% Einstein, Fermi, Heisenberg and the Birth of Relativistic Astrophysics 
% by Remo Ruffini

\chapter[From the 1920s to the 1930s]{From the 1920s to the 1930s}{}

\section{Introduction}

The introduction of special relativity  by Albert Einstein in 1905 \cite{einstein1905} signaled an epochal change in the understanding of physical laws. His presentation \textit{On the Electrodynamics of Moving Bodies} is based on a complete set of elementary observational facts, some simple considerations based on Euclidean geometry and 
a set of linear partial differential equations which are easily integrated analytically.
Introducing the concept of a space-time event as a basic element in the formulation of all physical laws, this short article still stands today as a monument of clarity, simplicity and scientific rigor. I often 
told %tell 
my students that understanding Einstein's  theory of special relativity is very difficult,  precisely because it is a new paradigm, in spite of its extreme simplicity.

Einstein's article introducing general relativity ten years later \cite{einstein1915}  is quite different: it uses the most sophisticated understanding of non-Euclidean Riemannian geometry, the nonlinear Lagrangian description of the fundamental interactions leading to a nonlinear set of partial differential equations in four dimensions which still do not admit a general solution over one hundred years later.  Most of all, general relativity proposed the revolutionary idea of geometrizing the gravitational interaction by introducing the physical concept of the equivalence principle.
In formulating general relativity Einstein took advantage of the geometrical success of the flat four-dimensional non-Euclidean spacetime introduced by Minkowski \cite{minkowski} for special relativity by extending it to a curved  Riemannian geometry  model for spacetime which behaves locally like Minkowski's spacetime.
He also used Hilbert's understanding of nonlinear Lagrangian theory \cite{hilbert} and employed the most elegant advanced mathematical and geometrical tool at the time, the absolute differential calculus, developed in the Italian schools of geometry by Luigi Bianchi \cite{bianchi,bianchi2}, Gregorio Ricci Curbastro \cite{riccicurb} and Tullio Levi-Civita \cite{levicivita}. The bridge between the physical insight of Albert Einstein and the results of these Italian geometers was made possible by the collaboration with his close friend Marcel Grossmann \cite{grossmann}. 

This is the most powerful synthesis of physics and mathematics ever encountered in the history of 
mankind. %homo sapiens. 
I often reiterate to my students that, like special relativity, general relativity is difficult to understand,  but now this is  indeed due to its conceptual, mathematical and physical complexity.
Contrary to the case of special relativity, where observational  verification was plentiful in view of its direct application to Maxwell's theory of electromagnetism, general relativity had very little observational evidence to support it.   
It took tremendous courage for anyone  to attempt to propose such a very difficult theory, so distant from the traditional approach to physics and  introducing as its foundation the revolutionary new idea of the geometrical interpretation of a physical interaction.

Soon after Einstein's equations were written,  a number of fundamental contributions appeared pointing out the possibility of inferring a new landscape for understanding physical phenomena in this novel geometrical approach.
An explicit solution was found by Karl Schwarzschild \cite{schw} corresponding to new physical phenomena occurring around a spherically symmetric distribution of matter. Similarly  Josef Lense and Hans Thirring \cite{lensethirring} pointed to the conceptually new idea of the dragging of inertial frames by a rotating object, and Willem de Sitter \cite{desitter} addressed  the first implications of general relativity for astronomy. 
These classic papers appeared in parallel with a wave  of three fundamental books giving a systematic  outlook to this new scientific era: the book of Wolgang Pauli ``Relativit\"atstheorie'' \cite{paulibook1}, later reprinted \cite{paulibook2}, the classic book of Hermann Weyl ``Raum-Zeit-Materie'' \cite{weylbook1}, later translated into English \cite{weylbook2}, and the  equally impressive book by Arthur S. Eddington ``Space, time and gravitation. An outline of the general relativity theory'' \cite{eddbook}. 
It is interesting that one of the first minds to lead the way in this new conceptual description of natural phenomena was a student at the Scuola Normale Superiore in Pisa: Enrico Fermi (see Fig.~\ref{fig:young_fermi}). He started from the analysis of gravitational and electrodynamical phenomena and succeeded in leaving behind an impressive  understanding of some  new issues raised by general relativity.


\begin{figure}
\begin{center}
\includegraphics[width =3in]{chap1_young_fermi2.pdf}
\caption{Young Enrico Fermi during the Pisa period (1918--1922).
}
\label{fig:young_fermi}
\end{center}
\end{figure}



\section{Fermi at the Scuola Normale Superiore in Pisa}

It is difficult to find a topic in the work of Enrico Fermi which has not yet been extensively discussed  either scientifically or historically. Nevertheless there are aspects precisely in  his earliest papers in the period when he was a student in Pisa and in the earliest part of his transition from Pisa to Rome spent in Florence, which have yet to be fully appreciated and which deserve additional attention today. They  were written in Italian and published in scientific journals which are not easily accessible, so we have translated them into English along with some others of particular relevance.\footnote{These are gathered together in a separate volume: {\it Fermi and Astrophysiacs-Volume 2}, edited by Remo Ruffini et al, World Scientific, 2017.}
% (see Chapter 2 of this volume and Appendix B). 
They deal mainly with fundamental issues of general relativity and classical electrodynamics and they help clarify and document those early years of his activity which contributed to creating his scientific personality. In his very first papers Fermi showed an outstanding interest in, knowledge of, and control over the mathematical techniques of the foundations of classical analytical dynamics and the theory of general relativity and also some interest in experimental work, necessary for obtaining his degree from the Scuola Normale in Pisa. Fermi mastered not only the physics of Einstein's then new theory but also the mathematical techniques of the tensor calculus of Tullio Levi-Civita and Gregorio Ricci-Curbastro, and a far reaching  interest in the knowledge of optics for X-ray instrumentation.
These papers
%, which we have translated into English, 
range from  classical electrodynamics and special and general relativity to the theory of adiabatic invariants, including some work on Roentgen X-rays which was a part of his thesis.


\begin{itemize}

\item[FI 1:] 
``On the dynamics of a rigid system of electric charges in translational motion'' (1);

\item[FI 2:]
 ``On the electrostatics of a homogeneous gravitational field and on the weight of electromagnetic masses'' (2);

\item[FI 3:] 
``On phenomena occurring close to a world line'' (3);

\item[FI 4:] 
``Correction of a contradiction between electrodynamic theory and the relativistic theory of electromagnetic masses'' (4c);

\item[FI 5:] 
``Masses in the theory of relativity'' (5);

\item[FI 6:] 
``On the mass of radiation in an empty space'' (10);

\item[FI 7:] 
``The principle of adiabatics and systems which do not admit action-angle coordinates'' (12);

\item[FI 8:] 
``Some theorems of analytical mechanics of great importance for quantum theory'' (13);

\item[FI 9:] 
``A theorem of calculus of probability and some application'' (38b);

\item[FI 10:] 
``Formation of images with Roentgen rays'' (7).

\end{itemize}

The article numbering in parentheses is that of the collected work of Fermi.\footnote{
\textit{Enrico Fermi: Note e Memorie (Collected Papers)},  
Accademia Nazionale dei Lincei and The University of Chicago Press, Vol.~1, 1961, Vol.~2, 1965;
Volume 1 is available on-line at:\\
\url{http://www.archive.org/details/collectedpapersn007155mbp}.\\
Both volumes are available at the Accademia dei Lincei website:
\url{http://www.lincei.it/modules.php?name=Content&pa=showpage&pid=125}.
}
Among these  articles are the details of Fermi's resolution in 1922  of the 4/3 problem in the classical theory of the electron which led to a mass-energy relation for the self-field contribution to the electron's inertial mass which violates Einstein's famous $E=mc^2$ formula. This work surprisingly still today is not well known nor presented either in current textbooks nor in those devoted to that specialized field. 
In order to analyze correctly the classical electron model in that early work, he developed  his  Fermi coordinates, so named by Synge, but not cited in Walker's later paper on the corresponding transport implicit in Fermi's work (later called Fermi-Walker transport).  Jumping momentarily ahead, let me just mention how Fermi-Walker transport has found a spectacular application and verification recently, some 90 years later,  in the NASA  ``Gravity Probe B'' experiment 
(see Fig.~\ref{fig_gpb}).


\typeout{perhaps need better quality conversion from jpeg to pdf: chap1_gpb.pdf}
\begin{figure}
\begin{center}
\includegraphics[width =4in]{chap1_gpb.pdf}
\vglue 0.5 cm
\caption{The Gravity Probe B (GP-B) gyro experiment, measuring the Fermi-Walker transport of the spins of four gyroscropes on board the satellite in a polar orbit undergoing dragfree (geodesic) motion around the rotating Earth through two effects, the small geodetic effect due to the mass of the Earth without considering its rotation, and the much smaller frame-dragging effect due to the rotation itself.\protect\cite{gpb} 
}
\label{fig_gpb}
\end{center}
\end{figure}



\section{The onset of general relativity in Germany and Italy}

While these conceptual scientific developments were taking place, the introduction of general relativity by Einstein had  encountered a  negative political climate in Germany. As we will see the interference of these political aspects greatly influenced the development of the scientific ideas. There is no better way to understand the climate in which Einstein's ideas were received in Germany, at the time Fermi was completing his studies in Pisa, than to reproduce the words used by Werner  Heisenberg:  

\begin{quotation}
\ldots In the summer of 1922, shortly before this scientific congress in Leipzig, the then foreign 
minister, Walther Rathenau, was murdered by nationalist terrorists.
It was a deliberate attempt to prevent any effort at a settlement.
Political passions again flared high, and the anti-Semitic movement began to direct 
its vengeance upon Einstein too, since he was a Jew, and enjoyed especially high esteem 
in the learned world of Germany. 
So just before the Leipzig session it was decided, at Einstein's request, that he himself 
should not speak there, but that von Laue should take over his lecture.
I did not know this when I went to Leipzig, and merely wondered at the ominous political 
excitement that was to be sensed among most of those attending the session.
When I sought to enter the great assembly hall to listen to Einstein's lecture, 
a young man thrust into my hand a red leaflet, reading more or less to the effect that 
the theory of relativity was a totally unproved Jewish speculation, and that it had been 
undeservedly played up only through the puffery of Jewish newspapers on behalf of Einstein, 
a fellow-member of the race.
I thought at first that this was the work of one of those lunatics, who do, of course, 
occasionally frequent such meetings.
But when I found that the red leaflet was being distributed by the students of one of the most 
respected of German experimental physicists, obviously with his approval, one of my dearest hopes disintegrated.
So science, too, could be poisoned by political passions; so even here it was not always a question 
solely of truth.
I became so agitated that I could no longer really take in the lecture.
I was sitting in the hall a long way from the rostrum, and quite failed to observe that 
von Laue was speaking in place of Einstein. Even after the meeting I made no attempt to seek out 
Eintein's acquaintance, but boarded the first train back to Munich. 
\ldots
\footnote{
From the book:
Werner Heisenberg, ``Encounters with Einstein: And Other Essays on People, Places, and Particles"
(Princeton University Press, Princeton, 1989), pp.~111--112.
}
\end{quotation}

In Italy, the theory of general relativity enjoyed great respect and interest among mathematicians. Indeed, from the beginning, the work of Einstein had profound roots in the Mathematics Institute in Rome, thanks to the work of Federigo Enriques, Guido Castelnuovo and especially Tullio Levi-Civita. It was through Marcel Grossmann that Einstein became aware of the scientific work on the absolute differential calculus of Gregorio Ricci-Curbastro and Levi-Civita, explained in great detail in the book by Sauer and Graf-Grossmann \cite{graf}, with introduction by Remo Ruffini. 

A first attempt at a theory of gravity based on the absolute differential calculus had been made in 1913 by Einstein and Grossmann \cite{eingross}.
The paper contained two sections: the first on the mathematical aspects of the problem, written by Marcel Grossmann, and the second on the physical aspects, written by Albert Einstein. 
To celebrate this ideal bridge between physics and mathematics in 1975 Abdus Salam and I established the Marcel Grossmann Meetings in his honor.\footnote{
The Marcel Grossmann meetings are held every three years in a location moving around in cities internationally: Trieste (MG1: 1975)  and (MG2: 1979), Shanghai (MG3: 1982), Rome (MG4: 1985) and (MG9: 2000), Perth (MG5: 1988), Kyoto (MG6: 1991), Stanford (MG7: 1994), Jerusalem (MG8: 1997), Rome (MG9: 2000), Rio de Janeiro (MG10: 2003), Berlin (MG11: 2006), Paris (MG12: 2009) and Stockholm (MG13: 2012), Rome (MG14, 2015).
}

In these years the contacts between Levi-Civita and Einstein, prior to and following the appearance of the equations of general relativity, grew very intense. This collaboration grew into a great mutual respect and friendship between the two. I remember Einstein's secretary, Helen Dukas, close to Einstein for so many years, recalling to me in Princeton a splendid sentence written by Einstein to Levi-Civita: ``I admire the elegance of your method of computation; it must be nice to ride through these fields upon the horse of true mathematics while the like of us have to make our way laboriously on foot.''  (See Fig.~\ref{chap1_fig1}).
There is no doubt that, without Levi-Civita, Einstein would not have been able to  formulate the field equations of general relativity. It is also clear  that the scientific imprint of the young Enrico Fermi in Pisa was strongly influenced by the work of Levi-Civita as is clear from his early papers. 
%we have translated and reproduced in Chapter 2. 


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_einstein_levicivita.pdf}
\caption{Einstein and Federigo Enriques at the University of Bologna.
}
\label{chap1_fig1}
\end{center}
\end{figure}



In addition to these common scientific interests there were the noble human contacts between Einstein and the families of Levi-Civita and Enriques. Recently a correspondence has been published of particular significance to this fact. Already in 1923 Federigo Enriques had written to Einstein  to invite him to transfer from Berlin to Rome and offering  him a position of Professor at the University of Rome and  to live in the building in Via Sardegna where Levi-Civita was also living. Here is Einstein's answer:   

\begin{quotation}
``Dear Colleague, your letter moved me deeply and I sincerely confess that I would prefer you and
the company of Levi-Civita to my colleagues I have here. Although there is a lot of anti-Semitism, for the moment I'm not suffering it. 
On the contrary, anti-Semitism forces one to be prudent and leads certain people to bother me less than they would under normal conditions. 
At my age it is not easy to change environment. There is no elasticity to blend with the new. For these reasons, despite the feelings of gratitude and 
sympathy I feel for you and your country that I have always loved in a special way, I cannot accept your affectionate offer. 
But if in the future the exacerbation of the situation forced me to have to leave my nest, I'll come to you with joy and full confidence. 
Your Albert Einstein."
\ldots 
\footnote{
Excerpt of the article on the newspaper ``Corriere della Sera'' by Maurizio Chierici: {\it ``Io e Einstein alla stazione\ldots ," a colloquio con la figlia del matematico Federigo Enriques} (April 10, 1992, p.~9), here in translation.
}
\end{quotation}


In the Rome Physics Institute  Einstein's theory of gravitation was instead never appreciated. This view was recalled to me by my close friend Arrigo Finzi, the sole exception to this general attitude. At the time Arrigo was a student in physics following the lectures of Fermi and had as his thesis advisor Tullio Levi-Civita in  mathematics. (See Figure ?? photo Bleuler Finzi RR in Silunte.) The work on general relativity was looked upon with some disdain, as pertaining mainly not to the field of physics but to the hybrid and, at that time, marginally scientific field of ``Fisica Matematica.'' There had been  one significant event also recalled by Arrigo in which Franco Rasetti, a member of Fermi's group,  gave 
a sarcastic tongue-in-cheek seminar to the physicists, with the mathematicians as guests apparently purporting measurements of general relativistic effects made possible by the new physics. At the end of the seminar when one of the mathematicians, Paolo Straneo, asked him for references, Rasetti turned to the physicists and shouted: ``You see, I told you they would believe all this nonsense!"




\section{The survival of general relativity from 1920 to 1960}

From the nineteen twenties  to the sixties, after the first waves of papers, books and observations confirming the novelties but also the paucity of general relativistic phenomena,  the theory of general relativity had lost its appeal among the general physics community all over the world. There had been  the first experimental tests of an astronomical nature:
the gravitational deflection of light, predicted as a consequence of the equivalence principle already in 
1911 \cite{einstein1};\footnote{
The final theory showed that the deflection is in fact twice the amount predicted in this paper.}
the anomalous  advance of the perihelion of Mercury, already explained by Einstein's theory in 1915 \cite{einstein2};
the gravitational red shift of spectral lines, predicted in the fundamental paper of 1916 \cite{einstein3}.

As for experimental tests of the theory of general relativity, already in 1932, Georges Darmois, a French mathematician who was a convinced supporter of Einstein's theory, discussed in his book ``La Th\'eorie Einsteinienne de la Gravitation, Les V\'erifications exp\'erimentales" (see Ref.~\cite{darmoisbook})
the results of the various experiments and concluded that they were not decisive (particularly those regarding the gravitational deflection of light).
The experiments utilizing solar eclipses would continue until 1952 (considering the years in which Fermi was still living). 
The first of them was the Sobral and Principe observation of the eclipse of May 29, 1919 directed by Eddington (see Ref.~\cite{sobralproc}).  The conclusion of Eddington himself was ``Although the material was very meager  compared with what had been hoped for, the writer (who it must be admitted was not altogether unbiased) believed it convincing'' 
[A.S. Eddington, Ref.~\cite{eddington2}, p.~116].
In Chandrasekhar's opinion ``\ldots  had he been left to himself, he would not have planned the expedition since he was fully convinced of the truth of the general theory of relativity'' 
[S. Chandrasekhar, Ref.~\cite{chandraedd}, p.~25; see also Ref.~\cite{sobralproc}]. 
As for the gravitational red shift of light, as we know, only the 1960s experiment of Pound and Rebka gave the conclusive answer.
The anomalous advance of the perihelion of Mercury was also the object of a number of attempts to explain it (including the oblateness of the Sun \cite{dicke1,dicke2}). This being the situation in the field of the experimental verification of general relativity, it is no surprise  that as the sophisticated experimentalist that Fermi had become after his transfer to Rome, he  considered, as we will see,  Einstein's theory to be far from having been demonstrated.

General relativity was kept alive in these years thanks to the intervention of a few remarkable physicists and mathematicians scattered around the planet in small and isolated ``scientific pockets." 
Even in  the absence of observational facts they were nevertheless convinced by the unique conceptual beauty of the theory. 
They clearly recognized the necessity of formulating a theory of gravitation consistent with the basic principle of relativistic invariance. 
Their contributions did not consist only of their appreciation of Einstein's theory and in teaching it: they also wrote a number of textbooks to save the message of Einstein for posterity.
There was a small group of scientists around Albert Einstein in Princeton including 
Luther P. Eisenhart \cite{eisenhart},
Kurt G\"odel \cite{godel},
Howard P. Robertson \cite{robertson}, 
Oswald Veblen \cite{veblen} 
and Hermann Weyl \cite{weyl1,weyl2,weyl3}, 
with their collaborators including 
Valentin Bargmann \cite{bargmann}, 
Peter G. Bergmann \cite{bergmann},
Banesh Hoffmann \cite{hoffmann2} 
and Leopold Infeld \cite{infeld} 
and students such as 
Joshua Goldberg \cite{goldberg}, 
Arthur Komar \cite{komar} 
and Abraham Taub \cite{taub}. 
A smaller group later developed around Ivor Robinson \cite{robinson} 
and Alfred Schild \cite{schild1,schild2} 
at the University of Texas in Dallas with the most remarkable addition few years later of Roy Kerr \cite{kerr}. 
In addition, there was George Y. Rainich \cite{rainich} 
in the East, 
George C. McVittie \cite{mcvittie} 
and Arthur G. Walker \cite{walker} 
in the Mid-West and 
Richard C. Tolman \cite{tolman} 
in California. 

In England there was a small number of highly qualified relativists following the tradition established by Arthur Eddington \cite{eddington1,eddington2,eddington3,eddington4,eddington5} 
including 
William B. Bonnor \cite{bonnor}, 
William H. McCrea \cite{mccrea} 
and Edward A. Milne \cite{milne1,milne2}, 
and later Hermann Bondi \cite{bondi1,bondi2} 
and Felix Pirani \cite{pirani1,pirani2}. 
In continental Europe a small group developed in theoretical physics around Wolfgang Pauli \cite{pauli}, 
Jean Becquerel \cite{becquerel}, 
Max Born \cite{born}, 
Th\'eophile de Donder \cite{dedonder1,dedonder2}, 
Paul A.M. Dirac \cite{dirac},
Pascual Jordan \cite{jordan1,jordan2}, 
Oscar Klein \cite{klein}, 
Max von Laue \cite{vonlaue1,vonlaue2}, 
Tullio Levi-Civita \cite{levicivita1,levicivita2,levicivita3}, 
Christian M\o ller \cite{moller}, 
Jan A. Schouten \cite{schouten1,schouten2,schouten3},
Erwin Schroedinger \cite{schroedinger1,schroedinger2},
Ernst C.G. Stueckelberg \cite{stueckelberg},
John L. Synge \cite{synge1,synge2}, 
Walter Thirring \cite{thirring1,thirring2} 
and Andrzej Trautman \cite{trautman}, 
while a more mathematical group developed around 
Henry Bauer \cite{bauer}, 
\`Emile Borel \cite{borel}, 
Elie Cartan \cite{cartan1,cartan2,cartan3}, 
Yvonne Choquet-Bruhat \cite{choquet}, 
Georges Darmois \cite{darmois},
Andr\'e Lichnerowicz \cite{lichnerowicz} 
and Marie-Antoinette Tonnelat \cite{tonnelat}.

Finally, some of the most significant contributions came from scientists from the Soviet Union, including Vladimir Fock \cite{fock}, 
Igor Tamm \cite{tamm}, 
Vitaly L. Ginzburg \cite{ginzburg} 
and of course Lev Davidovich Landau \cite{LL} and Evgeny Lifschitz \cite{lifshitz} 
and Isaak M. Khalatnikov \cite{khalatnikov}. 
There were also the contributions of  
Zhou Peiyuan \cite{peiyuan} 
in China, 
H. Takeno \cite{takeno} 
in Japan, 
and
V.V. Narlikar \cite{narlikar}, 
Amal Raychaudhuri \cite{raychaudhuri}
and Prahalad C. Vaidya \cite{vaidya} 
in India.


\section{Fermi from Pisa to Rome}

But let us return to Fermi and his transition from Pisa to Rome which signaled a drastic change of his scientific interests and his definite departure from his earlier interest in Einstein's theory of general relativity. 
After his thesis, Fermi had a temporary position at the University of Florence, while teaching one year  in Rome during the academic year 1923--1924. 
In 1925 an unpleasant  event occurred which may very well have been responsible for his change of heart concerning Einstein's theory.

A professor position had opened up in the field of ``Fisica Matematica"  at the University of Cagliari in Sardinia, and Fermi was confident of being chosen to fill it. Unfortunately for him the selection committee was divided into two factions, those who had mastered Einstein's theory and believed in it, and those who ``did not believe in it." Among the five Members of the selection Committee were Tullio Levi-Civita and Vito Volterra who strongly supported Fermi's candidacy. But Fermi lost.
The winner was instead Giovanni Giorgi, who had introduced the MKS system of units into physics.
It is a fact that for the rest of his life Fermi never used general relativity again with the sole exception of the critical reference to it in the Fermi-Turkevich paper, on which I will return,  and some interest in the last months  of his life, as referred to me by Murray Gell Mann. One can maintain that Fermi did not publish any other paper on this subject.\footnote{
As Edoardo Amaldi wrote \cite{amaldi}: ``Fermi had the habit of writing everything he was thinking or developing or computing directly into a notebook. He almost never wrote on unbound sheets of paper because he wanted to keep a record of everything he was doing.''
This habit was confirmed by other friends of Fermi (E. Segr\`e).
When Fermi left Italy in November 1938, Amaldi collected all the manuscripts and documents related to Fermi's scientific activities; after Fermi's untimely death he chose the Domus Galilaeana of Pisa as a depository for all these documents. It is a simple fact that among the manuscripts kept at Domus Galilaeana (regarding Fermi's Italian period) there is no material revealing any further interest in general relativity.
See Ref.~\cite{leone}.
} 
In 1926 Fermi was awarded the chair of theoretical physics in Rome created for him by Orso Mario Corbino, then a minister in the Mussolini government and  the director of the Rome Physics Institute. 
Fermi's transfer to Rome coincided with his many new  contacts he made with the German school of physics, first with Max Born and later enthusiastically with Werner Heisenberg. I comment below on  the recollections of those days I had the occasion to hear from Heisenberg himself.

From this Florence-Rome early period, we have translated into English two of his remarkable papers on statistical methods and the fundamental paper on the role of neutrinos in beta decay:

\begin{itemize}

\item[FI 11:] ``On the quantization of an ideal monoatomic gas" (30) (this paper set the basis for Fermi-Dirac statistics);

\item[FI 12:] ``A statistical method for the determination of some properties of the atom; this paper set the basis for the Thomas-Fermi model'' (43);

\item[FI 13:] ``An attempt to a theory of beta rays'' (80a); this paper set the basis for the theory of weak interactions.

\end{itemize}

It appears possible that, after the intense activity regarding the dawning of quantum mechanics,  and  the birth of  quantum statistics in his 1926 paper and in the corresponding one of P.A.M. Dirac \cite{diracfoot1}, 
Fermi wanted to concentrate all his efforts on the very fertile ground of nuclear and atomic physics. There, both from the theoretical and the experimental points of view, fruitful results abounded when compared with the then meager results in the experimental and observational verification of general relativity. In addition to the paucity and smallness of these effects, there was the tremendous mathematical difficulty of the theory, and a detachment from other fields of physics and astrophysics with the single remarkable exception of cosmology.
 The  Physics Institute was ``striking gold'' with Fermi and the outstanding physicists around him  in the field of nuclear physics. This topic has been covered by so many  books and  movies that I have no reason to enter in it in this  brief excursus of mine mainly directed towards astrophysics and general relativity.\footnote{Among these is the interesting book written by his wife Laura Fermi \cite{laurafermi}, the article by Edoardo Amaldi \cite{amaldiPR}, the book by Emiglio Segr\`e \cite{segre}, and the 1989 movie ``I Ragazzi di via Panisperna." 
} 


\section{Fermi and the problem of stellar interiors}

Except for his early work in Pisa, followed by the shock of the Cagliari affair, it is well known that in his research in Rome Fermi became extremely concrete and avoided speculation not supported by direct observational evidence. On one hand this gave the Rome school a sense of  realism and an urgent  quest for physical understanding.  On the other hand 
this attitude kept Fermi and the Rome group out of that group of scientists who were able to approach the many consequences  of Fermi-Dirac statistics for the final evolution of stars. 
It is appropriate here to attempt to justify this attitude by using Fermi's own words. Fermi was very knowledgeable about the physical status of atomic physics at the surface of stars but when it came to the analysis of their interiors, he would not enter into this topic to avoid having to ``resort to very risky hypotheses.'' Let us follow this particular attitude in his 1930 lecture delivered in Trento:\footnote{
See: ``Atomi e Stelle" \cite{fermiatomi}
in Note e Memorie, Vol.~I, article (60), pp.~355--360).
The above excerpt is in our own English translation. 
} 

\typeout{??why doesn't the quote environment work here??}
%\begin{quote}
{\it \leftskip 20pt
``\ldots As can be seen even from these brief hints, the physical state of the surface of stars, at least of many stars, is relatively well known.
If instead we want to say something about their interiors, we are forced  to resort to  very risky hypotheses.
Therefore all the theories about the interior of stars are very uncertain, however, they agree on the fact that in the interior of stars the temperature must be very high; it has been estimated to be on the order of magnitude of tens of millions of degrees.

At such a high temperature the properties of matter become very different from those we know. It is enough to consider that the kinetic energy of the motion of thermal agitation, being proportional to temperature, is a hundred thousand times greater than that at ordinary temperatures.
One understands then that molecules cannot exist in this situation; since even if for an instant by chance two atoms unite to form a molecule, they would immediately be pulled apart by violent collisions with the other particles. But even the structure of the atom is not resistant enough not to break under such violent shocks.
Consider for instance an iron atom; under normal conditions it consists of a nucleus surrounded by 26 electrons. But under the action of the bombardment almost all these electrons are pulled out of it and very probably only two of them remain within the nucleus while the other 24 disperse into the environment.
To conclude we can then imagine the matter inside a star to consist of a very disordered mixture containing a few nuclei accompanied by two or three electrons, and many free electrons moving in all directions with velocities on the order of those of cathode rays.
All that in an environment permeated by radiation at an enormous frequency whose intensity is so high as to produce a pressure which, according to Eddington, in some cases can arrive at breaking the structure of the star itself.

But all of what I have said is perhaps the result of pure imagination: no one has ever had and probably no one could ever have direct experience of this.
On the other hand the human mind wants to imagine even the things very far and very hidden; and maybe, without this tendency, the number of phenomena which human science has been able to understand would be even more limited.''

}
%\end{quote}
\vskip12pt

One additional factor which may have kept Fermi outside the field of astronomy is that both in Pisa and in Rome there was no astronomical teaching in the Physics Institute. 
%In Rome the astronomical observatory was very far from the university on the hills of Monte Mario where the Vatican Observatory had been %located previous to the unification of Italy, after which the great tradition of the Jesuit astronomers going back to the glorious activities of father Angelo Secchi were removed. 
The only astronomical lectures were in the Mathematics Institute closely linked to the courses of rational mechanics.
A factor in making this interaction with English speaking scientists problematic was the fact that at the time Fermi was fluent in German but only later learned English.\footnote{
John Wheeler recalled how Fermi in his quest for perfection in speaking English had asked the students in his class at the University of Chicago to correct his English mistakes. In order to overcome their reluctance to correct such a famous scientist, he offered them one penny for every correction. One penny was the optimal choice to break the ice, while a quarter would have led to too many interruptions and probably to chaos.
}

Indeed, during Fermi's  Rome period, a vast leap in understanding of fundamental astrophysical systems took place in Germany, England, and the USA, using precisely the concepts introduced by Fermi and later independently by Dirac in their jointly named quantum statistics. Of these I will just mention three key examples: white dwarf theory and its critical mass, neutron star theory and its critical mass, and the idea of gravitational collapse.


\section{Fowler and Stoner and the role of quantum statistics in white dwarf stars}

It was Ralph Howard Fowler who took the first step in applying Fermi-Dirac quantum statistics to the interiors of stars. This did not happen by chance. 
Fowler was the teacher of Paul Adrien Maurice Dirac.
Fowler introduced Dirac to quantum theory in 1923 and later on put Dirac and Werner Heisenberg in touch with each other through Niels Bohr. It was no surprise that as soon as Dirac published his paper on quantum statistics a few months after Fermi's paper, Fowler, who was at Trinity College and had worked with Arthur Milne on stellar spectra, temperatures and pressures, understood at once the role of quantum statistics in solving the problem of white dwarf equilibrium configurations. He understood that white dwarfs owe their stability to the quantum pressure of a degenerate electron gas \cite{fowler} (see the image of  R.H. Fowler in the 1927 Solvay Meeting group photo reproduced in Fig.~\ref{fig:solvay1927})).   
The role of special relativity and the ``exclusion principle'' for fermions was introduced into the study of white dwarfs by 
E.C.  Stoner \cite{stoner}, 
correcting an early work of W. Anderson \cite{andersonfoot1}.
Stoner clearly introduced the value of the critical mass of white dwarfs  
\[ %\begin{equation*}
M_{\rm crit}^{\rm Stoner} 
= \frac{15}{16}\sqrt{5\pi}\frac{M_{\rm Pl}^3}{\mu^2 m^2_n}
\approx  3.716 \frac{M_{\rm Pl}^3}{\mu^2 m^2_n}
\,,
\] %\end{equation*}
where $M_{\rm Pl} = \sqrt{\hbar c/G} \approx 10^{-5}$ g is the Planck mass, $m_n$ is the neutron mass, and $\mu = A/Z \approx 2$ is the average molecular weight of matter which shows explicitly the dependence of the critical mass on the chemical composition of the star.
Later the ``exclusion principle'' introduced by Stoner in the context of theoretical astrophysical considerations became known as the ``Pauli principle'' and was extensively applied to atomic physics \cite{nauenbergfoot1}.


\subsection*{The white dwarf critical mass}

This work was then followed by S. Chandrasekhar who, only 19 years old, had been accepted at the University of Cambridge as a student of Fowler. It was indeed on the ship from Madras to Southampton near the town of Genova that Chandra understood that special relativistic effects  are important in massive white dwarfs, and on his arrival in Cambridge he further refined Stoner's computations. It is interesting that in parallel and quite independently, one of the deepest papers on the nature of the physical equilibrium of stars was written in the Soviet Union by Lev Davidovich Landau.\footnote{
We reproduce his paper in Appendix \ref{appA_landau}.
}
Both papers of Chandrasekhar and Landau used the mathematical results contained in the monumental book of Emden ``Gaskugeln'' 
(Gas Spheres) \cite{emden}. 
Using the polytropic equation of state they pointed out that special relativistic effects were leading to the concept of a 
slightly smaller
critical mass for a white dwarf given by 
\[ %\begin{equation*}
M_{\rm crit}^{\rm Ch-L} 
\equiv M_0
= 2.015 \frac{\sqrt{3 \pi}}{2}\frac{M_{\rm Pl}^3}{\mu^2 m^2_n}
\approx  3.093 \frac{M_{\rm Pl}^3}{\mu^2 m^2_n}
\,,
\] %\end{equation*}
where the first numerical factor on the right hand side comes from the boundary condition $-(r^2 d u/dr)|_{r=R} = 2.015$ of the $n=3$ polytropic equation of Emden at the boundary $R$ of the star.
For $M > M_0$ no equilibrium configuration should exist. 

The  beautiful derivation by Landau was somewhat spoiled by the conclusion of the paper:  Landau correctly  derived the concept of the critical mass of a white dwarf but did not take this concept very seriously saying
{\it 
``for $M > M_0$ there exists in the whole quantum theory no cause preventing the system from collapsing to a point\ldots  As in reality such masses exist quietly as stars and do not show any such ridiculous tendencies we must conclude that all stars heavier than $1.5 M_\odot$ certainly possess regions in which the laws of quantum mechanics (and therefore of quantum statistics) are violated.''
}
The central role of the critical mass of white dwarfs in astrophysics had to wait many years until Fred Hoyle and William Alfred (Willy) Fowler forcefully presented the gravitational collapse of an overcritical white dwarf as giving rise to the type-I supernova phenomena \cite{hoyle}. 
 
The results by Chandrasekhar were criticized at the time by Arthur Eddington who considered the combination of special relativity and nonrelativistic quantum mechanics an ``unholy alliance.''\footnote{
{\it
``The theoretical study of very dense matter in white dwarf stars depends on a formula giving the minimum electron pressure $P_e$ for given electron density $\sigma$.
The ``ordinary'' degeneracy formula, first given by R.H. Fowler \cite{fowler}, is $P_e=K\sigma^{\frac53}$.
According to later investigations this is the limiting form of a ``relativistic'' degeneracy formula, intended to take account of the increase of the masses of the electrons at high velocities.
By the latter formula $P_e$ varies intermediately between $\sigma^{\frac53}$ and $\sigma^{\frac43}$, approximating to $\sigma^{\frac43}$ at the highest densities.

It should be noticed that this emendation has defeated the original purpose of Fowler's investigation. When putting forward the view that stellar matter might attain very great density, I was troubled by an apparent difficulty---there seemed no way in which the dense star could cool down when its energy supply ceased. 
The Fermi-Dirac theory was discovered soon afterwards, and Fowler applied it to the stellar interior, his main purpose being to show that it solved this difficulty. 
But the same difficulty is revived by Chandrasekhar's recent work \cite{chandrafoot1}.
Using the relativistic formula, he finds that a star of large mass will never become degenerate, but will remain practically a perfect gas up to the highest densities contemplated.
When its supply of subatomic energy is exhausted, the star must continue radiating energy and therefore contracting--presumably until, at a diameter of a few kilometers, its gravitation becomes strong enough to prevent the escape of radiation. 
This result seems to me almost a
}
reductio ad absurdum
{\it 
of the relativistic formula.
It must at least rouse suspicion as to the soundness of its foundation.

I do not think that any flaw can be found in the usual mathematical derivation of the formula.
But its physical foundation does not inspire confidence, since it is a combination of relativistic mechanics with non-relativistic quantum theory.

In the present paper this unholy alliance is examined\ldots ''
}
[from A.S. Eddington \cite{eddingtonfoot1}].
}
What I have found politically correct and to Eddington's credit is that in their scientific dispute, although Eddington was Plumian Professor and enormously more influential at the time than  Chandrasekhar, who was just a student at Cambridge, Eddington presented his alternative point of view clearly and did not object to the publication of Chandrasekhar's work which indeed follows his own paper  in the same issue of the \textit{Monthly Notices} \cite{chandrafoot1}.

[needs Jorge input here??]
 
Fermi could have been the ideal physicist to help clarify this Eddington-Chandrasekhar debate but in view of his attitude about the ``very risky hypothesis" to be adopted for the interior of the star, he did not enter into this matter,  just quoting  Eddington and leaving the Italian scientific community out of this most important field of research for many years to come. 
I still recall in my thesis discussion at the University of Rome in 1967 I had to witness the case of the Professor of Astrophysics
who knew perfectly well of the existence of Willy Fowler, but ignored the existence of R.H. Fowler and his fundamental contributions.\footnote{  
In fact, Willy Fowler was one of the lecturers of the XXXV Course of the International School of Physics ``E. Fermi,''  High Energy Astrophysics (1965), Director L. Gratton.
}

It has been only recently, as I will show later in this text,  that the dispute between Eddington and Chandrasekhar has been clarified exactly by applying the [insert reference to Tamm??] Tamm generalization \cite{tamm} of the Thomas-Fermi equation to the study of white dwarfs \cite{rotondo1,rotondo2} (see Appendices \ref{appA_PhysRevD_84_084007} and \ref{appA_PhysRevC_83_045805}).
The explanation was not easy to find  as I will explain later. 
At the end it was clear that both Chandrasekhar and Eddington had good reasons for holding their points of view but to resolve the question that they posed required almost 80 years of further theoretical development and work!



\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_sirius.pdf}
\caption{The image of Sirius A and Sirius B taken by the Hubble Space Telescope (available at \protect\url{http://hubblesite.org/gallery/album/pr2005036a/}). 
They form a binary system consisting of a white main sequence star (Sirius A) and a faint white dwarf companion (Sirius B, the small white dot to the lower left).
The distance separating Sirius A from its companion varies between $8.1$ and $31.5$ AU, while
their masses are similar: Sirius B is about as massive as the Sun, whereas Sirius A is about twice as massive, while its 
diameter is larger by a factor of $2\times10^2$ (about $3.4R_\odot$ versus $0.017R_\odot$). 
}
\label{chap1_sirius}
\end{center}
\end{figure}


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_eddington.pdf}
\caption{Sir Arthur Stanley Eddington, Plumian Professor at Cambridge (from 1913 to 1944). 
}
\label{chap1_eddington}
\end{center}
\end{figure}




\section{The neutron star critical mass}

This same attitude of refusing to look into the problem of the interior of stars kept  Fermi out of that select group of scientists  in the United States who laid the conceptual foundations from which later emerged the  the concept of a neutron star.
See, for instance, the classic papers reproduced in Gursky and Ruffini \cite{gursky} and Refs.~\cite{baade,landau1,landau2,landau3,chandrabook1,oppserber,oppvolkoff,oppsnyder,gamowfoot1,gamowfoot2}.


In 1934 one of the shortest and most memorable papers ever written in physics and astrophysics was published by two European scientists who had emigrated to the United States to become professors at Caltech, Walter Baade and Fritz Zwicky. The paper at once introduced three epochal concepts: the energetics of a supernova (see Fig.~\ref{chap1_crab_nebula}), the origin of cosmic rays from supernovae and the transition from a normal star into a neutron star as originating the supernova phenomenon.
  
\begin{quotation}
Supernovae flare up in every stellar system (nebula) once in several centuries. The lifetime of a supernova is about twenty days and its absolute brightness at maximum may be as high as $M_{\rm vis} = - 14^M$. The visible radiation $L_\nu$ of a supernova, is about $10^8$ times the radiation of our Sun, that is, $L_\nu = 3.78 \times 10^{41}$ ergs s$^{-1}$. Calculations indicate that the total radiation, visible and invisible, is of the order $L_r=10^7L_\nu = 3.78 \times 10^{48}$ ergs s$^{-1}$. The supernova therefore emits during its life a total energy $E_r > 3.78 \times 10^{53}$ ergs. If supernovae initially are quite ordinary stars of mass $M < 10^{34}$ g, $E_r/c^2$ is of the same order as $M$ itself. In the {\it supernova} process {\it mass in bulk is annihilated}. In addition the hypothesis suggests itself that {\it cosmic rays are produced by supernovae}. Assuming that in every nebula one supernova occurs every thousand years, the intensity of the cosmic rays to be observed on the Earth should be of the order $\sigma = 2 \times 10^{-3}$ erg cm$^{-2}$ s$^{-1}$. The observational values are about $\sigma = 3 \times 10^{-3}$ erg cm$^{-2}$ s$^{-1}$ (Millikan, Regener). With all reserve we advance the view that supernovae represent the transitions from ordinary stars into {\it neutron stars}, which in their final stages consist of extremely closely packed neutrons.
\footnote{
Abstract of the paper:
W. Baade, F. Zwicky: ``Supernovae and Comic Rays,'' in Proceedings of the American Physical Society (Minutes of the Stanford Meeting, December 15-16, 1933), \textit{Phys.\ Rev.} {\bf 4}, 138 (1934).
}
\end{quotation}


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in,angle=90]{chap1_crab_nebula.pdf}
\caption{The Crab Nebula. 
}
\label{chap1_crab_nebula}
\end{center}
\end{figure}


The concept of a neutron star came gradually, making its  first appearance in a fundamental paper by Friedrich Hund where the possibility of having a neutronization process in stellar matter was presented \cite{hund}. The first theoretical analysis soon followed  in a Newtonian treatment by George Gamow based on a self-gravitating set of neutrons described by degenerate Fermi-Dirac statistics. 
Actually Gamow did not publish the results in an article but inserted these considerations directly into a chapter in the second edition of his classic book on nuclear physics \cite{gamowfoot1}. Gamow correctly understood  that such configurations lead to the existence of a critical mass for a neutron star as soon as relativistic effects are manifested similar to the white dwarf case. He estimated such a mass to be approximately $1.5M_\odot$, and also in that work as we are going to show Gamow made a numerical mistake.

Years later when I had just arrived in Princeton, Eugene Wigner had noticed my great admiration for Gamow. He expressed in a subtle sentence in his well known ironic form: ``You admire so much Gamow, but you should be aware that Gamow used a special set of units $G$, $\hbar$, $c$, $\pi$ equal one!" It took me almost twenty five years to find out that Eugene was correct and that precisely in that first estimate of the critical mass of a neutron star indeed Gamow had missed a few crucial factors of $\pi$! The critical mass value should have been $5.75 M_\odot$  \cite{Henrik-Rueda-RR-M??}. % 
[work with German studentLudwig ask She Sheng  in Korean??]

The work on neutron stars was further developed in general relativity by Robert Oppenheimer and his students, under the same hypothesis of a degenerate neutron Fermi gas. The critical mass for gravitational collapse was then estimated to be $0.7M_\odot$ and further generalized to the case of a system of neutrons, protons and electrons in a book by John Wheeler and his group.\footnote{
See B. Kent Harrison, Kip S. Thorne, Masami Wakano, John A. Wheeler: ``Gravitation Theory and Gravitational Collapse'' (Univ. of Chicago Press, Chicago, 1965).
} 
As I will recall briefly, I expressed my reservation about this  treatment in my first meeting with Wheeler. I was  concerned and surprised that Fermi, who certainly had the knowledge to intervene in such  delicate issues, had never expressed an opinion on it. The existence and value of the critical mass as well as the physical parameters and the electrodynamical properties of such neutron stars were clearly dependent on the theoretical treatment.  Finally this problem  has found also a solution, not least thanks to the theoretical foundations of a generalized Thomas-Fermi model described by a properly formulated Einstein-Maxwell system taking into account all the fundamental interactions (see Refs.~\cite{rotondo1,rotondo2}, here reproduced in Appendices \ref{appA_PhysRevD_84_084007} and \ref{appA_PhysRevC_83_045805}) understood only 
very recently! %in recent months! 


\section{On continuous gravitational collapse}

A few months after addressing the problem of the equilibrium configuration of neutron stars, Oppenheimer soon boldly advanced in the study  of what would happen to a star with a mass larger than the critical mass in its continuous gravitation collapse.  The beautiful treatment by Oppenheimer and Snyder  \cite{oppsnyder} paradoxically triggered a bitter confrontation between Einstein and Oppenheimer 
(see Fig.~\ref{chap1_fig9}). %%{fig:einopp}). repeated incorrect reference to this figure...??
This confrontation was based on an equally  beautiful analytic solution of a system of many self-gravitating particles in circular orbits explicitly obtained by Einstein \cite{eincluster}  in the same year 1939. 
He showed how to construct a stationary self-gravitating system of many masses, each moving along a geodesic circular orbit about the center of the system under the influence of the gravitational field of all the other masses. Such a system has spherical symmetry and is referred to in the literature as an ``Einstein cluster.''
The spherical symmetry is guaranteed by the hypothesis that the normal to the orbital planes of the particles constituting every shell of the cluster are distributed at random in all directions and also the phase angles of the paths are subject to a random distribution.
In the Einstein model, all the particles are centrifugally supported, and what is not a priori clear and to me truly remarkable is that following Einstein's paper, it is always  to choose arbitrarily the number density of the particles or, equivalently, the energy density of the cluster and have an analytic self-consistent solution of Einstein's field equations for the metric corresponding to such a cluster.
Einstein explicitly considered the simplest case of a cluster with energy density decreasing with $r$ as $1/r^2$ far from the center.
He argued that the Schwarzschild radius can never be reached in physical reality since a cluster with a fixed number of particles cannot be arbitrarily concentrated
.
At the time the nature of the Schwarzschild radius was not yet understood. It was interpreted as a physical singularity. The role of the Schwarzschild radius with its horizon properties were understood by Finkelstein \cite{finkelstein} and later by Kruskal \cite{kruskal}. What Einstein was trying to show was the impossibility of reaching the Schwarzschild radius of the cluster.
Einstein clearly identified the stable clusters and the unstable ones. He gave special attention to the unstable orbits with radius smaller then  $6M$ and their reaching asymptotically the speed of light.
What actually Einstein had found was the existence of unstable circular orbits at three Schwarzschild radii, years before the 1949 work by Kaplan to whom such a result is commonly attributed \cite{kaplan}.
To fully appreciate the physical interpretation of such solutions it is sufficient to  examine these Einstein clusters clusters using the effective potential technique first introduced in the book of Stormer \cite{stormer} for the study of trajectories in the Earth's magnetosphere and later applied in general relativity to the study of the geodesics in a Kerr spacetime by Wheeler and myself \cite{rresro}. It the become clear that there are three different kind of orbits: stable, unstable and metastable \cite{pompi-geralico}. It then becomes  clear that the configurations with radius smaller than $6M$ are indeed not stable.  Clusters with selecteddensity and energy distribution fulfilling  can be found and their spacetime automatically determined using Einstein�s prescription. The crucial point, however, is that each cluster can reach a limiting stable configuration of equilibrium with maximum binding from which they indeed can undergo gravitational collapse to a black hole. 

The Einstein clusters represent an extremely interesting tool for probing the geometry of relativistic clusters (see also Bisnovatyi-Kogan and Remo Ruffini \cite{bk-rr}??):  in no way do they represent a counterexample to a black hole and in some cases they give the initial conditions for the formation of a black hole, fully supporting Oppenheimer approach \cite{??}! Having  addressed the physics of gravitational collapse for years, I was confronted to make an assessment about  Einstein's objections to  Oppenheimer�s work. I have postponed this task for a long time but finally we have succeeded with some collaborators to clarify the role of Einstein clusters  \cite{pompi-geralico}: the two approaches are indeed very different and address different aspects: the direct gravitational collapse by Oppenheimer  and some possible initial conditions leading to gravitational collapse by Einstein. 

Let us now turn to another fundamental contribution developed by Heisenberg and the northern European school of physics while Fermi was still in Rome, though not in direct contact,  which will have a major relevance for astrophysics for years to come.



\section{Tunneling from matter to antimatter and my meeting with Heisenberg}

While the work on nuclear physics and neutron physics was going on in Rome and in Berlin and the application of fermions to the study of self-gravitating systems in astrophysics was progressing both in Cambridge in England and United States there was a major topic of scientific interest in the northern European school of physics which in  time would become of marked importance in astrophysics. In some sense this work also finds a conceptual link in the paper of Fermi in the Pisa period on the electromagnetic energy of a charged particle.
As  Dirac introduced his theory of the electron \cite{diracref1,diracref2} 
in the framework of relativistic quantum theory, he realized the existence of positive and negative energy states. Only the positive energy states could correspond to the electrons, $e^-$. Dirac then proposed \cite{diracref2} that almost all possible states of negative energy are occupied with just one electron, in accordance with Pauli's exclusion principle and that the unoccupied states, ``holes" in negative energy states should be regarded as positrons, $e^+$.\footnote{
Actually initially \cite{diracref2,diracref3} 
Dirac believed that these ``holes" in the negative energy spectrum described protons, but later he realized that these holes represent particles with the same mass as an electron but with opposite charge, ``anti-electrons" \cite{diracref4}. 
The discovery of these anti-electrons  was made by Anderson in 1932 \cite{andersonref1} who named them positrons  \cite{andersonref2}.
}

Dirac pointed out in \cite{diracref3} the necessity of the annihilation process of an electron-positron pair into two photons, i.e., 
$$
e^+  + e^- \, \to \, \gamma_1+\gamma_2\,.
$$
He considered an electron under the simultaneous influence of two incident beams of radiation which induce a transition of the electron to states of negative energy. Then he calculated the transition probability per unit time, using the well established validity of the Einstein emission and absorption coefficients and he obtained the explicit cross-section of the annihilation process. Such a process is spontaneous, i.e., it occurs necessarily for any pair of electrons and positrons independently of their energy. The Dirac prediction was almost immediately observed \cite{klemperer}. 
Details can be found in Ref.~\refcite{RVXphysrep}, here reproduced in Appendix \ref{appA_rretal_phys_rep2010}.
Soon after the opposite process
$$
\gamma_1+\gamma_2 \, \to \, e^+  + e^-\,,
$$
namely the cross-section for the production of an electron-positron pair in the collision of two real photons, was given by Breit and Wheeler \cite{breitwhe}.
According to Dirac's theory of the electron, this process is caused by a transition of an electron from a negative energy state to a positive energy state under the influence of two light quanta on the vacuum. This process, differently from the one considered by Dirac, which occurs spontaneously, has a threshold due to the fact that the electron and positron mass is not zero: in the center of mass system there must be sufficient enery to create an electron-positron pair. Paradoxically this opposite process has not yet been directly observed in the laboratories (see Appendix of Ref.~\refcite{RVXphysrep}).


\begin{figure}[h]
\centering
\includegraphics[width=3.5in,angle=90,clip]{chap1_RVXfig2.pdf}
\caption{The mass-gap $2m_ec^2$  that separates the positive continuum spectrum ${\mathcal E}_+$ from the negative continuum spectrum ${\mathcal E}_-$.
}
\label{fig:chap1_RVXfig2}
\end{figure}


In Minkowski spacetime every relativistic wave equation of a free particle, as expressed by Dirac, gives rise to the familiar positive and negative energy spectrum and all the quantum states are stable (see Fig.~\ref{fig:chap1_RVXfig2}, details in Ref.~\refcite{RVXphysrep}).
In 1929 Oscar Klein, following Dirac's description of the matter-antimatter universe, studied a relativistic particle moving in an external step function potential leading to reflected and transmitted waves. He found a paradox that for a large enough value of the potential the reflected flux was larger then the incident one although the total flux was conserved: there was a contribution due to the tunneling of the wave function in the negative energy states. This was the origin of his famous  ``Klein Paradox:'' an electron scattered from a potential barrier on the order of the electron mass can tunnel between the matter and antimatter solution \cite{kleinref1} (see also Ref.~\refcite{dombey}).
In 1931 Fritz Sauter \cite{sauter} (see Fig.~\ref{fig:heisenbergetal} in the Preface) adopting the quantum tunneling phenomena just introduced by Gamow in the same year,
studied this problem by considering an electron moving in a potential barrier corresponding to a spatially confined constant electric field. Tunneling into the potential barrier leads to an exponential damping of the field. If the potential barrier is on the order of the electron mass, it is penetrated by the electrons and becomes more and more transparent by increasing the sharpness and depth of the potential well. In correspondence, the reflection of the wave function of the electrons decreases and the electrons tunnel into the negative energy states. By this ``level crossing'' an electron-positron pair is created at the expense of the electromagnetic energy of the background (see Fig.~\ref{fig:chap1_RVXfig3}, details in Ref.~\refcite{RVXphysrep}).

Also in 1931 Hans Euler (see Fig.~\ref{fig:euler}) in his celebrated diploma thesis \cite{eulerref1} 
realized that both the Dirac process and the Breit-Wheeler process had fundamental implications for light on light scattering, leading to a breakdown of the superposition principle. 
He called attention to the reaction
$$
\gamma_1\gamma_2 \, \to \, e^+e^- \, \to \, \gamma_1{}'\gamma_2{}'\,.
$$
If the energy of the photons is high enough, then a real electron-positron pair is created, following Breit and Wheeler \cite{breitwhe}, and once the electron-positron pair exists, two photons are then created following \cite{diracref3}. When the sum of energies of the
two photons is smaller than the threshold $2m_ec^2$, then the (above) reaction still occurs through a virtual electron-positron pair.
Under these conditions the light-light scattering implies a deviation from the superposition principle, and therefore the linear
theory of electromagnetism has to be substituted by a non-linear one. Maxwell's equations are then modified acquiring non-linear corrections due
to the Dirac theory of the electron.


\begin{figure}[h]
\centering
\includegraphics[width=3.5in,clip]{chap1_RVXfig3.pdf}
\caption{In the presence of a strong enough electric field the boundaries of the classically allowed states (``positive'' or ``negative'') can be so tilted that a ``negative'' is at the same level as a ``positive'' (level crossing). Therefore a ``negative'' wave-packet from the left will be partially transmitted, after an exponential damping due to the tunneling through the classically forbidden states, as a ``positive'' wave-packet outgoing to the right. 
%This figure is reproduced from Fig.~II in Ref.~\cite{1975mgm..conf..459D}, and 
%Here $\mu=m_ec^2, \epsilon V=V(z), \omega={\mathcal E}$.
}
\label{fig:chap1_RVXfig3}
\end{figure}


The need for a new nonlinear theory of electromagnetism going beyond the linear Maxwell theory  became a necessity. Max Born was the first to attempt to formulate such a nonlinear theory \cite{bornref1,bornref2,bornref3}. 
Soon after Heisenberg and Euler, following the pioneering work of Born, introduced a nonlinear Lagrangian by the introducing an effective dielectric constant and magnetic permeability \cite{eiseuler}. 
They further extended this idea by adopting the most general case of a complex dielectric constant. The crucial point was to relate the electron-positron pair creation process to the imaginary part of the Lagrangian.  The possibility  that electron-positron pair production could occur in the presence of a strong constant electric field was theoretically confirmed. In the presence of a strong constant electric field, the ``positive energy'' levels of the electrons exhibit a crossing with the ``negative energy'' levels---a ``level crossing" occurs as predicted by Sauter.
This leads to the phenomenon of electron-positron pair production out of the vacuum. They introduced correspondingly the concept of ``critical value of the electric field" at which vacuum polarization would occur: the characteristic strength for the electric field is $E_c = m_e^2c^3/(e\hbar)$, where $m_e$ is the electron rest mass, $c$ is the speed of light in vacuum, $e$ is the electron charge and $\hbar$ is the reduced Planck constant. 
A ``long march"  to reveal this process in heavy ion collisions in Earth laboratories then began \cite{HEi,HEii,HEiii,HEiv}. 
Two independent attempts to study these nonlinearities in electrodynamics were made by Born and Infeld \cite{bornref1,bornref2,bornref3} and by Euler and Heisenberg \cite{eiseuler}, leading the way to  the even greater revolution of quantum electrodynamics by Tomonaga \cite{tomonaga}, Feynman \cite{feynmanref1,feynmanref2,feynmanref3}, Schwinger \cite{schwingerref1,schwingerref2,schwingerref3} and Dyson \cite{dysonref1,dysonref2}.


\begin{figure}[h]
\centering
\includegraphics[width=3.5in,clip]{chap1_euler.pdf}
\caption{Hans Euler riding a bicycle.
}
\label{fig:euler}
\end{figure}


After my 1971 publication with John Wheeler of the article \textit{Introducing the Black Hole} (see Appendix \ref{appA_Ruffini2009p1645Phys_Today}), it became obvious to me, after some discussion with  Pietro Menotti, a visiting Italian theoretical physicist in Princeton,  that a natural place to test the Heisenberg-Euler process was in the gravitational collapse process leading to a black hole. I  went to see Heisenberg in his office at the Max Planck Institute in Munich.  
I discussed my article and some consequences of it with an enthusiastic Werner Heisenberg. I was very surprised to see him, unexpectedly small in stature, with a shiny gold $\hbar$ symbol on his tie, open to vigorously discussing the possible application I had proposed of his classic work with Euler to the physics of black holes. 
I had a splendid interaction with him: he was eager to tell me many anecdotes, in addition to discussing physics. He spoke of his many experiences with Fermi: from Fermi's timid approach in G\"ottingen and Leipzig as a young postdoctoral student to Fermi's authoritative role as the towering leader of the group in Via Panisperna after receiving the Chair of Theoretical Physics in Rome. And all this was described to me by Heisenberg recalling his stop in Rome on a trip back from Sicily to Germany filled with great memories. These contacts developed into a close friendship I had in the following years with him and his wife all the way up through a memorable trip to California in 1974 which I will recall later. 

[need to discuss a point with Jorge??]

\section{From quantum statistics to quantum field theories}

I have already described the key role played by the confrontation of opposing conceptual ideas between Eddington and Chandrasekhar  and also between Einstein and Oppenheimer. They were finally resolved satisfactorily in the intervening years and lead to a deeper understanding of the underlying physical and astrophysical phenomena.
But these were minor confrontations if one compare them to the major confrontation between Einstein  and Heisenberg in their vision of nature which still dominates the world of theoretical physics today and which perhaps finds in the new field of relativistic astrophysics some specific examples of collaboration and progress. To illustrate this point I will refer mainly to some reconstruction made by Heisenberg on the occasion of the 1927 and 1930 Solvay Meetings and let his words express the extremely important scientific exchanges and their unfortunate interruption around 1933. 
I have mentioned some of  the difficulties encountered by Einstein in the earlier development of general relativity and it is equally interesting to recall some of the difficulties encountered by Heisenberg in having his quantum field theory, developed with Jordan (see Fig.~\ref{jordan}) and Born, accepted by Albert Einstein. Some criticisms had already been presented by Einstein when in 1926 Heisenberg, at the time in Leipzig, had been invited to a colloquium in Berlin. 
His first meeting with Einstein is vividly recalled by Heisenberg:\footnote{
From the book:
Werner Heisenberg, ``Encounters with Einstein: And Other Essays on People, Places, and Particles"
(Princeton University Press, Princeton, NJ, 1989), pp.~112--114.
} 

\begin{quotation}
\ldots Berlin was then the citadel of physics in Germany. Here Planck, von Laue, Nernst and above all Einstein were teaching.
 Here Planck had discovered the quantum theory, and Rubens had confirmed it by his measurements of thermal radiation. 
And here Einstein, in 1916, had formulated the general theory of relativity and the theory of gravitation. Einstein would thus be in the audience; I would make his personal acquaintance.
[\ldots]
The lecture went off more or less as desired; there were good and helpful questions asked in the discussion that followed. I saw that I had secured Einstein's interest.
[\ldots]
For the first time, therefore, I now had the opportunity to talk with Einstein himself. On the way home, he questioned me about my background, my studies with Sommerfeld. But on arrival, he at once began with a central question about the philosophical foundation of the new quantum mechanics. He pointed out to me that in my mathematical description the notion of ``electron path" did not occur at all, but that in a cloud chamber the track of the electron can of course be observed directly. It seemed to him absurd to claim that there was indeed an electron path in the cloud chamber, but none in the interior of the atom. The notion of a path could not be dependent, after all, on the size of the space in which the electron's movements were occurring. I defended myself to begin with by justifying in detail the necessity for abandoning the path concept within the interior of the atom. I pointed out that we cannot, in fact, observe such a path; what we actually record are frequencies of the light radiated by the atom, intensities and transition probabilities, but no actual path. And since it is but rational to introduce into a theory only such quantities as can be directly observed, the concept of electron paths ought not, in fact, to figure in the theory. 

To my astonishment, Einstein was not at all satisfied with this argument. He thought that every theory in fact contains unobservable quantities. The principle of employing only observable quantities simply cannot be consistently carried out. And when I objected that in this I had merely been applying the type of philosophy that he, too, has made the basis of his special theory of relativity, he answered simply: ``Perhaps I did use such philosophy earlier, and also wrote of it, but it is nonsense all the same."

%He pointed out to me that the very concept of observation was itself already problematic. Every observation, so he argued, presupposes that there is an unambiguous connection known to us, between the phenomenon to be observed and the sensation which eventually penetrates into our consciousness. But we can only be sure of this connection, if we know the natural laws by which it is determined. If, however, as is obviously the case in modern atomic physics, these laws have to be called into question, then even the concept of ``observation" loses its clear meaning. In that case, it is the theory which first determines what can be observed.

\end{quotation}



\begin{figure}[h]
\centering
\includegraphics[width=4in,clip,angle=90]{chap1_kharkov1929.pdf}
\caption{Pascual Jordan's lecture at the Kharkov Conference in 1929 (courtesy of the Armenian Academy of Sciences).
In the first row in white shirt and tie is Viktor Ambartsumian, on his right Vladimir Fock and Dmitri Ivanenko (``sweet as a brioche'' in Gamow's words).
Further to his left also in white shirts are George Gamow and Lev Davidovich Landau. 
}
\label{fig:kharkov1929}
\end{figure}



An epochal Solvay Meeting took place in 1927 (see Fig.~\ref{fig:solvay1927}). 
There discussion between Heisenberg and Einstein took place and I quote here the words of Heisenberg:\footnote{
From the book:
Werner Heisenberg, ``Encounters with Einstein: And Other Essays on People, Places, and Particles"
(Princeton University Press, Princeton, NJ, 1989), pp.~115--117.
}

\begin{quotation}
\ldots  The spring of 1927 then saw the birth of the so called uncertainty relations, whereby the transition to a statistical interpretation  of quantum theory was finally completed. And hence they now formed the main topic of the discussion in Brussels. As I have already said, Einstein was unwilling to recognize the statistical interpretation; so he repeatedly tried to refute the uncertainty relations. These relations involve the statement that two determinants of a system, which must both be known at once in classical physics, in order to determine the system completely, cannot, in quantum theory, be exactly known at the same moment; and hence that between the uncertainties or inexactitudes of these quantities there are mathematical relations which prevent an exact knowledge of both quantities. Einstein kept on trying, during the congress, to refute the uncertainty relations by means of counter-examples, which he formulated in the shape of thought experiments. We were all living in the same hotel, and Einstein was in the habit of bringing along to breakfast a proposal of this kind, which then had to be analyzed. Einstein, Bohr and I would usually make our way to the congress hall together, so that even on this short walk a beginning could be made on anlysing and clarifying the assumptions. In the course of the day, Bohr, Pauli and I would frequently discuss Einstein's proposal, so that already by dinner-time we could prove that his thought-experiments were consistent with the uncertainty relations, and so could not be used to refute them. Einstein admitted this, but next morning brought along to breakfast a new thought experiment, generally more complicated than the previous one, which was now to effect the refutation. The new proposal fared no better than the old; by dinner it could be disproved. And so it went on for several days. In the end we---that is, Bohr, Pauli and I---knew that we could now be sure of our ground, and Einstein understood that the new interpretation of quantum mechanics cannot be refused so simply. But he still stood by his watchword, which he clothed in the words ``God does not play dice" to which Bohr could only answer ``But still, it cannot be for us to tell God, how he is to run the world." 
Three years later, in 1930, there was another Solvay Congress in Brussels, at which the same questions were discussed, and the general outcome was also much the same. So there we had to leave it, united in being different opinions. ``We agreed to disagree" as the British say. 
I then, unfortunately, did not meet Einstein for many years. For in the meantime the political horizon had again darkened; the National Socialists had come to power in Germany, and to Einstein it was plain that he neither could nor would remain any longer in Germany.
%\ldots 
\end{quotation}


\begin{figure}[h]
\centering
\includegraphics[width=5in,clip]{chap1_solvay1927_scan.pdf}
\caption{Fifth Solvay Conference on Quantum Mechanics, Brussels, 1927. 
(Photograph by Benjamin Couprie, Institut International de Physique Solvay, Brussels, Belgium.) In the last row W. Pauli, W. Heisenberg and R.H. Fowler, each next to the other. The complete set of pictures of the Solvay Meetings were donated by Dr.~Ernest Solvay to ICRANet on the occasion of receiving the Marcel Grossman Meeting Award in the Fourth Marcel Grossman Meeting in Rome in 1985.
From back to front and from left to right:
Auguste Piccard, \'Emile Henriot, Paul Ehrenfest, \'Edouard Herzen, Th\'eophile de Donder, Erwin Schr\"odinger, Jules-\'Emile Verschaffelt, Wolfgang Pauli, Werner Heisenberg, Ralph Howard Fowler, L\'eon Brillouin,
Peter Debye, Martin Knudsen, William Lawrence Bragg, Hendrik Anthony Kramers, Paul Dirac, Arthur Compton, Louis de Broglie, Max Born, Niels Bohr,
Irving Langmuir, Max Planck, Marie Curie, Hendrik Lorentz, Albert Einstein, Paul Langevin, Charles Eug\'ene Guye, Charles Thomson Rees Wilson, Owen Willans Richardson.
}
\label{fig:solvay1927}
\end{figure}



The 1927 Solvay Meeting was followed by the next one in 1930 when finally Fermi was also invited (see Fig \ref{fig:solvay1930}).
One can make the claim that these two meetings represented a separatrix. The last opportunity for a direct constructive interaction between Einstein's vision of a geometrical unifying approach to Nature and the quantum interpretation of Heisenberg took place there. The two worlds remained separate from each other for decades until forty years later they were brought back together 
in the unification of quantum  field theories and in the setting  of relativistic astrophysics.



\begin{quotation}
\ldots 
In the meantime the political horizon had again darkened; the National Socialists had come to power in Germany, and to Einstein it was plain that he neither could nor would remain any longer in Germany. He therefore spent a great deal of his time in travel abroad. Many universities all over the world counted themselves lucky if they could secure Einstein as a lecturer, or for a longer visit. The National Socialist revolution of 1933 then wrote {\it finis} to Einstein's stay in Germany. 
\ldots \footnote{
From the book:
Werner Heisenberg, ``Encounters with Einstein: And Other Essays on People, Places, and Particles"
(Princeton University Press, Princeton, NJ, 1989), p.~117.
}
\end{quotation}




\begin{figure}[h]
\centering
\includegraphics[width=5in,clip]{chap1_solvay1930_scan.pdf}
\caption{Sixth Solvay Conference on Physics, Brussels, 1930. Finally P.A.M. Dirac, W. Pauli, E. Fermi and W. Heisenberg were all together present at the meeting. 
E. Herzen, E. Henriot, J. Verschaffelt, C. Manneback, A. Cotton, J. Errera, O. Stern, A. Piccard, W. Gerlach, C. Darwin, P.A.M. Dirac, E. Bauer, P. Kapitsa, L. Brillouin, H. A. Kramers, P. Debye, W. Pauli, J. Dorfman, J. H. Van Vleck, E. Fermi, W. Heisenberg,
Th. De Donder, P. Zeeman, P. Weiss, A. Sommerfeld, M. Curie, P. Langevin, A. Einstein, O. Richardson, B. Cabrera, N. Bohr, W. J. De Haas.
}
\label{fig:solvay1930}
\end{figure}


\section{The decline of the  Fermi group in Rome}

1933 was precisely the year in which an gesture of solidarity with Einstein was again made by Enriquez and Levi-Civita   when he had expressed his interest to transfer to Rome. He made this request when the National Socialist Party came to power in Berlin and anti-Semitism became official policy. 

\begin{quotation}
\ldots 
``My father, says Adriana Enriques, turned to our uncle, Isaia Levi, very close to Mussolini. Mussolini receives my father: ``No, professor," he says. I'm not anti-Semitic: but why import a scientist from abroad when we have so many scientists to support in Italy?"
\ldots 
\footnote{
Excerpt of the article on the newspaper ``Corriere della Sera'' by Maurizio Chierici: {\it ``Io e Einstein alla stazione\ldots ," a colloquio con la figlia del matematico Federigo Enriques} (April 10, 1992, p.~9), in translation.
}
\end{quotation}

After the first glorious years of the group around Fermi at Via Panisperna 
\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_amaldi_fermi.pdf}
\caption{Fermi with some of his closest  collaborators in Rome: Oscar D'Agostino, Emilio Segr\`e, Edoardo Amaldi and Franco Rasetti (from left to right).
}
\label{chap1_fig8}
\end{center}
\end{figure}
the  Physics Institute was transferred to the Marconi Institute in the new campus of the University of Rome ``La Sapienza" (Studium Urbis), the situation there quickly deteriorated. I recall distinctively Ugo Fano, a friend and collaborator of Fermi, vividly remembering the departure of Fermi from Rome mainly motivated, in his opinion,  by the takeover of the Institute by Antonino Lo Surdo following the death of Orso Mario  Corbino (1937). 
In addition Fermi also had a threat hanging over his family due to the infamous racial laws.
In 1938 the president of the ``Accademia dei XL'' replied to a circular sent out by the minister Bottai, who requested a census of the members of the Academy of Jewish origin. After mentioning the members (G.E. Almansi, G. Castelnuovo, F. Enriques, G. Fubini, G. Levi, T. Levi-Civita and G. Morpurgo), he also mentioned that Fermi's wife was of Jewish origin (see Fig.~\ref{fig:bottai}). Also in 1938 Albert Einstein was dismissed as a foreign Member of the Academia Nazionale dei Lincei.The same happened to  Federigo Enriquez and Tullio Levi Civita as National Members. Einstein and Enriquez were readmitted in 1945. Unfortunately Levi Civita had passed away in 1942.
In 1939 Fermi's father-in-law, the admiral Augusto Capon, was expelled from the reserves of the Navy and in 1943 deported to Auschwitz and killed there.


\begin{figure}[h]
\begin{center}
\includegraphics[width =3.5in]{chap1_fermi_nobel.pdf}
\end{center}
\caption{Fermi and the King of Sweden Gustav V when Fermi was awarded the Nobel Prize on December 10, 1938.
As Edoardo Amaldi wrote, ``\ldots  The fact that Fermi was wearing the tailcoat, instead of the fascist uniform 
or the dress of the Italian Academy, and shook hands with the King instead of the giving the Fascist salute,
produced a wave of indignation in the press very rigidly controlled by the regime.''
[Edoardo Amaldi, Ref.~\protect\cite{amaldi}, p.~64].
}
\label{chap1_fig3}
\end{figure}


As is well known  the awarding of the Nobel Prize (see Fig.~\ref{chap1_fig3}) to Fermi coincided with his departure  for the United States (see Fig.~\ref{chap1_fig4}).
I consider his acceptance speech in Stockholm  to be of such a great beauty and actuality that we have reproduced it in 
Appendix A. \typeout{Appendix A NEEDS cross-reference}% 
The process of building up the elements, initiated by Fermi and later continued  by Segr\'e using the cyclotron,  is still  today extremely important in understanding the origin of the transuranic elements in an astrophysical setting through the $r$-process.

\begin{figure}[h]
\begin{center}
\includegraphics[width=3.5in,angle=90]{chap1_fermi_family.pdf} 
\caption{Fermi arrives with his family in New York on January 2, 1939.
}
\label{chap1_fig4}
\end{center}
\end{figure}

The 1938 racial laws of the fascist Italian government caused the final collapse of  the research on general relativity in the mathematics institute as well. It suffices here to recall the ban on the teaching activities of Tullio Levi-Civita and the deprivation of his membership in all scientific societies. He died isolated from the rest of the scientific world in his apartment in Rome in 1941.%
\footnote{
To get an idea of the ostracism which caused a real ``damnatio memoriae'' it's enough to have a look at an article of Francesco Severi (the founder and director of the Istituto Nazionale di Alta Matematica) in the review ``Primato,'' founded and directed by Giuseppe Bottai, Minister of Education, of October 15, 1942 bearing the title ``Matematica e civilt\`a.'' In the course of the article, the author had the occasion to make a survey of the Italian mathematicians of the last decades without even mentioning Vito Volterra and Tullio Levi-Civita. Remarkably, among the physicists, also Fermi is absent; he had already left Italy in 1938!
}

\begin{figure}[h]
\begin{center}
\includegraphics[width =3.5in]{chap1_bottai.pdf}
\end{center}
\caption{The census of the members of the ``Societ\`a Italiana delle Scienze'' of Jewish origin (Archive of the ``Accademia Nazionale dei XL''). 
Fermi is mentioned because his wife was of Jewish origin.
}
\label{fig:bottai}
\end{figure}



The sudden disappearance of Ettore Majorana in 1938 clouded the activities of the Rome group even further. 
For many years I have  attempted to understand the  mystery of his disappearance. Much of this understanding lies in my following the intricate way he obtained the chair of theoretical physics  from the Minister of Education Giovanni Gentile, whose son Giovanni Gentile, Jr.\ was competing with Majorana for the same chair (shown in the photo with Heisenberg in Fig.~\ref{fig:heisenbergetal} of the Preface).
The solution found for his chair was a direct call ``per chiara fama" from the minister, avoiding any scientific or medical examination. To me this was a key factor necessary to shed some light on this great mystery together with ``il mal di Napoli" recalled to me by Edoardo Amaldi the most eminent member of our faculty in Rome.  


\section{The Italian physics diaspora following 1938}

In time the  1938 racial laws destroyed  the development of physics in Italy by forcing many outstanding physicists to flee to the United States and Canada following Fermi's example. Among these were:

Sergio De Benedetti had gotten his physics degree in Florence (1933) and a few years later under the threat of Fascism made his way from Italy to the US after a few years in France with Ir\`ene Curie and Fr\'ed\'eric Joliot, leaving just before the arrival of the Nazis in 1940 to work in nuclear physics at a series of American research and academic institutions before settling at the Carnegie Mellon Institute of Technology, where many years later he invited me to give a colloquium. There he had been a pioneer in the use of positrons to study various states of matter  and  later was responsible for pioneering work on X-rays from pionic and muonic atoms.

Ugo Fano had studied mathematics at the University of Turin (1934) and soon became one of Fermi's closest collaborators in Rome as the youngest of the famous group of young ``Via Panisperna boys," named after the street where their physics institute was located prior to the transfer to its present location at the University of Rome  ``la Sapienza." Ugo had also collaborated with Heisenberg in Leipzig from 1936 to 1937 before his move to the US. In his case the transfer to the United States involved not only himself but an entire group of distinguished physicists and engineers in his family: his brother Roberto Fano  was a professor at MIT who was one of the founders of computer science and Ugo's wife Lilla Fano coauthored a series of books on the physics of atoms and molecules. I was introduced to Ugo by his nephew and my closest friend and astrophysics colleague Aldo Treves, while Aldo was  at MIT and I at Princeton. Ugo started at the National Institute of Standards and Technology in Washington, DC and moved to the University of Chicago in 1966.  He invited me to give a colloquium at the University of Chicago in 1972, a memorable event with the presence of many distinguished scientists, including  Valentin Telegdi and S. Chandrasekhar. 


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in,angle=90]{chap1_pontecorvo.pdf}
\caption{
The last photo I took of Bruno Pontecorvo (right) with Zel'dovich (left). I was having a discussion with Zel'dovich in his office in Leninsky Prospect when I asked him: how is Bruno? He did not answer but took his jacket with two gold medals and said ``Follow me and do not stop." He drove quickly to a hospital were he was greeted upon arrival and he almost ran to the third floor and knocked on a door which he immediately opened. Pointing to a surprised and happy Bruno he exclaimed: Remo, here is Bruno! 
}
\label{chap1_pontecorvo_moscow}
\end{center}
\end{figure}

Another Via Panisperna boy was Bruno Pontecorvo. He was born and studied initially in Pisa and transferred to Rome at the age of eighteen  where he was admitted to the third year of the physics curricula. He became the youngest and one of the closer collaborators of Fermi.  In 1936 he transferred to Paris and in 1940 after the Nazi invasion of Paris, he fled to the US, later moving to Canada. In 1948 he became a British citizen and worked at Harwell on the British atomic bomb project. In August 1950 he moved to the Soviet Union. My friendship with Bruno developed in a series of meetings I had with him arranged mainly through Yacov Borisovich Zel�Dovich in Moscow. Bruno and I shared a major common interest in the physics and astrophysics of neutrinos. The best testimony of our many scientific discussions together was captured in our video ``Il Caso Neutrino" made for Italian television, available on-line in both Italian and English at \url{http://www.icranet.org/videos/il\_caso\_neutrino.wmv}.
The friendship with him was also deepened by my many meetings with his brother in Rome: Gillo Pontecorvo. 
%See Fig.~\ref{chap1_fig_gpontencorvo}. 
%\Typeout{needs figure of Gillo Pontecorvo??} % NEEDS FIGURE
I met  Bruno him through the last years of his life both in Rome, see Fig.~\ref{chap1_pontecorvo_rome}
%\Typeout{needs figure of Bruno Pontecorvo and remo in rome??}  % NEEDS FIGURE
and in  the hospital in Moscow where I  took the last photo of him with Zel'dovich, 
see Fig.~\ref{chap1_pontecorvo_moscow}.


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_pontecorvo_rome.pdf}
\caption{
To insert. 
}
\label{chap1_pontecorvo_rome}
\end{center}
\end{figure}


Bruno Rossi studied at the University of Padova and got his degree from the University of Bologna. Soon after he initiated  the school on cosmic ray research at the University of Florence, where he obtained fundamental results on the makeup of cosmic rays, and also the first evidence for the existence of cosmic ray showers, performing his experiments in Ethiopia which was then an Italian colony. In 1938 he escaped Italy first to Copenhagen as a guest of Niels Bohr, then moved on to England and then to the US. In 1943 he was invited by Fermi to the University of Chicago, then went to Cornell University and then to MIT in Boston in 1946 where he remained until his retirement in 1970. In 1958 he joined the company America Science and Engineering as a consultant, in which capacity he called Riccardo Giacconi to initiate X-ray astronomy the next year. From 1974 to 1980 he returned to Italy as a Professor at the University of Palermo where he collaborated with Giuseppe Vaiana, a  distinguished space astrophysicist  from MIT who returned in that period to Palermo to become the Director of the Astronomical Observatory. My contacts with Bruno where quite intense during my period at Princeton and later through both Riccardo and ``Pippo" Vaiana. It was a pleasure to collaborate with Bruno in organizing various plenary sessions at The American Physical Society discussing the earliest results on the physics and astrophysics of neutron stars and black holes. Bruno was actually quite conservative in his approach then, unlike 
Riccardo Giacconi %\cite{??}  % NEEDS CITATION
and 
Herbert Gursky: %\cite{??}:  % NEEDS CITATION
he was happy to recognize the role played by white dwarfs  but not neutron stars and black holes in binary X-ray sources.

\vskip12pt [remo edit stops here]\\

Emilio Segr\`e, also a Panisperna boy, was born in Tivoli and studied under Fermi at the University of Rome ``la Sapienza." From 1932 to 1936 he held the chair of nuclear physics there and then moved to the chair in experimental physics at the University of Palermo. In 1938 he transferred permanently to the University of Berkeley. In 1974 Emilio returned to Rome during the final period of his life where he obtained again his original chair at  ``la Sapienza." He was an important member of the Manhattan Project during World War II and later won the Nobel Prize  with Chamberlain for the discovery of the anti-proton. Many were my encounters with Emilio: I found him to be a very serene person, with a peculiar sense of humour. His serenity is evident in his beautiful book on nuclei and particles \cite{segrebook}
through its very effective presentation
reflecting the style and the imprint of Fermi's teaching. Once in Princeton I had a student from Iran who was approaching his graduate research with this same imprint. His name was Bahram Mashhoon. I was puzzled by this until he told me that his undergraduate thesis advisor was Emilio, making him an authentic grandchild of the Fermi school. 

Franco Rasetti, another Via Panisperna boy already mentioned above, though not Jewish, moved to Canada in 1939 and later settled at John Hopkins University in Baltimore. He not only fled the absurd intellectual persecution in Rome but left physics altogether,  dedicating himself to the study of botany and trilobites!
Enrico Persico \cite{persicobook}, Fermi's close friend and fellow student from their university days together in Pisa,  remained in Italy after the imposition of the racial laws but moved to Canada a few years after the war taking Rasetti's position when Rasetti left for the US. However,  he returned to Rome a few years later to eventually have the Chair of Theoretical Physics formerly held by Fermi and much later by myself. He  was my professor of theoretical physics during my university studies. 

Among the very few scientists of Jewish origin who had decided to stay in Italy all the way through the Second World War was Arrigo Finzi, who had done his thesis with Tullio Levi-Civita on the Cauchy problem for the Einstein equations. When I asked him about his experiences in that period
under the Fascist regime he told me: ``Terrible! Terrible!" Soon after the end of the war Arrigo traveled  to the Institute for Advanced Study in  Princeton to discuss  his thesis  with Einstein. Later he was  one of the first settlers of the new state of Israel and became a Professor at the Technion in Haifa. While I was in Princeton he visited the NASA Institute for Space Science in New York where we often met. It was there were that Arrigo started his seminal work on what later became known as the dark matter component of the universe (see e.g., the recollections in the beautiful book of Sanders \cite{sanders} 
Arrigo almost every year visited me in Rome at ``la Sapienza" participating in scientific discussions. 
See Fig.~\ref{chap1_fig_finzi}.


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_fig_finzi.pdf}
\caption{Right to left: Arrigo Finzi, Gerald Tauber, myself and Konrad Bleuler in Greece.
}
\end{center}
\end{figure}

In Princeton I once strongly expressed  my opinion that one can hardly imagine the splendid development of physics in the US without the knowledge, dedication and enthusiasm of these authentic heroic scientific figures,  who fled from Italy before the war as a consequence of those terrible racial laws of the fascist government. The example and success of these scientists set a precedent that was followed  after the war by a large number of young physicists. This time they were not forced out of Italy by racial laws, but instead were attracted by the great intellectual stimulus, the scientific interests, and the American way of life with its many opportunities. Among them were Rosanna Cester, Tullio Regge, Riccardo Giacconi, Giuseppe Vaiana, Bruno Coppi, and myself in Princeton joining  Luigi  Crocco and later joined by the arrival of Enrico Bombieri.



\section{Fermi's contribution to Brazil and South America}

I will not speak of the particle physics development led by Fermi in the United States which has been celebrated in many books (see, e.g., Refs.~\cite{cronin,segre,lauraf}).
What I will talk about here, instead,  are some lesser known activities in Brazil inspired by Fermi before moving to the US which I have always found especially fascinating. 



\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_lattes.pdf}
\caption{Cesare Lattes (left) and Eugene Gardner (right) place photo-emulsions on the target probe of the 184 inch cyclotron at the University of California's Lawrence Radiation Laboratory for the detection of ``artificially" produced pi-mesons (March, 1948).
}
\label{chap1_fig7}
\end{center}
\end{figure}

In 1934 Gleb Wattaghin, 
born in the Ukraine but educated since childhood in Turin,  became the first physicist of the Italian school to transfer to Brazil. Giuseppe Occhialini was later sent by Fermi to join Wattaghin in  San Paulo in 1937. 
There a young student, Cesare Lattes, joined them. Cesare was the son of the former rabbi of Turin who had emigrated to Brazil due to  the insane racial laws of the Italian fascist government. Observations of cosmic rays were performed from Chacaltaya (1947) and the collaboration of Lattes and Occhialini with Powell and  Blackett was recognized internationally with the discovery of the pi-meson 
(Powell was awarded the Nobel Prize in physics in 1950 and Blackett in 1947). 
The description by Lattes of the discovery of the pi-meson is reproduced in Appendix \ref{appA_lattes}, see also Appendix \ref{appA_deandrade}, which also contains a paper on the scientific work of Lattes.


This sort of heroic ``wild" physics carried on by Lattes, and Occhialini from the mountain of Chattalquaia was  directly linked to analyzing phenomena occurring naturally in the universe, like their hunt for cosmic rays in the sky.  Soon after this activity  was followed by a high-precision physics of a different style under Earth-based ``controlled" laboratory conditions.
 One of the first examples of this equally important alternative style of research had again seen Lattes as one of the major protagonists identifying, with Eugene Gardner 
(see Fig.~\ref{chap1_fig7}), a multitude of  ``artificially" produced pi-mesons  at the 184-inch  Berkeley cyclotron built by Ernest Lawrence under ``controlled" conditions (see, e.g., Ref.~\cite{heilbron}). 

Comparing and contrasting these two styles of research---the �wild� one and the one performed under artificially �controlled-tame� conditions in the laboratory---it is often claimed that only those under controlled conditions in Earth-bound laboratory experiments guarantee the precision and reproducibility necessary in an experimental science. This is certainly not correct. In the case of Earth-bound experiments attention is directed to a single localized system which is studied through a series of events occurring at a specified location in space and for a time period in which the phenomenon can be submitted to direct measurement under artificially created circumstances under the control of the scientist. Such optimal conditions can be reproduced at will, leading to the essential reproducibility of the experiment required by the scientific method.

In the case of astrophysics the situation is apparently very different: the time scale of the phenomena under scrutiny occurring naturally independent of the observer�s is at times enormously long with respect to the lifetime of the observer and the specific events are hardly reproducible in a single system at a specific time. The analogous laboratory in this case is instead the entire universe and the system is not subject to the will of the scientist. However, it is possible to divide all astrophysical systems into equivalence classes and find, somewhere in the universe, a system that at a specific time of observation is undergoing the specific phenomenon of interest, a representative of its equivalence class.  As in Earth-based experiments, an astrophysical  ``experiment� also  requires special measurement techniques, and at times space technologies or observatories in a vast range of wavelengths are needed to analyze it. This can then be compared with other such events in its equivalence class to qualify for reproducibility and validation of the results.
 
Having established that the two methods are both equally valid from the point of view of their predictability  and reproducibility 
there is nevertheless an important difference. In Earth-based experiments the phenomenon is usually studied by itself, separate from any role that it might play in Nature if indeed it even occurs ``naturally.�  In astrophysics instead phenomena are observed occurring ``naturally,� so that the study of the phenomenon directly informs us about how it contributes to the actual working of our universe, i.e., there is no need to speculate further on how it might be used or not by Nature.



The physics developed under ``controlled" conditions  grew exponentially all over the world.
The work of Fermi as well as his anticipation of what would be found with accelerators has been well documented in the many testimonies found in the book edited by James Cronin \cite{cronin}. There the expectation by Fermi of the cost and energy of accelerators as a function of time (see Fig.~9.3 of that book) was reproduced and compared and contrasted with the energy versus time for actual accelerators (see its Fig.~9.5). Similarly interesting was his expectation for the largest possible accelerator in the future, the globotron as idealized by Fermi (see its Fig.~9.4).

It is not surprising that in Italy as well, this sort of ``controlled" physics became very popular,
first with the developments of the Frascati National Laboratories and then with CERN (see, e.g., Ref.~\cite{amaldi}) 
with the crucial and fundamental role in all these programs played by Edoardo Amaldi, one of Fermi's closest collaborators of in Rome (see Fig.~\ref{chap1_fig8}), and who had been my teacher. 
Soon an academic alliance materialized in the Physics Institute in Rome between the elementary particle physicists and the solid state physicists. They did not have any interest at that time  in carrying out genuine research in general relativity or on Einstein's field theories.

But without being carried away by ``big science,'' which is already well discussed in many books,
let us return to Fermi and his critical attitude towards the work in cosmology and in Einstein's theory that he had developed in Chicago after the Los Alamos bomb experience. As we will show, this will represent a very important seed planted by Fermi for the growth of the field of relativistic astrophysics.


\chapter[From the 1940s to the 1950s: the Fermi-Turkevich work]{From the 1940s to the 1950s: the Fermi-Turkevich work}{} 



\section{General relativity at the University of Rome ``la Sapienza" after the Second World War} 

What happened after the Second World War under the new conditions of the newly established  democracies? I will look first at the University of Rome and the birth there of particle physics and at the same time a timid new opening towards  Einstein's theory of general relativity. I will then return to the new Fermi period in the US after the achievement of the atomic bomb in Los Alamos and applying his great knowledge acquired in nuclear physics to cosmology. Many books have been 
written on the Manhattan Project
and I have nothing to add. On the work of Fermi and Turkevich much has still to be appreciated and I will give a presentation based on Fermi's own work. I will show how this work in due time has become fundamental to the entire field of relativistic astrophysics.
  



The disregard for Einstein's theory that had existed at the University of Rome between the world wars  continued to some extent even later,  both within the University and also in the city of Rome.
The latter can be illustrated by an anecdote which, although minor with respect to the atrocious racial laws, still reveals a lack of respect for the figure of Einstein.
At the time, there were three institutes in the Faculty of Science at the University of Rome  and correspondingly three  ``lauree'' or diplomas: ``Mathematics,'' ``Physics'' and also ``Fisica Matematica'' (mathematical physics). The last one was solely directed at creating the teaching staff for high schools, and had a lighter scientific curriculum and was attended primarily by women. A ``fisico matematico"  usually ended up teaching in high schools. 
A sort of epitome of  this depreciative attitude found its way into the naming of a street in Rome in honor of Einstein. The commission charged with selecting new street names gave great prominence to physicists and mathematicians alike in the Portuense District of the city. 

``Piazza Enrico Fermi'' is at the start of a major artery followed by ``Viale Guglielmo Marconi'' and even the four lane ``Via Quirino Majorana'' (after an obscure but locally influential physicist in Bologna, the uncle of Ettore Majorana). In that district, the shortest street,  without even an exit, a ``cul de sac'' as it is technically called, was dedicated in 1957 to Einstein with the name Via Alberto\footnote{
Later  corrected to Albert in 1995.
} 
(!) Einstein with  the explicative note ``Fisico Matematico'' in parentheses.
It is interesting that neither the name of Guglielmo Marconi nor that of Quirino Majorana was followed by any such note,
while the name of Enrico Fermi was indeed followed by ``Fisico'' (Physicist). 
See Fig.~\ref{chap1_fig5}.


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_streets.pdf}
\caption{Street signs in Rome dedicated to Guglielmo Marconi, Enrico Fermi  and Albert Einstein.
Einstein's street was initially named Via Alberto Einstein and then corrected decades later in 1995 to Via Albert Einstein.
}
\label{chap1_fig5}
\end{center}
\end{figure}


Somewhat the same attitude continued within the University of Rome after the war: we had witnessed the destruction of the school of geometry in the Mathematics Institute following the infamous racial laws of the fascist regime. An attempt to have a new beginning for Einstein's theory was made in 1959 by Carlo Cattaneo, who lectured in the Mathematics Institute in close contact with the French school of A. Lichnerowicz and Y. Choquet-Bruhat.
He gave an opportunity to students in the Physics Institute, myself included, to learn the formalism of general relativity. 

In the Physics Institute the newly developed field of particle physics soon became predominant. One reason for its clear success was the unprecedented high level of work around Oreste Piccioni in the last floor of the Physics Institute at the University of Rome.\footnote{This story was documented in a documentary film made for Italian RAI TV ``I ragazzi di via Giulia" directed by Adolfo Conti (2015), available on-line.}


Luis Alvarez, in his Nobel Lecture (1968), said:
``As a personal opinion, I would suggest that modern particle physics started in the last days of World War II, when a group of young Italians, Conversi, Pancini, and Piccioni, 
who were hiding from the German occupying forces, initiated a remarkable experiment. In 1946, they showed that the ``mesotron'' which had been discovered in 1937 by 
Neddermeyer and Anderson and by Street and Stevenson, was not the particle predicted by Yukawa as the mediator of nuclear forces, but was instead almost completely unreactive in a nuclear sense.''
Oreste left for the USA almost immediately after the discovery. I became his good friend in La Jolla.  Today I am still using the room where he did his experiment, as a working space for my graduate and undergraduate  students.
The wall of that room is filled with the signatures of distinguished visitors (see Fig.~\ref{chap1_figwheeleratg9}) including Oreste himself, who also signed the wall while visiting in 1989 (see Fig.~\ref{chap1_fig6}).

\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_g9_sign.pdf}
\caption{The signatures of Wheeler and Giacconi on the wall of the common room of the group G9 at the Department of Physics of the University of Rome ``la Sapienza." To the uppercase ``U" drawn by Wheeler representing the universe acquiring conscience from its own observations, Riccardo added a symbol of his X-ray mirror technique developed for the Einstein and Chandra telescopes. 
}
\label{chap1_figwheeleratg9}
\end{center}
\end{figure}



\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_g9_sign2.pdf}
\caption{Piccioni's signature on the same G9 wall.
}
\label{chap1_fig6}
\end{center}
\end{figure}


Indeed Oreste was one of the first young physicists who emigrated from Rome to the USA after the Second World War.
In addition to those already mentioned above, I would like to add 
Giuseppe Vaiana at the Harvard-Smithsonian Center for Astrophysics and 
Giancarlo Wick at Columbia University (see Wick in the photo with Heisenberg in Fig.~\ref{fig:heisenbergetal} of the Preface).


\section{The Fermi's leap in cosmology and in Einstein's world}

To illustrate the world of  cosmology  as a  precursor to the field of relativistic astrophysics and its relation to Einstein's theory of general relativity,  I use the well-known picture taken on the occasion of Einstein's seventieth birthday (see Fig.~\ref{chap1_fig9}).

\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_einstein70.pdf}
\caption{Albert Einstein's seventieth birthday (May 19, 1949).
From left to right:  H.P. Robertson, E. Wigner, H. Weyl, K. G\"odel, I. Rabi, A. Einstein, R. Ladenburg, J.R. Oppenheimer, G. Clemence.
}
\label{chap1_fig9}
\end{center}
\end{figure}


Some of the major predecessors of relativistic astrophysics are portrayed here. Robert Oppenheimer, standing to the left of Einstein, through his two classic papers with his students Robert Serber \cite{oppserber} and George B. Volkoff \cite{oppvolkoff} gave the basis for the treatment of neutron stars. It was indeed in solving this problem that the classic set of differential equations which have become known since as the Tolman-Oppenheimer-Volkoff equations (named also for Richard C. Tolman \cite{tolman1939}), or for short the TOV equations, were introduced.\footnote{
See footnote \ref{foot13}
} 
It was again Oppenheimer who courageously accepted the extreme consequences of the work of Landau, Chandrasekhar and Gamow that I spoke of earlier. The existence of a critical mass against gravitational collapse occurs as soon as the degenerate self-gravitating  Fermi gas supporting the equilibrium configuration becomes relativistic. With his graduate student Harland Snyder, Oppenheimer explicitly expressed the general relativistic equations governing the process of continued gravitational collapse \cite{oppsnyder}.
As I stated above,  this paper evoked a strong reaction by Einstein himself 
(see Fig.~\ref{chap1_fig9}), %{fig:einopp})??
and only recently has it been proven that the counterexample of the ``Einstein cluster" does not rule out the possibility of the occurrence of complete gravitational collapse to the Schwarzschild radius  and beyond.
The Oppenheimer-Snyder work evolved over time into one of the most important concepts of relativistic astrophysics: the black 
hole \cite{rr_intro_bh}. 

Two other scientific giants also appear in this picture: Isidor Rabi and Eugene Wigner, with whom I enjoyed and entertained a dialogue for years, in Princeton and New York, on the role of Einstein's theory in the foundations of relativistic astrophysics and especially on the measurable quantities in black hole physics. 

Returning to cosmology, portrayed in this  picture are three other giants who played a crucial  role in linking cosmology to Einstein's theory of general relativity: 
Howard Percy Robertson\footnote{See e.g., H.P. Robertson, T.W. Noonan:  \textit{Relativity and Cosmology},  W.B. Saunders Company (1968).}
who described the dynamical aspects of the evolving universe model discovered by Alexander Alexandrovich Friedmann,\footnote{
Friedman's two fundamental papers originally published in \textit{Zeitschrift f\"ur Physik} {\bf 10}, 377 (1922) and  {\bf 21}, 326 (1924), are reprinted in English translation in \textit{General Relativity and Gravitation} {\bf 31}, 1991, 2001 (1999).
} 
Hermann Weyl, who more than anyone else emphasized the close connections between Hubble's observations of the receding galaxies and the conceptual framework of a spatially homogeneous and isotropic universe satisfying Einstein's field equations \cite{weylbook2}, and finally Kurt G\"odel. 
I have  recently discussed the vigorous conceptual role of Weyl and G\"odel in probing the foundations of cosmology in the realm of general relativity (see Fig.~\ref{chap1_fig10}).\footnote{
See e.g., Ref.~\cite{rrsigismondi}. 
\label{foot36}
}
An excerpt regarding my interaction with Kurt G\"odel, as well as many discussions on the role of rotation in the universe, is given in Appendix \ref{appA_rem_godel}.


\begin{figure}[h]
\begin{center}
$\begin{array}{cc}
\includegraphics[width =2.5in]{chap1_godel1.pdf}&\quad
\includegraphics[width =2.5in]{chap1_godel2.pdf}\\[.4cm]
\quad\mbox{(a)}\quad &\quad \mbox{(b)}
\end{array}$\\
\end{center}
\caption{Kurt G\"odel and Albert Einstein (1954), together with
an original reprint of the classic paper dedicated by G\"odel to Einstein in honor of his seventieth birthday.
The copy was autographed to me by Kurt G\"odel in 1974 and is now at the ICRANet Center in Pescara.
}
\label{chap1_fig10}
\end{figure}


With his own style of research and particular attitude towards physics, Fermi was quite far removed from the questions these scientists were addressing,
but he jumped into their world to address cosmological nucleosynthesis
with three important tools:\\
1) the ability to use electronic calculating machines for the first time in an astrophysics context to integrate the system of rate equations.\\
2) a precise knowledge of the nuclear cross sections derived from the Los Alamos activities, some of them still classified, and\\
3) an expert knowledge of Einstein's field  equations which he had mastered in the early days in Pisa.

To reach a detailed understanding of his work,
it has been essential for me to read and translate into English the lecture he gave in Rome on October 7, 1949, which is reproduced in Appendix \ref{appA_fermi240_3}.  In the following paragraphs I will use his own words from that lecture  to illustrate the physical motivations which drove him in his fundamental work with Turkevich.
But first let me digress briefly to prepare the conceptual landscape in which this work was realized and recall the results of Friedmann and the Soviet-Russian school which were adopted by Fermi in his own work.


\section{The roots of relativistic cosmology in the Soviet-Russian school}

The view of cosmology as we understand it today was formulated by the Soviet-Russian school of physics,  profoundly rooted in the solution of Einstein's field equations first obtained by Alexander Alexandrovich Friedmann  
(Fig.~\ref{chap1_fig11}). From the conditions of homogeneity and isotropy for the three-dimensional space geometry, came a cosmological model for the universe with a definite beginning at a finite time in the past and drawing attention to the dynamical nature of space itself. Its success has  certainly been due to the identification of this dynamical expansion of space with the recession of galaxies observed by Hubble, a view forcefully expressed by Hermann Weyl.
It is interesting that, according to Sandage,
Hubble himself refused to believe such an explanation as long as he lived.


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_friedmann.pdf}
\caption{Alexander Alexandrovich Friedmann.
}
\label{chap1_fig11}
\end{center}
\end{figure}


At the end of World War II an equally important work appeared by Evgeny Lifshitz\cite{lifshitz} (Fig.~\ref{chap1_fig12}) and later by him and Isaac Khalatnikov\cite{khalatnikov} 
(see Fig.~\ref{chap1_khalatnikov}) 
who developed a novel theoretical approach to analyze the perturbations of a Friedmann universe in terms of scalar, vector and tensor harmonics in the quest for the solution of the problem of galaxy formation in the expanding homogeneous and isotropic Friedmann universe.\footnote{
The work of Lifshitz and Khalatnikov was further expanded in the study of the initial cosmological singularity by Belinski, Lifshitz and Khalatnikov. In recognition of this achievement, the $13^{th}$ Marcel Grossmann Award was granted to Belinski and Khalatnikov with the following motivation: ``for the discovery of a general solution of the Einstein equations with a cosmological singularity of an oscillatory chaotic character known as the BKL singularity.'' 
%See Fig.~\ref{chap1_fig_belinski??}. \Typeout{Belinski photo??}%  % NEEDS FIGURE, NEEDS CITATIONS??
%\begin{itemize}
%\item[]
%E. M. Lifshitz: On the Gravitational Stability of the Expanding Universe, \textit{J. Phys.\ USSR} {\bf 10}, 116 (1946),
%\item[]
%E. M. Lifshitz, I. M. Khalatnikov: Investigations in Relativistic Cosmology, \textit{Adv.\ Phys.} {\bf 12}, 185--249 (1963),
%\end{itemize}
}


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_khalatinikov-ruffini.pdf}
\caption{Isaac Markovich Khalatnikov with myself at MG13.
}
\label{chap1_khalatnikov}
\end{center}
\end{figure}

The time scale of the development of such perturbations was soon found to be too long to obtain the observed galactic structures. It was starting on the premise of this work by Lifshitz that  in 1946 George Gamow initiated a series of short articles exploring both the condition for the formation of the elements and of galaxies in a Friedmann cosmology. The work of Gamow was quite different in style from the rigorous and precise mathematical derivations  of both Friedmann and of Lifshitz.


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_lifshitz.pdf}
\caption{Evgeny Lifshitz.
}
\label{chap1_fig12}
\end{center}
\end{figure}


Gamow's papers were actually full of computational mistakes. His attitude was always to minimize the relevance of  precise computations in favor of developing the conceptual framework, so in his work we find some alarming statements like: ``Thus we have $\rho_{\rm mat}\Delta t\simeq10^{-4}\, g\,  cm^{-3}\, sec$ and not $\simeq10^{+4}\, g\, cm^{-3}\, sec$  as was given incorrectly in the previous paper because of a numerical error in the calculations''\footnote{
See Gamow's paper
\cite{gamow} reproduced in Appendix \ref{appA_gamow1}.
}
or again referring to formula (6) of his paper \cite{gamow},
``The fact that the above-calculated density and radii correspond closely to the observed values for the stellar galaxies strongly suggests that we have here a correct picture of galactic formation,'' whereas from that formula one can deduce a mass for a galaxy of only $10^3M_\odot$.
Nevertheless his papers are remarkable   for their physical intuition and for their attempt to identify  the basic physical process governing cosmological evolution.

It is well known that in the best cultural tradition of the Chinese classical paintings Chinese painters have often exercised themselves in expressing themes already expressed centuries earlier by other artists reproducing and reinterpreting their works faithfully and introducing minor stylistic differences in order to carry forward the conceptual and artistic message through the millennia. Similarly I recall the attitude of Titian's school (and also those of Rubens and van Dyck) reproducing attentively some of the works of great masters. In the same spirit I approached these works of Gamow trying to capture the concepts which allowed him to deduce from first principles the existence of the cosmological black body radiation, which he had the merit of predicting years before its actual observation. 
For almost ten years I read over and over again the paper ``The Origin of Elements and the Separation of Galaxies'' \cite{gamow},
and used it in my lectures for my class on theoretical physics at the University of Rome, enjoying the underlying strong conceptual logic which emerged despite the numerous numerical mistakes and some of the equally wrong estimates.

The often mentioned aphorism of Gamow was ``the details of the numerical accounting must be left to the shopkeepers.'' In this spirit I  focused on the underlying scientific message by Gamow, without being diverted by the often contradictory statements of the order-of-magnitude estimates or the too literal application of these ideas to explain  observational facts.  I discussed this attitude of Gamow with Eugene Wigner and Riccardo Giacconi. Both of them were quite critical. I already spoke of  Eugene's sentence: ``You admire Gamow so much: he used a special set of units $h$, $c$, $G$, $4\pi =1$!" and the fact that it took me almost 25 years to appreciate Eugene's sarcasm.
Recently discussing the text of the present manuscript with Riccardo, he fiercely criticized Gamow's attitude: the quest for precise computations and equally precise measurements is a must for serious physics and he found Fermi's critical attitude fully justified. In his opinion Fermi's reason for not publishing the results of his work with Turkevich was due to the desire just to teach Gamow how to do computations correctly. 
As we will see shortly Fermi's correct computations paradoxically lead to a deeper understanding of Gamow's conceptual framework.


\section{Fermi's criticism of Gamow's work}

There were three issues in Gamow's cosmology:\\
1) The formation of  all known elements by a neutron capture process in a Friedmann Universe,\\
2) the process of galaxy formation by the Jeans instability, and \\
3) the identification of a  Friedmann cosmology dominated in its early phases  by radiation as a description of the early universe. \\
Fermi addressed mainly the first issue and made some considerations on the third one. We cannot find any better way to illustrate Fermi's work than to  use his own lucid words excerpted from Appendix \ref{appA_fermi240_3}. I am sure everyone will enjoy reading them as we have ourselves in  translating them.

{\it
All the known matter is made up of various chemical elements each present with a different abundance, so the problem arises, first experimentally and then theoretically, of understanding for what reason some elements are abundant, others rare\ldots  What we are trying to establish are the amounts of the various chemical elements which are, so to say, in the whole Universe or, at least, in a large part of it and, obviously, the result which we may expect to obtain depends to a large extent on the samples taken for the analysis \ldots\ 
It is noteworthy  that, \ldots\ 
if the selection of the samples is made with suitable attention, the results are highly uniform even if derived from materials of very disparate origin. For instance, in some favorable cases, it is possible to assign the ratio of the cosmic abundance of two elements with a precision of the order of the 1 or 2$\%$\ldots\
That said it is interesting to consider the table reported here (Table~1) in which the numbers represent the relative abundances of the various elements.
}


\begin{table}[h]
\tbl{Relative abundance of the elements (Table 1 of the Fermi paper 240.3.)}
{\begin{tabular}{@{}crrrr@{}}
\hline
{} &{} &{} &{}\\[-1.5ex]
{} & A & Z & \vtop{\hbox{Atoms per $10^{4}$}\hbox{atoms of silicon}}\\[2ex]
\hline
{} &{} &{} &{}\\[-1.5ex]
H &1.01 &1 &$3.5\times10^{8}$\\[1ex]
He &4 &2 &$3.5\times10^{7}$\\[1ex]
Be &9.02 &4 &$2\times10^{-1}$\\[1ex]
C &12.01 &6 &$8\times10^{4}$\\[1ex]
O &16.00 &8 &$1\times10^{5}$\\[1ex]
Si &28.06 &14 &$10^{4}$\\[1ex]
Cl &35.46 &17 &$2.5\times10^{2}$\\[1ex]
Mn &54.93 &25 &$1\times10^{2}$\\[1ex]
Fe &55.85 &26 &$2.6\times10^{4}$\\[1ex]
Co &58.94 &27 &$1.6\times10^{2}$\\[1ex]
Ni &58.69 &28 &$2.0\times10^{3}$\\[1ex]
Cu &63.57 &29 &7\\[1ex]
Ga &69.72 &31 &$5\times10^{-3}$\\[1ex]
Sr &87.63 &38 &$10^{-1}$\\[1ex]
Cd &112.41 &48 &$2\times10^{-2}$\\[1ex]
Cs &132.91 &55 &$10^{-2}$\\[1ex]
Pt &195.23 &78 &$10^{-1}$\\[1ex]
Pb &207.21 &82 &$4\times10^{-3}$\\[1ex]
Th &231.12 &90 &$10^{-2}$\\[1ex] 
U &238.07 &92 &$3\times10^{-3}$\\[1ex]
\hline
\end{tabular}}
\label{tabch1_1}
\end{table}

{\it
\ldots
we represent in a diagram (Fig.~15) the relative abundance of the elements as a function of the atomic number. 
}

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{fermi240_fig_1.pdf}
\caption{The relative abundance of the elements as a function of the atomic number (Fig.~1 of the Fermi paper (240.3)).}
\label{chap1_fig_240_1}
\end{center}
\end{figure}

{\it
From this diagram one can see that immediately after the peak represented by hydrogen and helium there is a tendency to exhibit, though with high irregularity, a decreasing feature of the relative abundance of the elements. So that one who wanted to draw a curve through these points, neglecting the irregularities, could draw the curve shown in Fig.~15. And, if one wanted to trust that, having accounted for the exceptions, this curve represents with good approximation the relative abundance of the elements, one should also conclude that the relative abundance of each element is one of its essential characteristics like, for instance, its atomic number, its energy of formation or its mass. Then one forms the impression that the relative abundance of each element is really a property of its own, connected, as is obvious, both with the other properties of the element and with the mechanism, quite unknown, through which the element has been formed\ldots if we know the abundance of each element it is a question of trivial arithmetic to calculate the abundance of the isotopes\ldots  Obviously the idea of justifying all these facts, that is to justify the abundance of every single element and, for each element, the abundance of its isotopes, is, certainly, an extremely ambitious program and constitutes a problem whose solution is assuredly very far off.\\
}

And again let Fermi's words introduce the work of George Gamow:\\

{\it 
Nevertheless recently there have been attempts in this direction but with quite unsatisfactory results. This fact does not exclude that they are extremely interesting in the sense that they represent an attempt at research in the direction which most probably will be one of the most important in the future. On the other hand it is obvious that if the solutions obtained to date are not satisfactory one cannot exclude that in the future one cannot make conclusive steps along this road
\ldots\
we shall limit ourselves to speak here about 
\ldots\
the theory, due chiefly to Gamow, who being a joker as everybody knows, joined with two other physicists, Alpher and Bethe, with the aim perhaps of playing with the fact that the three names, read in the American way mangling the words, sound like the first three letters of the Greek alphabet. As a matter of fact, the essential contribution of the theory of which we are speaking was given by Gamow and in part by Alpher: Bethe, instead, appears to have been associated only to complete the play on words.
}
\\
(We have reproduced the article in Appendix \ref{appA_alpher_bethe_gamow}.)\\

Let us be guided by Fermi's words in the description of the formation of the elements by successive neutron capture in Gamow's theory:

{\it 
Refer to a $P$-$N$ diagram (Fig.~\ref{fig_2}) in which each element is represented by a point whose abscissa is equal to the number of its protons and whose ordinate is equal to the number of its neutrons. 

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{fermi240_fig_2.pdf}
\caption{$P$-$N$ diagram: each element is represented by a point whose abscissa is equal to the number of its protons and whose ordinate is equal to the number of its neutrons (Fig.~2 of the Fermi paper (240.3)).
}
\label{fig_2}
\end{center}
\end{figure}

As we have already said, all stable elements are located in a well defined zone. If we now assume that we submit a certain element to a ``bath'' of neutrons it may happen that its nuclei capture one of these neutrons. Thus, if the composition of this nucleus is represented by the point $A$ of Fig.~\ref{fig_3}, after the capture the newly formed nucleus will have a composition represented by the point $B$ which is obtained by taking from $A$ a step upwards (in fact $N$ is increased by one and $Z$ remains constant). 

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{fermi240_fig_3.pdf}
\caption{The mechanism of formation of heavy elements (Fig.~3 of the Fermi paper (240.3)).
}
\label{fig_3}
\end{center}
\end{figure}


The new nucleus will be able, in turn, to absorb another neutron and produce an element represented by the point $C$ and so on, until one ends up going out of the zone of stable elements. The newly formed unstable element will evidently be beta radioactive and then will disintegrate through a beta process which is a change of a neutron into a proton: the new representative point will therefore be obtained taking a step downwards (decrease of a neutron) and a step rightwards (increase of a proton). If now there are still neutrons present, the nucleus so formed will be able to absorb another neutron, then another neutron and after it will emit a beta ray; and in this way little by little we will climb up the slope of the stable elements. Thus little by little very heavy elements are formed through a mechanism of successive additions of neutrons to light nuclei assumed to be pre-existing.
}
\\

Fermi then recalls the theoretical hypothesis made by Gamow in the description of nuclear cross sections:\\

{\it 
At this point, if one  wants to be ambitious (and, as we shall see, Gamow puts forward demands even more ambitious than these), one can even hope to explain the formation of all the elements starting from only neutrons.

Let us assume, in fact, that in a region of space, at a certain instant, are contained some neutrons.
As is known, the neutron is not a stable particle, on the contrary its life time is quite short (it has not yet been measured very well but it cannot be appreciably different from 15 minutes) and therefore after about ten minutes, half of the neutrons will be decayed producing as many protons.
But neutrons and protons have a certain affinity and the neutrons tend to latch onto the protons in this way forming nuclei of deuterium.
In this way, starting initially from only neutrons, through their decay and association with the generated protons, it will be possible to form the first light nuclei and then, from them, with a process of the kind described above, one will arrive presumably at the formation of the heavy elements.

Gamow, simplifying (maybe too much) that which the experimental results really give, assumes that these cross sections for the capture of neutrons increase linearly for values of the atomic weight between 0 and 100 and then remain constant.
}\\

Fermi recalls an apparently  qualitative success of Gamow's theory in describing the abundance of elements with high atomic number:

{\it 
Therefore let us assume, for the time being, that the cross sections are really the ones Gamow claims.
In this case we can plainly write down the differential equations describing how heavier elements are successively formed.
Let us call $N_{a}$ the number of atoms with atomic weight $a$; the derivative of this number with respect to the time will depend on two terms: one which represents the increase in the number of atoms of weight $a$ due to the aggregation of atoms of weight $a - 1$ (and this will be a positive term proportional to $N_{a-1}$, 
to the cross section $\sigma_{a-1}$ of the element $a - 1$ and to the flux $\Phi(t)$ of the neutrons).
Then there will be a negative term which in the same way represents the decrease of $N_{a}$ due to the absorption of neutrons which changes the atoms $a$ into atoms $a + 1$. In a formula
\begin{equation}
\frac{dN_{a}}{dt} = \Phi(t)\left(\sigma_{a-1}N_{a-1}-\sigma_{a}N_{a}\right)
\qquad
\left(a=1,2,\ldots ,238\right)\ .
\label{eqch1_1}
\end{equation}
Equations like this must be written for every value of $a$ and a system will be obtained which we can solve, at a fixed neutron flux, deriving the way in which the abundances of the single elements evolve in time.

Of course the result one obtains depends on the time interval we choose in the sense that, if we fix a certain flux of neutrons, the material must be exposed to its action for a suitable time: in fact, if the time is too long, too many heavy elements are formed, if it is too short, too few elements are formed.
But, by ``cooking" so to say the material to the right point one succeeds in obtaining something which has a certain resemblance with the experimental data.
This resemblance arrives at such a point as to give, in the case of elements with high atomic number, a distribution of isotopes resembling the real one.
}\\
 
Fermi also recalls a crucial difficulty in Gamow's theory in describing the nuclear abundances of light elements:\\

{\it 
In the region of light elements the result is, instead, contrary to the experimental one but one can think that a successive heat treatment, even at not an exceedingly high temperature, might have modified the situation.
}\\

Fermi then describes the ``risky and almost certainly wrong statement \ldots\ connected with the theory of general relativity'' by Gamow:\\

{\it 
As we have said, Gamow was not content with these results and has taken a further step, a very risky and almost certainly wrong step.
Almost certainly wrong since the step one takes when, to explain the facts, one assumes very precise hypotheses.
In that case, as is obvious, the more precise the hypotheses are, the more easily one demonstrates that they are wrong.
At any way, Gamow resolved to determine the time in which the formation of elements described above has happened by resorting to the theory of the expansion of the universe.
This theory is connected with the theory of general relativity and we attempt to give a short account of it.
Unfortunately also for general relativity, as for other physical theories, there does not exist a single theory and this entails a certain freedom of choice, but at present this choice cannot be made on the reliable basis of experimental results. But if we base ourselves on the simplest one of the theories of relativity, that one without a cosmological term, we can construct as has been done, a theory of the expansion of the universe according to the following general lines.
}\\

In order to prove Gamow wrong on cosmological nucleosynthesis, Fermi paradoxically criticizes Gamow's procedure of adopting the validity of Einstein's equations and the use of a radiation-dominated Friedman cosmological model. As we know today these assumptions are precisely the ones which have credited Gamow's cosmology as the fundamental one for predicting the cosmological black body radiation. But let us use Fermi's words for a lucid description of Friedman cosmology:\\

{\it
One starts from the hypothesis, which has at least the merit of being very simple, that the energy density (matter and radiation) is uniform in the entire universe, at least when one averages over very large regions of it.
Furthermore one assumes that the space has a constant curvature; this means that the universe is homogeneous not only with respect to the energy density but also with respect to its geometrical properties.
From this hypothesis one can infer that the universe at a certainly well-defined time has the shape of a sphere or that of a pseudo-sphere; for particular reasons, connected with the present matter density, one must choose the pseudo-sphere, which is a sphere with an imaginary radius and obviously it is not possible to represent it by a figure.
But if for the moment we leave out of consideration the fact that the object of which we want to speak is a pseudo-sphere and not a sphere and furthermore if we limit ourselves to represent only three of its four dimensions (the time and two spatial coordinates) it will be possible (Fig.~\ref{fig_6}) to give an idea of how the Universe evolves expanding itself.
In Fig.~\ref{fig_6} the universe is represented by circles whose radius is increasing with time.

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{fermi240_fig_6.pdf}
\caption{The expanding universe: the universe is represented by circles whose radius is increasing with time (Fig.~6 of the Fermi paper (240.3)).
}
\label{fig_6}
\end{center}
\end{figure}

If now, by using the formulas of general relativity, one makes calculations, one can find a relation which connects the velocity of expansion of the radius, ${r = iu}$, of the pseudo-sphere with the energy density $w$:
\begin{equation}
	\left(\frac{du}{dt}\right)^{2} = c^{2}+\frac{Kc^{2}}{3}u^{2}w\ .
\label{eq_2}
\end{equation}

This formula says that the square of the time derivative of the modulus of the radius $u$ of the pseudo-sphere equals the square of the light velocity plus a term which contains the radius itself, the energy density $w$ and a constant $K$ related to the gravitational constant $G$ through
	\[	K=8\pi\frac{G}{c^{4}}\]
and having the value of about $2\times10^{-48}dyn^{-1}$.
If we now want to use this formula to describe the expansion of the universe when its radius is very small, we can see that the first term of the right hand side becomes negligible since the energy density increases much faster than the squared radius decreases.
Then formula (\ref{eq_2}) can be simplified in the following way:
\begin{equation}
	\left(\frac{du}{dt}\right)^{2}=\frac{Kc^{2}}{3}u^{2}w \ .
\label{eq_3}
\end{equation}

At this point Gamow made an interesting remark: if one admits that, when formula (\ref{eq_3}) holds, the energy is essentially radiation energy, one can, using the formula, obtain a relation between temperature and time which contains only universal constants.
In this way, one arrives at eliminating the arbitrariness due to the value of temperature at which nuclear reactions had taken place and given origin to the elements.
This arbitrariness might have allowed one to obtain, to a certain extent, any result whatsoever.
We give here, without proof, the formula which links temperature to the time elapsed since the instant when the Universe had infinitesimal size
\begin{equation}
	T=\left(\frac{3}{4Kc^{2}\sigma}\right)^{1/4}\frac{1}{\sqrt{t}}\;\;{\rm degrees} \ .
\label{eq_4}
\end{equation}
In this formula, $\sigma$ represents the Stefan's law constant, $T$ the absolute temperature and $t$ the time.
As we have already pointed out, this is an approximate formula and holds for values of $t$ not too large, for instance not exceeding a few million years.

If we substitute the constants appearing in formula (\ref{eq_4}) by their values, we obtain
\begin{equation}
	T=\frac{1.52\cdot10^{10}}{\sqrt{t}}\;\;{\rm degrees}
\label{eq_5}
\end{equation}
from which one sees
that when $t$ is, for instance, equal to one second, the temperature is, as one could have imagined, enormously high: of the order of $10^{10}$ degrees.
But it decreases very fast so that, after one thousand seconds, it is already reduced to the order of magnitude of one hundred million degrees and this value is low enough to stop strong nuclear phenomena.

Then the temperature varies with time following a well-defined law and the pseudo-radius of the universe varies with an equally determined law (it is proportional to the squared time) and therefore only one parameter is left undetermined: the density of neutrons; Gamow intends, by working on this single arbitrary parameter, to succeed in predicting the distribution of the abundances of the elements and indeed in a certain sense he succeeds.
As a matter of fact, he succeeds as long as one is content with a very rough analysis of his results, but as one tries to enter into details, immediately one runs into trouble and probably troubles would increase if it were possible to carry out this analysis which is extremely complicated to do.
}\\

This derivation explains why in the Fermi-Turkevich paper Fermi assumed a temperature dependence with the precision of three decimal places. In my first reading of the Fermi-Turkevich paper I was astonished that a scientist as concrete as Fermi could have ventured to assume such a precision.
I discussed repetitively this question with Wheeler without a clear conclusion, which is clearly explained above in the Fermi's own words.

\section{The Fermi and Turkevich paper}


As I already mentioned the  Fermi-Turkevich paper was never published by the authors in a scientific journal  and their results were only reproduced later in the review article  ``Theory of Origin and Relative Abundance Distribution of the Elements'' by Alpher and Herman \cite{alpher2}.\footnote{
See the excerpt Appendix \ref{appA_fermi_turk}.
} 
This article had the significant footnote ``We are indebted to Drs.\ E. Fermi and A. Turkevich for their cooperation and communication of unpublished results. The authors take the responsibility for the correctness of this transcription and interpretation of their work.''


The basic assumptions in the Fermi-Turkevich work were:
\begin{itemize}
\item[1)]
the initially radiation dominated Friedman cosmological model, following Gamow;
\item[2)]
the complete and detailed values for the reaction rates expressed in their Table XII (see below);
\item[3)]
the techniques of numerical integration of the rate equations by electronic machines.
\end{itemize}




\begin{figure}[h]
\begin{center}
\includegraphics[scale=.3,angle=-90]{chap1_tableXII.pdf}
%\caption{}
%\label{tableXII}
\end{center}
\end{figure}




The numerical integrations were made possible by the use of one of the first computers: the Maniac electronic machine  at Los Alamos. It is interesting that one of the possible reasons why the Fermi-Turkevich calculations were not published as a paper themselves was that, as mentioned by Yakov Borisovich Zel'dovich to me years later,  the cross sections involving tritium reactions were at the time secret because of their implications for nuclear bomb fusion processes. When it became possible to make them known Fermi considered the paper not so urgent as to need official publication, and it became a matter for a review article! This might have been a justification, but certainly in my opinion not the main one.\\

The major new result of Fermi and Turkevich in light element formation was summarized in their Figure 20 (see below) and is summarized by Fermi in the words\\


\begin{figure}[h]
\begin{center}
\includegraphics[scale=.5]{chap1_fig_20_fermiturk2.pdf}
\caption{Relative abundance of the very light elements as a function of time according to the non-equilibrium formulation of Fermi and Turkevich (unpublished). 
The nucleon concentration was taken to be $10^{21}$ cm$^{-3}$ at $t=1$ sec in an expanding universe dominated by radiation.
The relative abundances are the ratios of the number of nuclei of a given species in a volume $V$ to the total number of nucleons in that volume.
Since both quantities vary with the universal expansion in the same way the effect of the expansion is not evident.
(Fig.~20 of the paper ``Theory of Origin and Relative Abundance Distribution of the Elements'' by R.A. Alpher and R.C. Herman, \textit{Rev.\ Mod.\ Phys.} {\bf 22}, 153 (1950)).
}
\label{fig:20fermiturk2}
\end{center}
\end{figure}


\clearpage


{\it
``The first difficulties are met already in the lower region of the periodic system as soon as one asks oneself a little in detail in what manner the elements are gradually forming themselves. As we have already said, the first nucleus to be formed will be that of hydrogen, then through the merging of a proton with a neutron deuterium will be formed and then with the addition of another neutron tritium, which will decay through a beta decay into helium three. By addition of a new neutron helium three changes into helium four. Already here one meets a little difficulty because helium three capturing neutrons tends to break rather than to form helium four, nevertheless one can still think that at least a small fraction of helium three changes by capture of a neutron into helium four. But at this point the difficulty one meets is much more important because the nucleus of mass five does not exist: if one would try to form it by addition of a neutron to helium four it would break to peaces creating an insurmountable barrier which prevents the successive formation of elements through the addition of neutrons.''\\
}\\

Gamow wittily recalls the attempt to jump the mass 5 crevasse in his book \textit{The Creation of the Universe}.\footnote{
See
Ref.~\cite{gamow2}, p.~71.
}
I couldn't resist the temptation of reprinting in Fig.~\ref{chap1_fig13} the vignette in which Wigner proposes a way to jump across the mass 5 crevasse. In this figure Wigner is well identifiable by his famous ``please.'' He told me once: ``They accused me of being too polite''. Indeed this politeness was extreme. No one of us at Princeton university was ever able to enter a door after him: he was always entering any door last, following a well established Hungarian rule of survival!
In Fermi's words:\\

{\it
``In reality one can find some way to jump or even better to avoid this barrier, and it is the following: according to the formulas written above, in the time in which these phenomena should take place, the temperature, though already much decreased, is still on the order of $10^8$--$10^9$ degrees and at such high temperatures nuclear reactions can still take place in a conspicuous way and are produced by the collisions among the nuclei which move under the effect of thermal agitation. Thus it is not impossible to think that a nucleus of mass six can be formed, without the preliminary existence of a nucleus of mass five, by making a nucleus of deuterium react directly with a nucleus of helium four. As a matter of fact, this reaction is extremely unlikely, but not impossible, therefore it is not excluded that a small amount of lithium six is formed allowing, through successive additions of neutrons the formation of heavier nuclei. And many other difficulties of this type are met; for instance, also the nucleus eight does not exist in any stable form and this missing step will be jumped by a device of the kind already described.''
}\\


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_wigner.pdf}
\caption{Wigner's proposal for how to jump across the mass 5 crevasse.
}
\label{chap1_fig13}
\end{center}
\end{figure}



{\bf The impossibility of building heavy elements}\\

{\it
``But the difficulties do not end here, another one which cannot be passed over in silence is that, if one assumes an initial density of neutrons large enough so that they can form heavy elements in non negligible quantities, one finds that the ratio between helium and hydrogen has nothing to do with the actual one: one will have more abundant helium than hydrogen contrary to experimental evidence."
}\\

{\bf Fermi's negative conclusions about Gamow's work}\\

Let us now read the severe final remarks of Fermi:\\

{\it
``So it only remains sadly to conclude that this theory is unable to explain the way in which the elements have been formed in time, and this after all is what one should have expected. However, we must recognize the courage with which Gamow has set about constructing an attempt at a theory based on extremely determined hypotheses: the theory has failed and this means that some of his hypotheses are wrong, but the result he has obtained in this way (to be at least certain of having made a mistake) is certainly more remarkable than one that which could have been obtained from a theory so indefinite as to be able to explain a lot of experimental facts, exactly because of the great deal of arbitrariness contained in it, but that would not have made evident what are its incorrect points allowing them to be corrected and to proceed to the construction of new and more satisfactory theories.''
}\\

There is still the great pathos of why Fermi refused to publish his work with Turkevich: 
There is the possibility indicated by Zel'dovich that the paper contained at the time information of classified cross sections.
There is also the possibility mentioned by Riccardo Giacconi  that Fermi considered this work to be just a pedagogical  exercise meant to teach Gamow how to do the computations.
There is also the possibility that Fermi, being one of the greatest physicists who ever lived,  could not fail to appreciate in doing his work with Turkevich the tremendous beauty of Einstein's theory which through the confluence of many events of Faustian dimensions he was led to criticize.
The above sentence ``So it only remains sadly to conclude \ldots " can be a vehicle for the reader to evaluate this possibility.
There is also the possibility which I will consider below that Fermi could sense, in the Faustian game to discover knowledge of the fundamental  physical laws played between himself and Nature, he was feeling insecure. 

Paradoxically  Fermi failed to see the  importance of  the prediction   in Gamow's work of the existence of an initial radiation-dominated phase of the universe which will lead some ten  years later to a  new area of research called cosmological nucleosynthesis precisely starting from this work with  Turkevich. 
The issue of the formation of the heavy elements became in a certain sense peripheral to cosmology and was solved in the detailed work of stellar nucleosynthesis by a student of Fermi of German origin in Rome, Hans Bethe\footnote{
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/1967/bethe-lecture.html
}
and by William Alfred Fowler,\footnote{ % begin long footnote
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/1983/fowler-lecture.html
}
Margaret Burbidge, Geoffrey Burbidge, and Fred Hoyle \cite{hoyle4}. 
But  before leaving this topic let's consider some reactions to this work in the more general context of the scientific 
community.\footnote{
The Fermi and Turkevich paper has, nevertheless, indirectly influenced the developments of cosmology. The work was well known to a small number of influential scientists. It was certainly known to Bob Dicke at Princeton, as I found out in 1968, when I pointed out to him the diagrams of the abundance of the elements made by Fermi and Turkevich. Bob told me that he knew them and that they agreed with the ones he computed with Jim Peebles (see Ref.~\cite{peebles}, p.~5). 
In fact Peebles marginally quoted Fermi's work without explaining its fundamental relevance in Ref.~\cite{peebles2}.
I only replied that this was interesting, but that the Fermi-Turkevich work had preceded their contributions by almost two decades.
As we will see below, due to the beauty of its scientific approach, the numerical techniques adopted, and the importance of the results obtained, the work of Fermi and Turkevich has to be considered one of the fundamental contributions to relativistic cosmology.

I recall a review written by Chandrasekhar in 
\textit{Physics Today} (August 1974, p.~47) 
contrasting the textbook \textit{The Classical Theory of Fields} by Landau and Lifshitz with \textit{Gravitation} by Misner, Thorne and Wheeler. Chandra mentioned that all the statements of the MTW book could be found better and more succinctly expressed in the Landau-Lifshitz book. Although I don't completely share his opinion on this question, I could not help but have a similar feeling about the books of Steven Weinberg and the article by Fermi and Turkevich.
Paradoxically even the more copious and extended books by Weinberg on cosmology do not go much further than the basic equations and results given by Fermi. It is unfortunate  but significant that Fermi's work was only quoted 
in a footnote in \cite{??}  % NEEDS CITATION
and not at all in \cite{??}.  % NEEDS CITATION
That quote clearly shows that Fermi's work was known to Steven.  
} % end long footnote

\section{Zel'dovich's reaction to the work of Fermi and Gamow}

One of the most interesting reactions to this entire scientific adventure 
 was that of the Soviet colleagues. I had occasion many times  to discuss these issues in unforgettable and most pleasant meetings  with Zel'dovich and the outstanding friends around Evgeny Lifshitz in my many visits to Moscow in the 1970s.
\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_ruffini_zeldovich.pdf}
\caption{Dinner at home of Evgeny Lifshitz.
From left to right: Nina Ginzburg (wife of Ginzburg), Zinaida Lifshitz (wife of Lifshitz), Remo Ruffini, Evgeny Lifshitz, Yakov Zel'dovich, Angela Zel'dovich (one of the many wives of Zel'dovich), and Vitalyi Ginzburg.
}
\label{rr_lifs_zeld}
\end{center}
\end{figure}

 Let me  first recall some of the ongoing work at the time in the Soviet Union. 
The ``rocambolesque'' departure of Gamow  from Moscow on the occasion of the 1927 Solvay Meeting (see Fig.~\ref{fig:solvay1927}) had embittered all the Soviet scientists who had seen at once all their possibilities to travel abroad cut for years to come. The departure of Gamow was like a slap in the face to the Soviet system.\footnote{
See  Gamow's version of the matter in Appendix \ref{appA_autob_gamow} 
(from Chapter 6 of 
Ref.~\cite{gamow3}).
}

Motivated by ideological reasons, Zel'dovich told me that in order to prove the superiority of a truly Soviet thinker, he had proposed an alternative way to have a Friedmann universe initially at zero temperature as opposed to Gamow's idea of an initially radiation-dominated hot universe. The avoidance of the buildup of the heavy elements was obtained in the Zel'dovich approach by the existence of a background of degenerate neutrinos. We have reproduced his paper in Appendix \ref{appA_zeldovich}.

As Zel'dovich says there, ``The process $e^-+p=n+\nu$, which leads to the formation of neutrons at high matter density in the stars, turns out to be forbidden here, since the neutrino states that are energetically obtainable in this process are occupied. In the uniform model (closed or open) the neutrinos do not depart anywhere. Upon expansion such a substance turns into pure cold hydrogen'' \cite{zeldovich}. 
In this way the formation of neutrons would be completely avoided. The model would lead to a universe formed during its initial evolution  uniquely of cold hydrogen. 

The confrontation was quite clear: a cold universe developed by a Soviet scientist in Soviet Union as opposed to a warm universe developed by a fugitive Soviet scientist abroad!

The Zel'dovich approach was soon abandoned, as Igor Novikov told me years later, due to the evidence of the cosmological helium abundance and, more importantly, to the discovery of the cosmological black body radiation (see the Nobel lectures of Arno Penzias and Robert W. Wilson\footnote{
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/1978
}  
and George T. Smoot\footnote{
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/2006
}% 
). 

Interestingly, in our discussions (see Fig.~\ref{rr_lifs_zeld}) following the universal scientific success of the discovery of the cosmological black body radiation, Zel'dovich talked about the role of Gamow in science and politics finishing  with one question and one statement. First the question:
``How many Nobel Prizes Gamow received? One for physics and one for biology?''
Zel'dovich was clearly well informed of the great contribution of Gamow not only to astrophysics and nuclear physics, but also to biology for his studies on DNA structure \cite{gamow4}.
%}
In this question, however, Zel'dovich showed a clear sign of his isolation from the West: Gamow had not received any Nobel prize!
Nevertheless he was not ready to give up on the supremacy of Soviet science in view of the universal recognition by then of Gamow's ideas. Smiling he concluded with the statement:
``Certainly Gamow has been one of the greatest Soviet scientists.'' More of my discussion with Zel'dovich is given in Appendix \ref{appA_ruffinizeldovich}.




\section{The introduction of the name ``big bang''}

Let us return to an event organized by Gamow himself. In fact, even if Gamow does not say it in his autobiography, he went on a journey to Rome and got in touch with the Pontifical Academy of Sciences.
Felix Bloch told me that he was also knighted by the Order of the Maltese Cross. 
George Coyne, for many years director of the Vatican Observatory, told me that
Pope Pius XII was an admiring reader of the popular books of Gamow, especially the one ``One, Two, Three \ldots\  Infinity: Facts and Speculations of Science'' \cite{gamow5} 
and Gamow managed to enter somewhat into the inner circle of the Roman ``Curia'' in the Vatican.
It is an undisputed fact that Gamow's theory of the origin of the universe was adopted by Pope Pius XII in his address to the Academy on November 22, 1951.
Gamow, being a joker as everybody knows,\footnote{
See this phrase in Fermi's Rome lecture (Appendix \ref{appA_fermi240_3}).
}
mentioned the Pope's address at the beginning of his article in Physical Review:\footnote{
See the Gamow's paper \cite{gamow6} (\ref{appA_gamow2}).  
}
{\it ``It can be considered now as an unquestionable truth that 
from one to ten thousand million years ago, the matter of the (known) spiral nebulae was compressed into a relatively restricted space, at the time the cosmic processes had their beginning
and that during that stage
the density, pressure, and temperature of matter must have reached absolutely enormous proportions since
only under such conditions can we explain the formation of heavy nuclei and their relative frequency in the period system of elements.''
}
The reason for ``unquestionable truth'' was then clarified by a reference in the footnote:
``Address by Pope Pius XII to the Pontifical Academy of Sciences on November 22, 1951 (Tipografia Poliglotta Vaticana, Rome, 1951).'' The Pope's pronouncements are, by definition, unquestionable!
Fred Hoyle, present at the meeting, reacted with sarcasm to such a theory. He had his own competing theory of continuous creation in a steady state model of the universe (see, e.g., Refs.~\cite{bondi2,bondi3,hoyle2}).
Hoyle called Gamow's theory, derogatorily, a ``big bang.''
It is ironic that such a name, initially derogatory, has been adopted for the leading theory in cosmology.

In time Gamow's theory (whose roots trace back to Georges Lemaitre  in 1927, also scorned by Hoyle) was confirmed (see the Nobel lectures of Arno Penzias and Robert W. Wilson\footnote{
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/1978
}  
and George T. Smoot\footnote{
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/2006
} 
) and the steady state theory became the personal interest of only a small number of devoted scientists (see, e.g., Ref.~\cite{hoyle3}).


\section{General relativity after the death of Fermi and Einstein}

Fermi died on November 29, 1954.
One of the last messages he gave to Rosanna Cester at the Les Houches School (see Fig.~\ref{cester}), one of the young Italian Ph.D. students in the USA at the time, was simple and clear:
``Go to astrophysics, there is the future of physics!'' 
The last articles of Fermi, written with S. Chandrasekhar, are  dedicated to the field of astrophysics (see papers (261) and (262) of Fermi's collected works).


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_cester.pdf}
\caption{Enrico Fermi, Rosanna Cester, L\'eon Van Hove (from left to right).
}
\label{cester}
\end{center}
\end{figure}


On April 18, 1955 Einstein died.
Einstein had dedicated a large part of his final years in an attempt to unify electromagnetism and gravitation. 
I remember talking with my good friend Valentin Bargmann  about the Kaluza-Klein theory still amazed on the beauty of this attempt at unification and asking: ``Why it works so well?"
A beautiful last message was given by Einstein to my other good friend Abraham Taub. 
Abe asked Einstein: ``Why you give so much relevance to the unification of electromagnetism and gravitation,
when there exist so many additional interactions and particles, the electrons, positrons, pions \ldots ?"
Einstein simply answered:
``Abe, you are a pagan!''

The quest for unification had to wait for many years to come. I remember as a student a Professor of Rational Mechanics in Rome shouting ``nemmeno un cane lavora pi\`u sulle teorie unificate!" (not even a dog works any longer on unified field theories!). I had at that time, and I still have today, a great respect for any attempt to unify all fundamental interactions, and this topic still today occupies an essential part of my courses of theoretical physics. But at the time I considered that statement  to be inoffensive and simply obvious: after all, a dog cannot work on unified field theories! 

After the death of Einstein the enthusiasm for study of general relativity further diminished.
The field was plagued by many problems. 
I recall some of the major ones: 
\begin{itemize}

\item[1)]
It was extremely difficult to carry forward the problem of unification of all interactions in a geometrical form when the developments of quantum field theories and particle physics were practically developed independently in an alternative approach by the physics community. 

\item[2)]
The technical difficulty of handling the general relativistic field equations presented enormous mathematical difficulties and the  technical knowhow was restricted to a limited number of highly specialized mathematicians.
Due to these difficulties general relativity was increasingly in danger of not surviving.
I like to make a wild analogy with the Chinese language which  in that period was also on the verge of disappearing due to the technical difficulties in writing it.
As we will see a fundamental breakthrough came in both cases by the introduction of computers: this allowed one to write Chinese on a PC and  in total analogy it allowed any student to  evaluate all components of the Riemann tensor and the Christoffel symbols and geodesic orbits  in general relativity for arbitrary metrics, analytically and in the smallest fraction of a second,  thanks to techniques of algebraic manipulation.

\item[3)]
The absence at the time of the existence of physical phenomena in which general relativity could play a principal role and not just make a minimal almost infinitesimal modification to the existing theory.

\end{itemize}

This situation of intellectual disease in general relativity was well manifested by the words of Richard Feynman, by far the most brilliant student of John Wheeler, in the message he sent to his wife \cite{feynman}:

\begin{quote}
{\it 
``
I am not getting anything out of the meeting. I am learning
nothing. Because there are no experiments this field is not an
active one, so few of the best men are doing work in it. The
result is that there are hosts of dopes here and it is not good
for my blood pressure: such inane things are said and seriously
discussed that I get into arguments outside the formal sessions
(say, at lunch) whenever anyone asks me a question or starts to
tell me about his ``work.'' The ``work'' is always: (1) completely
un-understandable, (2) vague and indefinite, (3) something correct
that is obvious and self-evident, but worked out by a long
and difficult analysis, and presented as an important discovery,
or (4) a claim based on the stupidity of the author that some
obvious and correct fact, accepted and checked for years, is, in
fact, false (these are the worst: no argument will convince the
idiot), (5) an attempt to do something probably impossible,
but certainly of no utility, which, it is finally revealed at the
end, fails, or (6) just plain wrong. There is a great deal of ``activity
in the field'' these days, but this ``activity'' is mainly in
showing that the previous ``activity'' of somebody else resulted
in an error or in nothing useful or in something promising. It
is like a lot of worms trying to get out of a bottle by crawling
all over each other. It is not that the subject is hard; it is that
the good men are occupied elsewhere. Remind me not to come
to any more gravity conferences!
''
}
\end{quote}
The authentic resurrection of general relativity was just around the corner and its reincarnation came in the field of relativistic astrophysics, where also the work of Einstein,  Fermi and Heisenberg  acquired  new profound dimensions!

\chapter[The Birth of Relativistic Astrophysics]{The Birth of Relativistic Astrophysics}{} 

\section{From student in Rome to Princeton postdoc}

To introduce the birth of relativistic astrophysics I recall the personal experiences which motivated me to devote myself to this new field of research which was in its formative stages while I was a student.
 I studied at the University of Rome ``la Sapienza" at the Physics Institute ``G. Marconi," a building full of memories of Fermi: from the paraffin blocks to slow down neutrons, to the hall where he used to teach, to the tennis courts in the back where young professors of the Rome group, including Fermi,  practiced sport with vigor and tenacity. This obsession with winning in tennis characterized the rest of Fermi's 
life.\footnote{See Marvin Goldberger's remarks  on p.~156 of \textit{Fermi Remembered} \cite{cronin}.}

In 1964, introduced  by  Edoardo Amaldi,  I had the important experience of spending a period at CERN as a summer student, in view of starting my thesis  in particle physics at the Rome Institute. It was exciting to receive my first salary, to be in Geneva in a large international scientific community, structured with privileges and immunities, and learn about the construction of large experimental facilities. I was associated with a group studying the future accelerators, which  eventually became the storage rings some twenty years later. Every day I also was spending time in the beautiful library and, with another Italian summer student we started daily visits to different research groups asking about the goals of their research. We usually received  extensive and clear technical answers on their activities but systematically, concerning the final goal, we were sent to someone higher up in the hierarchical structure. We continued this inquiry stubbornly, step by step, day after day, until we reached the top of the hierarchical structure: we got an audience with the Director General Victor Frederick Weisskopf. It was just after lunch on a very warm August day. Weisskopf received us at the last floor of the then main building of  CERN: suddenly he did not feel well and went to rest. We were left alone wondering,  overlooking the distant landscape of the Sal\'eve mountain, our quest to learn the fundamental issue still unanswered.  
  
I was feeling a sense of frustration. Only recently by reading the note of Geoffrey Chew \cite{cronin}, did I find  expressed the sensation that was so strong in me at the time on the particle physics research: ``Theoretical physics has repeatedly generated beautiful mathematical structures to correlate certain categories of experimental measurements only to find these aesthetic marvels unable to cope with all measurements." I was feeling deeply the absence of an overall consistent theoretical framework.

I returned to Rome following the death of my father. To my teacher Edoardo Amaldi I indicated my lack of enthusiasm for pursuing research in particle physics experiments and my keen interest in addressing theoretical work in Einstein's theory of general relativity. There, in my opinion, existed a splendid self-consistent theory in quest for observational and experimental verifications.

Amaldi was first shocked and irate. He became red in the face (and this was the second time it had happened with me), but he finally approved with a memorable sentence: ``Ok, there is room  in Italy for one person in this field.'' I later realized that what appeared to me to be an enthusiastic approval by Amaldi  became in the view of the Physics Institute a clear limitation on my possible academic career in Italy.
 
I was personally attracted by the vivid appeal to the conceptual world of Albert Einstein which had started to be reintroduced in Rome in the Mathematics Institute. I was feeling a sort of claustrophobia in the physics developed under ``controlled'' artificial conditions of overwhelming dimensions. I was looking for a field  in which a significant conceptual contributions could be achieved, in a limited number of years, by the direct action of a few and possibly a single person.   

As a student I started to be more and more interested in the physics of the cosmos. 
I was accompanied in this experience by a new and increasing interest of Amaldi in general relativity. He was motivated by some preliminary results purported by Joe Weber on the detectability of gravitational waves \cite{weberfoot1}. 
We started a weekly two hour meeting where I was what Amaldi jokingly referred to as ``tutoring him'' on Einstein's theory.
At the time I was mainly using the second volume  (\textit{The Classical Theory of Fields}) of the theoretical physics series by Landau and Lifshitz. 

I was feeling that my attention to the cosmos and the theory of space and time was indeed very rewarding and I had the clear sensation that a new scientific era in physics was just on the verge of starting.

\section{The forerunners of a new scientific era of general relativity}

There had indeed been  some forerunners to this new era of general relativity:

\begin{itemize}

\item[1)]I already spoke of 
the work of Lifshitz and Lifshitz and Khalatnikov \cite{khalatnikov} 
on the perturbations of Friedmann cosmology using the technique of making scalar, vector and tensor perturbations of a Friedmann geometry in order to analyze the problem of galaxy formation.

\item[2)]
There had been of course in 1939, as I already recalled,  the set of outstanding papers  by Oppenheimer and his students on neutron stars, on the concept of critical mass against gravitational collapse as well as a first example of a description within general relativity of continuous gravitational collapse. In the absence of observational evidence and especially in view of the urgency of theoretical physics efforts related to World War II activities, these beautiful works had not been followed with the attention they merited. Attention again returned to the physics around the Schwarzschild radius in 1957 thanks to the work of Regge and Wheeler \cite{RW}. 
They studied  the stability of the Schwarzschild geometry introducing the complete set of scalar, vectorial and tensorial eigenfunctions in order to describe arbitrary perturbations of the Schwarzschild geometry.
This beautiful  work inspired by Wheeler and expressed mathematically by Regge, opened the way later to a very large number of physical applications in the following years, (see, e.g., the book of Rees, Ruffini and Wheeler \cite{rees}. 

\item[3)]
In 1959 along these lines came the work of Martin Kruskal \cite{kruskal}
obtaining for the first time the maximal extension of the Schwarzschild spacetime across the Schwarzschild horizon, thus overcoming  the difficulties of the so called Schwarzschild singularities and introducing the full extension of the Schwarzschild geometry. 
%(see Fig.~RR ??). % ruffini book kRUSKAL diagram?? % NEEDS FIGURE
In 1963 Roy Kerr presented in a two page article in \textit{Physical Review Letters} \cite{kerr} 
the first solution for a rotating object in general relativity, which came to be known as the Kerr metric. 
This paper was followed few years later by an equally epochal result of Newman and collaborators: the Kerr-Newman metric \cite{newman}. 

\end{itemize} 

\section{The beginning of relativistic astrophysics}

The new era started thanks mainly  to the technological developments at the  beginning of the space age launched in the USA by Dwight D. Eisenhower in  1955 and by  John F. Kennedy in 1961. An  enormous scientific and technological momentum was created by NASA with  the Apollo program of Werner Von Braun. This program was promoted in order for the United States  to make up quickly for the late start of its space program with respect to the Soviet one. 

\subsection*{The discovery of the first X-ray source outside the solar system}

As a byproduct of the NASA Program a team led by Riccardo Giacconi at American Science and Engineering in Boston had developed  a program to launch an  X-ray detector on board an Aerobee sounding rocket above the Earth's atmosphere. The goal was to determine the X-ray emission originating from the moon, for  reasons  not related to astrophysics but in a defense program. In June 1962 the detector was launched.  After looking at the moon the detector slew the entire sky and discovered a very intense X-ray source. Initially it was first  assumed that the source was located at the galactic center. It was then more closely positioned in the constellation of Scorpius, located at 9000 light years from the Earth and was properly called SCO X1. The first X-ray source outside the solar system  had been discovered  by Riccardo Giacconi, Herb Gursky, Frank Paolini and Bruno Rossi. There was outstanding evidence that this star was emitting a million time more energy  in X-rays than the sun emits at all wavelengths combined!

The discovery was not highlighted and the astrophysical and astronomical communities were not ready to accept its message.  Only Iosif Shklovsky in Soviet Union a few years later  indicated that the source had to be a neutron star accreting from a companion star \cite{shklovsky}. This was the first indication that the neutron stars conceived of by Gamow and by Oppenheimer and his school could indeed exist. Shklovsy was one of the leading astrophysicists in the Soviet Union at the Sternberg Astronomical Institute and the author of one of the most impressive books written on supernovae \cite{shklovsky2}. As we will see the work of Riccardo and Herb Gursky led to the one of the most fertile fields most quoted  not only in astrophysics but in all fields of scientific research.   

\subsection*{The discovery of the cosmological background radiation}

One of the first satellites to permit communications between Europe and the USA, the Echo satellites (see Figs.~\ref{echo_sat1} and \ref{echo_sat2}) (see, e.g., Ref.~\cite{elder}), 
led indirectly to the discovery of the cosmological background radiation (see Arno Penzias and Robert W. Wilson\footnote{
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/1978
}  
). 
An attempt by Dicke's group to claim discovery of this radiation ahead of  the Bell Lab group of Penzias and Wilson did not succeed, as the result of a direct intervention by  S. Chandrasekhar, as the editor of the \textit{Astronomical Journal}, he later told me. It is unfortunate that they succeeded, instead, in this context to minimize the impact of the Fermi and Turkevich work. 
\typeout{I do not understand this claim?? should be clarified.}


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in,angle=90]{chap1_echo_sat1.pdf}
\caption{Echo 2 undergoing tensile stress test in a dirigible hangar at Weekesville, North Carolina. 
}
\label{echo_sat1}
\end{center}
\end{figure}


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in,angle=90]{chap1_echo_sat2.pdf}
\caption{Arno Penzias and Robert W. Wilson close to the Bell Labs' Horn Antenna in Crawford Hill, NJ. 
}
\label{echo_sat2}
\end{center}
\end{figure}


The discovery of the cosmic background radiation  represented at once the confirmation that: 
\begin{itemize}

\item[1)]
The consideration's of George Gamow of an universe initially dominated by radiation was indeed correct.

\item[2)]
The Fermi-Turkevich computation of cosmological nucleosynthesis was essential to the comprehension of the material content of the universe (see, e.g., Ref.~\cite{kolb}). 

\item[3)]
The Einstein equations, ironically used with skepticism by Fermi, were indeed confirmed by direct observations to  really be  the theoretical basis for relativistic cosmology.

\end{itemize}

I mentioned already the irony of Fermi's attitude. He was motivated to prove Gamow wrong and Einstein's theory not trustable for cosmology. In his words the use of Einstein's theory was certainly wrong. On the other hand  he was actually the only physicist alive who had the knowledge to make the first model of cosmological nucleosynthesis. He knew the relevant cross-sections from the atomic and nuclear bomb projects and he had the first electronic computer facilities to integrate the equations and above all he had the physical understanding of how to approach the problem. As Murph Goldberger remarked, Fermi had a sports-like competition with Nature like in a tennis match: ``He regarded Nature as an adversary that he could win against in a similar way" \cite{cronin}. In this match on cosmological nucleosynthesis Nature won!
Nature used Fermi to perform the correct computation of cosmological nucleosynthesis, in spite of his misguided goal, 
and Fermi's work finally succeeded in proving both Einstein and Gamow right!



\subsection*{The discovery of pulsars and the identification of the  first neutron star}

The year 1967 marked the discovery of the first pulsar, observed at radio frequencies on November 28, 1967 by Jocelyn Bell Burnell and Antony Hewish \cite{hewish}.
Of all the pulsars observed the crucial one was the one discovered at the center of the expanding shell of the Crab Nebula. The explosion of the Crab supernova was observed by the Chinese and Korean astronomers starting July 4, 1054 A.D., and it was observed and recorded by Messier in his famous catalog  and it is truly incredible that thanks to the development of technology this astrophysical object is still today, almost daily,  presenting new discoveries: see, e.g., the discovery by Agile of the giant flare in 
September, 2010. %(Tavani X-ray ??).  % NEEDS CITATION
Just a few months after pulsars were discovered, a radio pulsar  was found  at the center of the Crab Nebula, followed soon after by its optical identification by 
two graduate students (??). 
The observation of this pulsar (see Fig.~\ref{chap1_fig15}) marked a dramatic turning point in the interests of the astronomical and astrophysical communities.
The role of neutron stars, studied within the framework of general relativity by Oppenheimer, came to the central stage of physics and astrophysics. There were plenty of discussions on the nature of pulsars: the major contenders to model them were rotating neutron stars versus vibrating white dwarfs. %(Ostriker ??). % NEEDS CITATION 
From the observed period of the Crab pulsar of $33$ ms and with first derivative $dP/dt=1.4\times10^{-15}$ ms per year \cite{comella} 
it soon became clear that the energy source of the electromagnetic radiation observed in the radio, optical, X and gamma rays from the pulsar NP 0532 was indeed powered by the rotational energy released by the spinning down of a rotating neutron star \cite{finzi}. 


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_crab.pdf}
\caption{The Crab Nebula. On the right side 33 images taken each one a millisecond apart: they  clearly  
show  the optical pulsation of the pulsar NP0532, discovered by W.J. Cocke, M.J. Disney and D.J. Taylor of Steward Observatory in Tucson, Arizona at Kitt Peak. The optical period precisely matched the radio period of 33.085 milliseconds.
}
\label{chap1_fig15}
\end{center}
\end{figure}


From that moment it became clear that neutron stars really existed  in our own galaxy. There were therefore  many  sources for which general relativistic effects were easily detectable.  Einstein's theory  became the conceptual backbone of the entire field of relativistic astrophysics.
Concurrently the work of Enrico Fermi on atomic physics,  as we will see, properly extended  to take into account general relativistic effects as well as all fundamental interactions, including the weak interactions  Fermi introduced 
in 1934 (see Appendix A and \cite{fermibetaAJP}), 
has given  origin to a new unified description of neutron stars overcoming some of the conceptual difficulties of  the Gamow and Oppenheimer-Volkoff description.
It is appropriate here to note that almost every year there has been a major discovery based on observations of the Crab  Pulsar and the associated supernova remnant 
(see Fig.~\ref{chap1_fig15}). 
Today  there is still a major outstanding feature of the Crab Nebula as yet unexplained: the emission of the shell of the supernova. It is  likely that this very complicated description of neutron stars which is currently emerging, with strong  electrodynamical effects,  will prove to be essential in explaining this phenomenon.


%The year 1965 marked the real birth of relativistic cosmology with the discovery by Arno Penzias and Robert W. Wilson\footnote{
%http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/1978.
%}  
%of the cosmic microwave background radiation (CMB).

Let us now return to the chronological recollection of some of my personal experiences at the beginning of the new era of relativistic astrophysics.


\section{The introduction of  boson stars}

In February 1967 I received my degree from the University of Rome discussing a thesis on massive scalar fields in general relativity and on the possibility of obtaining static self-gravitating equilibrium solutions. To integrate the equilibrium configurations, I made extensive  use of numerical techniques implemented on electronic computers, then a  novelty in general relativistic calculations. 
I succeeded in framing the problem but I did not obtain, at that time, explicit solutions.  
Amaldi encouraged me to go abroad with the promise of learning as much as possible and then return one day to Rome. I left when the first signs of the European version of the so-called ``cultural revolution'' affected the Rome Physics Institute, paralyzing the teaching and research activities for years. 
I was very fortunate in my first visit abroad, to Newcastle upon Tyne to attend a NATO conference on  the variation of the fundamental constants proposed by Dirac in his large numbers hypothesis \cite{diraclargeN}.  There I met Pasqual Jordan and had long discussions on his interpretation of the Dirac large numbers hypothesis. He invited me to Hamburg as a postdoctoral fellow of the Mainz Academy of Sciences.

It was a great experience to have every day contact and discussions with such a great physicist who had made the fundamental contribution of introducing second quantization into quantum field theory and who had inspired, with Eugene Wigner, the work of Fermi on the theory of beta decay.
%(see Fig.~??). % NEEDS FIGURE
%Insert in the caption: The lecture of Pasqual Jordan in Krakow.
\footnote{%
In this context, to understand better the historical contribution of Jordan,  I recall the anecdote recently given by C.N. Yang on p.~243 of \cite{cronin}:
``One day in the 1970s, I had the following conversation with Eugene Wigner in the cafeteria of Rockefeller University:\\
\begin{description}
  \item[Y:] What do you think was Fermi's most important contribution to theoretical physics?
  \item[W:] $\beta$-decay theory.
  \item[Y:] How could that be? It is being replaced by more fundamental ideas.
            Of course it was a very important contribution which had sustained the whole field for some forty years: Fermi had characteristically swept under the rug, and focused on what can be calculated. It was beautiful and agreed with experiment. But it was not permanent. In contrast, the Fermi distribution is permanent.

  \item[W:] No, no, you do not understand the impact it produced at the time. Von Neumann and I had been thinking about $\beta$-decay for a long time, as did everybody else. We simply did not know how to create an electron in a nucleus.
  \item[Y:] Fermi knew how to do that by using a second quantized $\psi$?
  \item[W:] Yes.
  \item[Y:] But it was you and Jordan who had first invented the second quantized $\psi$.
  \item[W:]  Yes, yes. But we never dreamed that it could be used in real physics.
\end{description} 
}

When I arrived in Hamburg, Jordan was working on his scalar-tensor theory of gravitation generalizing Einstein's theory and Kaluza-Klein theory with the presence of a massless scalar field and trying to obtain expressions for the changes of the fundamental constants. He had naturally taken a keen interest in my work on a massive self-gravitating scalar field  in general relativity. It was in the many discussions following my presentations in his seminar that I reformulated the equations I had written  in Rome, modifying a term in  the energy-momentum tensor and obtaining finally explicit numerical ground state solutions of the Einstein-Klein-Gordon equations: 
the first example of a boson star had emerged.
This was to the great surprise to some members of the  Jordan group who were  using analytical procedures in an attempt to obtain a theorem about the nonexistence of solutions of the above equations: I had just formulated the explicit solutions.

That summer I attended a colloquium in Paris at the Institute Henri Poincar\'e and in a small lecture room I met John Wheeler, Charles Misner and Paul Dirac. It was a great opportunity during the breaks to be alone with Dirac in an empty auditorium and be able to ask his opinion after some thirty years about his initial hypothesis of the changing with time of the fundamental constants based on his ``large numbers" hypothesis. Dirac was not very talkative. After some minutes of silence, he simply answered: ``What, do you mean the $10^{20}$, $10^{40}$ coincidences?", to which I answered ``Precisely" and after some additional minutes of intense silence a simple answer ``It is true." I kept thinking about the scalar-tensor theory approach to this problem by Jordan.

To Wheeler I presented the first result of my boson star solutions and, having himself worked on the self-gravitating solution of the Einstein-Maxwell equations in his theory of 
geons \cite{wheelergeons}, 
I was not surprised by his great interest in my work. I also expressed to him my concern about some of the statements he had made in a recent book on gravitational collapse with 
Harrison, Thorne, and Wakano \cite{wheeleretal1965}. I was since that time convinced, although unable yet to prove, that some global description of neutron stars was needed along the lines of what I had just found for boson stars. In the case of bosons I had found an explicit  solution for the global description of the system and the results were totally different from those obtained by a local description using an equation of state.  
Misner tried to give a simple answer to my questions. I replied that more attention should be given to the equation of state of neutron stars, especially if one departs from the overly simplistic model of Oppenheimer and Volkov, mathematically correct, but a  physically untenable solution for a system of self-gravitating neutrons neglecting the weak interactions. I was already concerned at the time that a nonlocal description of a neutron star was needed if the electromagnetic structure and the beta equilibrium should be enforced. We decided to continue to discuss this topic in the future. At the time I had no theoretical means to prove this conjecture, and, as I will show, this issue was solved only recently: 45 years later!

After all these encounters,
I was confident that general relativity would have a great future in the domain of relativistic astrophysics. I expressed this feeling to Leopold Halpern while walking to Notre Dame. 
He answered at once: ``No doubt about!''
Leopold became one of my closest  friends in the following years.


\section{My 1967 arrival in Princeton}

In September I moved to Princeton and I was received warmly by John Archibald Wheeler (see Fig.~\ref{chap1_fig16}) as a post-doctoral fellow.  
For this initial period Amaldi had found for  me a postdoctoral fellowship of the newly born European Space Organization (ESRO), granted to me by the then director general Pierre Auger. The agreement was to keep Amaldi and his group informed on the developments of gravitational wave detectors.

\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_einstein_yukawa_wheeler.pdf}
\caption{Albert Einstein, Hideki Yukawa and John Archibald Wheeler.
Photo taken at the Institute of Advanced Study in Princeton in Marquand Park (1954) and 
dedicated to me by Wheeler with the words ``To Remo Ruffini, companion in the search for the deeper meaning of Einstein's great theory, with warm regards, John Wheeler, 5 April 1968."  
}
\label{chap1_fig16}
\end{center}
\end{figure}


Soon after arriving in the USA, I visited Joe Weber in Maryland and established excellent contacts with him. But I could not help having doubts about his results. I was astonished that he had not yet computed the cross-section of his detectors, something Fermi would have done as a first step. In view of the relevance that this experiment represented in the following years for the Physics Department in Rome, I will briefly comment on it before returning to the field of relativistic astrophysics.
 We soon computed, with Johnny, the cross-section of the gravitational wave resonant bars using a Breit-Wigner formula 
(see chapter 7 of the book by Rees, Ruffini and Wheeler \cite{rees}). 
It soon became clear that the detection rate of the so-called Weber events  was  unjustifiable on the basis of our theoretical considerations.

During this initial  period  Brandon  Carter visited us in Princeton
coming from Cambridge, England, having
just published a  fundamental paper, ``The Global Structure of the Kerr Family of Gravitational Fields" \cite{carter}.
There he a system of first order differential equations  describing charged test particle motion in the Kerr-Newman geometry. Johnny identified the crucial role of an effective potential technique, originally developed by Stormer in the study of the orbits in the Earth aurorae \cite{stormer}, for studying the trajectories of Carter's differential equations. This gave us the opportunity for an immediate application of  numerical techniques by computers, to discover the physical and astrophysical content of this set of mathematical equations. This work characterized an entire new era (see, e.g., the book of Rees, Ruffini and Wheeler \cite{rees}
and the appendices therein).
The innermost stable circular orbits in the Kerr geometry, later abbreviated to ISCOs, were immediately computed analytically by me and Johnny. Both the Carter and the Ruffini-Wheeler results were later  rewarded by a named problem in the last edition of the Landau-Lifshitz  textbook \textit{The Classical Theory of Fields} \cite{LL}
and became one of the most quoted concepts in the physics of binary X-ray sources.


\begin{figure}[h]
\centering
\includegraphics[width=3.5in,angle=90,clip]{chap1_kn_orbits.pdf}
\caption{Motion of a cloud of uncharged particles corotating about an extreme spinning charged black hole. The orbits are stable. The constants of the motion are $E = 0.968$, $\Phi = 2$, $Q = 10$. The initially vertical grid lines indicate isochronous points (as seen from infinity). [Fig.~10 of Ref.~\protect\refcite{coccorr}.]
}
\label{fig:chap1_kn_orbits}
\end{figure}

Later the integration of five particles around a Kerr black hole, numerically integrated  by an undergraduate student in Princeton, Mark Johnston, led to the beautiful image (see Fig.~\ref{fig:chap1_kn_orbits}).
This image was later interpreted by the artist Pierelli in a silver sculpture he named
TEST (Traction of Events in Space Time) \cite{TEST}
given to the recipients of the Marcel Grossmann Awards, while the image itself became the symbol of ICRA and ICRANet.
See Fig.~\ref{fig:TEST}.


\begin{figure}[h]
\centering
\includegraphics[width=3.5in,clip]{chap1_test3.pdf}
\caption{The sculpture TEST by Pierelli. 
}
\label{fig:TEST}
\end{figure}





\section{Stanford: Everitt, Fairbank and Schiff, the great triad}

After a year  in Princeton I took a trip to California before returning to Italy. I drove to Stanford along the northern route and  returned along the southern one: an unforgettable trip that gave me a lasting impression of the dimensions of that beautiful country. 
At Stanford I met Felix Bloch, the former assistant of Heisenberg in Leipzig 
%(see Fig.~??) % NEEDS FIGURE??
who had founded the Physics Department at Stanford and I enjoyed many reminiscences with him of George Gamow, Quirino Majorana, Edoardo Amaldi and the founding of CERN among many other topics. 
Indeed Amaldi and Piere Auger,
%(see Fig.\ref{??}), % NEED FIGURE 
following the idea of Isidor Rabi to establish international physics  laboratories,  were essential  in proposing the institution of CERN in Geneva and Felix had been for some years its first Director General. Felix is actually the only physicist I have ever met who knew of Quirino Majorana, the uncle of the better known Ettore Majorana, and his experiments in Bologna  to test screening of  gravity.

I also found very fascinating my discussions with Bob Hofstadter, formerly at Princeton, and I appreciated his enthusiasm in proposing to use in space some of the sodium-iodide crystal detectors  he had developed to detect X- and gamma rays at the accelerators in Stanford. His eagerness was clearly reiterated almost daily: ``Remo,  try to find a way to see up there in the universe some of the phenomena  we have observed here in the laboratory.� Years earlier Bob had made a proposal to NASA to fly a sodium-iodide instrument  which could have detected the Crab Nebula pulsar in X-rays prior to the radio observations!  This dream of Bob  became a routine reality decades later. 

Stanford gave me the possibility to establish very powerful connections with three very different men: Leonard Schiff, Bill Fairbank and Francis Everitt.    I had studied Schiff�s classic textbook on quantum mechanics. How great it was finally to meet him and find him to be a really friendly guy with a characteristically inviting smile. 
%See Fig.~??. % NEED FIGURE SCHIFF
Having played a crucial role in guiding Bob Hofstadter's Nobel-prize-winning measurements of 
nuclear form factors \cite{??}, % NEED CITATION  
Schiff had turned to general relativity in his mid-forties and written several elegant papers, most impressively his investigation of the meaning of experiments for testing Eddington's formulation of general relativity and, above all, his exact calculation of the geodetic and frame dragging precessions of a gyroscope in 
earth orbit \cite{??}. % NEED CITATION 
Tragically  he met an early death in 1971 just two months before my extended visit to Stanford in 1971--1972 arranged at his invitation. 

% in progress Remo here

Bill Fairbank was an outstanding source of ideas and discoveries: above all the quantized magnetic flux in superconductors which together with Josephson�s prize winning superconducting tunneling led to that marvelous measuring instrument: the superconducting quantum interference device or SQUID (see, e.g., ``Near Zero: New Frontiers of Physics'' \cite{nearzero})ref).  My interaction with Bill proved to be one full of enthusiasm and common scientific interests. Among the many topics we discussed and planned, we agreed that the most direct way to gauge Joseph Weber's alleged discovery of gravitational waves was to develop a more massive detector, cooled not just to 2 degrees Kelvin but all the way to  a few millidegrees Kelvin and utilizing SQUID detectors. I informed Amaldi in Rome of this program.

Francis Everitt had gotten his Ph.D. in paleomagnetism with Blackett in London, proving among other things that 300 million years ago in carboniferous times  BMMMMMM?? had been 10 degrees south of the Equator  and then had gone on to discover the ``third sound" in superfluid helium with Atkins at the University of Pennsylvania \cite{??}. % NEED CITATION 
When I met him he was well into the design of what some would call ``the impossible experiment:" the NASA Gravity Probe B (GP-B) mission, to measure the two effects Schiff had calculated.
The extraordinary conjunction of physics and engineering was then beginning to develop a low temperature space laboratory working at helium temperature 
%(see Fig.~\ref{??}) % NEED FIGURE
 and using essentially the SQUID technology for read out 
%(see Fig.~\ref{??}). % NEED FIGURE
This project reached completion 37 years later with the satellite launch in 2004, and was brought to its ultimate success with a very sophisticated  data analysis leading to its final report in 2011  \cite{everitt2011}. My friendship and overlapping scientific interests with Francis have been of the great joys of both our lives still continuing today through ICRA and ICRANet. Many graduate students,  both at Stanford and in Rome,  joined us in following this great experiment from its start to his completion both in its theoretical and experimental aspects. 

After that epochal trip to  Stanford,  instead of returning to Italy I stayed in Princeton for nine more years, first as a member of the Institute for Advanced Study, then as an instructor and assistant professor at Princeton University, and again as a member  of the Institute for Advanced Study. 
An occasion to develop our collaboration further came that same year in September when  Hermann Bondi, who had just been nominated the Director General of ESRO, invited John Wheeler,  myself, Leonard Schiff and Francis to an international meeting in Interlaken. 
%on ... % NEEDS COMPLETION
This gave Wheeler and I the occasion to write our report in the following two years. % NEEDS COMPLETION

%\Typeout{DELETE OR NOT THE REST OF THIS SECTION??}
I came back to Stanford later for a semester to oversee the developments of the gravitational wave experiment and also to have interactions with Francis. I informed Amaldi and I suggested duplicating the Stanford facility in Rome to check for coincidences. I was motivated in this decision by three different reasons:
1) to give a definite answer to Weber's contentions by an experimental work in a regime with a very clear signal-to-noise ratio,
2) to introduce in Italy the new technology of low temperature physics and the use of SQUIDs introduced by Bill, and
3) to foster interest in the field of relativistic astrophysics and in the sources of gravitational waves, which I was developing in Princeton (see chapter 7 and appendix A). % NEEDS CROSS-REFERENCE
Indeed the results are well known: the Rome-Stanford experiment showed the inconsistency of Weber's result, low temperature techniques were widely used in the Physics Department in Rome, even developing magnetometers to scan the brain, and some theoretical activity was later transplanted to ICRA and ICRANet.


My interest in gravitational waves had waned and I was putting all my effort into the new field of relativistic astrophysics, white dwarfs, neutron stars and black holes, as I will describe below. It was indeed a pleasure, in the following years, to illustrate to Vicky Weisskopf at MIT, who meanwhile had become a close friend,  the results of my research at the Institute for Advanced Study and at  Princeton University. 



\section{Introducing the black hole}

In Princeton we used to work with enormous energy (see Figs.~\ref{rr_wheeler1}--\ref{rr_wheeler4}).
First I finished my research on boson stars \cite{ruffinibosonstars}  and then began to look at gravitational waves from pulsars 
\cite{rrpulsars}.
Our style of research was new,
 based on the extensive application of computer techniques I had learned in Rome. Numerical analysis implemented on computers was used to answer specific physical issues related to the final evolution of stars and to gravitational waves and cosmology. 
All these theoretical activities were anchored in direct confrontation with the large amount of data that was starting to flow in thanks to the new space technologies.
The main message of Wheeler was let us not stop at neutron stars but proceed on to black holes (see the paper \cite{rr_intro_bh}, reproduced in Appendix \ref{appA_Ruffini2009p1645Phys_Today}). 
Indeed we moved to the new physics of the simplest and most complete physical object in the universe, the black hole! (See Fig.~\ref{wimmer}.)
In that paper for the first time the emphasis was not on the mathematical aspects of the Kerr-Newmann solution but new physical processes were addressed, like the concept of the ergosphere, the reversible and irreversible transformations of black holes and the relevance of binary star systems for their possible future observation.
In view of the urgency of these developments I postponed my interest in further studying neutron stars till later on.

\begin{figure}[t]
\begin{center}
\includegraphics[width =3in]{chap1_wimmer.pdf}
\caption{Artist's conception of the black hole by Helmut Wimmer, used as the cover of the \textit{Physics Today} magazine containing the 1971 article ``Introducing the black hole" by Ruffini and Wheeler.
}
\label{wimmer}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in,angle=90]{chap1_rr_whe_and_coll.pdf}
\caption{Johnny Wheeler, Remo Ruffini and collaborators at Princeton in 1970.
}
\label{rr_wheeler1}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_rr_whe_chr_phd.pdf}
\caption{Demetri Christodoulou being addressed by Eugene Wigner at his Ph.D. thesis defense at Princeton in 1971,
with David Wilkinson, Johnny Wheeler and Remo Ruffini looking on.
}
\label{rr_wheeler2}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in,angle=-90]{chap1_rr_whe.pdf}
\caption{Remo Ruffini and Johnny Wheeler at Princeton around 1970.
}
\label{rr_wheeler3}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in,angle=90]{chap1_rr_whe_chr.pdf}
\caption{Demetri Christodoulou, Johnny Wheeler and Remo Ruffini in Princeton around 2003.
In the background one sees the phrase
``Raffiniert ist der Herrgott, aber boshaft ist er nicht" (Subtle is the Lord, but malicious he is not) written in charcoal from the fireplace by Einstein and later carved into the marble mantle.
}
\label{rr_wheeler4}
\end{center}
\end{figure}

A testimony of this period of research is the book of Rees, Ruffini and Wheeler \cite{rees}. 
The first ten chapters were written by Johnny and myself as an ESRO report which was the outcome of our participation in  GR3 in Tiblisi.\footnote{
Chapter 1: Introduction.
Chapter 2: The physics of a superdense star.
Chapter 3: Pulsars.
Chapter 4: Supernovae.
Chapter 5: Black holes.
Chapter 6: Quasi-stellar objects.
Chapter 7: Gravitational radiation.
Chapter 8: The three traditional tests of relativity.
Chapter 9: The retardation of light as it passes by the Sun on its way to and return from Venus.
Chapter 10: Relativistic effects in planetary and lunar motions.
}
We had the greatest opportunity and joy to have as coauthor Martin Rees, who joined us in this book with the following eight chapters,\footnote{
Chapter 11: The expanding Universe.
Chapter 12: The evolving Universe.
Chapter 13: The microwave background: the primordial fireball.
Chapter 14: The fate of fluctuations: galaxy formation.
Chapter 15: The mystery of the missing mass: the content of the Universe.
Chapter 16: Cosmic background radiation.
Chapter 17: ``Non-canonical'' models and the very early Universe.
Chapter 18: The ``large numbers'': coincidence or consequence?
}
followed by a ninth chapter written by Johnny entitled ``Beyond the end of time.''
A series of the latest developments in this field moving so quickly in those days was directly summarized by reproducing some publications of papers which had just appeared when the book was printed.
Actually the Tbilisi meeting turned out to be a very important experience: it marked the first encounter of Johnny and myself  with Andrei Sakharov, Yakov  Zel'dovich and all their many young collaborators including Rashid Sunyaev, Gena Bisnovaty-Kogan, Valery Chechetkin and especially my unforgettable friend Victor Schwartzmann (see Appendix \ref{appA_ruffinizeldovich}).

% bob edit

In the States we were blessed  by three very important factors. 
%
\begin{itemize}

\item[1)]
First there was the presence at Princeton University of some exceptional students and post-docs, including the undergraduate students 
James A. Isenberg, Robert T. Jantzen, Robert Leach, Mark Johnston, Paul McGuire, and Richard Hanni,  and the graduate students 
Jacob Bekenstein, Demetrios Christodoulou, Bahram Mashhoon, Hans Ohanian, William G. Unruh, Robert M. Wald and Frank J. Zerilli.
There were also gifted visiting students from France, first Nathalie Deruelle, followed one year later by Thibault Damour. 
Of course among the permanent academics at Princeton at the time were such giants as Valentin Bargmann, Kurt G\"odel, Martin Kruskhal, Tullio Regge and Eugene Wigner, and this ambiance was also often refreshed by the witty remarks of another very learned outsider
to the field of relativistic astrophysics, Freeman Dyson. 

\item[2)]
Second there was the splendid development of space science at American Science and Engineering and later at Harvard University by the group led by Riccardo Giacconi and Herbert Gursky. 
Discussions with Riccardo and Herbert were occurring nearly every day by phone. 
I still remember an old fashioned professor who  in a physics department meeting denounced the ``scandal'' that I had spent 264 dollars in one month on telephone calls to Cambridge, Massachussetts.
The chairman of the department, Murph Goldberger, took a more relaxed attitude and invited me to proceed as needed.

\item[3)]
Finally there was the knowledge of physics, the enthusiasm, and the dedication of John Wheeler to create this local resonance in Princeton. Through him we were
connected to a small group of scientists visiting Princeton with extensive experience  in  physics acquired and tested in the study of nuclear and thermonuclear processes. 
 The most important among them for me  were Michael May and especially Jim Wilson, with whom I collaborated strongly in the years that followed.
Knowing Johnny's experience, I expressed the feeling that quite apart from the moral and political aspects of the event, to see a nuclear explosion should be, from a physicist's standpoint, a formidable experience. 
He told me: ``Ask the French, since they are still experimenting in the atmosphere.''
I did not follow his advice, but a few years later we  indeed reached the possibility of observing the largest nuclear explosions in the universe,   realized in gamma ray bursts, as I  will speak of shortly.

\end{itemize}

A similar enthusiasm characterized the twin group of relativistic astrophysics in Moscow gathered around Yakov Zel'dovich with such young collaborators as Rashid Alievich Sunyaev, Gennady (``Gena") Bisnovatyi-Kogan, Valeri Chechetkin, and Victor Schwartzmann,  whom I have already mentioned and also, of course, Igor Novikov.
I recall some some of the moments with Zel'dovich in \cite{ruffinizeldovich2009} 
reproduced in Appendix \ref{appA_ruffinizeldovich}.


\begin{figure}[h]
\begin{center}
\vglue 3in 
\includegraphics[width =3in]{chap1_remo1972award.pdf} %width?? % NEEDS FIGURE
\caption{
Remo Ruffini receiving the Cressy Morrison Award from the New York Academy of Sciences in 1972. 
}
\label{fig:remo1972award}
\end{center}
\end{figure}

\section{The identification of the first black hole candidate}

The 1972 Les Houches Summer School gave me the opportunity return to my study of neutron star configurations of equilibrium by introducing an alternative approach based on the gravitational Thomas-Fermi equations. Other important results were presented there like the idea of live versus dead black holes, the absolute upper limit to the critical mass of neutron stars of 3.2 solar masses, and the relevance of binary X-ray sources. As we will see,  a  new understanding of neutron stars would later  be obtained from the gravitational Thomas-Fermi equations.
The launch of the first X-ray satellite Uhuru by Giacconi and his group in 1970 had as its crowning achievement the first identification of a black hole candidate in 1973 \cite{leachruffini,josephhenrylectures}, namely in the Cygnus X-1 binary system  within our own galaxy.


\begin{figure}[h]
\begin{center}
\vglue 3in 
\includegraphics[width =3in]{chap1_giacconi_nobel.pdf} %width?? % NEEDS FIGURE
\caption{
Riccardo Giacconi receiving the Nobel Prize in 2002. 
}
\label{fig:giacconi}
\end{center}
\end{figure}



Another important event was  the 1974 meeting of the AAS in San Francisco that I organized with Gursky.
For the first time gamma ray bursts were introduced in a large public event at this meeting \cite{gursky}. 

Finally, in 1974 we held the Enrico Fermi Varenna Summer School where all these successes were summarized and avenues for future research were opened \cite{giacconi}.
I presented all these results at the Solvay Meeting in 1974 \cite{rr_solvay} (see Fig.~\ref{fig:solvay1973}).

From the three small groups in Princeton, Cambridge, England and Moscow, the seeds of relativistic astrophysics were spread to all the universities worldwide: there are very few universities where there is no scientific interest in black holes. From less than a hundred scientists initially working in this area, the  number has grown exponentially to the thousands, the tens of thousands, the hundreds of thousands who are engaged in various aspects of relativistic astrophysics.
This has also been the result of a parallel development in observational technology on the ground, underground and in space. It suffices here to recall the enormous progress of the Hubble Space Telescope, and of ESO during the leadership of Riccardo Giacconi for ground-based observatories and from space. Similarly from space, in addition to the already mentioned NASA program, there were also programs by ESA and the space agencies in Russia, Japan, India and more recently Brazil.
I will not try to cover any of these developments which have taken place since the Princeton days and which are well summarized and documented  in the  above mentioned books. I will focus  instead on some lesser known activities outside the US that  I have witnessed and in which the work of  Fermi, Einstein and Heisenberg  has led to fundamental new results in relativistic astrophysics and I will address now only the new frontier in this field.


\begin{figure}[h]
\centering
\includegraphics[width=5in,clip]{chap1_solvay1973_scan.pdf}
\caption{Sixteenth Solvay Conference on Physics, University of Brussels, 1973.
}
\label{fig:solvay1973}
\end{figure}



\section{Kyoto and some influences of Fermi and Heisenberg in Japan}

After my experience at the Institute for Advanced Study and as an assistant professor at Princeton University, using a generous Alfred P. Sloan Fellowship awarded to me by a committee led by T.D. Lee, I went to visit other groups in Japan and  Australasia. I had been very eager to accept an invitation from Hideki Yukawa and Humitaka Sato to visit Kyoto. I went first  to 
Takehara
to see the relativity group then headed by Kenji Tomita which had moved there from Hiroshima University at the end of World War II.
The director of the physics department there had been a student of Heisenberg and was one of 0.01 percent to survive at the blast site. He decided to move the department to his house at the beach at the small fishing village of Takehara.
I gave lectures at Yukawa Hall in Kyoto and a book introducing black holes to Japanese students and the public was published by Humitaka and myself \cite{sato} (see Fig.~\ref{fig:rrsatobook}).

% Figure 3.  book with Sato
\begin{figure}[h]
\centering
\includegraphics[width=5cm]{chap1_rrsatobook}  
\caption{
The cover of the book
``Black Holes" by Humitaka Sato and Remo Ruffini, in Japanese (Chuo Koron-Sha, Tokyo, 1976).} 
\label{fig:rrsatobook}
\end{figure}

To me the most interesting thing in this revealing experience was to understand the different research paths followed by this Oriental school, so different from our Rome school imprinted by Enrico Fermi.  Of course the two schools were not so  independent since much of the towering work in quantum field theory had been developed in Japan already under the direct influence of Werner Heisenberg and that imprint was clearly recognizable. I enjoyed each single day in Kyoto  by looking at the beauty of the small waterfalls and  stone gardens around the ancient wooden temples in the concentric  hills of Kyoto forming an almost perfect parabola which made its focus the perfect target for an atomic bomb explosion. I often gratefully  recalled in my mind the anecdote that John Wheeler, 
influenced by his wife Jeanette, was  one of the main actors 
in defusing the possibility of using Kyoto as the first target in Japan for the atomic bomb, a weapon created with the basic scientific contributions of Enrico Fermi. ``Jeanette would never have forgiven me for that."


\section{My last meeting with Heisenberg talking about Einstein and Fermi}

In the summer of 1974 Werner Heisenberg came to the United States and we met first in Washington.
I then invited him and his wife to meet me  in Stanford. We had a leisurely series of walks in the fields around the campus and up in the woods in Ladera during which we had the opportunity to discuss many points of both physics and history.  
First Heisenberg was very interested in understanding better the connection between the Heisenberg-Euler process he had developed to describe the polarization of the vacuum  around a compressed nucleon and some work I was doing with Thibault Damour on vacuum polarization around a Kerr-Newman black hole. Thibault and I later published that work which served as the basis for the explanation of the energy source for GRBs, the blackholic energy,  and  for the idea of the ``dyadotorus'' \cite{dyado}. 
It was  also very pleasant to talk about the historical aspects of his paper with Hans Euler. He told me that the paper had two parts, one of physics, which was simple,  and another in which the Euler constant appeared in one of the formulas, and this was quite difficult.
Heisenberg  also told me the story of the tragic end of Hans Euler, who was 
a descendant of the famous mathematician by the same name. As a young man he had been 
engaged to a Jewish girl who had been taken to a labor camp. He decided to finish with all the nonsense going on in his life and volunteered for the Luftwaffe where he was among the first killed on the Russian front at the beginning of World War II.

Paradoxically Heisenberg was mainly  interested in talking about my work but I was eager to let him know that I had great respect for Chandrasekhar's work  and I intended to invite Chandra to our school of Varenna. Initially Heisenberg appeared not to be interested. But since I was insisting he concluded: ``Yes, you are correct,  in my last visit with Fermi walking on  the campus of Chicago we crossed paths with Chandra and Fermi turned back to introduce him to me, maybe you are correct, we should recognize his work more."  
I wrote to Chandra a few months after his Nobel Prize in 1983, ``Heisenberg would have been most satisfied."
 
Heisenberg was at times  a quite unusual person. He enjoyed telling stories and I was eager to record them in my mind. He told me about the time at Farm Hall where they were kept secluded at the end of the war. He had received an order not to reveal his identity to anyone. One evening he was taking a walk in the garden and a guard challenged him to identify himself. The first thing he did was to shout ``Don't shoot!" Then he approached the guard and explained the order he had received. The guard accepted this explanation, which would have been the end of the discussion for any normal German person following orders,  but not for Heisenberg. He went on with the guard saying ``They have ordered me not to reveal my name but they did not order to me not to ask you who you think I am." To this the guard answered: ``We do not know your name but we do know  the name of the man with the white moustache: Marechal Petain!"  The man with the white moustache was  Max Von Laue.

Some of the comments of Heisenberg were unexpected to say the least. Staring at the Bay Bridge from San Francisco to Berkeley he noticed: ``The last time I visited San Francisco that bridge was not here." True. I asked him the dates of his last visit: it had been 1929 and the bridge had  indeed been built in 1933. Difficult to imagine in our very mobile world! There were also many more points about his own involvement in the German bomb project which were quite simple and revealing, but this would need an additional paragraph I am not willing to write today.  

One last point I was eager to discuss with him was about Einstein and general relativity. I was quite direct in asking Heisenberg: ``If you had not discovered the principle of indeterminacy and introduced the matrix formulation of quantum mechanics, certainly somebody else would have discovered them independently, but do you think that if Einstein had not introduced general relativity, somebody else would have done it?" Heisenberg did not answer and asked me: ``Why do you ask such a question?" and to that I explained my profound belief that ``Someone could have been forced by electron experiments to introduce the indeterminacy principle, but in the case of general relativity it needs such a profound mixture of understanding of mathematics and  physics  intuition  which led Einstein to his equations, without any experimental support." To that Heisenberg said: 
``Mathematics? Einstein did not know any mathematics."  The ancient rivalry between Berlin and Leipzig was not yet over!  

We agreed that he would have given the inaugural lecture at our Varenna Summer School on July 21, 1975 bridging the gap of the Heisenberg-Euler work from nuclear physics to astrophysics. In fact this could not happen since he became very ill and on July 7, the secretary canceled his lecture. He died the following winter.

% bob edit

\section{Back to Rome and the Fermi Chair}

Finally in 1978 Edoardo Amaldi called me back to Rome for a chair of theoretical physics: one of the three into which the original Fermi chair had been split. 
Amaldi had been in contact with me during the years I had spent in the USA and he had developed, with my suggestions, 
an experimental group with the goal of detecting gravitational waves in an Earth-based bar detector experiment.
I tried to make clear that the style of research now was necessarily in the domain of ``wild'' physics, but the style of research adopted in Rome was more closely related to the one of ``controlled'' physics.  In my opinion the physics of gravitational waves had to be seen in the context of  relativistic astrophysics, which had the largest horizons ever opened to human inquiry through X-ray binaries, active galactic nuclei and more recently gamma ray bursts. Amaldi was more interested in an approach to improve the sensitivity of the previous experiments in the laboratory as in particle physics. However, there is a big difference between gravitational wave experiments and laboratory experiments in particle physics: usually a new experiment improves on a previous successful experiment and this was not the case for gravitational waves. The Weber experiment was shown to be incorrect precisely by the joint Stanford-Rome experiment.  
It was indeed in  the ``wild'' setting of astrophysics  that the first evidence for the existence of gravitational waves was given by observations of a binary pulsar analyzed by R.A. Hulse and J.H. Taylor.\footnote{
See their Nobel lectures at
http://nobelprize.org/nobel$\underline{\phantom{t}}$prizes/physics/laureates/1993/.
}

Upon my return to Rome one of my main objectives was to maintain  contact with Riccardo Giacconi and his research group. Riccardo had moved from Harvard to Baltimore to build and direct the Space Telescope Institute. 
One of the first contacts I established through Herb Gursky was with the Vatican Observatory (Specola Vaticana in Italian) in Castel Gandolfo near Rome
and its director George Coyne. Near Tucson in Arizona the Specola built the prototype telescope of a new generation of multiple mirror telescopes  and in Castel Gandolfo it had one of the best scientific libraries in the world. Our collaboration became stronger and stronger.

One of my principal scientific activities was the connection with Abdus Salam,  ICTP and the newly born Third World Academy of Science (TWAS). Abdus and I enthusiastically participated  in research relating particle physics and relativistic astrophysics and we also  started a teaching program in the former summer camp of the English troops in the Karakorum Mountain Range in Pakistan, a memory of the Kipling times, in the splendid mountain village of Nathiagali. There professors and researchers from a wide range of developing countries from the Philippines to India,  Egypt, and Morocco participated each year in the lectures we organized with some of the leading scientists in physics and astrophysics. This experience near the Swath Valley gave me the opportunity to become knowledgeable of that marvelous part of our planet and its history and culture. Each trip from Rome to Nathiagali was a 
great adventure with the crossing of the Khyber Pass! 
There was an additional very important special side of Abdus: he had been a close friend of 
Chou En-Lai (see Fig.~\ref{salam}). Thus he  was able to introduce me to the Chinese Academy and in the last thirty five years I have dedicated  particular attention to developing  scientific collaborations with Chinese scientists. 


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_salam.pdf}
\caption{Abdus Salam and 
Chou En-Lai.
}
\label{salam}
\end{center}
\end{figure}
\section{China from 1979 on}

I had the good fortune  to enter China in 1979 and meet Fang Lizhi and his wife and scientist colleague Li Shuxian. It was the beginning of an intense experience in science, in culture and  in approaching  the many facets of the role of scientists in society, following Galileo's teaching and example. 
Just as I was nearing completion of this memoir in 2012 Fang Lizhi died.  
Much has been written in the international press about him. I recall here only three aspects more related to his academic life and the Rome Physics  Department at large and then in the next subsection I recall  an anecdote relating Fang to Fermi. 

\subsection*{Our small book on relativistic astrophysics}

During that  first visit I delivered lectures in campuses all over China and we decided to collect them  into a small 184 page book in Chinese to be priced at less then 1 Yuan \cite{rrfang}. 
This book initiated into relativistic astrophysics many Chinese students who in the meantime  have become recognized leaders in the field both in China and internationally. 

\subsection*{MG3 in Shanghai}
 
In 1982 we succeeded in organizing the first international scientific meeting in China: the Third Marcel Grossmann Meeting in Shanghai. 
It was one of the great efforts in my life, with the help of Fang and Zhuo Pei-Yuan, then president of the Chinese Academy of Science and Technology (CAST), to get accepted an extension of a basic paradigm in the Chinese way of thinking: the motto ``Friends from all over the world are welcome" became ``Scientists from all over the world are welcome." This allowed, among others, the participation of Israeli scientists in this scientific celebration of Einstein's ideas. 
Achieving the final agreement for the travel document between myself and the Chinese ambassador in Rome represented the culmination of one of the most difficult experiences in my life. It was reached recalling the great historical friendship between Italy and China quoting three names: Marco Polo, Matteo Ricci (Ri Ma To) and Enrico Fermi. I will return to this shortly.

\subsection*{The establishment of ICRA and the Fang chair in Rome}

In 1985 it became clear that we had to create a structure to formalize these collaborations and it was with the help of Antonio Ruberti, the Rector of the University of Rome ``La Sapienza," that we created the first international consortium of universities and research centers operating in the field of relativistic astrophysics.  We founded the International Center for Relativistic Astrophysics (ICRA) in Rome which was soon officially recognized by the President of Italy.  
The original members were Francis Everitt for Stanford University, George Coyne for the Specola Vaticana, Riccardo Giacconi for the Space Telescope Institute, Fang Lizhi for the University of Hofei, Abdus Salam for the ICTP and TWAS, and myself for the University of Rome. 
%(see image on wall (Fang) Fig.~??). % NEEDS FIGURE

In 1989 Ruberti, then Minister of Research and University, promoted ICRA's request to create
a chair in theoretical physics at the University of Rome ``la Sapienza" in order to have Fang Lizhi transfer to Rome.
The Physics Department accepted under the condition that two additional Chairs be established, one devoted to particle physics  and one to solid state physics. Finally, only two were created. Fang accepted instead to go to the University of Arizona at Tucson (see, e.g., Ref.~\cite{kissinger}). 

\section{Fermi and China} 
 
I have spoken about events in Fermi's life in Italy and in Europe and his influence in the Americas and in Japan.  Before closing I would like to discuss some influence Fermi had in China: this is the case in which two of Fermi's Chinese students and collaborators had an unprecedented  impact on science at the international level and triggered the scientific  development of the largest nation in the world: China.
During my second visit there I went to Kun Ming: it was quite an experience to see this beautiful location on the border of a lake, having been so vividly described by Marco Polo. 
There was a train line constructed by the French reaching this town from Hanoi. There was also a beautiful university where two young students studied physics  during World War II,  their families having escaped from the east of China 
ahead of the Japanese invasion. Their names were Tsung Dao Lee and Cheng Ning Yang. At the end of the war they transferred to the USA: T.D. Lee was followed in his Ph.D. thesis by Fermi and C.N. Yang became Fermi's assistant.
 
The remarkable scientific career of these two young Chinese scientists is well recorded in the history of science. 
After Nixon's visit to China in 1972, Lee and Yang frequently went back to China to deliver lectures based on the Fermi tradition and today they are spending the greater part of their time in China organizing scientific centers and activities. 
As I have already mentioned I had many occasions to interact with T.D. Lee and, as I will mention in the conclusions, even today our scientific paths cross in the study of the final evolution of stars like white dwarfs and neutron stars. 

It was during the Third Galileo-Xu Guangqi Meeting in 2011 that I had another pleasant meeting with C.N. Yang. 
This also gave me the opportunity to see Beijing University again, having originally seen it in 1978 after the cultural revolution with all its libraries , now renewed and reaching a new splendor. Next to the Zhou Pei-yuan Institute are the offices of the C.N. Yang Center. 
We talked about our common friend Isidor Rabi and his role in collaborating with Eisenhower as President of Columbia University prior to the latter's election as President of the USA. We also talked about Fermi's role in formulating his theory of beta decay, of the adventures of the A-bomb and  H-bomb projects and many other topics. 
This also gave me the chance to introduce him to our ongoing projects with ICRANet. 

In the imperial  Chinese tradition of the past, in each town in China there was a place in which every year the best young astronomers were examined and selected and brought to the imperial palace to perform their study and research. 
Great credit goes to T.D. Lee  for having reactivated this selection process on a large scale and having sent the most qualified young students not to the imperial palace in Beijing but to the leading universities in the USA for many years.\footnote{
\url{http://en.wikipedia.org/wiki/CUSPEA}
}
A similar program was carried out by C.N. Yang. 
In my opinion these experiences, as well as the ones we developed with Fang in ICRA and ICRANet,  have  been  a significant component in guaranteeing that most impressive scientific, technological and industrial development that the entire world admires today in China. 
In some sense this authentic scientific and cultural evolution of modern China was triggered directly and indirectly  by the influence of Fermi. 

Returning to the main topic of Fermi and astrophysics, it is interesting that according to T.D. Lee Fermi's original critical attitude expressed in his Trento lecture on the interior of stars was evolving towards the end of his life. As recalled by T.D. Lee in a talk held at a joint meeting of the APS and AAPT in February, 2010 ``Remembering Enrico Fermi," Fermi was beginning to warm up towards astrophysics in his final years: Fermi asked Lee during his Ph.D. thesis the approximate temperature of the Sun at its center. Lee replied, ``Ten million degrees." Fermi asked: ``How do you know?" Lee told him he had looked it up. Fermi asked if he'd verified the number and Lee replied, ``It's really complicated. It's not so easy to integrate these equations." Fermi suggested that Lee build a huge specialized slide rule that would enable the solution of two radiative transfer equations, one that involved the 18th power of the temperature, and the other that involved the reciprocal of temperature to the 6.5th power. Over the next few weeks Lee built a slide rule that was 6.7 feet long and carried out the necessary integration. ``It was great fun." 

And a final story about  Fang and Fermi's Los Alamos work.
In 1956 at the age of twenty  Fang had received his physics diploma from Beijing University and was immediately inducted into China's secret nuclear bomb project where his first assignment was to reproduce Fermi's result on the plutonium pile.
He was dismissed from this project in 1958 but
in 1992 Fang had an unexpected insight into that work when I showed him Robert Serber's newly declassified Los Alamos Primer: \textit{The First Lectures on How to Build an Atomic Bomb}.\cite{losalamos} 
Fang exploded in laughter when he saw there the same incorrect value of the neutron yield that the Chinese had received from the Soviets. He said the coincidence of the two incorrect values was impossible unless the Soviets had somehow earlier gotten the \textit{Primer} themselves---an early case of nuclear information proliferation! 



\section{From ICRA to ICRANet}

In  2005 we founded the International Center for Relativistic Astrophysics Network (ICRANet), the first international organization dedicated to promote international scientific cooperation and undertake research in relativistic astrophysics. 
Its headquarters are in  Pescara, Italy on the coast of the Adriatic Sea.
The member states of ICRANet are Armenia, Brazil, Italy, and the Vatican, but it also includes as member institutions  the University of Arizona in Tucson, Stanford University and ICRA in Rome. Fang was a cofounder and the first President of its Steering Committee and Riccardo Giacconi the first President of the Scientific Committee. Among the activities promoted by ICRANet have been the Galileo-Xu Guangqi (GX) meetings, held annually alternating between China and the West with a maximum of 137 participants from China and 137 scientists from the West. GX1 was held in Shanghai, GX2 in Nice, and GX3 in Beijing. ICRANet today has four centers:  Nice, Pescara, Rio and Yerevan.  
I am teaching theoretical physics and doing research in relativistic astrophysics at the University of Rome through the support of ICRA and more recently of ICRANet. Many of my former students and collaborators have obtained research and teaching positions in universities and research institutes around the world and I still hope to have at least one of them at the Physics Department of the University of Rome ``la Sapienza'' to share our serene scientific experience 
\Typeout{serene scientific experience??}%
with a  Physics Department which has had a quite complicated past.  But this brings us to another topic that I will not elaborate on here.   
To conclude I will instead outline some ongoing activities of ICRA and ICRANet and show how some of the seeds described above are today growing beyond what anyone could have imagined.


\section{The fundamental role of the theories of Fermi, Einstein and Heisenberg for understanding the final evolution of stars and the composition of the universe}

One of the greatest challenges of astrophysics today is to understand the largest explosions in the universe: gamma ray bursts (GRBs). 
We believe that these explosions occur during the formation of a black hole and that in them we are witnessing for the first time the release of ``blackholic energy" (see Appendix \ref{appA_rr_kerrfest}).
The enormous energy emitted up to $10^{55}$ ergs allows these systems to be observed up to 
the redshift $Z=8$ which in the current understanding of our universe corresponds to distances from the Earth of about $2.61\times10^{29}$ cm$\,\approx8.5\times10^{10}$ pc.
Understanding these systems, which emit an energy equivalent to  a few solar masses within a few seconds, has required overcoming many conceptual difficulties, 
opening new areas of research,
and
extrapolating  our current scientific knowledge to as yet unobserved domains.
As I will show, these developments are rooted in some of Fermi's work once
reformulated in an essential way in the context of Einstein's theory of general relativity. 

The central role in modeling this phenomenon is played by the generalization of the Thomas-Fermi theory.
Initially conceived in the nonrelativistic approximation, this theory was first applied in the domain of atomic physics. It was first generalized to the relativistic regime in the case of heavy nuclei to encompass relativistic effects as well as the weak interactions.

\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_dyadotoro.pdf}
\caption{The ``dyadotorus,'' i.e., the region in the Kerr-Newman geometry where vacuum polarization processes may occur, leading to the creation of electron-positron pairs [see C. Cherubini, A. Geralico, J. A. Rueda H. and R. Ruffini, Ref.~\protect\cite{dyado}]. 
The corresponding release of energy is the most powerful way to extract energy from black holes, which appears to be the energy source for the most transient and most energetic events in the universe, the GRBs.
}
\label{fig:dyadotoro}
\end{center}
\end{figure}


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_satellites.pdf}
\caption{The flotilla of satellites exploring the universe with X-ray and gamma ray telescopes.
}
\label{satelliti}
\end{center}
\end{figure}


It was further generalized to a unified relativistic treatment involving electromagnetic, gravitational, strong, and weak interactions within the context of Einstein-Maxwell field theory subject to quantum statistics.
I developed this program by having in my ear one additional sentence of  Eugene Wigner,
which took me almost thirty years to appreciate fully: ``The Thomas-Fermi theory \textit{vorks} much better than it should."

In confronting the many conceptual difficulties along the way to understanding GRBs,
it has been necessary to formulate new paradigms \cite{bianco}. 
For the first time it has been necessary to study macroscopic systems of up to a fraction of a solar mass, moving at ultrarelativistic velocities with Lorentz gamma factors 
$200\leq\gamma\leq6000$, 
a phenomenon which is unprecedented in physics and astrophysics.
These difficulties have manifested themselves in a variety of ways. They have forced us:
\begin{itemize}

\item[1)]
To solve many relativistic problems, e.g., just to mention a few, the equations of motion, the relativistic equations of hydrodynamics, the collision between ultrarelativistic baryons with the circumburst medium of the source and all the relativistic computations of the emission from a shell at ultrarelativistic velocities, and the 
crucial description of the correct equitemporal surfaces of the system.

\item[2)]	
To make  the classical astronomers aware that although the GRB emission takes place on time scales of a few seconds 
and, occasionally, as short as a fraction of a second, still the system cannot be treated as a single phenomenon: there are drastically different physical phenomena occurring at time scales shorter than a second, as measured in the arrival time of the observer. 
Hardest for a classical astronomer to understand is the concept that the time integrated spectrum during such a brief time could overshadow many fundamental phenomena and in fact it is necessarty to analyze the instantaneous spectra on the even shorter time scale of a fraction of a millisecond. 
It is even harder to get them to understand that during a fraction of a second in the arrival time at the detector, the exploding material in the laboratory frame of the GRB event actually travels distances on the order of light years!
Similar difficulties also exist for making particle physicists aware that we are indeed observing $10^{53}$--$10^{54}$ baryons at $10$--$100$ TeV interacting with a target of protons $10^{40}$ cm in size and 
$10^{22}$ g in mass.

\item[3)]	
To make the general scientific community aware that indeed through the analysis of the different eras of a GRB we can have information about the phases prior to the gravitational collapse of the core of the progenitor, the phases just following the formation of the black hole and the early emission of the GRB as well  as to observe  the expansion of the GRB in the circumburst medium and make a ``tomography" of that medium.
This allows the detection, through flares of a few seconds, of the structure of interstellar clouds of $10^{14}$ cm in size and $10^{22}$ g in mass.
Fig.~\ref{fig_luca} shows one of the most successful examples of such an analysis. It is interesting that Fermi made one of the first pioneering investigations on the structure of these interstellar clouds (see papers (237), (238) and (265) reproduced in Chapter 3).
Today we are observing precisely these features in galaxies at billions of light years from the Earth and finding similar features in galaxies  trillions of light years away. 

\end{itemize}

There are so many new ideas that have emerged from this investigation, it is hard to know where to start in listing them. 
For the analysis of neutron stars which participate in some of the GRB progenitors and for the black holes which are at the basis of the GRB description there are 
many. For example:
%
\begin{itemize}

\item[1)]
Many new ideas have been characterized by the introduction of specific new terms which have been adopted in the language as well as in textbooks.    To recall a few examples, I just mention:
 the reversible and irreversible transformation of black holes \cite{christodoulou1,christodoulou2}, 
which have led to the analogies between black hole physics and thermodynamics and especially to the concept of the irreducible mass of a black hole \cite{leshouches}; 
the ergosphere of a black hole determining the region in which the rotational energy extraction process from a black hole can  take place, essential for the understanding of the jet formation in galactic and extragalactic sources \cite{rresro}; 
the mass energy formula for the Kerr-Newmann geometry, at the basis of the energetics of  GRBs; 
the dyadosphere of a black hole \cite{rryamada,preparata}
from the Greek ($\delta\upsilon\alpha\varsigma$, $\delta\upsilon\alpha\delta o\varsigma$) the region of creation of electron-positron plasma around a black hole; 
the proto-black hole, the collapsing core prior to the black hole formation \cite{rrcospar}; 
the neo-neutron star, the young neutron star originating in the gravitational collapse leading to a supernova in a binary system giving rise to both the supernova and the GRB \cite{negreiros}. 

\item[2)]
From this list I would just like to briefly explain the dyadotorus \cite{dyado} 
(see Fig.~\ref{fig:dyadotoro}).
This is the region around a rotating magnetized black hole in which pair creation occurs and gives birth to an electron-positron plasma. 
Indeed this concept has its origin in Fermi's work on the electromagnetic contribution to the mass of a charged sphere (see paper (4c) reprinted in translation in {\it Fermi and Astrophysics}), properly extended to general relativity and to the black hole. 


\item[3)]
It is interesting that in this quest to reach a maximally self-consistent formulation of concepts of relativistic astrophysics, I had for years a cogent question: had there  been a strong disagreement on the possible existence of black holes by Albert Einstein raised by the work of Oppenheimer and Snyder? 
Having worked for so many years on black holes I had been intrigued by this problem for a long time and a new line of investigation on this issue was started
only recently  when  I re-examined a truly exceptional paper by Einstein \cite{eincluster} (see Appendix \ref{appA_einstein_clusters}). 
It should be studied by everyone working in general relativity.
Indeed the ``Einstein cluster" allows one to obtain regular solutions for a spherically symmetric cloud of particles in circular orbits and corresponding to an arbitrary distribution of density.
Some of the pioneering concepts of circular orbits in the Schwarzschild geometry were indeed obtained by Einstein 10 years earlier than the results attributed to Kaplan in the literature \cite{kaplan}.
What we have recently proved is that in no way do Einstein's considerations preclude the formation of black holes but on the contrary, the Einstein clusters give origin to the onset of unstable configurations which can indeed be considered as the initial value problem for the formation of the black holes \cite{pompi} (see Appendix \ref{appA_rr_GX2_clusters}).
In this sense both the work of Oppenheimer and Snyder %(see Fig.~\ref{fig_oppsnyder})
and Einstein agree when the rigor of the equations are followed instead of a subjective interpretation of their results.    

\end{itemize}

%\begin{figure}[h]
%\begin{center}
%\includegraphics[width =3in]{chap1_oppenheimersnyder.pdf}
%\vglue 3 cm
%\caption{Oppenheimer and Snyder. TO INSERT}
%\label{fig_oppsnyder}
%\end{center}
%\end{figure}


\begin{figure}[h]
\begin{center}
\includegraphics[width =3in]{chap1_grbs.pdf}
\caption{The main features of GRB 090618: a first emission episode characterized by a nonrelativistic expanding thermal emitter and a second emission episode representing the canonical GRB.
The main spikes observed in the canonical GRB originate from the interaction of the relativistic plasma with nearby interstellar clouds, characterized by a common density of $\sim 10^{22-24}$  g. The energetics and the distance of GRB 090618 permitted all the satellites observing at the time to detect this very luminous GRB. They are shown in the bottom of the figure.}

\label{fig_luca}
\end{center}
\end{figure}


Among the extrapolation to yet unobserved domains of current scientific knowledge, one of the most fruitful activities has come from the extrapolation to new fields motivated by overcoming logical inconsistencies encountered in the existing theoretical treatments of some physical and astrophysical systems. 
I have already reviewed some issues in the treatment of white dwarfs left unsolved for decades.
I am going to review some of the most recent results on the structure of neutron stars which finally answer some of the doubts I had for years on the validity of existing treatments present in all textbooks and which clearly point to a new electromagnetic structure for neutron stars:
\begin{itemize}

\item[1)]
The generalization to relativistic regimes of the Feynman, Metropolis and Teller treatment of compressed atoms by solving the relativistic Thomas-Fermi treatment in a Wigner Seitz cell \cite{rotondo2}
(see Appendix \ref{appA_PhysRevC_83_045805}) 
has allowed us to obtain a new equation of state for white dwarfs consistent with strong, weak, electromagnetic interactions and quantum statistics within a self-consistent treatment in general relativity \cite{rotondo1} 
(see Appendix \ref{appA_PhysRevD_84_084007}).
Certainly Fermi who was the advisor of the Ph.D. thesis of T.D. Lee on white dwarfs  would have appreciated this result. 
Quite apart from obtaining a consistent theoretical treatment, which is a necessity from a conceptual point of view, this work offers a new understanding in a many year long effort to comprehend phenomena such as anomalous X-ray pulsars (AXPs) and soft gamma ray repeaters (SGRs) \cite{malheiro} 
(see Appendix \ref{appA_11020653_malheiro}).

\item[2)]
One of the mysteries to me has been why Fermi did not approach the problem of neutron stars in his US period. 
It is not possible that just by looking at the Oppenheimer-Volkoff work he did note the impossibility of treating such systems by neglecting the role of the strong and especially of the weak interactions. 
Also his initial reluctance to look at the interiors of stars which we have seen earlier should have been overcome by the conceptual challenge of studying the ground state of a self-gravitating system of protons, neutrons and electrons from first principles. 
I also considered the  possibility that his complicated personal relations with Oppenheimer could have kept him away from such a topic. 
As our re-examination of this work progressed I have started to consider an additional possibility. 
Using a Thomas-Fermi treatment of a neutron star we have shown that an overcritical electric field should exist between the core and the crust of a neutron star \cite{rrpath}. 
We have then  examined a simple model of superheavy nuclei within Newtonian physics  following the work of Popov and collaborators, applying it instead to the case of neutron stars using an ultrarelativistic solution of the Thomas-Fermi atom \cite{popov,rotondo3} 
(see Appendix \ref{appA_Rotondo_et_al_2011_IJMPD}). 
We have concluded that a Newtonian approximation confirms the existence of an overcritical electromagnetic field between the core and crust of neutron stars. 

\item[3)]
The generalization of all these results to the case of general relativity was then mandatory.
We first solved the problem of a system of neutrons, protons and electrons in beta-equilibrium \cite{rotondo4} 
(see Appendix \ref{appA_rotondo_et_al_PLB2011}), 
reaching the conclusion that the traditional condition of local charge neutrality in all current treatments of neutron stars was conceptually incorrect and that a global description, based on the general relativistic generalization of the Thomas-Fermi equation and the implementation of the condition of global charge neutrality, was a necessity.

The traditional Tolman-Oppenheimer-Volkoff equations then became conceptually unacceptable and a solution of the Einstein-Maxwell system of equations became a necessity.
We then introduced the contributions of the strong interactions and proposed for the first time the global system of equations \cite{ruedaNPA} 
(see Appendix \ref{appA_rueda_et_al_NPA2011}) and finally we have integrated the system, obtaining  a new range of parameters for the mass, radius, and moment of inertia of a neutron star.


\end{itemize}

For all these configurations we have confirmed and computed the overall critical field at the interface between the core and the crust of a neutron star \cite{belvedere} 
(see Appendix \ref{appA_belvedere_et_al_2012}).
I consider this to be one of the most complex problems ever approached and solved in theoretical physics.

In order to proceed to solve the origin of the blackholic energy to be created in the formation of black holes, the consideration of this electromagnetic structure in neutron stars is essential, and the process of formation and collapse of this structure may well lead to an explanation not only of GRBs but also  of the emission of the supernova remnant in the supernova process.

Coming back to Fermi it is clear that this theoretical work which encompasses all of the fundamental interactions could not have been approached in the 1950s. 
I have asked myself if Fermi did not confront it since he could see the objective difficulty in formulating a consistent theoretical approach. 
What certainly I can imagine is that both Fermi and Wigner would agree about the validity of the above-mentioned sentence: ``The Thomas-Fermi theory works much better than it should."  

Indeed, in addition to his greatest theoretical understanding, Fermi, being both an experimentalist and a theorist, would have been very pleased in seeing the unprecedented display of space, ground and underground missions dedicated to GRB observations.
The latest and most important mission is dedicated in his name: the Fermi Satellite.
All these together represent one of
the greatest observational and experimental efforts ever developed in the history of our planet (see Fig.~\ref{satelliti}). 


\section{Discussion with Murray Gell'man}

It was indeed a great pleasure to have Murray Gell-Mann as a guest of ICRANet in our newly restored center at Villa Rati in June, 2012. This gave me the chance to discuss with him some of the questions raised above regarding Fermi, Einstein, Heisenberg, and GRBs.

First Gell-Mann confirmed that in 1950 Fermi  was again becoming interested in general relativity and proposed to him as a Ph.D. thesis topic studying the effects of general relativity in the structure of the galaxy. Gell-Mann instead turned to particle physics, which we all know led to his great achievements later.

Looking back, two things stand out, Fermi's prescience and the enigma of timing. In 1950, general relativity was nearly a closed branch of mathematics, beautiful but sterile. Ten years later, all was changed. Space, radioastronomy, and other new technologies led to amazing discoveries. Theory was dramatically alive. Some of this we have already noted but another area first studied in connection with Mach's principle by Hans Thirring, the role of rotation in relativity, suddenly gained new life in the early 1960s through Leonard Schiff and Roy Kerr.

Schiff came to gravity from nuclear theory via virtual particles and the equivalence principle. Turning next to experimental foundations, he raised a storm by arguing that the three famous Einstein tests prove much less than was thought. Amazingly, he then conceived two entirely new tests, measures of the de Sitter geodetic effect and Lense-Thirring frame dragging effect by gyroscopes in Earth orbit. 

Thus began one of the most difficult experiments in the history of science, which I have followed with fascination since my first visit to Stanford in 1968. Fig.~\ref{fig_gpb} shows the two predicted effects in a polar orbit defined with respect to the chosen guide star IM Pegasi, geodetic precession by 6.606 milli-arcseconds per year and frame-dragging precession by 39 micro-arcseconds per year. The experiment involved four electrically suspended gyroscopes and a reference telescope mounted in a quartz block with a magnetic gyro readout based on the London moment of a spinning superconductor. The measured geodetic and frame-dragging precessions were 6.600 $\pm$ 0.017 arcseconds and 39 $\pm$ 7 milli-arcseconds per year, with all four gyroscopes in full agreement within the limits of their respective error ellipses. In 1953, Einstein observed that frame-dragging and two other effects, ``\ldots  which are to be expected in accordance with Mach's ideas, are actually present according to our theory, although their magnitude is so small that confirmation of them by laboratory experiments is not to be thought of.''  
Fifty years later, space and cryogenics together made the experiment possible.


Kerr's exact solution for the metric around a rotating black hole came in 1963. Near the hole, frame-dragging is enormous. This was a topic we studied intensely in the 1960s at Princeton and Stanford, discovering the beautiful orbit-patterns that form a sculptural icon for the Marcel Grossmann Award. Returning to Fermi, one might imagine with the large rotating mass of the galaxy that it too might produce large frame dragging effects. In fact, the characteristic ratio $a/m$ is much smaller than for the Earth, so much smaller that there is nothing really to consider. Gell-Mann was correct to choose particle physics. 

Gell-Mann and I also discussed the new equation of state of the neutron star. He was surprised by our interest in neutron stars instead of quark stars but also on this point the discussion was extremely fruitful. It is well known that there is an enormous difference between quark stars and the traditional TOV treatment of neutron stars. However, when the correct treatment of the neutron star is done, the two pictures are rather similar.

The last point was a more general discussion about GRBs and their daily occurrence. It is a priori one of the most profound aspects of GRBs that although they appear at a daily frequency as local phenomena, indeed they originate from very low probability effects occurring once in a hundred million years in each galaxy and only the fact of the possible fractal structure of the universe and its observed homogeneity and enormous dimensions leads to a phenomena which occurs once a day. The big mystery to understand is what the role of these GRBs is in the possible evolution of the species and of life in the universe.


%\begin{flushright}
%Remo Ruffini
%\end{flushright}



\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_AVIAOWAT.pdf}
\caption{Gleb Wataghin.
}
\label{chap1_AVIAOWAT}
\end{center}
\end{figure}


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_CRibeiro-CLattes-GOcchialini.pdf}
\caption{C. Ribeiro, C. Lattes, G. Occhiolini.
}
\label{chap1_CRibeiro-CLattes-GOcchialini}
\end{center}
\end{figure}


\begin{figure}[h]
\begin{center}
\includegraphics[width =4in]{chap1_Lattes-panair.pdf}
\caption{
C. Lattes. 
}
\label{chap1_Lattes-panair}
\end{center}
\end{figure}

\setcounter{chapter}1
\endinput



