Philosophy of Gravity and Gravity of Philosophy

Gennady Gorelik

The Attraction of gravitation: new studies in the history
of general relativity

/ John Earman, Michel Janssen, John D. Norton, editors.

Boston : Birkhauser, 1993. [Einstein studies ; v. 5].
P. 308-331.

1. First Steps in the General Theory of Relativity

2. One and a Half Decades under the Symbol
*h*
and the Year 1937 under the Banner of Marxism

3. Fock's Work on Motion in GTR

4. The Contribution of Nikolaus Copernicus
to the General Theory of Relativity

5. Fock's "Theory of Space, Time and Gravity"
against the Background of His Gravity, His Time, and His Space

6. Principles of Relativity and Complementarity
for the History of Physics

V. A. Fock Chronology (Gravitational, Philosophical, Social)

Vladimir Aleksandrovich Fock (1898-1974) was one of the main participants in the history of the general theory of relativity (GTR) in Russia. His teachers, A. A. Friedmann and V. K. Frederiks, were the pioneers of GTR in Russia (Vizgin and Gorelik 1987). He studied the famous Friedmann paper on nonstatic cosmology in manuscript form and translated it, at the author's request, into German. He elaborated a description of the spinor field in GTR (Fock 1929). In 1935 he was an "opponent" (judge) of Matvey Bronstein's thesis—the first deep investigation of quantum gravity. He independently of Einstein, Infeld, and Hoffman (1938) solved the problem of motion in GTR. He is the author of the first Soviet monograph on GTR. And, finally, he was an energetic and tireless participant in the discussions during the 1950s and 1960s on understanding GTR.

However, despite Fock's authority in physics due to his scientific abilities, his attitude toward GTR was not shared by many even in the USSR. This concerned his attitude toward cosmology, the role of coordinate conditions and especially privileged systems of reference, the principles of relativity and equivalence and the philosophical status of GTR.

His stand on the last issue seems to be the most enigmatic because he unequivocally declared his adherence to dialectical materialism and connected it with his understanding of GTR. Such an attitude did not attract sympathy among physicists, although Fock's human dignity and honesty were beyond doubt. Besides, in Stalin's time, Fock was the main defender of quantum and relativistic physics in the USSR.

This situation has already attracted the attention of historians (Graham 1982, 1987). Here I shall try to reveal the roots of Fock's position in his scientific activity proper and to analyze the nature of the communication gap between Fock and his physicist colleagues.

To do this, it is necessary to take into account the following factors:
Fock's specific methodological stand, which was intermediate between theoretical
physics and mathematics; his predisposition to a philosophical world view;
his inclination to schematism or mathematization in life outside natural
science; and finally the relatively narrow empirical basis of GTR in the
1930s to 1950s. It is not easy to discuss these factors in academic terms
since they manifested themselves in horrible social circumstances. They
were embodied concretely in Fock's personality—he was an honest, dignified,
fearless and, strange as it may seem, law-abiding person. To reveal these
elements of the explanation and to connect them in a united scientific-psychological
complex, one should consider the evolution of Fock's views.

Vladimir Fock (1898-1974) |
Anna Kapitsa's cartoon caricaturing Vladimir Fock's attitude to Peter Kapitsa's way of handling math. The date is February 5, 1953. It was the seventh year of Peter Kapitsa's disgrace. Vladimir Fock was visiting the Kapitsas, a few weeks before Stalin's death. |

**1. First Steps in the General Theory of Relativity**

Fock (1963) recalled the following of his early acquaintance with GTR:

The earliest documented testimony of Fock's interests in GTR is his handwritten summary of his lecture in a philosophical circle dated 1922.What should be noted especially is that this summary is half philosophical. Fock begins with:

(a) *an* object being seen from different
viewpoints;

(b) an object being seen by moving observers; its mass and dimensions.

If two observers see differently, it is clear that they see not the whole object but facets of it.

One had to admit as really existing not space
and time separately but their combination; instead of *r ^{2}*
and

Physics strives to break up phenomena into the simplest elements. But the simplest elements are not commonplace to us; besides that, they (as the simplest) are undefinable. The familiar (i. e., having properties of familiar objects) are only rather complex combinations of these elements. But so far as we have not given definitions for elements, there are no definitions for these combinations either.

And we give a definition for the latter. We take
the quantity *G _{mn} .* We do not say that it is equal to
zero when matter is absent, but in another way: being equal to zero means
that matter is absent, i. e., absence of matter is a symptom of

In 1922 in Soviet Russia the philosophical approach to natural science
was still a purely private affair. To lecture at a philosophical circle
meant a certain predisposition to a philosophical outlook. It is difficult
to attribute Fock's view in 1922 to some *-ism* (e. g., to intersubjective
idealism or mathematical realism), but one can definitely say that in Fock's
position there is no dialectical materialism (which he would master and
appropriate in the mid-1930s). His striving to comprehend the epistemological
bridge between physical reality and theory is beyond doubt.

In the philosophical viewpoint of the 24-year-old theorist, it is possible
to see some ideas of the classics of relativity. However, Fock's approach
to GTR seems highly independent (unlike the first Russian review on GTR
by Frederiks (1921)). Instead of the ideas of general relativity, covariance
and equivalence, which were usual for the majority of accounts of GTR,
in Fock's account what prevails is the geometrical approach, based on the
concept of absolute space-time. The other interesting feature is this:
Fock mentions "the possibility of finite but boundless space" and does
not mention the possibility of a nonstatic universe, while Friedmann's
popular (1923) book was finished the day (!) before Fock's lecture, and
it talked about this new possibility with enthusiasm. Friedmann's famous
paper (1922) was dated May 29.

**2. One and a Half Decades under the Symbol h
and the Year 1937 under the Banner of Marxism**

In the following one and a half decades Fock was busy with quantum theory on the whole. His important work on including the Dirac equation into GTR (1929) did not concern questions of principle in GTR.

Some interesting traits for the relativistic portrait of Fock may be revealed in his participation in the defense of M. P. Bronstein's thesis in 1935 (Gorelik and Frenkel 1985). Fock assessed highly this investigation, which was concerned mainly with the quantization of weak gravitational fields. He did not, however, attach importance to one of Bronstein's conclusions, which may have been the most interesting from the general physical and philosophical points of view, but the least definite mathematically. Based on a quantum-relativistic analysis of the measurability of the gravitational field (beyond its weakness and nongeometrical character), Bronstein deduced that, in a complete theory of quantum gravity, the concepts of space and time would have to be generalized radically. In Fock's words of 1935, one can see some distrust of GTR: he admits that the theory (of strong fields) may be changed and doubts the special role of the gravitational radius. (See Gorelik and Frenkel 1985.)

Fock took up the Einstein theory of gravitation in full measure at the end of the 1930s, preceded by some important events in his philosophical and social biography.

At the beginning of the 1930s, Fock discovered dialectical materialism
for himself (hereafter I shall use the common Soviet abbreviation *Diamat).
*We
know from A. D. Aleksandrov's testimony (Aleksandrov 1988, 1989) that Fock
read Lenin's book *Materialism and Empirio-Criticism* in 1932 and
found in it something interesting and important for him (and he regretted
that this book was inculcated in a "police" way). Two decades later Fock,
in the introduction to his book on GTR, remarked:

In answering an official questionnaire in 1938, Fock wrote that he was descended from nobles, although he could have given a much less dangerous reply, because his father was a scientist-forester. Fock also informs us: "Since birth I have lived in Leningrad, did not take part in the revolutionary movement, <...> was not repressed by Soviet power." [Personal file of V. A. Fock. Archives Acad. Sci. USSR 411-14-127].

There are some inexactitudes here. In the first place, having entered Petrograd University in 1916, Fock in 1917 voluntarily joined the artillery school and then went to the war front (in 1918 he was immobilized because of advancing deafness). In the second place, Fock was arrested twice: in 1935 for one day and in 1937 also for only a few days (in the latter case he was released as a result of P. Kapitsa's courageous letter "upstairs").

For Fock, 1937 was also filled with many other events that were not
very scientific. He was active in preventing a special session of the Academy
of Sciences concerned with the philosophical basis of modem physics (Gorelik
1990). The initiator of this session was the 65-year-old electrical engineer
academician, V. F. Mitkevich. Having old-fashioned (meta-) physical views
and having obtained new-fashioned political skills, he officially proposed
organizing a special meeting "for the struggle for the materialistic foundations
of physics and against physical idealism." He had named V. A. Fock (together
with I. E. Tamm and Ya. I. Frenkel) as a physical idealist and an opponent
of *Diamat.*

Before 1937 Fock did not express his philosophical views publicly but had expressed unequivocally his opinion about the poor scientific level of books by Mitkevich and his fellow campaigner A. K. Timiryazev in a review (Fock 1934) published in the leading popular-scientific journal.

It was this review that was attacked (three years later!) by an aggressive and prolific journalist, V. E. Lvov. He seemed to take into account Fock's arrest and charged him not only with idealism but also with adherence to fascist methods!

Fock had to defend himself and his science. He sent three letters. In the first one, addressed to the Leningrad public prosecutor, Fock demanded prosecution of Lvov for libel and defamation. The second letter was addressed to the Central Committee of Communist Party, and there Fock wrote about the harm done by Lvov to Soviet science. In the third, a seven-page letter of February 13, 1938 to the Presidium of the Academy of Sciences, Fock, without any delicacy, expressed his misgivings about Mitkevich's efforts and insisted on abolishing a (quasi-) philosophical academy session devoted to physics. Judging by all that is known, it was Fock who was the main force in preventing this harmful session (Gorelik 1990).

In the same letter, Fock wrote about the desirability of good philosophical
discussion of the new physics based on *Diamat.* He was sincere in
writing these sentiments, for we have Fock's manuscript "Does Quantum Mechanics
Contradict Materialism?" (23 pp.), dated November 1937. The discussion
of 1937 became the subject of the article (Fock 1938a) published in the
journal *Under the Banner of Marxism.*

In 1937 Fock was parted from many of his colleagues, who became the victims of the Great Terror. In August, M. P. Bronstein was arrested. When Fock heard about this he went personally to Bronstein's home to learn exactly what had happened (Gorelik and Frenkel 1990). In 1937, this was a very courageous and unusual act. He also signed letters in defense of repressed scientists.

Ten years later Fock wrote the official review of works by D. Iwanenko and A. Sokolov on quantum gravity, which were being presented for the Stalin prize. In this review Fock mentioned the name of M. P. Bronstein, then "an enemy of the people," many times. In particular,

**3. Fock's Work on Motion in GTR**

The year 1939 was a landmark in Fock's biography. He became a full member of the Academy of Sciences and his interests in fundamental physics had moved from quantum theory to gravitation. In 1939, Fock (1939a) published a long paper on motion in GTR. Without discussing the entirety of this important work (Havas 1989), I shall single out only a few essential points for our theme.

Fock begins with the difference between his and Einstein's points of view on GTR as a whole. For Fock, GTR is the foremost theory of gravitation and therefore must be applied to phenomena in which gravitation dominates, "i. e., to phenomena of an astronomical scale," but not to problems on an atomic scale. But at the same time he assesses very skeptically (or worse) "the so-called cosmological problem": "In the modem state of knowledge, any attempt to consider the Universe as a whole has to be of a speculative character."

Fock based his approach on the following: "in the atomic world it is observed that electrical forces greatly dominate the forces of gravity," "the great successes of quantum mechanics during the last 10-15 years and the complete fruitlessness of Einstein's attempt to explain elementary particles by means of a unified field theory." Nevertheless, Fock concludes:

Now let us return to Fock's paper itself, to one of its elements which was of a purely mathematical nature but later acquired considerable physical and even philosophical meaning. This element is the coordinate condition

* Dx_{n}*
=

where ** D** is the covariant D'Alembertian (there are different
forms of this condition). The corresponding coordinate systems are called

One of the main peculiarities distinguishing Fock's work from Einstein-Infeld-Hoffmann's corresponding work is its view on the choice of coordinate systems. The physical statement of the problem, with the aim of correlation with Newton's equations of motion and post-Newtonian terms, leads to such conditions as the weakness of the gravitational field, its insular character (planetary system), and Euclidean character at infinity. But to solve the field equations of GTR it is necessary to add coordinate conditions, having chosen sufficiently definite coordinate systems.

For Einstein, with his understanding of GTR, the choice of coordinates was a question of technique or mathematics. And Einstein's choice leads to such a laborious pathway to the solution that the computations could not go into the publication and were cited from a complete manuscript in the Princeton Institute.

Fock, having chosen harmonic coordinates, found, as he wrote, "a much simpler" pathway to the solution. Already in the paper of 1939 he attempted to base his choice on more than mathematical grounds.

Having mentioned de Donder and Lanczos, "who first (in 1921, 1923) had pointed out the simplification reached by means of harmonic coordinates," Fock does not limit himself to pure mathematics. In his words,

**4. The Contribution of Nikolaus Copernicus to the
General Theory of Relativity**

The first postwar testimony of Fock's reflections on gravity is his rather short paper (1947) dedicated to Copernicus's jubilee. Why did he write on Copernicus? There are no other traces of Fock's interest in the history of science outside the twentieth century.

It is possible to point out several very different causes. In the ideological life of the postwar USSR, the most "militant materialism" reigned. Idealism (crossed with anti-patriotism and cosmopolitanism) was attacked in different fields of science. Debates over the state ideology of Marxism-Stalinism became very leaden, strictly black and white, or, more exactly, red and white. The list of saints and enemies of progress had been formed, and Copernicus had one of the most respectable places among the heroes of science. The state attention to the great Polish founder of the new astronomy was strengthened by state political interests in Eastern Europe.

In Soviet ideology, the positive Copernicus was indissolubly connected with the negative Ptolemy. In a paper, the first in the jubilee volume, Idelson (1947), side by side with a profound analysis of Copernicus's works, had to mention also "the wise words of comrade I. V. Stalin," which consisted only of the phrase "decayed system of Ptolemy."

And it is the pair "Ptolemy-Copernicus" that cast a shadow on general relativity. Of course, the shadow was due not to these classics themselves but to the soldiers of the cause of the one true philosophy. Being ignoramuses in physics, they looked for philosophical mistakes only in popular texts. In such texts dealing with GTR, in order to explain the basic ideas (or for effect), the equal correctness of Ptolemy's and Copernicus's points of view was asserted, e. g., Friedmann 1923; Einstein and Infeld 1938.

In contrast with other articles of the jubilee volume, Fock did not base his article on an appropriate historical interest in 400-year-old events. In spite of the title of his article, it was not his aim to illuminate the relationship between Copernicus and Ptolemy by means of GTR. To the contrary, he preferred to use a controversy, solved long ago, in order to illuminate his understanding of GTR as a geometric theory of gravity. A second and no less important aim was to defend Einstein's theory against ignorant and malicious critics.

In short, in Fock's article of 1947 were present all the main elements of his treatment of GTR (which henceforth he named "Einstein's theory of gravity"):

(2) the possibility of introducing

as space and time coordinates those variables
which are quite analogous to the rectangular Cartesian coordinates and
the time coordinates of the special theory of relativity (harmonic coordinates)....
The essential condition for this is the requirement of pseudo-euclidean
geometry of space-time at infinity...; this requirement is satisfied for
systems of masses like a solar system. (Pock 1947, p. 185)

Fock's argumentation, which has been recounted many times since, is
well known due to his monograph of 1955 (2nd edition in 1961 and English
editions in 1959, 1964). That is why we may consider only the principal
relevant circumstances from 1947 to the mid 1950s.

**5. Fock's "Theory of Space, Time and Gravity" against
the Background of His Gravity, His Time, and His Space**

The next publication on the theory of gravitation that Fock prepared was in 1948. It was based on his pre-war work. In addition to concrete results, he also developed his understanding of the fundamental ideas of Einstein's theory. Admitting the historical, heuristic role of the principle of equivalence, Fock denies its validity in the complete theory. He also denies any particular physical role of covariance and general relativity as a more general relativity than in the special theory of relativity. For Fock, Einstein's theory is solely a geometrical theory of gravity. In his words: "I gave a detailed account of my point of view on Einstein's theory of gravity because Einstein's point of view, which I consider as wrong, is dominant up to today" (Fock 1950. p. 70).

The end of the 1940s and the beginning of the 1950s in the USSR were
not very suitable years for pure, subtle theory. Soviet physics found itself
under the strongest social pressure. After a notorious session of VASHNIL
in 1948 had devastated Soviet biology, a similar session was prepared for
physics. The unhealthy ambitions of some physicists in unhealthy social
conditions were embodied in the struggle against "physical idealism, anti-patriotism
and cosmopolitanism." In this struggle, V. Fock was of course on the side
of genuine science, defending relativistic and quantum physics and scientific
ethics (Gorelik 1991). He based this activity also on *Diamat *(Fock
1949).

It was at this same difficult time that discussion of the foundations of relativity was revived by publication in 1950 of lectures delivered by L. I. Mandelshtam in the 1930s (Mandelshtam died in 1944). In these lectures, in particular, an operational approach to physical concepts was used and attention was paid to conventional elements in the definitions of the special theory of relativity. Fock, in his review (1951), gave a high estimate of the scientific and pedagogic significance of Mandelshtam's lectures but criticized the operational and conventional elements.

The question, however, which had been the subject of a methodological analysis of a physical theory for Fock, became a crime for ignorant philosophical overseers. They attacked "bourgeois idealism" on the whole, "reactionary Einsteinism" (Maksimov 1952) in particular and Mandelshtam with his school as "the seed-bed of idealism in USSR" especially; to "physical idealism" it was easy to add also anti-"cosmopolitan" arguments because there were a great many Jews among Soviet physicist-theorists. One of the highest ranking among these philosophical overseers was A. A. Maksimov (1891-1976).

The main defender of genuine science was the academician Fock, whose
arguments were both scientific and *Diamatic.* He demolished Maksimov
in the leading philosophical journal (Fock 1953a)—and Maksimov was on the
journal's editorial board.

It was in just such a social atmosphere that Fock went on to elaborate his treatment of Einstein's theory of gravity.

In a sense, 1955 became the year of summation. In that year Fock's monograph
*The
Theory of Space, Time and Gravity* was published, but for our theme
a much less scientific article written by Fock for the principal Soviet
newspaper *Pravda* is more interesting. This article was entitled
"Half a Century of Great Discovery. About the Theory of Relativity by Albert
Einstein." We have the good fortune of looking at this article through
the eyes of two remarkable contemporaries—academicians Igor Tamm and Vladimir
Fock—because of letters they exchanged on November 13 and 17, 1955. [Personal
file of V. A. Fock. Archives Acad. Sci. USSR 1034-3-691: 31-32; 1034-3-160:
8-10].

Judging from the correspondence they kept (the earliest letter is dated 1929) and the testimony of their colleagues, these outstanding Soviet theorists were connected by a mutual respect in both scientific and moral spheres.

The manuscript of Fock's article was sent to Tamm from *Pravda*
for his information. It was his reaction to this article that led to Tamm's
letter. Having recalled Fock's anti-Maksimov article of 1953 approvingly,
Tamm expressed his doubts about the appropriateness of a polemic with Einstein
and the discussion of his philosophical errors in a jubilee newspaper article.
In the same letter Tamm invited Fock (with great respect for his "fundamental
works in quantum electrodynamics and theory of space and time") to take
part in investigations on quantizing space-time. This idea attracted Tamm's
attention very much then.

Fock's letter, clear and detailed, answers all Tamm's remarks in the
following way. He had not intended to write a praising, jubilee article,
he explained, but a critical review of a published book (the Russian translation
of Einstein's *The Meaning of Relativity).* The article turned out
to be rather difficult, but its subject was fairly difficult too. "Einstein
is a great physicist, but he is not a very good mathematician," Fock wrote.

(a) it amounts to official recognition in our country of the theory of relativity as a great discovery and great achievement of human genius,

(b) this recognition is made without grovelling and with reasonable criticism,

(c) the philosophical sins of Einstein are mentioned but have been forgiven.

On November 30, 1955 there was an open session of the Academy of Sciences
of USSR, dedicated to the 50-year jubilee of the theory of relativity.
An introductory speech was made by Tamm. His closest colleague, V. L. Ginzburg,
delivered the paper "Experimental Testing of the General Theory of Relativity,"
and Fock delivered a paper on the equations of motion. These papers, together
with some others, comprised the memorial volume *Einstein and Modern
Physics.* Fock's viewpoint is represented in the volume very lucidly
and in a way that is especially convenient for us. It is in two components:
critical and constructive.

The volume includes Einstein's "Autobiographical Notes," which were translated and commented on by Fock. He begins with Einstein's philosophical views; however, his reduction of the many-colored ("extremely inconsequent") philosophical palette of the great physicist into the sharp dichotomy of the terms "materialism--idealism" seems to be a ritual duty. In considering Einstein's pathway to the theory of gravity, Fock does without philosophy at all. He criticizes Einstein's reasonings, "which finally led him to his gravitation theory of genius," and criticizes his "logical inconsistencies," "incorrect use of terms," etc. The questions are, as before, in relativity, covariance, and equivalence (Fock 1956b).

Fock's paper on the equations of motion contains the following constructive statements. For isolated (insular) systems, it is possible to state "conditions determining the coordinate system uniquely, with an indeterminacy up to a Lorentz transformation (harmonic coordinates)." For Einstein's theory, the harmonic coordinate system has a significance in principle, because "the existence of such a system reflects the objective properties of the space-time continuum." The introduction of harmonic coordinates allows the recovery of the equations of motion of masses taking into account their inner structure, all ten classical integrals of motion including relativistic corrections, and the gravitational potentials at large distances.

What reception did Fock's position find with his colleagues?

In Tamm's article there is only one phrase indicating that " 'the special and general theories of relativities' may be not very good terms." In opposition to Fock, one can see the great importance attached by Tamm to cosmology.

A more definite opinion was expressed in Ginzburg's paper, although he also avoided "fundamental questions on space and time, geometry and the theory of field in their connection with the general theory of relativity." According to Ginzburg (1956), GTR is "first of all a relativistic theory of gravity" for which the principle of equivalence is "the basic physical statement," and the principle of general relativity in itself is not physical. Nevertheless, referring to Einstein, who had to admit this last point in 1918, Ginzburg stated that he does not agree with "the opinion of Fock, who says that the 'theory of gravity was incorrectly understood by its author' " (Ginzburg 1956, p. 136).

A straightforward opponent of Fock (and possibly more Einsteinian than Einstein himself) was L. Infeld, who, in the same memorial volume, wrote:

**6. Principles of Relativity and Complementarity for
the History of Physics**

Thinking over the communication gap between Fock and Tamm (as expressed in their letters), or, more generally, between Fock and his physicist colleagues, both in scientific-methodological and in social-philosophical spheres, one should avoid a quick and simple judgement over who was right and who was wrong. Both positions were pure and honest, but the difference that could not be removed stemmed from the difference in their personalities.

To comprehend this situation, a historian of physics might take a lesson from the experience of 20th-century physics. In our case one might take a lesson from a short article written by Fock himself. While summing up the theory of relativity and quantum mechanics epistemologically, and their experience of dealing with non-absolute truths, Fock concluded:

Now it is time to connect the fairly heterogeneous events from Fock's biography as described above. To connect them with one life line, first of all, it is necessary to describe his frame of life references. One should begin with the vectors characterizing his scientific standpoint, because, for a genuine scientist, and for Fock especially, these vectors are the most important.

According to the prominent experimental physicists P. Kapitsa and D. Rozhdestvensky, who knew Fock very well, "This is a man detached from common life due to his almost absolute deafness. The whole of his life is persistent work with scientific problems"; "Fock thinks by mathematical images and it is very difficult for him to go deeply into the mentality of an experimentalist or average man, in spite of his permanent readiness to help everybody who asks him" (Kapitsa 1989, p. 124; Frenkel 1990, p. 150; [Personal File of V. A. Fock] Archives Russian Acad. Sci. 411-14-127, p. 6 [note 1]). This is, why one should turn to Fock's philosophy and social conduct only after having considered his scientific psychology.

If one had to characterize the foundation of Fock's frame of mental references in two words, they seem to be "mathematicity and sobriety." One may consider as key his phrases such as "The correct mathematical framing of a physical problem always must ensure the uniqueness of a solution" (Fock 1956c, p. 160). Mathematicity itself does not exclude a romantic attitude to physics (e. g., H. Weyl), but Fock was an anti-romantic.

Without taking this into account, it would be rather comical to see Fock criticizing Einstein's intermediate inferences that led to his theory of genius. Here Fock recalled Einstein's confession that his mathematical intuition was not sufficiently strong (Fock 1956b, p. 79). But a physicist would prefer to recall other words of Einstein: "Unless one sins against logic one generally gets nowhere; or, one cannot build a house or construct a bridge without using a scaffold which is really not one of its basic parts" (Einstein 1953, p. 147).

Fock had "the means of observation" to appreciate Einstein's achievements of genius and he did admit that Einstein had achieved his results by means of these "incorrect" concepts and inferences, but to go mentally into this incorrect practice was, for Fock, precluded by his mathematical powers. It was quite clear to Fock (as well as to his colleague-geometricians) that in Riemann geometry, the zero-curvature case has the most symmetry, that the principle of equivalence cannot be formulated inside GTR.

If there are perfect, exactly defined mathematical structures, why should one not set aside logically dubious constructs without exact mathematical meaning, regardless of their historical merits? If the building is finished, why should one not take the scaffold away?

This applies to the principle of equivalence and to the idea of general relativity, which were important for creating GTR but then dissolved in its mathematical structure. The same applies to the operational analysis of definitions, by means of which L. Mandelshtam introduced the special theory of relativity (STR) in his lectures. For a mathematician, in the latter case, to describe Minkowski space is quite enough. But for a physicist, even aside from pedagogics, it is not enough.

Einstein modeled physics with the following epistemological scheme:

E =>A => S => E,

where *E is* the variety of immediate experiences of the senses,
*A*
is a system of axioms, and *S* are statements deduced (Einstein 1952,
p. 137). Mathematical physics (as represented by Fock) reigns over the
section *A*® S, while theoretical physics
deals with the sections *E *=> A and *S *=> E.

Fock reproached Einstein by saying "his general inferences proceed as
if they did not take into account that any physical theory is approximative
in essence" (Fock 1956b, p. 74). The physicist-theorist looking for a new
system of axioms certainly does have to forget that it is approximate.
At the same time, in order to be prepared for the coexistence and succession
of different axiom systems, he should pay special attention to the section
*E
*=>
A.

Fock's attitude toward cosmology was especially revealing, if one remembers that nonstatic cosmology was born in front of him. Of course, his concern was not with the mathematical side of cosmological solutions, but rather with their physical meaning. In 1939 he disassociated himself from cosmological speculations and even reproached them. Later, and up to the end of his life, Fock mentioned formally or described very briefly the mathematics of cosmological applications of GTR, but certainly, in his heart, there were no kind feelings for relativistic cosmology. Cosmology as "a model of the world on the whole" he considered philosophically unsatisfactory; he wrote about "risky extrapolation" and questioned the applicability of GTR to "cosmologically huge regions of space and time" (Fock 1955, p. 464; 1967, p. 33; 1973, p. 72).

What were the causes of such an attitude to cosmology, besides the well-known discrepancy of the Hubble age with the data of geo- and astrophysics? (It had to be especially important for the sober-minded Fock.) One can see the main causes in his "mathematical sobriety" and in the pressure of his own scientific experience.

It is difficult to read without a smile Fock's explanation for his colleagues:

To be important for mathematical uniqueness is not equivalent to being important in the history of physics. But for Fock, who was sure that the mathematically correct formulation of a problem is unique, the absence of boundaries and the non-unique extrapolation of cosmological conditions could not replace the clear boundary conditions in the island problem (isolated system).

The theoretical necessity of the relativistic generalization of celestial mechanics was based on a centuries-old, solid foundation, but behind cosmology stood only irresponsible speculations.

Such a position had to be strengthened by Fock's scientific success in solving the island problem. And his attitude toward harmonic coordinates, by means of which he had solved the island problem, had to be strengthened also by his results concerning the conservation laws for the insular system.

Let us pay attention to what Fock said about the ten conservation laws (commonly, in other treatments of GTR, only four laws of conservation of energy and momentum are discussed). In classical mechanics and STR the existence often conservation laws is connected with the 10-dimensionality of the Galileo and Poincare groups, or with the 10-dimensionality of the set of Cartesian inertial frames of reference, and, finally, with the four-dimensionality of space-time. This connection is produced in a most clear and profound way by Noether's theorem (which Fock, however, did not use).

Generalizing the equations of motion and conservation laws for insular systems placed Fock's results on a solid, historically scientific base (in which Fock included also Copemicus's theory). This stimulated Fock to "ontologize" his successful method of solving the problem—harmonic coordinate systems. It is impossible, however, to build Fock's analysis (of the insular system by means of harmonic coordinates) straightforwardly in a cosmological setting. A Euclidean character at infinity is incompatible with any non-trivial cosmology. "So much the worse for cosmology," Fock thought, perhaps.

Some elements of Fock's understanding of GTR were adopted, especially by geometrically orientated physicists (the meaning of the principle of equivalence and general covariance, necessity of coordinate condition). Fock's belief that harmonic coordinates were privileged in principle and comparable with Einstein's equations in significance remained unadopted.

(Fock's interpretation of GTR allows, however, for adaptation to common modem treatments necessarily including cosmology. Harmonic coordinates may be transformed into the idea of a standard coordinate system generated by the inner metrical structure of the given space-time [such coordinates were first introduced by Riemann himself]. Based on metrical coordinates, it is possible in a general geometry to introduce a 10-dimensional quasi-group, generalizing the ordinary Poincare group for the variable curvature case. With the help of this construction, one can realize the correspondence between GTR, STR, and Newtonian gravity in terms of the island situation and the ten conservation laws of energy-momentum-moment [Gorelik 1988].)

Having described the scientific part of Fock's frame of reference, we can pass to its social-ideological part. The latter occupied, of course, not much time. From Fock's texts and from testimonies of those who knew him (Aleksandrov 1988, 1989; Feinberg 1990; Fock 1991, 1993) emerges the image of a scholar absorbed in his science and, beyond science, honest and self-respecting, responsible and fearless, sympathetic and rather schematic, or mathematical.

If a man belongs to science with his whole mind and heart, it seems probable that, in his life outside science, he is guided by his professional methodology as far as possible. But what if his professional methodology proves to be insufficient in his scientific field? What if, for example, he fails to find a common language with colleagues in spite of great efforts? There is no other way to explain this failure apart from some external factors, though Fock himself hardly would have attributed philosophy to external factors.

Fock learned *Diamat* at the beginning of the 1930s. His textbook
was Lenin's *Materialism and Empirio-Criticism.* It is difficult to
reconstruct exactly Fock's understanding *of Diamat* from his texts,
which contain few quotations. Undoubtedly Fock found in *Diamat* something
important and interesting for himself, in spite of police inculcation,
a flood of quasi-philosophy, abusive polemics, and anachronisms.

Fock was not alone in his relation with *Diamat.* There is no room
in this chapter for a general discussion of Marxist philosophy, its natural-scientific
roots, and the socialist prejudices of physicists. Here one must notice
only that, among Soviet physicists, there existed various individual combinations
of attitudes to different components of Marxist or Soviet ideology, to
dialectical and historical materialism, and to the theory and practice
of Soviet socialism. Adherence to one part might be accompanied by indifference
to another and hostility to a third.

Fock belonged with those who, being predisposed to a philosophical view,
found a good base in *Diamat.* Behind Fock's *Diamat,* however,
one could, with some imagination, recognize something close to Platonic
(true mathematical) idealism: Fock believed in the existence of one true
philosophy as the most general scheme or quintessence that uniquely realized
the evolution of scientific knowledge.

Such an attitude radically differs from the one of (the physicist) Einstein, who supposed that the physicist has the right (or even obligation) to philosophical opportunism, taking, depending on circumstances, the positions of realist, idealist, positivist... (Einstein 1949).

In speaking about Fock's social psychology, one should take into account that, to Niels Bohr, he seemed to resemble Pier Bezukhov. Perhaps due to Fock's European roots, to the honest, fearless, and profound hero of L. Tolstoy, one should also add a somehow not-so-Russian respect for law, regularity, and stubbornness.

Fock seemed to be satisfied with the theoretical postulates of Soviet power. To judge the conformity of beautiful schemes with social practice was more difficult for Fock than for his colleagues (most of whom kept social illusions for a long time). Apart from the previously mentioned "detachment from life" and deafness, his own biography might prevent him from seeing social reality. Was he not twice arrested and did not justice "triumph" twice?!

Fock perceived the Stalinist terror (the true scale of which was unknown)
as a natural disaster, saying that "cowardice does not influence the probability
of arrest" (Aleksandrov 1988, p. 489), and he fearlessly defended those
who found themselves under this probability. When social reality (personified,
for example, by A. Maksimov) invaded his science, Fock acted resolutely
and, as his letter to Tamm shows, rather deliberately. But beyond his own
science his judgements were fairly schematic. He wrote in this schematic
way, for example, about the conservation of energy in Fock 1949. Some of
his judgments in the social field were even more schematic and conforming
to the "logic" of Soviet newspapers.

Having limited ourselves to this description of Fock's frame of reference, let us, based on this frame, look at the last three decades of Fock's life in the theory of gravity.

Fock persistently, without sparing effort, explains his (true) understanding of Einstein's theory of gravity, including also certain mathematical clarifications (Fock 1953b, 1956a, 1956b, 1967). The answer to Fock was silence or evasive words or repetition of old words, mathematically meaningless, although sanctified by the great physicist. When, in scientific discussion, scientific arguments are exhausted, additional reasons are sought beyond science. And the direction of the search is prompted by the socio-cultural atmosphere around the scientist through his own world view. As a result,

A historian who has attempted to account for a communication gap between outstanding scientists and has found an explanation in the difference of their frames of mental references runs the danger of being accused of superciliousness. After all, he claims to see what the scientists in question failed to see.

To ward off such accusations one can recall once more Fock's article
of 1971 and designate as complementary scientific creativity and the ability
to shift easily from one scientific frame of reference to another. The
former demands of a scientist to stand firmly within his own frame of reference.
There is no doubt that Fock's frame of reference led him to outstanding
scientific achievements, and the cooperation of different frames of mental
reference is necessary for the successful development of science.

Anon., ed. (1979). *Albert Einstein i teoriya gravitatsii.*
Moscow: Mir. Aleksandrov, Aleksandr D. (1988). "Vladimir Aleksandrovich
Fock" [Russian]. In

Aleksandrov, A. D., *Problemy nauki i pozitsiya uchenogo.*
Leningrad: Nauka, pp. 489-496.

——— (1989). Interview given to G. Gorelik, October 17, 1989.

Einstein, Albert (1949). "Remarks Concerning the Essays
Brought Together in This Co-operative Volume." In *Albert Einstein: Philosopher-Scientist.*
Paul A. Schilpp, ed. Evanston: The Library of Living Philosophers, pp.
683-684.

——— (1952). Letter to Solovine, May 7, 1952. *Letters
to Solovine.* New York, 1987. pp. 135-139.

——— (1953). Letter to Solovine, May 28, 1953. *Letters
to Solovine.* New York, 1987. p. 147.

Einstein, Albert and Infeld, Leopold (1938). *The Evolution
of Physics.* New York: Simon and Schuster.

Einstein, Albert, Infeld, Leopold, and Hoffmann, Banesh
(1938). "Gravitational Equation and the Problem of Motion." *Annals of
Mathematics* 39: 65-100.

Feinberg, Evgeniy. (1990). Interview given to G. Gorelik, February 28, 1990.

Fock, Mikhail. (1991). Interview given to G. E. Gorelik, April 15, 1991.

———(1993). "Recollections about Father" [Russian]. *Voprosy
Istorii Estestvoznania i Tekniki.* 2: 80-87; 3: 90-98.

Fock, Vladimir. (1922). [Summary of the lecture for the philosophical circle, September 6, 1922]. Archives Academy of Sciences USSR 1034-1-191: 1-3.

——— (1929). "Geometrisierung der Diracschen Theorie des
Elektrons." *Zeitschrift fur Physik* 57: 261-277.

——— (1934). "For Truly Scientific Soviet Book" [Russian].
*Sorena*
3: 132-136.

——— (1937). "Does Quantum Mechanics Contradict Materialism?" (November 1937) [Russian]. Archives Academy of Sciences USSR 1034-1-361.

——— (1938a). "On the Discussion on Problems of Physics"
[Russian]. *Pod znamenem marksizma* 1: 140-159.

——— (1938b). Letter to Presidium of Academy of Sciences USSR, February 13, 1938. In Gorelik 1990, pp. 27-29.

——— (1939a). "On Movement of Finite Masses in the General
Theory of Relativity" [Russian]. *Zhumal experimental'noi i teoreticheskoi
fiziki 9:* 375-410; [in French] *Journal of Physics of USSR* 1:
81-116.

——— (1939b). "Albert Einstein (On His 60-Year-Jubilee)"
[Russian]. *Priroda 1: *95-97.

——— (1940). Letter to the journal "Pod znamenem marksizma" on the review by Ernest Kolman (No. 2, 1940) of Landau 1939. Archives Academy of Sciences USSR 1515-2-98.

——— (1947). "The System of Copernicus and the System of
Ptolemy in the Light of the General Theory of Relativity" [Russian]. In
*Nikolay
Kopemik.* Naum I. Idelson, ed. Moscow: Nauka, pp. 180-186.

——— (1949). "Basic Laws of Physics in the Light of Dialectical
Materialism" [Russian]. *Vestnik Leningradskogo universiteta* 4: 34-47.

——— (1950). "Some Applications of the Ideas of Lobachevsky's
Non-Euclidean Geometry to Physics" [Russian]. In A. P. Kotelnikov and V.
A. Fock, *Nekotorye primeneniya idey Lobachevskogo v mechanike i fizike.
*Moscow:
Nauka, pp. 48-86.

——— (1951). "Review of the Book: Mandelshtam, L. I., *Polnoe
sobranie trudov. *Vol. 5. Moscow, 1950" [Russian]. *Uspekhi fizicheskikh
nauk 45:* 160-163.

——— (1953a). "Against Ignorant Criticism of Modem Physical
Theories" [Russian]. *Voprosy filosofii* 1: 168-174.

——— (1953b). "Modem Theory of Space and Time" [Russian].
*Priroda*
12: 13-26.

——— (1955). *Theory of Space, Time and Gravity.*
[Russian]. Moscow: Nauka.

{Fock, V. A. The theory of space, time, and gravitation.
2d rev. ed. Translated from the Russian by N. Kemmer. New York, Macmillan,
1964. xi, 448 p.}

——— (1956a). "Half-century of the Great Discovery" [Russian].
*Pravda*
April 15, 1956.

——— (1956b). "Remarks on Einstein's Creative Autobiography"
[Russian]. In *Einstein i sovremenaya fizika.* Igor E. Tamm, ed. Moscow:
Nauka, pp. 72-85.

(1956c). "Equations of Motion of System of Heavy Masses
Taking into Account Their Inner Structure and Rotation" [Russian]. *Ibid.*
p. 160-162.

———(1963). "A. A. Friedmann's Works in the Theory of Gravitation
by Einstein" [Russian]. *Uspekhi fizicheskikh nauk* 80: 353-356.

———(1966a). "The Grundprinzipien der Einsteinschen Gravitationstheorie."
In *Deutsche Akademie der Wissenschaften z*u* Berlin. Einstein Simposium*
November 2-5, Berlin, pp. 27-37.

———(1966b). "Comments" [on Graham 1966]. *Slavic Review*
25: 411-413.

———(1967). *Einstein's Theory and Physical Relativity*
[Russian]. Moscow: Znanie.

———(1971). "Principle of Relativity to Means of Observation
in Modem Physics" [Russian]. *Vestnik Akademii Nauk SSSR* 4: 8-12.

———(1973). "Quantum Physics and Philosophical Problems"
[Russian]. In *Fizicheskaya nauka i filosoftya.* Mikhail E. Omel'anovsky,
ed. Moscow: Nauka, pp. 55-77.

Frenkel, Viktor, ed. (1990). *Fiziki o sebe.* Leningrad:
Nauka. Frederiks, Vsevolod K. (1921). "General Principle of Relativity
by Einstein" [Russian]. *Uspekhi fizicheskikh nauk* 2: 162-188.

Friedmann, Aleksandr. (1922). "Uber die Krummung des Raumes."
*Zeitschrift
furPhysik* 21: 326-332.

——— (1923). *World as Space and Time* [Russian].
Petrograd: Iskra.

Ginzburg, Vitaliy. (1956). "Experimental Testing of General
Theory of Relativity" [Russian]. In *Einstein i sovremennaya fizika.*
Igor E. Tamm, ed. Moscow: Nauka, pp. 123, 136.

——— (1973). "General Relativity and Copemicus's Heliocentric
System" [Russian]. *Voprosy filosofii* 9, 10.

Gorelik, Gennady. (1988). "Dimensionality of Space-Time
and Poincare Quasi-group" [Russian]. In *Einsteinovsky sbornik 1984-1985.*
Igor Yu. Kobzarev, ed. Moscow: Nauka, pp. 271-300.

——— (1990). "Philosophical Problems of Soviet Physics
in 1937" [Russian]. *Voprosy Istorii Estestvoznania i Tekniki* 4:
17-31.

——— (1991). "University Physics and Academy Physics" [Russian].
*Voprosy
Istorii Estestvoznania i Tekniki 1:* 31-46.

——— (1993). "V. A. Fock; Theory of Gravitation and Philosophy"
[Russian]. *Priroda* 10. (In press.)

Gorelik, Gennady, Frenkel, Viktor. (1985). "M. P. Bronstein
and Quantum Gravity" [Russian]. *In Einsteinovsky sbornik 1980-198].*
Igor Yu. Kobzarev, ed. Moscow: Nauka, pp. 291-327.

——— (1990). *Matvey Petrovich Bronstein (1906-1938).*
Moscow: Nauka.

Graham, Loren R. (1966). "Quantum Mechanics and Dialectical
Materialism." *Slavic Review 25:* 381-410.

——— (1982). "The Reception of Einstein's Ideas: Two Examples
from Contrasting Political Cultures." In *Albert Einstein. Historical
and Cultural Perspectives. The Centennial Symposium in Jerusalem.* Princeton:
Princeton University Press, pp. 107-138.

———(1987). *Science, Philosophy and Human Behavior in
the Soviet Union.* New York.

Havas, Peter (1989). "The Early History of the 'Problem
of Motion' in General Relativity." In *Einstein Studies.* Vol. 1,
Don Howard and John Stachel, eds. Boston: Birkhauser, pp. 234-277.

Idelson, Naum. (1947). "Life and Creative Work of Copernicus"
[Russian]. In *Nikolay Kopernik.* Naum I. Idelson, ed. Moscow: Nauka,
pp. 5-42.

Infeld, Leopold (1956). "My Recollections about Einstein"
[Russian]. In *Einstein i sovremennaya fizika.* I. Tamm, ed. Moscow:
Nauka, pp. 197-260.

Kapitsa, Pyotr. (1989). *Pis'ma o nauke.* Moscow:
Nauka.

Kozhevnikov, Aleksey. (1988). "V. A. Fock and the Method
of Secondary Quantization" [Russian]. In *Issledovaniya po istorii fiziki
i mekhaniki, 1988.* Grigorian, Ashot T., ed. Moscow: Nauka, pp. 113-138.

Maksimov, Aleksandr. (1952). "Against the Reactionary
Einsteinism in Physics" [Russian]. *Krasny Flot* June 12.

——— (1973). "About Some Negative Phenomena at the Frontline of Philosophy " [Russian]. Archives Academy of Sciences USSR 1515-4a-327: 72.

Mandelshtam, Leonid. (1950). *Polnoye sobranie trudov.*
T. 5. Moscow: Nauka.

Markov, Moisey, ed. (1979). *Einstein i filosofskie
problemy fiziki XX veka. *Moscow: Nauka.

Medvedev, Boris. (1977). *Nachala teoreticheskoy fiziki.*
Moscow: Nauka. Miroshnikov, Mikhail I. ed. (1978).

*V.* *A. Fock. K 80-letiyu so dnya rozhdeniya.*
In *Trudy Gosudarstvennogo Opticheskogo Instituta.* Vol. 43. Leningrad.

Tamm, Igor, ed. (1956). *Einstein i sovremennaya fizika.
Sbornik pamyati A. Einsteina.* Moscow: Nauka.

Vizgin, Vladimir and Gorelik, Gennady (1987).
"The Reception of the Theory of Relativity in Russia." In *The Comparative
Reception of Relativity.* Thomas F. Glick, ed. Boston: Reidel, pp. 265-326.

**V. A. Fock Chronology (Gravitational, Philosophical,
Social)**

1898 Born in St. Petersburg into family of a noble-scientist

1916 Enters Petrograd University

1917 Volunteers for frontline of World War Returns to the University

1922 Translates Friedmann's paper on cosmology into German

1922 Gives lecture at philosophical circle on GTR

1927 Rockefeller grant-holder in Gottingen and Paris

1929 Riemannization of Dirac's equation

1932 Corresponding member of Academy of Sciences USSR

Professor at Leningrad University

Publishes the first Russian textbook on QM

Reads (with interest) Lenin's *Materialism and Empirio-Criticism*

1934 Publishes a very critical review of physics books by the most prominent "materialists" and anti-relativists

1935 First (one-day) arrest

1935 Examines M. Bronstein's thesis on quantum gravity

1937 Second (five-day) arrest

1938 Successful struggle to prevent quasi-philosophical and anti-relativistic session in Academy of Sciences USSR

1939 Full member of Academy of Sciences USSR

1939 Paper on problem of motion in GTR

1939 Jubilee article about A. Einstein

1946 Stalin prize for the work on propagation of radio waves

1947 Formulates in the main his own attitude to GTR

1947 Defends Copernicus from super-relativism and relativity from super-materialism

1940s-50s Defends quantum and relativistic physics (on
behalf *of Diamat) *and defends scientific ethics

1955 Takes part in the Bern jubilee conference on GTR

1955 Monograph *Theory of Space, Time and Gravitation*

1955 Article "Half-century of the Great Discovery" for
newspaper *Pravda*

1960s Persistently explains his attitude to GTR and expresses
his adherence to *Diamat*

1974 Dies