Vladimir Fock: Philosophy of Gravity and Gravity of PhilosophyIn: The
Attraction of gravitation: new studies in the
history of general relativity 
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
(18981974) 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, lawabiding person. To reveal these elements
of the explanation and to connect them in a united
scientificpsychological complex, one should consider the
evolution of Fock's views.

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. 
Fock (1963) recalled the
following of his early acquaintance with GTR:
A. A. Friedmann and V.
K. Frederiks, professors in Petrograd University, were the
first who familiarized Russian physicists, who worked in
Petrograd, with the theory of gravitation recently created by
Einstein. This was at the very beginning of the 1920s when the
blockade of Soviet Russia had just been broken and scientific
literature from abroad began to arrive. In the Physical
Institute of the University a seminar gathered where, among
other things, lectures on Einstein's theory were delivered.
The participants of the seminar were teachers and students in
their last year (and at that rime there were very few). The
basic speakers on the theory of relativity were V. K.
Frederiks and A. A. Friedmann, but sometimes also Yu. A.
Krutkov, V. R. Bursian and others spoke. I remember the talks
of Frederiks and Friedmann clearly. The style of these talks
was different: Frederiks deeply understood the physical side
of the theory, but did not like the mathematical computations;
Friedmann stressed not physics, but mathematics. He strived
for mathematical rigor and attributed great importance to the
full and exact formulation of the initial preconditions. The
discussions that arose between Frederiks and Friedmann were
very interesting.
This
recollection, with its "duet of acting characters"—mathematics
and physics—as we shall see, can tell us much about Fock's
position itself. In spite of the important role of Frederiks
in the assimilation of GTR in Russia, one may doubt the depth
of his physical comprehension of GTR. On the other hand, "the
full and exact formulation of the initial preconditions" was
very characteristic of Fock himself.
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:
I am going to give an
account of the physical foundations of the theory of
relativity and to point out some contacts with philosophical
problems. But I consider myself to be an ignoramus in
philosophy, and therefore I do not claim to solve, or even to
put philosophical questions in correct form. In this respect I
wait for the assistance of my listeners.
After a few
words about the historical origins of GTR, Fock turns to
the leading thread: the
search for the really existing in the nature. The really
existing is defined as being perceived by all identically.
Examples:
(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 t^{2} the interval r^{2} — c^{2}t^{2}
really exists.
Fock
summarizes the content of general relativity in the following
way:
Geometry has absorbed
physics. From the formal point of view it is all the same, but
it is more satisfactory for our intuitions. As well now the
physicist believes in the existence of atoms and electrons
neither more nor less than in the existence of common "large"
objects. If he was a "naive realist," he has remained the
same. But he replaced entities that he considered before as
really existing. It is possible to go further.
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 G_{mn} being equal to
zero.
From this
short text one can draw some important conclusions.
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 mid1930s). His striving to comprehend the
epistemological bridge between physical reality and theory is
beyond doubt.
In the philosophical viewpoint
of the 24yearold 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 spacetime. 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.
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 quantumrelativistic
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
EmpirioCriticism 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:
The philosophical side
of my views on the theory of space, time and gravitation was
formed under the influence of the philosophy of dialectical
materialism, in particular under the influence of Lenin's Materialism
and EmpirioCriticism. The teaching of dialectical
materialism helped me to approach critically Einstein's point
of view concerning the theory created by him and to think it
out anew. This teaching helped me also to understand
correctly, and to interpret, the new results obtained by me. I
would like to state this here, although this book does not
explicitly touch philosophical questions. (Fock 1955, p. 16)
Before
considering the interaction between Fock, Diamat, and
the theory of gravity, let us get acquainted with some facts
from Fock's biography which may seem to be irrelevant at first
glance.
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 scientistforester. 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 41114127].
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
65yearold electrical engineer academician, V. F. Mitkevich.
Having oldfashioned (meta) physical views and having
obtained newfashioned 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
popularscientific 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 sevenpage 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,
Whatever causes
compelled the authors to avoid mentioning Bronstein's
achievements, their work may not be considered as the
construction of the quantum theory of gravitation, for this
theory was created by Bronstein 11 years earlier. [Personal file of V. A. Fock.
Archives Acad. Sci. USSR 10341549].
The facts
pointed out here provide a social portrait of Fock and will
help us to understand his attitude to GTR better.
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 socalled
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 1015 years and
the complete fruitlessness of Einstein's attempt to explain
elementary particles by means of a unified field theory."
Nevertheless, Fock concludes:
One should admire the
creation of Einstein's genius, which is so rich in physical
content in spite of its seeming abstractness. I hope this
paper will help to reveal the physical content of this
remarkable theory.
In a popular
article, dedicated to Einstein's jubilee, Fock (1939b)
expressed his position in stronger words, both in criticism in
relation to cosmology and in appreciation of Einstein: "one of
the greatest modem scientists, whose name is known and dear to
every educated man and is shining equally as the name of
Newton." In 1939 such enthusiastic appreciation of a
"bourgeois" scientist known for his "idealistic" philosophical
and "bourgeoisliberal" political views, was already very
exotic.
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} = 0,
where D is the
covariant D'Alembertian (there are different forms of this
condition). The corresponding coordinate systems are called harmonic.
One of the main peculiarities
distinguishing Fock's work from EinsteinInfeldHoffmann'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
postNewtonian 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,
Harmonic coordinates are
the nearest in their properties to ordinary rectangular
coordinates and ordinary time in the Minkowski "world." That
is why, in these coordinates, the GTR formulas are the
clearest.
Fock supposes
that the harmonic coordinate system "deserves the name of
inertial," because he considers it
most probable that from
Euclideanness at infinity and from its harmonic character (in
connection possibly with some additional conditions like the
radiation condition), our coordinate system is defined
uniquely, with the indeterminacy of an ordinary Lorentz
transformation.... As it seems to me, the possibility of
introducing, in the general theory of relativity, uniquely
defined inertial coordinate system deserves to be noted.
Judging from
the content of Fock's paper (1939a), it seems that the paper
is not merely the solution of a certain problem, but the
beginning of a large program of work. The war interrupted this
work, however, and Fock came to be busy with more applied
physical problems.
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 antipatriotism and cosmopolitanism)
was attacked in different fields of science. Debates over the
state ideology of MarxismStalinism 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
"PtolemyCopernicus" 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 400yearold 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"):
(1) the radical devaluation of the
principles of general relativity, covariance and equivalence;
(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 pseudoeuclidean geometry of
spacetime at infinity...; this requirement is satisfied for
systems of masses like a solar system. (Pock 1947, p. 185)
Based on this,
Fock firmly rehabilitated "the immortal creation of
Copernicus—the heliocentric theory of the solar system."
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.
The next publication on the
theory of gravitation that Fock prepared was in 1948. It was
based on his prewar 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, antipatriotism
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 seedbed 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 physicisttheorists. One of the highest
ranking among these philosophical overseers was A. A. Maksimov
(18911976).
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 10343691: 3132; 10343160:
810].
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 antiMaksimov 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
spacetime. 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.
His mathematical errors
have to be pointed out. For Einstein's reputation it is useful
to cleanse his theory of erroneous statements. It would be a
tactical mistake to keep silent about Einstein's erroneous
philosophical statements. The only way for physics to get
immunity from philosophical attacks is to admit philosophical
errors by physicists themselves and to separate these errors
from the entity of theory.
Fock
concluded:
Publication in a leading
newspaper of an article about Einstein signed by
me—independently of its intelligibility—1 consider as very
useful because:
(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.
In these
letters the discussion concerned only the social status of
GTR. But, in just a few weeks, the possibility had arisen of
giving an account of their true scientific views.
On November 30, 1955 there was
an open session of the Academy of Sciences of USSR, dedicated
to the 50year 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 manycolored ("extremely
inconsequent") philosophical palette of the great physicist
into the sharp dichotomy of the terms "materialismidealism"
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
spacetime 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:
I am not in agreement
with Professor Fock that one should add certain conditions to
the theory of relativity, the conditions picking out harmonic
systems. During my visit in the Soviet Union (1955), I, to my
great surprise, have been convinced that Professor Fock stands
apart in this question, and that physicists of such caliber as
Landau, Tamm, and Ginzburg are in disagreement with his
attitude. (Infeld 1956, p. 238)
This
discrepancy, this communication gap between Fock and his
physicist colleagues, was maintained for many years, up to his
death, in spite of his persistent efforts to elucidate his
viewpoint (Fock 1967; Ginzburg 1973). One may find clear
testimony of the failure of his efforts in the volume
published in the USSR on Einstein's centenary that collected
major works in the theory of gravity (Albert Einstein i
teoria gravitatsii, 1979). This volume contains two of
Fock's papers (1929, 1939a), but on the volume's jacket there
is the phrase: "... general theory of relativity, i. e.,
mechanics of arbitrary accelerated system...."
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 scientificmethodological and in socialphilosophical
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 20thcentury 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
nonabsolute truths, Fock concluded:
As the history of the
development of science shows, general principles established
for one field of knowledge may be applicable also in other
fields. I believe that such general character is possessed by
the principle of relativity to the means of observation.
In this is its philosophical meaning. (Fock 1971)
Of course, in
the history of science, to determine a "frame of reference" or
"means of observation" for an outstanding scientist is much
more difficult than in special relativity or in quantum
mechanics. But only after having determined the "direction
vectors" of the scientist's world view and having tied these
vectors to his unique personality can a historian hope to
comprehend his life path.
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.
41114127, 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 antiromantic.
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 colleaguegeometricians) that in Riemann
geometry, the zerocurvature 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 physicisttheorist 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 wellknown discrepancy of
the Hubble age with the data of geo and astrophysics? (It had
to be especially important for the soberminded 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:
In any field theory,
formulated by means of partial differential equations,
boundary conditions (or conditions which can replace them) are
as important as the equations themselves; without such
conditions the field cannot be determined. (Fock 1956b, p. 79)
—isn't this a
student's question?!
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 nonunique 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 centuriesold, 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
10dimensionality of the Galileo and Poincare groups, or with
the 10dimensionality of the set of Cartesian inertial frames
of reference, and, finally, with the fourdimensionality of
spacetime. 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 nontrivial 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
spacetime [such coordinates were first introduced by Riemann
himself]. Based on metrical coordinates, it is possible in a
general geometry to introduce a 10dimensional quasigroup,
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 energymomentummoment [Gorelik 1988].)
Having described the scientific
part of Fock's frame of reference, we can pass to its
socialideological 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 selfrespecting, 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 EmpirioCriticism. 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 quasiphilosophy, 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
naturalscientific 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 notsoRussian
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 sociocultural atmosphere around the scientist
through his own world view. As a result,
It is possible that the
difference between the points of views of the two schools
[Einstein's and Fock's] on given, concrete questions is not
incidental but connected with the difference in their general
philosophical directions. (Fock 1955, p. 472)
With regard to
another frame of reference (call it "Tamm's"), one must say
that, among its inhabitants, there were no specialists in GTR
comparable with Fock. These inhabitants were
physicisttheorists who could not ignore the
laboratoryNewtonian experience behind the abstract Riemannian
constructions of GTR and could not look at the physical world
from inside Riemannian spacetime. Apart from this, these
physicists could not see through the mud just recently thrown
at "reactionary Einsteinism."
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.
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———
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265326.
1898 Born in St. Petersburg into
family of a noblescientist
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 grantholder 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
EmpirioCriticism
1934 Publishes a very critical
review of physics books by the most prominent "materialists"
and antirelativists
1935 First (oneday) arrest
1935 Examines M. Bronstein's
thesis on quantum gravity
1937 Second (fiveday) arrest
1938 Successful struggle to
prevent quasiphilosophical and antirelativistic 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
superrelativism and relativity from supermaterialism
1940s50s 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 "Halfcentury of
the Great Discovery" for newspaper Pravda
1960s Persistently explains his
attitude to GTR and expresses his adherence to Diamat
1974 Dies