Remarks on Albert Einstein’s Creative Autobiography

V. A. Fock

Albert Einstein’s creative autobiography, written by him in his 68th year,*) is a remarkable document. It contains no, or almost no, biographical material proper—no account of the external events of his life. Einstein speaks almost exclusively about the development of his scientific ideas and about his views on those scientific questions that consistently interested him over the course of his life. But this is precisely what gives Einstein’s work its special value, since it makes it possible to penetrate into the creative laboratory of the great scientist.

In addition to concrete scientific questions, Einstein also touches in his work upon general questions. The autobiography therefore makes it possible to judge Einstein’s philosophical views and his views on the aims and tasks that confront any physical theory.

It is true that it is difficult to say whether these views belong to the period of Einstein’s life that is discussed in this passage of his autobiography, or whether they took shape toward the end of his life and merely gave retrospective illumination to his work. The latter possibility is indicated by certain words of Einstein’s at the beginning of his work (p. 71). Be that as it may, Einstein’s views on the general questions of physics are of considerable interest.

Let us first say a few words about Einstein’s philosophical views. In his scientific work Einstein was a spontaneous materialist. But at the same time, throughout his life, and especially in his youth, he was under the influence of Mach’s idealistic philosophy. In his philosophical statements Einstein is extremely inconsistent: among his statements one can find both standard positivist formulations and timidly expressed materialist ones (see, for example, the definition of the subject matter of physics on p. 100).

*) The autobiography was first published in a collection issued in the USA in 1949 in honor of Einstein’s seventieth birthday.

It should be noted that Einstein’s philosophical views evolved rather in the direction of materialism. If in the book The Meaning of Relativity, written mainly in 1921–1922, Einstein’s positivist philosophical credo is formulated without any reservations, then in his autobiography, written by him around 1947 or 1948, there is even a series of critical statements directed at positivism (p. 88), which, however, is not always criticized from a materialist standpoint.

Einstein’s views on the tasks of physical theory are extremely interesting, although by no means indisputable (p. 78). In Einstein’s opinion, a theory must not only explain facts but must also possess an inner perfection, expressed in the simplicity and logical harmony of its fundamental foundations. Only this inner perfection can make a theory convincing. Agreement with experimental facts proves nothing as yet, since facts can be explained, with a given degree of accuracy, by means of different theories, provided only that the latter are adjusted in an appropriate way. If different theories explain the given facts equally well, then in choosing between them the decisive criterion is simplicity. One cannot ascend from facts to theory, for this path is ambiguous. A theory must be constructed speculatively and only then tested against facts. The main thing necessary for constructing a theory is general principles of a logical character; facts are needed only for refining the details. Einstein expressed such views on physical theory more than once.

As far as can be judged from the autobiography, Einstein set as the goal of his life the discovery of general physical principles (see, for example, p. 89). In their generality these principles should be similar to the first and second laws of thermodynamics; they should be applicable to the entire totality of physical phenomena. It should be noted that Einstein was not interested in approximate theories with a limited domain of applicability. In his general reasoning he seemed not to take into account that essentially every physical theory is approximate. True, in his statements concerning particular theories he was, by force of circumstance, compelled to speak of them as stages on the path to truth. But then he again and again returned to the idea of a universal physical theory that would encompass everything: gravitation, the structure of elementary particles, the electromagnetic field, and all other fields. In Einstein’s opinion, such a theory could be created, in the main, by a speculative path.

In what follows we shall attempt to examine critically those ideas of Einstein’s which seem to us controversial or contain controversial points. Such a critical approach to the ideas of the brilliant scholar may seem overly bold. However, one must remember that in the history of physics there have often been cases when the author of a physical theory

REMARKS ON A. EINSTEIN’S CREATIVE AUTOBIOGRAPHY

did not fully understand the true significance of his discovery. This applies especially to major discoveries of a fundamental character, which have exerted a considerable influence on the further development of science. The significance of such discoveries becomes fully apparent only later, and often this is revealed not by the author of the discovery himself, but by someone else.

A good example here is Maxwell’s theory of electromagnetism. (This example is cited by Einstein himself in his autobiography, pp. 78–79.) In creating his theory, Maxwell thought that he was constructing the mechanics of the ether, and only Lorentz, who pointed out that the electromagnetic field represents an independent reality, understood the true meaning of Maxwell’s theory. One may say, paradoxical though it sounds, that Maxwell himself did not fully understand the true meaning of Maxwell’s theory. Similarly, Lorentz did not fully understand the true meaning of the Lorentz transformations: he thought that they were only formal transformations serving to simplify the equations. The true meaning of the Lorentz transformations was discovered by Einstein (and Lorentz also agreed with Einstein’s interpretation). De Broglie did not understand what de Broglie waves were; a statistical interpretation of the wave function was given only later. Such examples can be multiplied.

All this gives us the right to apply critical analysis to the works of Einstein himself as well.

Speaking of the years of his study, Einstein criticizes mechanics as the foundation of physics (pp. 79–82). Of course, this criticism is entirely justified and, at the present time, can meet with no objections; in Einstein’s own words, it is only of methodological interest. But with the criticism of mechanics as the foundation of physics, Einstein links criticism of Newtonian mechanics itself, conducted from Mach’s point of view; and here, in our opinion, there are debatable points. Einstein, apparently, later abandoned Mach’s opinion that all inertia must arise from the interaction of masses, although for a long time he considered it correct. However, Einstein’s objections to the privileged character of inertial systems in Newtonian mechanics (p. 80) seem to us unfounded. The analogy proposed by Einstein with the singling out of the vertical direction (p. 81) rather confirms than refutes the privileged character of inertial systems. In fact, from the point of view of Einstein’s theory of gravitation, which already represents a further stage, space in a gravitational field is nonuniform, and the singling out of the vertical direction in the case considered by Einstein is entirely legitimate. In objecting to the Newtonian notion of absolute space as a certain active participant in all mechanical processes (p. 80), Einstein leaves to the word “absolute” only the Newtonian interpretation (absolute = not subject to the influence of masses and their motions).

Meanwhile, the conception of absolute space as an active participant in mechanical processes could have been preserved if by absolute space one understood any space possessing its own objective properties (for example, a definite metric), even if these properties were subject to the influence of masses and their motions.

Here and in what follows Einstein uses the concept of “rigid” (accelerated and unaccelerated) reference systems. This concept, however, does not have a satisfactory definition. Still, when considering Newtonian mechanics its use is still permissible.

We have dwelt on Einstein’s critique of Newtonian mechanics because this critique, and in particular the critique of the concept of inertial systems, serves Einstein as preparation for the substantiation of the theory of gravitation, to which he will turn at the corresponding point in his creative autobiography (p. 94 ff.).

Einstein relates with extraordinary vividness the profound impression made on him by Maxwell’s theory (p. 82). He then proceeds to Planck’s formula and its justification (pp. 84—87), and also to the theory of Brownian motion (pp. 87—88) and its connection with the theory of radiation (Brownian motion of a mirror, p. 88).

Einstein writes (p. 89) that after 1900 he began to despair of the possibility of digging down to true laws by means of constructive generalizations of known facts. He came to the conclusion that only the discovery of a general formal principle (similar to the principle of the impossibility of a perpetual-motion machine of the first and second kind) could lead to reliable results. Such a restrictive principle, comparable with the principle of the nonexistence of a perpetual-motion machine, was indeed found by Einstein (p. 89 ff.). This is the principle of relativity, more precisely, the principle of the invariance of the laws of physics with respect to Lorentz transformations (p. 91). This principle underlies Einstein’s theory of relativity. The great significance of this theory is universally recognized, and we shall not dwell on it. It is more interesting to analyze the critical remarks made by Einstein himself about his theory.

First of all Einstein notes (p. 92) that the theory introduces (besides four-dimensional space) two kinds of physical objects, namely: 1) measuring rods and clocks, and 2) everything else; and this, in his opinion, is illogical. Such an opposition of measuring rods and clocks to everything else requires explanation. Apparently Einstein understands by this the opposition of space—time, on the one hand, to forms of matter, on the other, and wishes to point out the illogicality of such an opposition. Then this will be the same thought about the interconnection of space, time, and matter that Einstein expressed in other places as well (for example, in criticizing the Newtonian concept of absolute space). Only here this thought is expressed, so to speak, in positivist form: the behavior of measuring rods

and clocks is regarded not as something secondary, conditioned by the properties of space and time, but as primary, as the definition of these properties.

Another remark by Einstein, made in connection with the preceding one, is also of interest. Einstein says (p. 92) that the postulates of the theory of relativity are not so strong that sufficiently complete equations for physical processes could be derived from them. The fact that Einstein considers it necessary to emphasize this, in our view obvious, point shows that at first he thought otherwise. Undoubtedly, Einstein at first hoped that from the principle he had found it would be possible to derive absolutely everything, including the theory of quantum phenomena and the nature of inertia. This is confirmed by the following words of Einstein (p. 93): “The fact that the special theory of relativity represents only the first step in the necessary development became clear to me only when I attempted to represent gravitation within the framework of this theory.” Having become convinced that the principle underlying the “special” theory of relativity is not yet the universal key to all physical laws, Einstein did not lose faith in the existence of such a universal principle and continued tirelessly to search for it throughout his life. For a time it seemed to Einstein that he had found it in the form of the requirement of general covariance of equations, but this too proved to be an illusion. The remarkable theory of gravitation discovered by Einstein does not follow from the requirement of general covariance alone, and the property of general covariance is not its monopoly. On the other hand, it is precisely only a theory of gravitation, and not the universal “theory of the unified field” which, as Einstein hoped, was supposed to include within itself the theory of all known fields, the theory of elementary particles, and the theory of quantum phenomena.

Einstein’s searches for a “theory of the unified field” continued until the end of his life.

Let us return to Einstein’s autobiography, to those of his reflections which ultimately led him to his brilliant theory of gravitation. In the main, the chain of his reasoning is as follows (pp. 94–95).

Having established the fact of the equality of inertial and gravitational mass, Einstein proceeds to consider the behavior of bodies in an “accelerated reference system” and arrives at the conclusion of the equal rights of all reference systems—inertial and non-inertial—which in turn leads him to the requirement of general covariance of equations. Relying on this requirement, Einstein ultimately arrives at his equations of gravitation.

The first and the last links of this chain are correct: the fact of the equality of inertial and gravitational mass is beyond doubt, as are the final equations of gravitation. But Einstein’s intermediate arguments do not withstand criticism, since they contain a number of logical inconsistencies. Let us analyze these arguments in more detail.

First of all, the concept of an accelerated frame of reference as a rigid material system is inapplicable in the theory of relativity. The term “accelerated frame of reference” can be understood there only in the mathematical sense, as a certain coordinate system. Meanwhile, in Einstein’s arguments, “accelerated frames of reference,” understood precisely as material systems, play the most fundamental role. Even if this difficulty is set aside, the attempt (p. 94) to interpret the apparent gravitational field in an accelerated system as “true” (in quotation marks or without quotation marks) appears unconvincing. One can speak of the indistinguishability (or equivalence) of fields of acceleration and gravitation only under a purely local consideration. If, however, fields are considered not locally, but with boundary conditions taken into account, then an apparent gravitational field (arising from acceleration) can always be separated from a true one.

In any case, the transition from the law of equality of inertial and gravitational mass to the local equivalence of fields of acceleration and gravitation represents, in our view, rather a loss of generality than a real step forward in the argument.

The mixing of local consideration with nonlocal consideration constitutes a definite (logical and mathematical) error on Einstein’s part. At the beginning of the arguments on p. 94 a reservation is made that the arguments refer to fields of small spatial extent; but already one paragraph later the same conclusions are applied to gravitational fields extending arbitrarily far. Meanwhile gravitational fields extending arbitrarily far and not bounded by boundary conditions are impossible*). Consequently, the premise from which Einstein draws the conclusion about the meaninglessness of the concept of an inertial frame falls away. Contrary to Einstein’s opinion, the concept of “acceleration with respect to space” retains its meaning.

In formulating his conclusion, Einstein says (p. 94) that the basic requirement of the special theory of relativity (the invariance of laws with respect to the Lorentz transformation) is too narrow, i.e. that one must require the invariance of laws also with respect to arbitrary transformations of coordinates.

This formulation is based on the idea that general covariance is an extension of the principle of relativity. Yet the one has no relation whatever to the other. The principle of relativity is the expression of the property of homogeneity of space—time**). Homogeneity manifests itself in the existence of a group of transfor-

*) In every field theory formulated by means of differential equations in partial derivatives, boundary conditions (or conditions replacing them) are just as important as the equations themselves; without them the field cannot be determined.

) See my work, “The Concepts of Homogeneity, Covariance and Relativity in the Theory of Space and Time,” Voprosy filosofii, No. 4, p. 131, 1955.

observations, which leave unchanged the values of the coefficients \(g_{\mu\nu}\) in the expressions for the square of the interval. In Galilean coordinates these transformations have the form of Lorentz transformations. The property of homogeneity can be formulated both in Galilean coordinates and in a generally covariant way. It is already clear from this that this property has no relation whatsoever to general covariance.

The confusion of mathematical concepts allowed by Einstein*) is also manifested in the fact that in the word combinations:

a) invariance of the laws with respect to Lorentz transformations;

b) invariance of the laws with respect to arbitrary transformations;

the words “invariance of the laws” are used in different senses. In case a) this concept also includes the constancy of the quantities \(g_{\mu\nu}\) (the condition \(g'_{\mu\nu}=g_{\mu\nu}\)), whereas in case b) this condition is not included, and the quantities \(g_{\mu\nu}\) are also subjected to transformation (according to the tensor rule).

The indicated confusion of concepts is also manifested in the incorrect use of the word “relativity” (on this see below).

According to Einstein (p. 95), “the general theory of relativity proceeds from the following basic proposition. The laws of nature must be expressed by such equations as would be covariant with respect to the group of continuous coordinate transformations. This group here thus takes the place of the group of Lorentz transformations of the special theory of relativity.”

This formulation of Einstein’s is also based on a misunderstanding. Two theories can be compared with respect to covariance only if this term is given the same meaning in both cases. If what is meant is the covariance that is connected with homogeneity (\(g'_{\mu\nu}=g_{\mu\nu}\) for \(x'_{\mu}\ne x_{\mu}\)), then the “special” theory possesses it and the “general” theory of relativity does not. If, however, what is meant is formal covariance (\(g_{\mu\nu}\) are transformed according to the tensor rule, and \(g'_{\mu\nu}\ne g_{\mu\nu}\)), then both theories, the “special” and the “general,” are in the same position, since both admit a generally covariant formulation**). In the sense of covariance these two theories are not at all in the relation of particular to general (and if they are, then the advantage is rather on the side of the “special” theory, which admits transformations for which \(g'_{\mu\nu}=g_{\mu\nu}\), whereas the “general” theory, generally speaking, does not admit them).

*) When one has to point out Einstein’s mathematical errors, one involuntarily recalls his admission that his intuition in the field of mathematics was not sufficiently strong (p. 76).

**) A generally covariant formulation of the “special” theory is given by Einstein himself on p. 96 (on this see below).

With these latter transformations, which express the homogeneity of space, the principle of relativity is connected. Therefore the confusion, allowed by Einstein, of the concepts of covariance expressing homogeneity and formal covariance leads him to an incorrect use of the terms “relativity” and “principle of relativity” in a sense that has nothing in common with homogeneity. Einstein also uses the terms “special relativity” and “general relativity.” But in the first phrase the word “relativity” is understood in the sense of homogeneity, while in the second—in the sense of covariance*); meanwhile these two concepts are completely different.

In any case, Einstein’s assertion that general covariance is the fundamental proposition of his new theory (see also p. 95) is incorrect. Einstein himself senses the weakness of this thesis of his. On the same pp. 95–96, a few lines below, he half renounces it and supplements the requirement of covariance with the requirement of simplicity of the theory. Of course, this changes the matter. The principled simplicity and inner perfection of Einstein’s theory of gravitation are not subject to doubt; it is precisely these qualities that make his theory convincing.

The thesis originally advanced by Einstein that general covariance is the distinctive feature of the “general theory of relativity” is in fact refuted by Einstein himself, who on p. 96 gives a brilliant, in its brevity, generally covariant formulation of the “special theory of relativity.”

It is extremely interesting that, having written his famous equations

\[ R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = -\chi T_{\mu\nu}, \tag{*} \]

which for the first time made it possible to understand the nature of universal gravitation, Einstein immediately, disappointed, calls them (p. 98) a “provisional way out of the situation” and “nothing more than a theory of gravitation.” Such a disappointed assessment of his own greatest achievement appears to us to be in no way justified. It is necessary, however, to sort out its sources.

It seems to us that the source of Einstein’s disappointment is his general attitude, of which we spoke above: his belief in the possibility of creating, by a speculative route, a universal physical theory that would encompass everything. When Einstein constructed his so-called “special” theory of relativity, he experienced disappointment when he became convinced that this theory does not give everything and that, for example, quantum phenomena alone cannot be explained by it. When Einstein constructed his so-called “general”

*) This follows clearly, if only from the fact that Einstein calls (p. 99) the group of continuous transformations with respect to which the field equations are covariant (generally covariant), the “group of general relativity.”

the theory of relativity, he again experienced disappointment, having become convinced that this is “no more than a theory of gravitation” and that it does not include a theory of all fields existing in nature (Gesamtfeld).

Let us return to Einstein’s statements on the theory of gravitation. In his theory Einstein regards as final (p. 98) only the case of a pure gravitational field, when the mass tensor is equal to zero and the equations reduce to \(R_{\mu\nu}=0\). It seems to us, however, that precisely this case is unreal. The source of the gravitational field is always masses. The equations \(R_{\mu\nu}=0\), considered not locally but together with boundary and initial conditions, must lead to the Galilean character of all space. The only way out of the situation can be the admission of singular points of the field, but this is equivalent to the implicit introduction of the mass tensor \(T_{\mu\nu}\). Therefore the only correct form of the equations of gravitation appears to us to be the equations (*).

Einstein’s works that established the connection between the equations of gravitation and the laws of motion of masses are very important. (Analogous works were also carried out in the USSR, but apparently Einstein did not know of them.) Of particular interest is Einstein’s consideration (p. 99), in which the fundamental significance of the nonlinearity of the field equations is emphasized: only thanks to their nonlinearity can the field equations lead to definite laws of motion.

It should be noted that the preference following from Einstein’s general views, which he gives to the equations \(R_{\mu\nu}=0\) over the complete equations (*), leads him to the fact that he confines himself to the laws of motion for singular points (i.e. for point masses), thereby denying himself the possibility of studying the influence of the internal structure of bodies on their motion. The restriction to the case of point masses reflects Einstein’s striving to construct, without resorting to quantum mechanics, a theory of elementary particles as singular points of the field. Meanwhile there is no doubt that the laws of motion for masses following from the equations of gravitation are applicable where gravitation plays the predominant role, i.e. on astronomical, and by no means on atomic, scales.

It is quite astonishing that Einstein, who did so much for quantum theory in the initial period of its development, took a negative position with respect to modern quantum mechanics. Einstein tries to justify his negative position also in his autobiography (pp. 100–102). For this purpose he again sets forth the substance of his dispute with Bohr, which arose in 1935.

The essence of this dispute is as follows. If a system consisting of two subsystems is described, according to Schrödinger, by a wave function, then a measurement on one subsystem (and the associated action upon it) changes the state of the second subsystem even

in the case when there is no direct force interaction between the two subsystems. In this Einstein sees a paradox and concludes from it the incompleteness of quantum mechanics. Bohr denies the presence of a paradox here, but his explanation, correct in its physical part, is unsatisfactory philosophically, since it has a positivist tinge.

Einstein’s error consists, in our opinion, in the fact that Einstein denies (declares telepathy, p. 102) all interactions except force interactions. Meanwhile, from various fields of science and life one can adduce many diverse kinds of interactions which are all non-force interactions. We shall confine ourselves to the following examples. A person who is a member of a collective experiences an interaction (not a force interaction, of course) with the other members of the collective, and their fate—for example illness or death—inevitably affects him as well (“changes his state”). In the case of the death of subordinates (“the first subsystem”), the state of the superior (“the second subsystem”) inevitably changes, if only because he ceases to be a superior; in this the former superior may remain whole and unharmed (the absence of direct force action*). An example from another field can be obtained by considering interaction by means of a signal (a telegram); the effect of the telegram has no connection whatever with the energy expended on its transmission, and in this sense the interaction may also be called non-force, in contrast to the purely force interaction between an electric power station and an enterprise consuming electric energy.

In the field most important for us—the field of quantum mechanics—a non-force interaction is, for example, the interaction expressed by the Pauli principle. Another kind of quantum-mechanical non-force interaction is the interaction between two particles having a common wave function (the case considered by Einstein). Thus, the existence of non-force interactions is not open to doubt. But if they are acknowledged, then the dilemma considered by Einstein also disappears (points of view \(A\) and \(B\), pp. 101–102), and with it falls the paradox that led him to the opinion of the incompleteness of quantum mechanics.

We have seen that the denial of non-force interactions is an error. This error is very reminiscent of the one of which Einstein speaks (p. 73), recalling his early childhood: it then seemed to him that action could be transmitted only through contact, and the behavior of the compass needle made upon him the impression of a miracle, which he remembered for his whole life. In his mature years, quantum-mechanical non-force interaction seemed to Einstein a miracle, and he likewise did not accept this “miracle.”1

The final pages of the autobiography (pp. 103–105) Einstein devotes to a formal generalization of his theory of the gravitational field—a generalization which, in our opinion, has no physical meaning. The aim of these attempts by Einstein remained the construction of a theory of a single universal field (Gesamtfeld). It must be stated that here Einstein was following the wrong path, and that his nearly thirty years of effort ended in complete failure. Einstein’s belief in the possibility of finding, by speculative means, a universal principle providing the key to all the laws of physics did not justify itself.

Einstein accomplished so extraordinarily much in his lifetime that his individual errors and failures can in no way obscure his great achievements from us. Without him, physics would not be what it is today. Not only in our eyes, but also in the eyes of future generations, Albert Einstein will appear as a colossal figure, standing in the same rank as the greatest minds of all time.

1. This (or a similar) example belongs to A. D. Aleksandrov. ↩