Just short of 101 years ago, Einstein and Bergson met each other publicly in Paris for a "grand debate", at least as the papers would present it. If we are to take the minutes as a more accurate account, it went more like this. Einstein was welcomed for a Q&A session with French scholars. Bergson, being present (and the celebrity philosopher of the concept of time), was compelled to speak and so he raised a question for Einstein who provided a curt reply, as his French wasn't extraordinary.
Now this meeting can be read about here or in Jimena Canales' book-length treatment The Physicist and the Philosopher. Her book notes a variety of the social and historical background factors to this debate, of which there are many insights. For example, German scholars had been ejected from Allied universities during the First World War, and this is one of the first examples of a German scientist being welcomed into a French intellectual setting following the war. While this is interesting, I was more curious about the philosophical contentions, which the book does not discuss at much length.
Out of curiosity, and as I could find no translation readily available, I decided to use this weekend to translate the minutes of this meeting from French into English. Perhaps this may be of use to whoever stumbles across this post. The original French can be found here (public domain).
The scene of this meeting is very easy to picture, especially for those who have attended honorarium sessions given for celebrity professors. The grandiose gestures and perhaps excessive deference given by the hosts to their guest. Random scholars with pet projects jumping in with idiosyncratic questions that try to wedge their thoughts into the grand master's work. The grand master himself being rather socially awkward but coming off with the insouciance of an aloof mastermind.
This comic portrait is interesting from another angle, however. Albert Einstein remains to this day the poster boy of genius, as much as he was in his own day. (So much so Roland Barthes even wrote a semiotic analysis of Einstein's brain as the symbol of genius itself). A universally acclaimed mind whose stardom transformed physics from one mere science into the noblest, most esoteric science for the layman. In the public imagination, physics has become the smartest profession for quite some time.
At any rate it is here that Einstein meets Henri Bergson (1859-1941). As some background, Bergson was the celebrity first-rate genius of his generation. Before he was eighteen, he won a national mathematics competition and a scientific prize for an unrelated achievement. Despite his talent for the natural and mathematical sciences, he opted to dedicate his studies to classics. He wrote a critical study on the Latin poet Lucretius before publishing two dissertations Time and Free Will alongside a thesis on Aristotle written in Latin. In terms of intellectual breadth, Bergson was more than a match for Einstein. In terms of depth, that is the open question.
Bergson was regarded by his contemporaries (including William James) as one of the greatest philosophers of all time, even ranking as the next greatest in the succession of Plato, Descartes, and Kant. Many intellectual or literary celebrities of their day do not withstand the test of time. Read any poem by Poet Laureate Alfred Austin to see why this may be the case.
That being said, it is not clear if Bergson belongs in this category. The intransigent brilliance of his thought is rather striking when you read him.
Instead, he seems to be one of those thinkers of the twilight, whose senescence corresponds with the withering of philosophical prestige. As classics and philosophy diminished in the West, to be replaced in the public mind by the physicist. A Shakespearean tale in its own way.
There may be multiple senses in which Einstein begins his remarks by asking, "Is the time of the physicist the same as that of the philosopher?"
Session of April 6th, 1922
The Theory of Relativity
Mr. X. Leon - The date of April 6th, 1922 will be momentous in the Annals of our Society and it is for her an honor to receive the presence of the genius author of the theory of special and general relativity.
One of the most eminent founders of the French Society of Philosophy, our very missed instructor Emile Boutroux, recalled even in 1920 to the Academy of Moral and Political Sciences, "That is had constantly, since its origin, sought to bring together in frequent and familial meetings, not only philosophers and the friends of philosophy, but like in the Review of Metaphysics and Morals, the scientists and the philosophers". Never will it be able to congratulate itself more [than now]. And if it is true, like Mr. Boutroux added, that in these talks "it is not rare that a thinker exposes more than in his written studies, his intimate principles and his veritably guiding ideas", never in the existence of our society has it received a more brilliant consecration.
I would have therefore scruples to delay the moment when you all are going to hear the words of the great thinker of whom Langevin has said so justly that he "has opened to us a new window to eternity", if I did not considere it my duty to express to Mr. Einstein, on behalf of the members of this Society, our profound gratitude for the modesty with which he accepted to come speak with us.
Let me tell him: he is no stranger to the scientists and the philosophers who are here. It was in the beginning of 1911 that our colleague Winter published his book Method in Philosophy and Mathematics, where he was the first to signal to the public the importance and profundity of the views of Mr. Einstein. In the month of April in the same year, during the session of the 4th International Congress in Bologna, Langevin, with his admirable mastery, revealed, first in an oral presentation to the astonished but singularly captivated philosophers, the mysteries of special relativity. In October, an apostle of the new Gospel, he took it up again, under a slightly different form, the exposition of the discoveries of Mr. Einstein before the members of the French Society of Philosophy. And just yesterday, at this extraordinary session where Mr. Einstein had been invited and it was for all the attendants a great disappointment that he was not able to come, the most memorable session was without doubt that of Miss Wrinch, Enriques, Langevin, Painleve discussed the question of the most recent forms of the theory of relativity.
Today we are overjoyed to resume the discussion in the presence of the giant himself; however, one regret grips our heart.
The French Society of Philosophy counted among its founding members one other scientist of genius: he was called Henri Poincare.
Now you know the fundamental role that Poincare played in the creation of what was called the new mechanics, by showing the part of the agreement which existed in classic mechanics and in introducing certain fecund notions, for example the quantity of electromagnetic movement or the pressure known as "Poincare pressure".
Better yet, in his Lessons on electricity and optics published more than twenty years ago, in 1901, Henri Poincare examined the theories of Hertz, of Helmholtz, of Larmor, of J.J. Thompson, of Lorentz, and his preferences went to the conceptions of the celebrated Dutch physicist. Speaking in particular on Michelson's experiment, he wrote these truly prophetic lines:
"I regard it very probable that optical phenomena depend only on the relative movements of material bodies and not on the quantities [merely] close to the order of the square or on the cube of the aberration, but strictly [so]. As the experiments become more exact, this principle will be verified with more precision. A well-made theory should be able to demonstrate the principle at once in all its rigor. Lorentz's theory does not do so yet. Of all those which have been proposed, it is the closest to doing so."
The solution expected by Poincare, Mr. Einstein provided in his 1905 essay of special relativity; he accomplished the revolution that Poincare had foreseen and presented at a time when the development of physics seemed to lead to an impasse.
What a spectacle it would have been to meet today, in this compound with these two creators of worlds, sons of different countries, and what light might h ave sprung from it in this search for truth, which beyond the limits of borders, affirms the universality of the human spirit and realizes the approval of all intelligence!
Mr. Langevin - The theory of relativity is first of all a physical theory; it starts from known facts and leads to the prediction of new facts; it is essentially experimental. Born from contradictions which arose between electromagnetic theory and mechanics, it is the sole one which gives an account of known facts and allows us to predict others. The theory is not only experimental by its origin, but it is still so by its method. It only incorporates abstract elements of physics given by observable quantities, provided by experience, and it rejects any absolute arbitrariness.
For these reasons, it was necessary to give up the classification of human knowledge proposed by Auguste Comte. Comte placed at the base of our immediate concepts an absolute space and time upon which he built mechanics, physics, physicochemical science and their consequent biology; for him physics had essentially [existed] for the theater of Euclidean space where an absolute time reigned. The new conception is wholly different: it is a fusion of geometry and physics making impossible the existence of an absolute space-time. This notion of a space and of a time independent of each other led to paradoxical consequences when one wanted to give the notion of simultaneity a precise meaning, valid for all observers, whatever their motion may be in relation to each other.
The theory of special relativity rests on two fundamental axioms: the principle of relativity and the principle of the constancy of the speed of light. According to the first principle, the equations translating the laws that govern phenomena must have the same form for all systems of inertia in uniform translation with respect to each other; this principle is founded on experience which is always found confirmed in all the domains of physics. The isotropy of the speed of light, otherwise called the constancy of c when one passes from one Galilean system to another, is a consequence of the laws of electromagnetism that no one can reasonably dream of contesting, and is directly verified by experiments of Michelson's kind. In the new kinematics, time has lost its absolute character; the notion of simultaneous events far from one another loses all meaning. Moreover, the principle of causality is unaffected if we admit that no one exists capable of traveling with a speed higher than the fundamental speed c.
But the theory of general relativity goes further and philosophy is no stranger to its development; it is philosophy which drove Einstein to think that reality had no need of systems of reference, that the laws of nature could take a form where these systems of reference would not intervene, in other words a form invariable to the changes of coordinates. But, if we reflect well on it, our only knowledge of the external world rests on the observation of absolute coincidences, each having a meaning independent of any system of coordinates and determinism requires that the course of phenomena is nothing else than a succession of similar coincidence chained from one to the others. The laws which translate this linking up must translate this chain must necessarily be able to assume an invariable form.
For special relativity every system of inertia had its own particular time. In general relativity, to the contrary, the systems of inertia disappear and this disappearance entails the impossibility of a time that is common to a whole system of reference. Only the notion of proper time subsists measured by the arc of the trajectory of the universe which describes a determined material point; but it is not possible to establish in a univocal way the relations between the proper times and the different material points or, what amounts to the same thing, among the four coordinates which defines the situation of an event within a certain system of reference, one is not able to say that one of them represents time.
The notion of causality becomes delicate and is made the object of a deep discussion on the part of Hilbert. Hilbert, as a mathematician, has searched for how one should particularize the choice of the system of coordinates so that one of the variables could play the role of time. It is only in static cases that the decomposition of the universe into space and time is possible, but the space thus obtained is not Euclidean. Its nature depends on that which it contains. In non-static cases the decomposition into space and into time is absolutely impossible.
One can see how much interest the theory of relativity can present for philosophers who are occupied with these obscure conceptions of space and of time. It offers another philosophical interest from an axiomatic point of view, that is to say by the nature of the axioms who serve as its basis. We have already seen that the theory of special relativity is built on the axiom of relativity understood in the Galilean sense, and on the axiom of the constance of the speed of light. Concerning general relativity, Hilbert stated two fundamental postulates: (1) All the the laws of physics can be put in a Hamiltonian form; in other words, there exists a function of quantities which characterizes the state of the universe, called tensor density of the action of the universe, whose integral is extended to a determined region of the universe which must remain stationary in the course of phenomena. This Hamiltonian principle, purely originating in mechanics, extended by Larmor to electromagnetic phenomena, is the only flotsam which has survived in the middle of the general upheaval of physics; it was thus natural to give him a privileged place. (2) The preceding integral is invariable for changes in the system of reference.
But current trends are going even further. The action still includes two parts: a geometric part relative to the gravitation by means of which the law of motion of free bodies takes a geometrical form (every body left to itself follows a geodesic in the space-time in which it is found) and a physical part, providing laws relative to phenomena other than gravitation. This physical part is incidentally electromagnetic, because all known phenomena other than gravity seem to fit into the electromagnetic framework.
To arrive at this point, it was necessary to abandon a certain number of postulates; one may be tempted to abandon new ones to go further; this is what Weyl and Eddington have done; the two parts geometric and physical were joined into one solely of a geometric nature, but the way followed by Weyl and Eddington is no longer, as with Einstein, of a purely experimental nature; the goal of which they fixed themselves, this was to find a geometry as general as possible that it could then be compared with reality. In the research of these geometries, it was essential to introduce the least possible number of postulates; as for comparison with the facts, she could not be done by means of a general method, and only trial-and-error could lead to an identification of geometric beings with physical beings. The theory of Weyl will succeed possible in giving physical meaning to all the geometric elements which it introduces; to the contrary, that of Eddington seems too general. It still contains geometric elements to which the author was unable to give a physical meaning, but perhaps these unknown elements correspond to phenomena whose existence we do not yet suspect.
To conclude, we must say that the edifice built by Einstein is the only one today that rests in a sure way on experience, which accounts for all known phenomena and which allows us to predict others.
Mr. Hadamard - The physicists today are so fluent in mathematical questions that they can do without mathematicians and the latter have nothing more to say. I will insist simply on the fact that from a logical point of view everything fits together in the theory of relativity; however, it is from the logical point of view that one is tempted to attack the theory of the current moment, because it is revolutionary and completely upsets our traditional and inherited conceptions of space and time.
When it comes to a physical theory, three questions are posed. At least that is what my philosophy professor once used to teach me:
- Is the theory logical with itself, in other words, does it contradict itself in any part?
- Is this in accordance with the facts?
- Does it agree with the facts better than the pre-existing theories?
Ah well, as as far as the first question is concerned, the mathematician cannot find the slightest contradiction in the theory of relativity; in reality, special relativity is even a logical consequence of the Maxwell-Lorentz equations; a contradiction in this theory could not exist without a contradiction in theirs. However, there is no contradiction in the equations of electromagnetism.
Questions 2 and 3 cannot concern the mathematician, and it is for the physicist to respond to them.
Mr. Einstein - I have only one word to say on the subject of Mr. Hadamard's remarks. Mr. Hadamard says that a physical theory must first be logical and then consist with experimental facts. I do not believe this is sufficient and, in every case, it is not evident a priori. To say that a theory is logical, this signifies that it is made up of symbols who are linked to each other by means of certain rules, and to say that the theory conforms to experience, signifies that one possesses the rules of correspondence between symbols and facts. Relativity is the issue of experimental necessity; this theory is logical in this sense which can be given a deductive form, but it is still necessary to know the clear rules which make its elements correspond to reality; there is then three postulates, and not two, as Mr. Hadamard thought.
Mr. Hadamard - To put it differently, that which we are examining is a logical theory and the ensemble of rules which make it correspond to reality.
Mr. Cartan - Mr. Einstein has stated the laws of the universe starting from a certain mathematical expression: the ds^2 which is a quadratic differential form with four variables. For the analyst, all interest is placed on the differential invariables which are attached to this ds^2. The geometer is especially interested in some of these simplest differential invariants, those which define what he called the curvature. As for the physicists, they are only concerns with the invariables which are susceptible to a physical interpretation; they have called them tensors. The fundamental tensor is the energy-quantity-of-movement tensor provided by experience. But geometry shows that there exists a second tensors which, equal to zero, expresses that the laws of the speed of light are the same as in special relativity; this tensor is also zero in the law of gravitation with a scalar potential. Like the matter tensor, it has ten components and is as simple as it is in the sense that it does not contain derivatives of potential of an order higher than the second, and that the derivatives of the second order enter linearly. The matter tensor presents an interest for physics. I ask Mr. Einstein if the second order is also of interest? So far it has no physical meaning, and there is a kind of disagreement between geometry and nature.
Mr. Einstein - What is this tensor?
Mr. Cartan - The components are the real and imaginary parts of the coefficients of a certain ternary quadratic form whose meaning is difficult to give in common language.
Mr. Painleve - It is certain that one cannot find a logical contradiction in the theory of special relativity, but considerable difficulties arise when one passes from one system of inertia to another. I would like to point out these absolutely essential difficulties which come from the fact that the correspondence between time and the fixed observer who changes the system of inertia is no longer univocal. This lack of univocal correspondence prevents an application of reasoning reciprocally and creates a fundamental dissymmetry. I would like to insist on this point, because I believe that no one, save Mr. Langevin, had noticed it sufficiently.
Mr. Langevin - I would like to point out this lack of symmetry, I have made stand out in the 1911 Congress of Philosophy of Bologna, as well as in my course at the College of France.
Mr. Paul Levy - The only observable realities are those which result from the presence of bodies in the universe. To simply my reasoning, let me suppose there are infinitely flat beings on the surface of a sphere. The measurements that they will make with the rules will show that they are on a surface with constant curvature. But one could tell them they are wrong, that they are on a surface with zero curvature. They will that it is their instruments that have been modified and which provide them with a non-Euclidean geometry. This is how, instead of saying that the sun creates a curvature of space, I believe it preferable to say that it modifies the rules, that these undergo a longitudinal contraction when they radially approach the sun. The question is which of these two languages is more convenient. I do not want to say that the one I propose corresponds to reality better than the other. I only fear that one attributes to the other languages an objective meaning which it does not have.
Mr. Einstein - Geometry is an arbitrary conception. one is always free to adopt that which one wants, in particular a Euclidean geometry. But the Euclidean concepts do not have physical meaning and cannot serve us physicists. More than that, the relation between the real continuum and imagined geometric space is not univocal and one cannot say that one of the ways of speaking is preferable to the other.
Mr. Langevin - The process of Mr. Paul Levy is nothing else than the representation of a non-Euclidean space on a Euclidean one. It is the process of the chart.
Mr. Paul Levy - The experiment does not make it possible to say which is the true representation.
Mr. Perrin - I agree entirely with the views of Mr. Langevin and think that the theory has the greatest importance in all the domains of physics.
Mr. Jean Becquerel - On the subject of the gravitational field of a material center, it seems interesting to me to point out a work of G. Mie, who showed that our logical representation of the universe is an orthogonal projection, in a ten-dimensional Euclidean continuum, of the continuum of Hilbert on any Minkowski universe parallel to the universe asymptotically. This interpretation leads to the Schwarzschild formula without arbitrary function. The result of Mie shows that the coordinates employed by Schwarzschild are those with which the aspect of the universe, for the physicist, becomes the most intuitive.
Mr. Einstein - One can always choose such a representation as one choose if one believe it is more useful than another for the work that one proposes, but this has no objective sense.
Mr. Brunschvicg - Mr. Einstein, in accepting the invitation of our society, has kindly indicated the problems on which he would agree to bring us some precision; he notably pointed out the relationship between the theory of relativity and the Kantian conception of science. It is in order to obtain this precision that I have been asked to speak here. And this is for me the occasion to say, simply, brutally perhaps, my emotion to greet among us a man who, by his work in science and in philosophy (and for other reasons on which I do not insist, but on which he knows well that we are thinking about), enlarges our idea of humanity. The name of Einstein has already taken rank among those geniuses who allows us to transform them according to a Platonic image, which will be particularly relevant here, the sensible light in the intelligible light.
Now, taking the Kantian world as a base of reference, I would like to try to define, in a few words, what is, for the philosophers, the scope of the transformation brought about by the discovery of the Einsteinian world.
The Kantian world has, on the one hand, a container: space and time. On the other hand, a content: matter and force. There are thus two kinds of questions to study successively: problems of container, which are the object of the "Transcendental Aesthetic"; problems of content which are the object of the "Analogies of Experience" in the "Transcendental Logic". The first concerns mathematics; the second concerns physics. The latter can only be dealt with when the former has been resolved.
The Einsteinian world is characterized by the fact that it no longer allows the separation of container and content. We are no longer dealing with the space of Kant, the intelligible norm and the receptacle of the real, which would constitute itself by itself, would close in on itself, while waiting for things to come fill it, even less to the arithmetic time, which is conceived of as empty and homogeneous, by analogy with a space which is itself empty and homogeneous. And not much more is there a universe of the physicist which would be defined by its content, independently of the spatial and temporal forms in which it takes place. Thus it is no problem which relates to the matter considered as substance in itself, or of the force considered as a cause in itself.
Now that this transformation provokes an intense intellectual joy in the philosopher, one word allows us to comprehend it. The Kantian conception threw us into antinomies; the Einsteinian conception delivers us from them. The first two antinomies of Kant are called by him "mathematical antinomies": they make evident the rational necessity and also the equally rational impossibility to conceive of the finitude of space and time, to pose a simple and indivisible element. Mathematics was thus made to pay incomparable services which are now returned to the science of physics, in the embarrassment of the inextricable difficulties of the philosophy of physics. In fact, when it was a question of deciding how one could pass from the the framework of space and time to the realities of matter and motion, one hit insoluble contradictions -- witness Descartes defining motion as a pure relation, and yet treating it as the absolute of reality -- witness Laplace relying on the Newtonian mechanics and yet conceiving of the universe as a power to dilate or retract without beings placed inside being able to perceive it, by who knows what miracle, they would be on the outside of the universe, following his own singular and striking expressions, the "observers".
However, all these embarrassments disappear, as if by magic, with the doctrines of relativity. Why? Because they do not know the pure mathematics, the space taken apart from what fills it, the time taken apart from what passes, in a word the system of measurement which would be defined as measuring. The operation of measurement consists in putting the process of measurement and the thing to be measured in a relation so close that one could not determine the characters of the one without reference to the properties, intrinsic and objective, of the other. There is no longer a philosophical problem which posed touching the entity of time, dragging itself painfully by the tug of space. The world, following Mr. Einstein, is without place and without reversal; it is constituted in one piece by the progressive correlation of mathematics and physics, which does not leave at any moment of intellectual work, to remain on hiatus, which does not involve any fissure between the position of the space-time continuum and the reality that determines its characteristics.
From this point of view, the arrival of relativity does mark a revolution - but in the literal sense of the metaphor, as an achievement of the process of thought - that we see taking space with Kantian relativism, where space, because of the paradox of symmetrical object, is a form of intuition which names a content where the cause claims the experience of an irreversible time. With Kant, already, the parallelism of ideas and things changes in connection, in reciprocity; with Mr. Einstein this connection, this reciprocity, acquires an unsuspected depth, because relativity is made to appear more abstract an expression of the reality of physics, at the same time that it specifies the meaning of pure instrument of work, which belongs to mathematics. If it is inevitable that we speak on mathematicians, we must as physicists. And then, by the solidarity henceforth established between the "Transcendental Aesthetic" and the Analytic, they would disappear, for to speak again in the Kantian language, the contradictions of the "Dialectic".
Mr. Einstein - About Kant's philosophy, I believe that every philosopher has their own Kant, and I cannot answer what you have just said, because the few indications that you have given me do not suffice for me to know how you interpret Kant. I do not believe, for my part, that my theory agrees on all points with the thought of Kant as it appears to me.
What seems to me the most important in the philosophy of Kant, is that he speaks of a priori concepts to build science. Now one can oppose two points of view: the a priori-ism of Kant in which certain concepts pre-exist in our consciousness and the conventionalism of Poincare. These two points of view agree on this point that science needs, in order to be built, arbitrary concepts. As to know if these concepts are given a priori, or are arbitrary conventions, I cannot say anything.
Mr. Le Roy - Our friend Xavier Leon urges with all force that I speak. With his amiable insistence, I could not refuse. But basically I have nothing to say; and it is this alone I will explain in two words.
For the philosopher, in whatever way, besides, he conceives of their existence, there is a space and a time, objects of intuition, which pre-exist the measure that one makes of them and which remain distinct from measurement. For the physicist, on the contrary, especially in the perspective where the theory of relativity is placed, space and time are defined by their very measurement; they are, in the end and to the letter, two sets of measurement operations. To these sets, how could one impose a priori a system of any characters, determinations, laws, or internal relationships? The point of view of the philosopher and of the physicist are one and the other legitimate; but they lead us to pose, under apparently similar terms, two problems which are in reality entirely different.
I estimate in particular that the problem of time is not the same for Mr. Einstein as for Mr. Bergon. There were several remarks to make on this point. But, Mr. Bergson being among us, this is not for me to make them, and my intervention will have had all the effect I desire if it leads Mr. Bergson himself to speak.
Mr. Bergson - I came here to listen. I did not have the intention of speaking. But I cede to the amiable insistence of the Philosophical Society.
And let me start by saying how much I admire the work of Mr. Einstein. It seems to me that it is as important to philosophers as to scientists. I see in it not only a new physics, but also, in certain respects, a new way of thinking.
A complete deepening of this work should naturally carry the theory of general relativity as well as the theory of special relativity on the question of space as well as on that of time. Since we have to choose, I would take the problem that especially interests me, that of time. And since we should not speak about time without taking into account the hour, and that the hour is quite advanced, I will restrain myself to summary indications on one or two points. It will force me to leave aside the essential.
Common sense believes in a single time, the same for all beings and for all things. Where does this belief come from? Each of us senses duration: this duration is the very flow, continuous and indivisible, of our interior life. But our interior life includes perceptions, and these perceptions seem to us to be part of the perceptions, and these perceptions seem to us to be part of both ourselves and of things. We thus extend our duration to our immediate material surroundings. As, moreover, this environment is itself surrounded, and so on indefinitely, there is no reason, we think, for our duration to not also be the duration of all things. Such is the reasoning that we outline vaguely, I would say almost unconsciously. When we bring it to a higher degree of clarity and precision, we represent ourselves, beyond what one could call the horizon of our external perception, a consciousness whose field of perception would encroach on ours, then, beyond this consciousness and its field of perception, another consciousness situated in an analogous way in relation to it, and so on, indefinitely. All these consciousnesses, being human consciousnesses, seem to us to live in the same duration. All their external experiences would thus take place in the same time. And as all these experiences, encroaching on one another, have, two by two, a common part, we end up representing from ourselves a single experience occupying a single time. From then on we can, if we wish, eliminate human consciousnesses that we had arranged from far away like so many relays for the movement of our thought: there is only the impersonal time where all things flow. Here is the same reasoning in a more precise form. Whether we remain, however, in vagueness or seek precision, in both cases the idea of a universal time, common to consciousness and to things, is a simple hypothesis.
But it is a hypothesis that I believe to be well-founded, and which, in my opinion, has nothing incompatible with the theory of relativity. I cannot undertake the demonstration of this bridge. It would be necessary first to study more much thoroughly than I have just done real duration and measurable time. It would be necessary to take one by one the terms which fit in the formulas of Lorentz and look for their concrete meaning. One would thus find that the multiple times which is the question in the theory of relativity is far from able to to pretend all have the same degree of reality. As one would advance in this study, one would see how the relativist conception, which corresponds with the point of view of science, and of the conception of common sense, which translates roughly the data of intuition intuition or consciousness, complete each other and lend each other a mutual support. It is true that it would be necessary, along the way, to dissipate a very serious confusion, to which some commonly accepted interpretations of the relativistic theory owe their paradoxical form. All this would lead us too far.
But all that I cannot establish for the time in general, I ask your permission to at least give a glimpse of it for the particular case of simultaneity. Here one will painlessly see the relativistic point of view does not exclude the intuitive point of view and even necessarily implies it.
What is usually meant by the simultaneity of two events? I will consider, to simplify it, the case of two events which would not have duration, which would not themselves be flows. This being said, it is obvious that simultaneity implies two things: (1) an instantaneous perception and (2) the possibility, for our attention, to share itself without dividing itself. I open my eyes for a moment: I perceive two instantaneous flashes starting from two points. I say simultaneous because they are one and two at the same time: one, as my act of attention is indivisible, two insofar as my attention is distributed between them and they duplicate without splitting. How can the act of attention be one or several at will? How does a trained ear perceive at each moment the global sounds given by the orchestra and still however disentangle, if it pleases, the notes given by two or several instruments. I do not take it upon myself to explain it. It is one of the mysteries of the psychological life. I simply state it; and I point out that by declaring the notes given by several instruments are simultaneous we express: (1) that we have an instantaneous perception of the ensemble; (2) that this ensemble, indivisible if we want, is divisible, if we wish it, also: there is a single perception, and there are nevertheless several. Such is simultaneity, following the sense of the word. It is given intuitively. And it is absolute, in that it does not depend on any mathematical convention, or any physical operation such as a setting of the clocks. It is never observable, I recognize this, between neighboring events. But common sense does not hesitate to extend it [simultaneity] to events as far away as one would like one from to the other. It is said, instinctively, that the distance is not absolute, that is "large" or "small" according to the point of view, according to the term of comparison, according to the instrument or organ of perception. A superman with with immense vision would perceive the simultaneity of two instantaneous events "enormously distant" as we perceive that of two "neighboring" events. When we speak of absolute simultaneities, when we represent to ourselves instantaneous slices of the universe which would gather, so to speak, definitive simultaneities between events as distant from one another as one would like, it is to this superhuman consciousness, coextensive to the totality of things, that we think.
Now, it is incontestable that the simultaneity defined by the theory of relativity is of a completely different order. Two events more or less distant, belonging to the same system S, are said here to be simultaneous when they occur at the same time, when they correspond to the same indication given by two clocks which are found respectively by each of them. Now these clocks have been set one to the other by an exchange of optical signals, in the hypothesis that the signal has the same trajectory to go out and to return. And it is without doubt, if one places themselves at the point of view of the observer inside the system, who holds it as immobile. But the observer inside another system S', in motion with respect to S, takes their own system as a system of reference, and sees the first one as the one in motion. For them, the signals that come and go between the two clocks of the System S do not have, in general, the same trajectory going outward and on the return. And consequently, for them, the events that take place in this system when the two clocks mark the same time are not simultaneous, they are successive. If one takes the simultaneity of this bias--and this is what the theory of relativity does--it is clear that the simultaneity has nothing absolute, and that the same events are simultaneous or successive according to the point of view from from which they are considered.
But, in positing this second definition of simultaneity, are we not obliged to accept the first one? Don't we implicitly admit this one next to the other one? Let us call the two events that are compared E and E', [and] H and H' the clocks respectively placed next to each of them. Simultaneity, in the second sense of the word, exists when H and H' mark the same time. And it is relative, because it depends on the operation by which these two clocks are set one to each other. But, if such is the simultaneity between the indications of the two clocks H and H', is it thus the simultaneity between the indication of clock and H and event E, between the indication of clock H' and event E'? Evidently not. The simultaneity between the event and the indication of the clock is given by the perception which unites them in an indivisible act. It consists essentially in the fact--independent of all clock-setting--that this act is one or two at will. If this simultaneity did not exist, the clocks would be useless. They would not be manufactured, or at least nobody would buy them. Because we only buy them to know what time it is and "to know what time it is" admits a correspondence not between the indication of a clock and another indication of the clock, but between an indication of the clock and the moment where it is found, the event that is accomplished, something that is ultimately not an indication of the clock.
You will tell me that the simultaneity intuitively observed between any event and this particular event which is an indication of the clock is a simultaneity between two neighboring events, very close, and that the simultaneity which you are generally concerned with is that of distant events one from the other. But, once again, where does proximity begin, and where does remoteness end? Savant microbes, posted respectively at points E and H, would find the distance between them enormous, that is to say the distance between the clock and the event which we declare "neighboring". They would build microbial clocks that they would synchronize by an exchange of optical signals. And when you come to tell them that your eye simply observes a simultaneity between the event E and the indication of the clock H which is "close" to it, they would answer: "Oh no! We do not admit that. We are more Einsteinian than you, Mr. Einstein. There will be no simultaneity between the event E and the indication of your human clock H if our microbial clocks, placed at e and H, mark the same time. And this simultaneity could be a succession for an observer external to our system; it will have nothing of the intuitive or the absolute."
I do not otherwise object to your definition of simultaneity any more than I object to the theory of relativity in general. The observations I have justed presented (or rather sketched, for I would be led far afield if I wanted to give them a rigorous form) have a completely different object. What I want to establish simply is this: once the theory of relativity is admitted as a physical theory, everything is not completed. It remains to determine the philosophical meaning of the concepts it introduces. It remains to search for the point at which one renounces intuition, at which point one remains attached to it. It remains to place the part of the real and of the conventional in the results to which it leads, or rather in the intermediaries that it establishes between the position and the solution of the problem. By doing this work which concerns time, one perceives, I believe, that the theory of relativity is not incompatible with the ideas of common sense.
Mr. Einstein - The question is posed thus: Is the time of the philosopher the same time of the physicist? The time of the philosopher, I believe, is a psychological and physical time all at once. Now physical time can be derived from the time of consciousness. Primitively, individuals have the notion of simultaneity of perception. They could get along and agree on something about which they perceive. It was a first step towards objective reality. But there are objective events independent of individuals, and one passes from the simultaneity of perceptions to the events themselves. And in fact, this simultaneity has for a long time not led to any contradiction because of the greatness of the speed of light. The concept of simultaneity could therefore pass from perceptions to objects. From there to deduce a temporal order in the events was not a far gap, and instinct made it fact. But nothing in our consciousness allows us to conclude the simultaneity of events because these are only mental constructions, logical beings. There is only a psychological time different from the time of the physicist.
Mr. Meyerson - I would like to ask Mr. Einstein for clarification on two particular points which, by the way, are less related to the substance of his conceptions than to the way in which they are often presented and the conclusions that one seems to draw from them.
So we often hear about a four dimensional universe in terms that imply that these four dimensions are similar in nature. This is not the case, of course. To realize this, we only need to state that space, with Mr. Einstein, not being a point of infinity, we must, by continuing to move in a straight line, after a very long time obviously (one billion years, we are told, at the speed limit, which is that of light), to return to the same place. It is obvious then that if it had to be the same time, we must, in a future as distant as one would want, find the present moment. It would be the very ancient conception of the Grand Year of the first thinkers of Greece and of Heraclitus in particular, a conception of which we find reflections in modern philosophers and scientists, with Nietzsche and Mr. Arrhenius, but which here would be presented with all the fullness and all the rigor that the Ancients lent it. This is not at all the opinion of Mr. Einstein, whose universe is, as you know, "cylindrical". That is to say it comprises a curvature for the three spatial dimensions, while the fourth dimension, that of time, is free from it. But it is not only this cyclical return, even in the very long term, as Mr. Einstein foresees it for space, which is impossible for time, it is -- we all know it -- any return, any backward movement. We move in time in a different way than we do in space. No doubt, since the principle of relativity, something changed in this regard. Time no longer flows uniformly for everyone, and if a traveler were to return after completing a trip accomplished at a speed of an order approaching that of light, their watch would not agree with those of the people who stayed behind. But there would however be a limit to this divergence, because this traveler could never go back in time. "One cannot telegraph into the past" Mr. Einstein rightly says to us, and the principle of entropy is, in the prodigious upheaval imposed on the conceptions that we believe by those most firmly established by the theory of relativity, one of two great principles of the old physics which remain, the other one being, as you know, that of lesser action.
The true situation, from this point of view, seems to be me to be the following. Einsteinian mechanics implies reversibility. But this is not a trait which is proper to itself. On the contrary, in classical mechanics, the phenomenon also appears reversible. In both cases it is, moreover, very obviously, a consequence of our deep tendency to spatialize time, a tendency that is here expressed by the simple statement that we use, to represent it, of a numerical duration--because any number is susceptible to be decreased as well as increased. You know that, in the field of classical mechanics, irreversibility is obtained with the help of statistical considerations. They can obviously be maintained in Einsteinian mechanics. Perhaps one can also, in this ordering of ideas, combine, as one might say, the principle of relativity [with] the quanta hypothesis. In any case, it seems appropriate to avoid, as far as this particular structure of the dimension is concerned, all equivocation and speak not about a universe with four dimensions, but rather of 3 + 1 dimensions, as Mr. Weyl did, but remembering that this discrepancy is not only related to the fact that, in the the formula of the interval, the variable of time is preceded by a sign different from those of the three spatial variables, but also, and even more importantly, to this fact of irreversibility. Our illustrious guest is enjoined himself by us to consider [this] beyond the symbols, the physical realities. Now it is here a reality in the first place, because not more in the empire of Einstein than of Newton, we will neither walk backwards nor digest before having eaten.
The second question is a little more complex. It is common enough to represent the theory of relativity as being the accomplishment, the concretization of some sort, of the program sketched by Mach. This is quite right in some respects, because, as far as the perfect relativity of motion in space, Mach was one of your genuine precursors. You will excuse me for briefly recalling to my colleagues of the Society of Philosophy of what this is all about. The whole world is familiar with the rotating vase experiment of Newton: at first, that is to say, when the wall is already revolving with a high speed, but has not yet communicated its motion to the water, the surface of this one remains flat. Then the liquid, coming to turn along the turn, rises toward the sides. It is therefore, concluded Newton, [the case] that the rotary motion is an absolute motion, that is to say, contrary to the one caused by attraction and which depends on the masses, it depends on the intimate essence of space itself. This is what Mach disputed. For him, the motion also depends on the masses present in space. If the centrifugal motion of water is apparently independent of the rotation of the walls, it is because the mass of these is relatively small. "Nobody could say what would happen if the walls become more and more massive until they reached, for example, a thickness of several kilometers." It is on this point that Mr. Einstein's theory added precision to Mach's conception. In effect, here gravity and inertial motion, instead of being entirely separate, as with Newton, are found to the contrary to be intimately combined, and one arrive at a calculation of what the masses would have to be to move around a body to provoke in it manifestations of a centrifugal force perceptible to our instruments of measure.
But this aspect of Mach's theory, however highly interesting it may be, is not his principal point, and if we want to qualify the set of conceptions of this thinker of relativists, it is by thinking of something different from the relativity of space. Mach is, in effect, above all a successor to Auguste Comte. For him, as for the founder of positivism, science is only a collection of rules, of laws. It only knows and ought to search for the definition of relationships, the relations between things and it must resolutely set aside all that aims at knowledge of things themselves, know which is declared metaphysical. Besides, you know that positivism, since the first disciples of Auguste Come, has often tried to force entry in a close rapport with an extreme idealism (such as in Taine, for example, with the doctrine of Hegel), by connecting the non-research of the thing to its non-existence outside consciousness. It must not surprise us, the confusion that favors the use of the somewhat ambiguous term of relativity, it is not surprising to see the supporters of this doctrine trying to find support in the conceptions of Mr. Einstein, in proclaiming that relativity of space proves the relativity of our knowledge in any order of ideas and shows us, consequently, to what extent it would be in vain to penetrate into the interiority of things, as the atomic theories pretend to do. There indeed is the real crucial point of the whole question. Comte, pushed by his powerful scientific instinct, had, by a happy illogic, declared atomism a "good theory". But already John Stuart Mill had perceived that, in order to follow the principles of positivism with more rigor, one must abstract the object and seek to establish direct relations between our sensations, and Mach showed himself resolutely hostile to atomic theories. For him, as for the energistic school that followed him, the ideal of a science is thermodynamics because it seems to renounce any figuration of matter which it deals with and limits itself to deducing its statements from two abstract principles. This attitude was manifest in a very pronounced way in the last years of the nineteenth century and at the beginning of the current century, when the discoveries which revealed the discontinuity of matter and thus provoked a return to atomistic conceptions. In the eyes of the energists, this powerful evolution, which constituted an immense progress of knowledge, appeared as a disastrous setback. I will not try here to show you to what extent these pretensions on which, you all know, science has passed resolutely to the order of the day, were vain. I will limit myself to note that between Mach's conceptions in this order of ideas and the theory of Mr. Einstein there seems to be no really intimate or necessary link. One could well be a partisan supporter of the relativity of space and still be convinced nevertheless, as Malebranche had established, that no science is possible without posing, beforehand, the object remaining outside consciousness, and that, consequently science could not dispense with specifying how it conceives of this object through the modifications which the progress of our knowledge imposes on this image. It seems to me, moreover, that the attitude of Mr. Einstein himself confirms this way of seeing. In effect, this evolution toward atomism which I mentioned earlier and which has so displeased the good-natured energists, Mr. Einstein has powerfully contributed to this. In 1905, almost at the same time as his first work on relativity, he published an essay where, without knowing the results of Gouy, nor, in general, Brownian motion, he determined the amplitude of molecular motion, and his formulas were then, as is well known, used by Mr. Perrin. In the same way, when the Council of Physics in 1911, then with regard to the phenomena of black radiation, so strange, so embarrassing for the atomic physicists, a purely phenomenist attitude had been expressly suggested to the assistants. On the contrary, Mr. Einstein insisted with great clarity on the necessity to represent that which we know of these phenomena "in a concrete form" that is to say by a figuration in space with the help of a mechanism which is really able to explain the observations. He moreover, reasserted that this image had to be as complete and as coherent as possible and pointed out the difficulties and implausibilities which one runs up against in this order of ideas by adopting the hypothesis of Mr. Planck. I do not thus believe that I am going too far to assume that Mr. Einstein is himself far from sharing, in this domain, the opinions of Mach. But I believe that, the particular point of interest which this question presents, is not only a point of view of the theory of our scientific knowledge, of epistemology, but also from the point of view of philosophy in general, and given also the possibility of the confusion of which I spoke, some clarifications from the mouth of the same author of relativity.
Mr. Einstein - In the continuum of four dimensions it is certain that not all directions are equivalent. On the other hand, there does not seem to be much relation from the logical point of view between the theory of relativity and Mach's theory. For Mach there are two points to distinguish: on the one hand, there are things which we cannot touch. They are the immediate data of experience. On the other hand, there are concepts that we can on the contrary modify. Mach's system studies the relations which exist between the data of the experiment. The set of these relations is, for Mach, science. This is a wrong point of view. In short, what Mach has made is a catalogue and not a system. As much as Mach was a good mechanic, he was also a deplorable philosopher. This short-sighted view of science led him to reject the existence of atoms. It is likely that if Mach were still alive today, he would change his mind. However, I would like to say that, on this point: concept can change--I am in complete agreement with Mach.
Mr. Pierson - I would like, with regard to the enticing confrontation between psychological duration and Einsteinian time, point out that there are cases where this confrontation is experimentally realized, when the psycho-physiologist studies, by a scientific method, the impressions of duration, of succession, of simultaneity.
However, for a very long time, astronomers had already recognized that it was impossible to rely on psychological simultaneity to determine precisely a physical simultaneity, when it was a question, by the method of eye and ear, of specifying the position of a star in the reticule of a telescope at the moment of a pendulum's beat. This indeed the type of concrete experiment pointed out by Mr. Bergson to show the possible intervention of the impressions of duration in determinations relative to physical time.
Now, we know that it is physiologically impossible to obtain an exact mental translation from a physical simultaneity between heterogeneous sense-impressions. In effect, the latency of transformation of the external stimulus into nerve impulses and the time of the propagation of this influx, change with the regions of the body and the organs of the senses put into play, without counting cerebral variations, complex and irregular. But there is more, let us suppose that two points of the retina receive luminous impressions. It seems that, in these conditions, the perceived simultaneity will be a certain hint, within the limits of a given approximation, of physical simultaneity. But it is enough that the luminous impressions have a different intensity for it [to appear] to be nothing. I was able to determine a difference of the intensities such as the weakest luminous excitation, physically preceding the strongest by a few hundredths of a second, which is in reality notably perceived as posterior. Thus the determinations of succession or psychological simultaneity cannot in any case be used for a measurement of physical time, which requires a spatial translation, following a scientific rule which Mr. Bergson has rightly brought to light. It is by the coincidence or the non-coincidence of lines left by the coincidence of lines left by signal-devices on a surface animated by a faster or slower movement that we judge it to be physical simultaneity. taking into account all the useful correction. For these measurements of time as for all the others, it is visual acuity which intervenes. ANd thus the Bergsonian duration seems to me to remain foreign to physical time in general and particularly to Einsteinian time.
Mr. Bergson - I am entirely in agreement with Mr. Pieron: the psychological observation of a simultaneity is necessarily imprecise. But, to establish this point by laboratory experiments, it is necessary to resort--imprecise still-- to statements of psychological simultaneity: without them no reading of the apparatus would be possible.
Translation completed with assistance from DeepL.
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