CHAPTER IX

CHAPTER IXEINSTEIN OR NEWTON?

EINSTEIN OR NEWTON?

Recent discussion of Relativism at the Academy of Sciences—Traces of the privileged space of Newton—The principle of causality the basis of science—Examination of M. Painlevé’s objections—Newtonian arguments and Relativist replies—M. Painlevé’s formulæ of gravitation—Fecundity of Einstein’s theory—Two conceptions of the world—Conclusion.

What are these “special signs” by which the Newtonian conception of nature recognises that we are in touch with the privileged space which Newton called absolute space, and which seemed to him the real, intrinsic, exclusive frame of phenomena?

These signs or criteria are implicitly at the root of the development of classic science, but they for a time remained in the shades of the discussions provoked by Einstein’s theory. Leaving aside for a moment other, and perhaps less noble, cares, M. Paul Painlevé, addressing the Academy of Sciences at Paris, has with brilliant success drawn attention to the arguments, ancient yet ever robust, which constitute the strength of the Newtonian conception of the world.

Let us from this point speak of the absolute time and space of Newton and of Galileo as privileged space and privileged time, in order not to expose our flanks further to the metaphysical objections—not without justification—which the qualification “absolute” provokes.

Why is classical science, the mechanics of Galileo and Newton, founded upon privileged space and privileged time? Why do they refer all phenomena to these unique standards, and consider them adequate to reality? It is on account of the principle of causality.

The principle may be formulated thus: Identical causes produce identical effects. That means that the initial conditions of a phenomenon determine its ulterior modalities. It is briefly a statement of the determinism of phenomena, and without that science is impossible.

It is, of course, possible to be captious on the point. Conditions entirely identical with given initial conditions can never be reproduced or discovered at a different time or in a different place. There is always some circumstance that will be different; for instance, the fact that in the interval between the two experiments the Nebula in Andromeda will have come several thousand miles nearer to us. And we have no influence on the Nebula in Andromeda.

Happily—this saves the situation—distant bodies have, it seems, only a negligible influence on our experiments. That is why we can repeat them. For instance, if we to-day put a gramme of sulphuric acid in ten grammes of soda-solution (one-tenth), they will in the same period of time produce the same quantity of sulphate of sodium that they would have done a year previously in the same conditions of temperature and pressure; in spite of the fact that meantime Marshal Foch sailed for the United States.

Thus the principle of causality (like causes, like effects) is always verified, and never found at fault. It is therefore an empirical truth, but in addition to this it imposes itself on our mind with irresistibleforce. It even imposes itself upon animals. “The scalded cat avoids hot water,” is proof enough. In any case, not science only but the whole life of man and animals is based upon it.

It is a consequence of the principle that if the initial conditions of a movement present a symmetry, this will appear again in the movement. M. Paul Painlevé insisted strongly on this in the course of the recent discussion of Relativism at the Academy of Sciences. The principle of inertia in particular follows from this statement: a body left to itself far from any material mass will, by reason of symmetry, remain at rest or travel in a straight line.

It will certainly follow a straight line for a given observer (or for observers moving with uniform velocities relatively to the first). The Newtonians say that the space of these observers is privileged.

On the other hand, for another observer who is, relatively to them, moving at an accelerated velocity, the path of the moving body will be a parabola, and will no longer be symmetrical. Therefore the space of this new observer is not privileged space.

It seems to me that the Relativists might reply to this as follows. You have no right to define the initial conditions for a given observer, then the subsequent movement for another observer who is moving with accelerated velocity. If you thus define your initial conditions relatively to the latter, the moving body at the moment when it is released is not free for this observer, but falls in a gravitational field. It is therefore not surprising that the motion produced seems to him accelerated and dissymmetrical. The principle of causality is not wrong for either observer.

One might also give a different definition of the privileged system,saying: it is that relatively to which light travels in a straight line in an isotropic medium. But in that case the rays from the stars travel in a spiral for an observer fixed on a turning earth, and the Newtonians would infer from this that the earth turns relatively to their privileged space. Einsteinians will reply that the space in which the rays travel is not isotropic, and that they are diverted from the straight line in it by the turning gravitational field which causes the centrifugal force of the earth’s rotation. They will always find an escape which will leave the principle of causality intact.

It seems difficult, therefore, to give unanswerable proof of the existence of the privileged system when we start from the principle of causality. Each party retains its position.

On the other hand, there is evidential value, a keen and convincing penetration, in the second part of the criticism which M. Painlevé directs against the principles of Einstein’s theory.

Let us sum up the argument of the distinguished geometrician. You, he says to the Einsteinians, deny all privilege to any system of reference whatever. But when you want to deduce, by calculation, the law of gravity from your general equations, you cannot do it, and you really do not do it, except by introducing scarcely disguised Newtonian hypotheses and privileged axes of reference. You only reach the result of your calculation by sharply separating time and space as Newton does, and by referring your gravitating moving objects to purely Newtonian privileged axes, in the case of which certain conditions of symmetry are realised.

To this fine and profound criticism which M. Painlevé raises may be added that of Wiechert, who has pointed out various other hypotheses introduced by Einstein in the course of his calculations.

In a word, Einstein seems not to have kept entirely clear of the Newtonian premises which he repudiates. He has not the disdain for them that one would suppose, and he does not hesitate to have recourse to them occasionally for the purpose of helping out his calculations. That is rather to pay a little reverence to the idols you have burned.

In reply the Einsteinians will doubtless say that, if they introduce Newtonian axes in the course of their arguments, it is to make the results of calculation comparable to the result of experimental measurements. The axes introduced into their equations have for the Relativists the sole privilege of being those to which experimenters refer their measurements. But we must admit that that is no small privilege.

That is not all. The principle of General Relativity amounts to this: All systems of reference are equivalent for expressing natural laws, and these laws are invariant to any system of reference to which they are related. That means in effect: There are relations between objects of the material world which are independent of the one who observes them, and particularly of his velocity. Thus, when a triangle is drawn on paper, there is something in the triangle which characterises it and which is identical, whether the observer passes very quickly or very slowly, or at any speed and in any direction whatever, beside the paper.

M. Painlevé observes, with some reason, that in this form the principleis a sort of truism. It is a severe verdict, yet it expresses a certain fact. The real relations of external objects cannot be altered by the standpoint of the observer.

Einstein replies that it is at all events something to have provided a sieve by which we may sift the laws and formulæ which serve to represent the phenomena that have been empirically observed: a criterion which they must pass before they are recognised as correct. This is true. Newton’s law, in its classic form, did not meet this criterion. This proves that it was not quite so obvious. A truth that was unknown yesterday has become to-day a truism. So much the better.

In expressing one of the conditions which must be satisfied by natural laws the theory of Relativity at least has what is called in philosophical jargon a “heuristic” value. But it is none the less true, as M. Painlevé points out with great force and clearness, that the principle of General Relativity, considered in this light, would be unable to provide precise laws. It would be quite consistent with a law of gravity in which the attraction would be in inverse proportion, not to the square, but to the seventeenth or hundredth power, or any power whatever, of the distance.

In order to extract the correct law of gravitation from the principle of General Relativity we have to add to it the Einsteinian interpretation of the result of the Michelson experiment—to wit, that relatively to any observer whatsoever light travels locally with the same velocity in every direction. We have also to add various hypotheses which M. Painlevé regards as Newtonian.

To the critical discussion of Relativity which he so brilliantlypresented at the Academy of Sciences M. Paul Painlevé added a valuable mathematical contribution of which the chief result is the following: It is possible to excogitate other laws of gravitation than that offered by Einstein, and all of them will fulfil the Einsteinian conditions.

The learned French geometrician indicated several of these, especially one of which the formula differs considerably from that of Einstein, yet equally and precisely explains the motions of the planets, the displacement of the perihelion of Mercury, and the deviation of rays of light near the sun.

This new formula corresponds to a space that is independent of time, and it does not involve the consequence that Einstein’s formula does in regard to the shifting toward the red of all the lines in the solar spectrum. The verification or non-verification of this consequence of Einstein’s equation, of which we pointed out the difficulties (perhaps insurmountable) in a previous chapter, thus acquires a new importance.

It is a remarkable thing that many of the formulæ of gravitation given by M. Painlevé lead to the conclusion, differently from that of Einstein, that space remains Euclidean even near the sun, in the sense that measures are not necessarily contracted.

All this light on the astronomical horizon seems like the dawn of a new era in which observations of unprecedented delicacy will provide tests that are calculated to give a more precise and less ambiguous form to the law of gravitation. There are great days—or, rather, great nights—in store for the astronomer.

As far as the principles are concerned, the controversy will go on. It must end in something like the following dialogue:

The Newtonian: Do you admit that at a point in the universe that is far away from all material masses a moving object left to itself must follow a straight line? If so, you recognise the existence of privileged observers—those for whom the line is straight. For another observer the line is a parabola. Therefore his point of view is wrong.

The Relativist: Yes, I grant it; but in point of fact there is no point in the universe where there is no influence of distant material masses. Therefore your moving object left to itself is a mere fiction, and I am not going to base science upon an unverifiable piece of imagination. The whole aim of the Relativist is to rid science of everything that has no experimental significance. As to the observer who sees the moving object in question describe a parabola, he will interpret his observation to mean that the object is in a gravitational field.

The Newtonian: You are therefore compelled to admit that far away from all matter, far from all heavenly bodies, there can be what you call a gravitational field, that it varies according to the velocity of the observer, and that it can be very intense in spite of the distance of the heavenly bodies, and even, at times, increase with that distance. These are strange and absurd hypotheses.

The Relativist: They are strange, but I defy you to prove that they are absurd. They are less absurd than to localise and set in motion a point that is isolated and independent of any material mass.

The Newtonian: For my part, I can easily imagine a single material point in the universe having a certain position and a certain velocity in it.

The Relativist: For my part, on the contrary, if such a material point existed, it would be absurd and impossible to speak of its position and its motion. It would have neither position nor motion nor rest. Such things can exist only with reference to other material points.

The Newtonian: That is not my opinion.

The Impartial Spectator: In order to know which of you is right we should need to try an experiment on a material point that is withdrawn from the influence of the rest of the universe. Can you try this experiment?

The Newtonian and the Relativist(together): No, unhappily.

The Metaphysician(coming up like the third thief in the fable): Then, gentlemen, I advise you to return to your telescopes, your laboratories, and your tables of logarithms. The rest is my affair.

The Newtonian and the Relativist(together): In that case we are quite sure we shall never learn anything further about it than we know or believe now.

Meantime, it is impossible to exaggerate the importance of the new light thrown on the question of Relativity by the intervention of M. Paul Painlevé at the Academy of Sciences. It will have a lasting and prodigious echo.

Will Einstein’s fine synthesis be defeated? Shall we see it sink in the controversies, doubts, and obscurities of which we have given a short account? I think not.

When Christopher Columbus discovered America, it was all very well to tell him that his premises were wrong, and that if he had not believed that he was sailing for the Indies he would never have reached a newcontinent. He might have replied, after the style of Galileo: “I discovered it, for all that.” The method that gives good results is always a good method.

When we have to plunge into the depths of the unknown to discover something new, when we have to learn more and better, the end justifies the means. When he reminds us of optics, mechanics, and gravitation, now bound up together in a new sheaf, of the deviation of light by gravity which he foretold against all expectation, of the anomalies of Mercury which he was the first to explain, and of his improvement of the Newtonian law, Einstein has the right to say, with some pride: “There is what I have done.”

It is said that the paths by which he attained all these fine results are not devoid of unpleasant false turns and quagmires. Well, there are many ways to Rome and to truth, and some of them are not perfect. The main thing is to get there. And in this case the truth means ancient facts brought into a new harmony, and new facts set forth in prophetic equations and verified in the most surprising manner.

If discussion of principles—if theory, which is only the servant of knowledge—shrugs its servile and disloyal shoulders a little over Einstein’s work, at all events experience, the sole source of truth, has justified him. Brilliant formulæ that Einstein had not foreseen are now discovered to explain the anomaly of Mercury and the deviation of light. It is good: but we must not forget that the first of these correct formulæ, that of Einstein, went boldly in advance of the verification.

New trenches have been won in the war against the eternal enemy, the unknown. Certainly we have now to organise them and create more directroads to them. But to-morrow we shall have to advance again, to gain more ground. We shall have, by any theoretical device that we can, to state other new facts, unknown but verifiable facts. That is what Einstein did.

If it is a weakness of Einstein’s teaching to deny all objectivity, all privilege, to any system of reference whatever, while utilising such a system for the necessities of calculation, it was at all events a weakness shared by the great Poincaré. To the day of his death he rebelled energetically against the Newtonian conception. The support of such a genius, whom one finds involved in all our modern discoveries, is enough to secure some respect for the Relativist theory.

If we have on the one side Newton and his ardent and persuasive apologist, equipped with a fine mathematical genius, Paul Painlevé, we have on the other side Einstein and Henri Poincaré. Even in earlier history we have Aristotle against Epicurus, Copernicus against the Scholastics, at the same barricade. It is an eternal war of ideas, and it may be endless if, as Poincaré believed, the Principle of Relativity is at the bottom only a convention with which experience cannot quarrel because, when we apply it to the entire universe, it is incapable of verification.

It is the fertility of the Einsteinian system which proves that it is strong and sound. Are the new beings with which it has peopled science—the discoveries predicted by it—legitimate children? The Newtonians say that they are not. But in properly ordered science, as in an ideal State, it is the children that matter, not their legitimacy.

At all events the vigorous counter-offensive of M. Painlevé has driven back to their lines the over-zealous apostles of the new gospel, whothought that they had pulverised classic science beyond hope of recovery. Each side now remains in its positions. There is no longer any question of regarding the Newtonian conception of the world as a piece of childlike barbarism. A different conception is now opposed to it—that is all. The war between them is as yet undecided, and may remain for ever undecided, as the weapons with which it might be possible to bring it to an issue are sealed up for ever in the arsenal of metaphysics.

Whatever may happen, Einstein’s teaching has a power of synthesis and prediction which will inevitably incorporate its majestic system of equations in the science of the future.

M. Émile Picard, perpetual secretary of the Academy of Sciences, and one of the luminous and profound thinkers of our time, has asked if it is an advance “to try, as Einstein has done, to reduce physics to geometry.” Without lingering over this question, which may be insoluble, like all speculative questions, we will conclude with the distinguished mathematician that the only things which matter are the agreement of the final formulæ with the facts and the analytic mould in which the theory casts the phenomena.

Considered from this angle, Einstein’s theory has the solidity of bronze. Its correctness consists in its explanatory force and in the experimental discoveries predicted by it and at once verified.

What changes in theories are the pictures we form of the objects between which science discovers and establishes relations. Sometimes we alter these pictures, but the relations remain true, if they are based upon observed facts. Thanks to this common fund of truth, even the mostephemeral theories do not wholly die. They pass on to each other, like the ancient runners with their torch, the one accessible reality: the laws that express the relations of things.

To-day it happens that two theories together clasp the sacred torch. The Einsteinian and the Newtonian vision of the world are two faithful reflections of it: just as the two images, polarised in opposite directions, which Iceland spar shows us in its strange crystal both share the light of the same object.

Tragically isolated, imprisoned in his own “self,” man has made a desperate effort to “leap beyond his shadow,” to embrace the external world. From this effort was born science, and its marvellous antennæ subtly prolong our sensations. Thus we have in places approached the brilliant raiment of reality. But in comparison with the mystery that remains the things we know are as small as are the stars of heaven compared with the abyss in which they float.

Einstein has discovered new light for us in the depths of the unknown. He is, and will remain, one of the light-houses of human thought.

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Footnotes:[1]Albert Einstein, born in 1879, is a German Jew of Würtemberg. He studied in Switzerland, and was an engineer there until 1909, when he became professor at Zurich University. In 1911 he passed to Prague University, in 1912 to the Zurich Polytechnic, and in 1914 to the Prussian Academy of Science. He refused to give his name to the manifesto in which ninety-three professors of Germany and Austria defended Germany’s war-action.—Trans.[2]Physics, bk. iv, ch. xiv.[3]De Natura Rerum, bk. i, vv. 460 ff.[4]It is assumed that the ship is not rolling or pitching, and that there is no vibration in the train.[5]The best definition of the second that can be given is the following: it is the time which light takes to cover 186,000 miles in empty space and far from any strong gravitational field. This definition, the only strict definition, is further justified by the fact that there is no better means of regulating clocks than luminous or Hertzian (which have the same speed) signals.[6]In the geometrical calculus or representation that may be substituted for this the hypotenuse of the triangle is the distance in time, each second being represented by 300,000 kilometres.[7]As an example of an identical force acting during periods of time successively equal to 1, 2, or 3, we may take three guns of the same calibre, but of lengths equal to 1, 2, and 3, and of which the charges, or rather, their propulsive forces, are identical and constant. It is found that the initial velocities of the shells are, in relation to each other, 1, 2, and 3.[8]De Natura Rerum, bk. ii, vv. 235-40.[9]It is obvious that we assume the projectile to be without rotation: that is to say, the Columbia cannon must not, in our hypotheses, be rifled. This is indispensable, for if the projectile turned, there would be centrifugal effects which would greatly complicate both the phenomena and our argument.[10]It goes without saying that in all this we assume that the luminous ray travels in a homogeneous medium.[11]We are, of course, imagining the earth as perfectly circular, without irregularities.[12]It goes without saying that we assume the observer to have a retina with instantaneous impressions.

Footnotes:

[1]Albert Einstein, born in 1879, is a German Jew of Würtemberg. He studied in Switzerland, and was an engineer there until 1909, when he became professor at Zurich University. In 1911 he passed to Prague University, in 1912 to the Zurich Polytechnic, and in 1914 to the Prussian Academy of Science. He refused to give his name to the manifesto in which ninety-three professors of Germany and Austria defended Germany’s war-action.—Trans.

[2]Physics, bk. iv, ch. xiv.

[3]De Natura Rerum, bk. i, vv. 460 ff.

[4]It is assumed that the ship is not rolling or pitching, and that there is no vibration in the train.

[5]The best definition of the second that can be given is the following: it is the time which light takes to cover 186,000 miles in empty space and far from any strong gravitational field. This definition, the only strict definition, is further justified by the fact that there is no better means of regulating clocks than luminous or Hertzian (which have the same speed) signals.

[6]In the geometrical calculus or representation that may be substituted for this the hypotenuse of the triangle is the distance in time, each second being represented by 300,000 kilometres.

[7]As an example of an identical force acting during periods of time successively equal to 1, 2, or 3, we may take three guns of the same calibre, but of lengths equal to 1, 2, and 3, and of which the charges, or rather, their propulsive forces, are identical and constant. It is found that the initial velocities of the shells are, in relation to each other, 1, 2, and 3.

[8]De Natura Rerum, bk. ii, vv. 235-40.

[9]It is obvious that we assume the projectile to be without rotation: that is to say, the Columbia cannon must not, in our hypotheses, be rifled. This is indispensable, for if the projectile turned, there would be centrifugal effects which would greatly complicate both the phenomena and our argument.

[10]It goes without saying that in all this we assume that the luminous ray travels in a homogeneous medium.

[11]We are, of course, imagining the earth as perfectly circular, without irregularities.

[12]It goes without saying that we assume the observer to have a retina with instantaneous impressions.

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