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 irresistible
force. 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 principle
is 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 brilliantly
presented 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 new
continent. 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 direct
roads 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, who
thought 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 most
ephemeral 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.
_Printed in Great Britain by
Hazell, Watson & Viney, Ld.,
London and Aylesbury._