Newton’s law, but the correction is trifling except in rare cases. But
Einstein’s _theory_ of gravitation is fundamental and far-reaching
and if it is substantiated it will revolutionize physics and radically
affect our ordinary conceptions of the universe. The verification of a
prediction does not necessarily prove the truth of the hypothesis that
led to the prediction. Many a scientific discovery has come out of a
false assumption. Just as a miner may reopen an abandoned gold mine
or work over his dump heap to get more out of it, so scientists often
return to an old theory which they had abandoned for a more fruitful
hypothesis.
THE WEIGHT OF LIGHT
It is interesting to see that our modern physicists show a disposition
to adopt a corpuscular or emission theory of light not unlike the
conception which Newton steadfastly and vainly defended against the
undulatory theory. Professor Thomson, of Cambridge, reminds us that the
crucial experiment between the two theories was the test made by Bennet
in 1792 to determine if light exerted any pressure on a body when it
struck it as it would if light consisted of minute particles driven
straight forward with great velocity. Bennet found no such pressure
and the corpuscular theory was regarded as disproved. But it was later
found that the undulatory theory also involved such a pressure, and
recent experimenters have proved and measured it. As Professor Thomson
says:
It is perhaps fortunate that Bennet had not at his command more
delicate apparatus. Had he discovered the pressure of light, it would
have shaken confidence in the undulatory theory and checked that
magnificent work at the beginning of the last century which so greatly
increased out knowledge of optics.
Of course any modern form of the emission theory of light must
account, as Newton’s did not, for such phenomena as interference and
polarization, which are so satisfactorily handled by the undulatory
theory. That is, it must combine the best features of both. Professor
Thomson shows that only an exceedingly small fraction of the ether is
concerned in the forward movement of light, in other words, “the wave
front must be more analogous to bright specks on a dark ground than to
a uniformly illuminated surface.” He does not, however, go so far as
Planck in regarding it as proved that radiant energy of all kinds has
a unit or atomic structure, the color of the light depending on the
size of these particles.
The discovery of the pressure of a beam of light has led to some
startling conclusions. For example, what shall be done with Newton’s
law that action and reaction are equal? When a gun is fired the kick of
the gun is balanced by the momentum of the projectile. When a reflector
throws a beam of light into space, the kick of it is there all right
but where is the projectile, if light is merely the undulation of an
imponderable fluid? We may suppose that the light strikes some dark
body out in space, transmits its impulse to that and Newton’s laws is
satisfied, but it may be a long time before such a body is encountered
and it may never be: at any rate a law that remains in a state of
innocuous desuetude for several thousand years is not good for much.
We must then assume that light has mass since it has inertia and
momentum. But if light has mass it must have weight; that is, it must
be attracted by gravitation. The eclipse observations confirmed this
deduction. Newton would have expected something of this, for he says in
his _Opticks_:[6]
Query 1.--Do not Bodies act upon Light at a distance, and by their
action bend its Rays, and is not this action (_caeteris paribus_)
strongest at the least distance?
The observed deflection of light due to the sun’s gravitation is
greater than Newton would have anticipated but it would have been still
more disconcerting to the nineteenth-century physicists, for in giving
up Newton’s emission theory they had come to regard light as merely a
form of motion in a weightless medium, the ether. Disembodied energy,
like heat and light in ethereal space, was regarded as having no mass
or weight. Twentieth-century physicists are coming to the opposite
view, that the mass of a body is the measure of its internal energy.
If so, mass is not constant but changes with composition, temperature,
structure, electrification and motion.
As Einstein himself expresses it:
It is evident that it is not possible to attribute an absolute
sense to the notion of acceleration, no more than to the notion
of velocity. It is only possible to speak of the acceleration of
a material point in connection with a body taken as the body of
reference. It follows from this that there is no sense in attributing
to a body a “resistance to acceleration” in the absolute sense, like
the resistance of inertia in the classical mechanics. Further, this
resistance of inertia ought to be so much the greater when there is,
in the neighborhood of the body, more inert masses not in accelerated
movement. On the other hand, this resistance ought to disappear when
these masses participate in the acceleration of the body.
Now it is altogether remarkable that the equations of the
gravitational field contain these different aspects of the resistance
of inertia, which one might call the _relativity of inertia_.
The progress of science is continually toward a dematerialization
of matter. Physical analysis resolves the crude, heavy, solid stuff
that our senses show us into finer and finer particles farther and
farther apart until these practically disappear into mere points of
irradiating influence. First the mass is divided into the molecule and
this again into the atom, assumed, at the time it was invented, to be
the ultimate unit of matter. But recently the atom has been shown to
be a sort of solar system, but more complex, composed of hundreds of
electrons, corpuscles of electricity, whose radius is calculated to be
1/10,000,000,000,000 of a centimeter (a centimeter is so ---- long).
“But the size of the centers of disturbance, which in Einstein’s theory
are associated with matter, bears to the size of the electron about the
same proportion as the size of the smallest particle visible under the
most powerful microscope to that of the earth itself.”[7]
The old axiom was, “matter cannot act where it is not.” The new version
might rather read: “matter cannot act except where it is not.” That is
to say, attention is now directed to the space surrounding a material
body or electrical corpuscle.
Although we laymen are not concerned with the niceties of astronomical
measurements there is an aspect of this conflict of theories that
does interest us. The theory of Newton or, to go back further, of
Galileo, that the earth moves around the sun, altered profoundly the
philosophical and religious beliefs of the world, and the theory
of Einstein is much more far-reaching and revolutionary in its
metaphysical implications than the former. Professor Planck, who has
just received the Nobel Prize for his discoveries in physics, said of
Einstein’s first paper:
It surpasses in boldness everything previously suggested in
speculative natural philosophy and even in the philosophical theories
of knowledge. Non-Euclidean geometry is child’s play in comparison....
The revolution introduced into the physical conceptions of the world
is only to be compared in extent and depth with that brought about by
the Copernican system of the universe.
MUTABLE THEORIES AND STABLE FACTS
There is a feeling very prevalent among the general public interested
in such things that the foundations of modern science are being swept
away by the recent discoveries. The layman has been led to believe
that such laws as gravitation, the conservation of matter and the
immutability of the elements are the most certain and absolute truths
of science. But now he hears reputable men of science talk calmly about
the decay of matter and the transformation of one element into another,
and gravely consider a theory which makes invalid Newton’s three laws
of motion. It surprises, even shocks, him, as much as it would to
have a convention of bishops discuss the question of whether there
is a God, or the Supreme Court agree to set aside the Constitution
of the United States, or a congress of physicians resolve that all
medicine does more harm than good. He knows that the mere broaching of
such heretical views in these assemblies would be met with a storm of
indignation and that all the weapons of contempt, ridicule and even
personal spite would be directed against the rash innovator. Therefore
he is astonished and puzzled to see that in the scientific world these
revolutionary theories are received with interest and even pleasure,
and in the criticism to which they are subjected there is scarcely a
trace of animosity. And he does not see why men of science who have
accepted doctrines apparently contradictory to their former teachings
do not appear shamefaced and apologetic before the public, like augurs
whose tricks had been exposed.
The difficulty of the layman arises from his not understanding how a
scientist looks at his science; not realizing how firmly he holds to
its facts and how loosely he holds to its theories. The scientist never
bothers his head with the question whether a particular theory is true
or false. He considers it simply as more or less useful, more or less
adequate, succinct and comprehensive. A theory is merely a tool, and
he drops one theory and picks up another at will and without a thought
of inconsistency, just as a carpenter drops his saw and picks up his
chisel. He will say that the earth moves around the sun one moment, and
the next will revert to the theory of Chaldean astronomers, because it
is more convenient, and say “the sun rises.”
Really, the new discoveries are not so upsetting to science as they
appear to the general public. Unexpected and revolutionary as they are,
no page of millions that record the experiments and observations of
science is invalidated. No man’s work is proved wrong. Revolutions in
science do not destroy; they extend.
In the reaction of public opinion toward any novel and revolutionary
idea there are three stages observable.
1. That it is not true.
2. That it is not new even if it is true.
3. That it does not make any difference anyhow.
The first is merely the natural and instinctive reaction against any
disturbing intellectual innovation. It is a flat denial inspired by
that unconscious neophobia or xenophobia that possesses all of us
more or less. The second stage is the effort at compromise in which
usually both the advocates and opponents of the new idea coöperate by
endeavoring to prove that it is not so novel and unprecedented as was
at first assumed but fits in very fairly with our accepted notions, in
fact may be regarded as a supplement or even a natural development of
them. The third stage, like the second, is designed as an attempt to
disarm opposition by allaying alarm in the conservative mind.
The second line of argument has a good deal of validity, for even the
most startling and original idea will be found on closer examination
to have its roots deep in the ground of the past and to have been
approximately anticipated many times before. The third line of argument
also contains some truth for we find everyday life does go on in much
the same way, although it may seem that the foundations have been
knocked from under our mental, moral or social universe by some new
notion. Yet as the popular mind gradually accepts and adapts itself to
the novel conception we generally find that its influence is even more
far-reaching than was at first anticipated.
In the case of the Copernican theory it took about two centuries for
the controversy to pass through the three stages and the mind of the
public to become readjusted to the new conception of the earth’s
revolution. In the case of the Darwinian theory of evolution the
process was accomplished in about fifty years. The Einstein theory
is more subversive of ordinary ideas than either of the others so it
would naturally take longer to soak in. But the modern mind seems to
be subject to acceleration and we see in the two months since the
notion has been sprung upon the public that all three of the lines of
argument are appearing at once and so the controversial period may run
its course in five years though it will be longer before its indirect
influence upon our fundamental philosophy and habits of thought are
fully felt.
SCIENTIFIC VERSUS LEGAL LAWS
In all such discussions we must bear in mind that “law” in the
scientific sense of the word means, not a commandment or a rule, but
merely a way of working. It is a concise description of how things
behave. There are no laws _in_ Nature; there are only laws
_of_ Nature; that is to say, laws drawn out of Nature (or, if you
prefer Latin to Anglo-Saxon, laws deduced from Nature) by man for his
own convenience in thinking. Physical laws are therefore essentially
psychological; mere memory schemes, calculating machines. The law
of gravitation is no more gravity than the funny wriggles that my
stenographer is making in her notebook are the sounds I am uttering.
To change geometries does not require any such effort as to change
cars. It means merely changing our minds. But this is harder for some
of us than it ought to be. Here is where the theory of relativity
will be of use to us. Poincaré, the French mathematician, cousin of
the late President, said: “These two propositions, ‘the earth turns
round’ and ‘it is more convenient to suppose the earth turns round’
have the same meaning. There is nothing more in the one than in the
other.” If Galileo and his inquisitors had understood the Principle of
Relativity it might have saved them both trouble; the former temporary
imprisonment and the latter everlasting disgrace. A revolution in
science is simply a change in mental attitude. Maybe a political
revolution is no more.
It is disconcerting to the layman to be told, first, that matter
consists of solid round atoms in empty space; next, that it is made
of mere particles of electricity and negative at that; then that it
is constituted out of strains in the ether; again, that the atoms are
bubbles in the ether; and finally, that there is not any ether. But
these various hypotheses are like the crayon strokes that an artist
makes about a figure he is trying to draw. They are all attempts at
preliminary sketches for mental pictures of natural phenomena. We do
not call the geographers inconsistent and contradictory because one
colors Massachusetts red on the map and another colors it green. All
scientific hypotheses are put to the pragmatic test of which works the
best in unlocking the secrets of Nature. Is “wheat” or “sesame” the
magic word? Whether we call a dog “Fido” or “Towser” depends not on
which name is shorter or sounds better but on which the dog answers to.
If gravitation comes to heel better when we say “Einstein” than when
we say “Newton,” all right, we’ll change. I trust that these frivolous
illustrations will not lead my readers to accuse me of treating gravity
with levity.
The layman--and with him must be included all those who have merely
learned science but not used it--talks a great deal about “the laws
of Nature,” which he regards as abstract, immutable, universal and
eternal edicts, part of which are transcribed into the textbooks. To
the working scientist they are only more or less convenient formulas;
in the ultimate analysis only mnemonic symbols for stringing together
facts to make them easier to handle, like _vibgyor_, for the
spectrum colors. He knows that most of them are limited in their
scope and only approximate in their accuracy. His chief delight is in
discovering these limitations and irregularities. He regards these
“laws” with no awe or reverence. He has no attachment for any of
them--unless it happens to be one that he has formulated himself. If he
finds a new hypothesis that works better he throws the old one aside
as he does his old model dynamo, or keeps it around as handy still for
doing some of the common work of the laboratory. It is, to recur to
our example, just as “true,” using the word in its ordinary sense, to
say that the sun goes around the earth as to say that the earth goes
around the sun, for all motion is relative, and we can regard either
body as the stationary one or both as moving, as we choose. When we say
that the statement that the earth moves around the sun is the “true”
one, we merely mean that it is the more convenient form of expression,
for on this hypothesis the paths of the earth and the other planets
become circles (or more accurately speaking, irregular and eccentric
spirals) while on the other and older hypothesis their paths are very
complicated and difficult to handle mathematically. The theory that
the earth moves is not only simpler than that of a stationary earth,
but it is wider in its scope. It explains more, that is, it connects up
with other knowledge, such as the flattening at the poles. Copernicus,
then, did not discover a new fact about the solar system. He only
invented a lazier way of thinking about it.
The man of science invents an hypothesis whenever he needs one in his
business. It is to him merely a new tool, a _novum organum_. If
there is not an ether it would be necessary to create one. So he did
it. He had to have a noun for the verb “undulate.” When he had created
it he saw it was not good. The properties with which he endowed it were
self-contradictory, and it refused either to move with the earth or to
pass through it. But these theoretical inconsistencies do not bother
the physicist much. In spite of them the ether is a handy thing to have
about the laboratory. The scientist does not abandon a theory because
it has inconsistencies any more than he divorces his wife because she
has inconsistencies. Certainly the physicist did not consider himself
presumptuous in thus inventing ether for his own convenience. He knew
that the ordinary man had in the same way invented “matter” long ago
for his own convenience. It is a crude, inadequate and impossible idea,
this naïve conception of matter as something solid, heavy, hard,
inert, indestructible, impenetrable, colored and surfaced; but it is
good enough for part of the people all of the time and for all of the
people part of the time. The physicist himself uses it for everyday.
Only in his rigorous moments does he come down to bed-rock and say,
with Poincaré, “Mass is a co-efficient which it is convenient to
introduce into calculations.”
But when the physicist thus reduces matter to a small italic _m_
some people are sure to say that he is denying the existence of
matter. What would they say about Riemann who considers matter to be
holes in the ether? A definition is a different thing from a denial.
There are people among us who deny the existence of matter and they
call themselves “Scientists,” too, but they are not the ones who are
devoting their days and nights to the study of the workings of matter
in order to make it the servant of man.
A professor of chemistry would not think of asking his students if
the atomic theory is true any more than he would ask them if the
atomic theory is blue. He does not care whether they believe the
atomic theory or not. He only wants them to be able to use the atomic
theory for getting certain valuable results. Consequently, he watches
with interest and without apprehension the progress of discovery in
radio-activity which is undermining the old conception of the atom.
He would be glad to get rid of the atomic theory if he could find
something better because after all it is a clumsy thing and will not
hold half the facts he wants to put into it. He would have no more
hesitation about dropping it than he has in setting down one beaker
to pick up a larger one when what he has in the first is frothing
over. He does not want to spill anything, but he does not care what
vessel it is in. Revolutions in science never go backward and they
differ from political revolutions in that nothing worth saving is
lost in transition. The new theory must always include all that the
old one does and more. In their struggle for existence, formulas
fight like snakes; the one that can swallow the other beats. Now a
four-dimensional universe can take in a three-dimensional universe and
have space to spare for whatever the narrower conception could not
include so it seems likely to prevail.
We now know how to sympathize with those poor frightened people who
lived in the times of Copernicus and Galileo when they were told that
the solid earth on which they stood was not supported by anything,
but whirling about and rushing around through empty space and that
half the time they hung with their heads down over immeasurable space
with nothing to hold on to. But they got used to it in time and lived
happily ever after. So may we.
For the benefit of those who want to get their information at first
hand I append an article by Dr. Einstein himself which appeared in the
London _Times_ of December 13, 1919, and in _Science_ of
January 6, 1920:
TIME, SPACE, AND GRAVITATION
_By Dr. Albert Einstein_
I respond with pleasure to your Correspondent’s request that I should
write something for the _Times_ on the Theory of Relativity.
After the lamentable breach in the former international relations
existing among men of science, it is with joy and gratefulness that I
accept this opportunity of communication with English astronomers and
physicists. It was in accordance with the high and proud tradition of
English science that English scientific men should have given their
time and labor, and that English institutions should have provided the
material means, to test a theory that had been completed and published
in the country of their enemies in the midst of war. Although
investigation of the influence of the solar gravitational field on
rays of light is a purely objective matter, I am none the less very
glad to express my personal thanks to my English colleagues in this
branch of science; for without their aid I should not have obtained
proof of the most vital deduction from my theory.
There are several kinds of theory in Physics. Most of them are
constructive. These attempt to build a picture of complex phenomena
out of some relatively simple proposition. The kinetic theory of
gases, for instance, attempts to refer to molecular movement the
mechanical, thermal, and diffusional properties of gases. When we say
that we understand a group of natural phenomena, we mean that we have
found a constructive theory which embraces them.
But in addition to this most weighty group of theories, there is
another group consisting of what I call theories of principle. These
employ the analytic, not the synthetic method. Their starting-point
and foundation are not hypothetical constituents, but empirically
observed general properties of phenomena, principles from which
mathematical formulæ are deduced of such a kind that they apply to
every case which presents itself. Thermodynamics, for instance,
starting from the fact that perpetual motion never occurs in ordinary
experience, attempts to deduce from this, by analytic processes, a
theory which will apply in every case. The merit of constructive
theories is their comprehensiveness, adaptability, and clarity, that
of the theories of principle, their logical perfection, and the
security of their foundation.
The theory of relativity is a theory of principle. To understand it,
the principles on which it rests must be grasped. But before stating
these it is necessary to point out that the theory of relativity is
like a house with two separate stories, the special relativity theory
and the general theory of relativity.
Since the time of the ancient Greeks it has been well known that in
describing the motion of a body we must refer to another body. The
motion of a railway train is described with reference to the ground,
of a planet with reference to the total assemblage of visible fixed
stars. In physics the bodies to which motions are spatially referred
are termed systems of coördinates. The laws of mechanics of Galileo
and Newton can be formulated only by using a system of coördinates.