SCIENCE IN A NO-THOROUGHFARE
_Scientific truth and mathematics—The precise function
of Einstein—Michelson’s experiment, the Gordian knot
of science—The hesitations of Poincaré—The strange,
but necessary, Fitzgerald-Lorentz hypothesis—The
contraction of moving bodies—Philosophical and
physical difficulties._
It would be foolish to pretend that we can penetrate the most obscure
corners of Einstein’s theories without the aid of mathematics. I
believe, however, that we can give in ordinary language—that is to
say, by means of illustrations and analogies—a fairly satisfactory
idea of these things, the intricacy of which is usually due to the
infinitely subtle and supple play of mathematical formulæ and equations.
After all, mathematics is not, never was, and never will be, anything
more than a particular kind of language, a sort of shorthand of thought
and reasoning. The purpose of it is to cut across the complicated
meanderings of long trains of reasoning with a bold rapidity that is
unknown to the mediæval slowness of the syllogisms expressed in our
words.
However paradoxical this may seem to people who regard mathematics as
_of itself_ a means of discovery, the truth is that we can never
get from it anything that was not implicitly inherent in the data which
were thrust between the jaws of its equations. If I may use a somewhat
trivial illustration, mathematical reasoning is very like certain
machines which are seen in Chicago—so bold explorers in the United
States tell us—into which one puts living animals that emerge at the
other end in the shape of appetising prepared meats. No spectator could
have, or would wish to have, eaten the animal alive, but in the form
in which it issues from the machine it can at once be digested and
assimilated. Yet the meat is merely the animal conveniently prepared.
That is what mathematics does. By means of a marvellous machinery the
mathematician extracts the valuable marrow from the _given facts_.
It is a machinery that is particularly useful in cases where the wheels
of verbal argument, the chain of syllogisms, would soon be brought to a
halt.
Does it follow that, properly speaking, mathematics is not a science?
Does it follow at least that it is only a science in so far as it is
based upon reality, and fed with experimental data, since “experience
is the sole source of truth.” I refrain from answering the question, as
I am one of those who believe that everything is material for science.
Still, it was worth while to raise the question because many are too
much disposed to regard a purely mathematical education as a scientific
education. Nothing could be further from the truth. Pure mathematics
is, in itself, merely an abbreviated form of language and of logical
thought. It cannot, of its own nature, teach us anything about the
external world; it can do so only in proportion as it enters into
contact with the world. It is of mathematics in particular that we may
say: _Naturæ non imperatur nisi parendo._
Are not Einstein’s theories, as some imperfectly informed writers have
suggested, only a play of mathematical formulæ (taking the word in the
meaning given to it by both mathematicians and philosophers)? If they
were only a towering mathematical structure in which the _x_’s
shoot out their volutes in bewildering arabesques, with swan-neck
integrals describing Louis XV patterns, they would have no interest
whatever for the physicist, for the man who has to examine the nature
of things before he talks about it. They would, like all coherent
schemes of metaphysics, be merely a more or less agreeable system of
thought, the truth or falseness of which could never be demonstrated.
Einstein’s theory is very different from that, and very much more than
that. It is based upon facts. It also leads to facts—new facts. No
philosophical doctrine or purely formal mathematical construction ever
enabled us to discover new phenomena. It is precisely because it has
led to such discovery that Einstein’s theory is neither the one nor the
other. That is the difference between a scientific theory and a pure
speculation, and it is that which, I venture to say, makes the former
so superior.
Like some suspension bridge boldly thrown across an abyss, Einstein’s
theory rests, on the one side, on experimental phenomena, and it leads,
at the other side, to other, and hitherto unsuspected, phenomena, which
it has enabled us to discover. Between these two solid experimental
columns the mathematical reasoning is like the marvellous network of
thousands of steel bars which represent the elegant and translucent
structure of the bridge. It is that, and nothing but that. But the
arrangement of the beams and bars might have been different, and the
bridge—though less light and graceful, perhaps—still have been able
to join together the two sets of facts on which it rests.
In a word, mathematical reasoning is only a kind of reasoning in a
special language, from experimental premises to conclusions which are
verifiable by experience. Now there is no language which cannot in some
degree be translated into another language. Even the hieroglyphics of
Egypt had to give way before Champollion. I am therefore convinced that
the mathematical difficulties of Einstein’s theories will some day be
replaced by simpler and more accessible formulæ. I believe, indeed,
that it is even now possible to give by means of ordinary speech an
idea, rather superficial perhaps, but accurate and substantially
complete, of this wonderful Einsteinian structure which ranges all the
conquests of science, as in some well-ordered museum, in a new and
superb unity. Let us try.
* * * * *
We may resume in the few following words the story of the origin, the
starting-point, of Einstein’s system.
1. Observation of the stars proves that interplanetary
space is not empty, but is filled with a special medium,
ether, in which the waves of light travel.
2. The fact of aberration and other phenomena seems to prove
that the ether is not displaced by the earth during its
course round the sun.
3. Michelson’s experiment seems to prove, on the contrary, that
the earth bears the ether with it in its movement.
This contradiction between facts of equal authority was for years
the despair and the wonder of physicists. It was the Gordian knot of
science. Long and fruitless efforts were made to untie it until at last
Einstein cut it with a single blow of his remarkably acute intelligence.
In order to understand how that was done—which is the vital point of
the whole system—we must retrace our steps a little and examine the
precise conditions of Michelson’s famous experiment.
I pointed out in the preceding chapter that Michelson proposed to study
the speed of a ray of light produced in the laboratory and directed
either from east to west or west to east: that is to say, in the
direction in which the earth itself moves, at a speed of about eighteen
miles a second, as it travels round the sun, or in the opposite
direction. As a matter of fact, Michelson’s experiment was rather more
complicated than that, and we must return to it.
Four mirrors are placed at an equal distance from each other in the
laboratory, in pairs which face each other. Two of the opposing
mirrors are arranged in the direction east-west, the direction in
which the earth moves in consequence of its revolution round the sun.
The other two are arranged in a plane perpendicular to the preceding,
the direction north-south. Two rays of light are then started in the
respective directions of the two pairs of mirrors. The ray coming from
the mirror to the east goes to the mirror in the west, is reflected
therefrom, and returns to the first mirror. This ray is so arranged
that it crosses the path of the light which goes from north to south
and back. It interferes with the latter light, causing “fringes of
interference” which, as I said, enable us to learn the exact distance
traversed by the rays of light reflected between the pairs of mirrors.
If anything brought about a difference between the length of the two
distances, we should at once see the displacement of a certain number
of interference-fringes, and this would give us the magnitude of the
difference.
An analogy will help us to understand the matter. Suppose a violent
steady east wind blew across London, and an aviator proposed to cross
the city about twelve miles from extreme west to east and back: that is
to say, going with the wind on his outward journey and against it on
the return journey. Suppose another aviator, of equal speed, proposed
at the same time to fly from the same starting-point to a point twelve
miles to the north and back, the second aviator will fly both ways at
right angles to the direction of the wind. If the two start at the same
time, and are imagined as turning round instantaneously, will they both
reach the starting-point together? And, if not, which of them will have
completed his double journey first?
It is clear that if there were no wind, they would get back together,
as we suppose that they both do twenty-four miles at the same speed,
which we may roughly state to be 200 yards a second.
But it will be different if, as I postulated, there is a wind blowing
from east to west. It is easy to see that in such circumstances the
man who flies east to west will take longer to complete the journey.
In order to get it quite clearly, let us suppose that the wind is
travelling at the same speed as the aviator (200 yards a second). The
man who flies at right angles to the wind will be blown twelve miles
to the west while he is doing his twelve miles from south to north.
He will therefore have traversed _in the wind_ a real distance
equal to the diagonal of a square measuring twelve miles on each
side. Instead of flying twenty-four miles, he will really have flown
thirty-four in the wind, the medium in relation to which he has any
velocity.
On the other hand, the aviator who flies eastward will never reach his
destination, because in each second of time he is driven westward to
precisely the same extent as he is travelling eastward. He will remain
stationary. To accomplish his journey he would need to cover _in the
wind_ an infinite distance.
If, instead of imagining a wind equal in velocity to the aviator (an
extreme supposition in order to make the demonstration clearer), I had
thought of it as less rapid, we should again find, by a very simple
calculation, that the man who flies north and south has less distance
to cover in the wind than the man who flies east and west.
Now take rays of light instead of aviators, the ether instead of
the wind, and we have very nearly the conditions of the Michelson
experiment. A current or wind of ether—since the ether has
been already shown to be stationary in relation to the earth’s
movement—proceeds from one to the other of our east-west mirrors.
Therefore the ray of light which travels between these two mirrors,
forth and back, must cover a longer distance in ether than the ray
which goes from the south mirror to the north and back. But how are we
to detect this difference? It is certainly very minute, because the
speed of the earth is ten thousand times less than the velocity of
light.
There is a very simple means of doing this: one of those ingenious
devices which physicists love, a differential device so elegant and
precise that we have entire confidence in the result.
Let us suppose that our four mirrors are fixed rigidly in a sort of
square frame, something like those “wheels of fortune” with numbers on
them that one sees in country fairs. Let us suppose that we can turn
this frame round as we wish, without jerking or displacing it, which is
not difficult if it floats in a bath of mercury. I then take a lens and
observe the permanent interference-fringes which define the difference
between the paths traversed by my two rays of light, north-south and
east-west. Then, without losing sight of the bands or fringes, I
turn the frame round a quarter of a circle. Owing to this rotation
the mirrors which were east-west now become north-south, and _vice
versa_. The double journey made by the north-south ray of light
has now taken the direction east-west, and has therefore suddenly
been lengthened; the double journey of the east-west ray has become
north-south, and has been suddenly shortened. The interference-fringes,
which indicate the difference in length between the two paths, which
has suddenly changed, must necessarily be displaced, and that, as we
can calculate, to no slight extent.
Well, we find no change whatever! The fringes remain unaltered. They
are as stationary as stumps of trees. It is bewildering, one would
almost say revolting, because the delicacy of the apparatus is such
that, even if the earth moved through the ether at a rate of only three
kilometres a second (or ten times less than its actual velocity), the
displacement of the fringes would be sufficient to indicate the speed.
* * * * *
When the negative result of this experiment was announced, there was
something like consternation amongst the physicists of the world.
Since the ether was not borne along by the earth, as observation had
established, how could it possibly behave as if it did share the
earth’s motion? It was a Chinese puzzle. More than one venerable grey
head was in despair over it.
It was absolutely necessary to find a way out of this inexplicable
contradiction, to end this paradoxical mockery which the facts seemed
to oppose to the most rigorous results of calculation. This the men of
science succeeded in doing. How? By the method which is generally used
in such circumstances—by means of supplementary hypotheses. Hypotheses
in science are a kind of soft cement which hardens rapidly in the open
air, thus enabling us to join together the separate blocks of the
structure, and to fill up the breaches made in the wall by projectiles,
with artificial stuff which the superficial observer presently mistakes
for stone. It is because hypotheses are something like that in science
that the best scientific theories are those which include least
hypotheses.
But I am wrong in using the plural in this connection. In the end
it was found that one single hypothesis conveniently explained the
negative result of the Michelson experiment. That is, by the way, a
rare and remarkable experience. Hypotheses usually spring up like
mushrooms in every dark corner of science. You get a score of them to
explain the slightest obscurity.
This single hypothesis, which seemed to be capable of extricating
physicists from the dilemma into which Michelson had put them, was
first advanced by the distinguished Irish mathematician Fitzgerald,
then taken up and developed by the celebrated Dutch physicist Lorentz,
the Poincaré of Holland, one of the most brilliant thinkers of our
time. Einstein would no more have attained fame without him than Kepler
would without Copernicus and Tycho Brahe.
Let us now see what this Fitzgerald-Lorentz hypothesis, as strange as
it is simple, really is.
But we must first glance at a preliminary matter of some importance. A
number of able men have declared—after the issue, let it be said—that
the result of the Michelson experiment could only be negative _a
priori_. In point of fact, they argue (more or less), the Classic
Principle of Relativity, the principle known to Galileo and Newton,
implies that it is impossible for an observer who shares the motion
of a vehicle to detect the motion of that vehicle by any facts he
observes while he is in it. Thus, when two ships or two trains pass
each other,[4] it is impossible for the passengers to say which of the
two is moving, or moving the more rapidly. All that they can perceive
is the relative speed of the trains or ships.
[4] It is assumed that the ship is not rolling or pitching, and that
there is no vibration in the train.
The men of science to whom I have referred say that, if Michelson’s
experiment had had a positive result, it would have given us the
absolute velocity of the earth in space. This result would have been
contrary to the Principle of Relativity of classical philosophy and
mechanics, which is a self-evident truth. Therefore the result could
only be negative.
This is, as we shall see, ambiguous. There is, if I may say so, a flaw
in the argument which has escaped the notice even of distinguished men
of science like Professor Eddington, the most erudite of the English
Einsteinians. It was he who organised the observations of the solar
eclipse of May 29, 1919, which have, as we shall see, furnished the
most striking verification of Einstein’s deductions.
In the first place, if Michelson’s experiment had had a positive
result, what it would have indicated is the velocity of the earth in
relation to the ether. But, for this to be an absolute velocity, the
ether would have to be identical with space. This is so far from being
necessary that we can easily conceive a space—to put it better, a
discontinuity—between two stars that contains no ether and across which
neither light nor any other known form of energy would travel.
When Eddington says that “it is legitimate and reasonable,” that it is
“inherent in the fundamental laws of nature,” that we cannot detect any
movement of bodies in relation to ether, and that this is certain “even
if the experimental evidence is inadequate,” he affirms something which
would be evident only if space and ether were evidently identical. But
this is far from being the case. If Michelson’s experiment had had
a positive result, if we had detected a velocity on the part of the
earth, should we have discovered a velocity in relation to an absolute
standard? Certainly not. It is quite possible that the stellar universe
which is known to us, with its hundreds of thousands of galaxies which
it takes light millions of years to cross, may be contained in a sphere
of ether that rolls in an abyss which is devoid of ether, and is sown
here and there with other universes, other giant drops of ether, from
which no ray of light or anything else may ever reach us. It is, at
all events, not inconceivable. And in that case, assuming that the
ether has the properties attributed to it by classic physics, even if
we had detected the movement of the earth in relation to it, we should
not have discovered an absolute movement, but at the most a movement
in relation to the centre of gravity of our particular universe,
a standard which we could not refer to some other which would be
absolutely stationary. The Classical Principle of Relativity would not
be violated.
Hence, whatever may have been said to the contrary, the issue of
Michelson’s experiment might, in these hypotheses, be either positive
or negative without any detriment to Classical Relativism. As a matter
of fact, it was negative, so nothing further need be said. Experiment
has pronounced, and it alone had the right to pronounce.
These distinctions were not unknown to Poincaré, and he wrote: “By the
real velocity of the earth I understand, not its absolute velocity,
which is meaningless, but its velocity in relation to the ether.”
Therefore the possibility of the existence of a velocity discoverable
in relation to the ether was not regarded as an absurdity by Poincaré.
He said: “Any man who speaks of absolute space uses a word that has no
meaning.”
It is worth while noticing that in all this the development of
Poincaré’s ideas betrays a certain hesitation. Speaking of experiments
analogous to those of Michelson, he said:
“I know that it will be said that we
are not measuring its absolute velocity, but its velocity
in relation to the ether. That is scarcely satisfactory.
Is it not clear that, if we conceive the principle in
this fashion, we can make no deductions whatever from it?”
From this it is evident that Poincaré, in spite of himself and all his
efforts to avoid it, was disposed to find the distinction between space
and ether “scarcely satisfactory.”
I must admit that Poincaré’s own argument seems to me not wholly
satisfactory, or at least not convincing. “Nature,” says Fresnel,
“cares nothing about analytical difficulties.” I imagine that it cares
just as little about philosophical or purely physical difficulties. It
is hardly an incontestable criterion to suppose that a conception of
phenomena is so much nearer to reality the more “satisfactory” it is to
us, or the better it is found adapted to the weakness of the human
mind. Otherwise we should have to hold, whether we liked or no, that
the universe is necessarily adapted to the categories of the mind;
that it is constituted with a view to giving us the least possible
intellectual trouble. That would be a strange return to anthropocentric
finalism and conceit! The fact that vehicles do not pass there, and
that pedestrians have to turn back, does not prove that there are no
such things as no-thoroughfares in our towns. It is possible, even
probable, that the universe also, considered as an object of science,
has its no-thoroughfare.
Clearly one may reply to me that it is not the universe that is adapted
to our mind, but the mind that has become adapted to the universe in
the evolutionary course of their relations to each other. The mind
needs in its evolution to adapt itself to the universe, in conformity
with the principle of minimum action formulated by Fermat: perhaps the
most profound principle of the physical, biological, and moral world.
In that respect the simplest and most economical ideas are the nearest
to reality.
Yes, but what proof is there that our mental evolution is complete and
perfect, especially when we are dealing with phenomena of which our
organism is insensible?
* * * * *
Experiment alone has proved, and had the right to prove, that it
is impossible to measure the velocity of an object relatively to
the ether. At all events, this is now settled. After all, since it
is evidently in the very nature of things that we cannot detect an
absolute movement, is it not because the velocity of the earth in
relation to the ether is an absolute velocity that we have been unable
to detect it? Possibly; but it cannot be proved. If it is so—which is
not at all certain—it is in the last resort _experience_, the
one source of truth, which thus tends to prove, indirectly, that the
ether is really identical with space. In that case, however, a space
devoid of ether, or one containing spheres of ether, would no longer be
conceivable, and there can be nothing but a single mass of ether with
stars floating in it. In a word, the negative result of Michelson’s
experiment could not be deduced _a priori_ from the problematical
identity of absolute space and the ether; but this negative result does
not justify us in denying the identity _a posteriori_.
Let us return to our proper subject, the Fitzgerald-Lorentz hypothesis
which explains the issue of the Michelson experiment, and which was
in a sense the spring-board for Einstein’s leap. The hypothesis is as
follows.
The result of the experiment is that, whereas when the path of a ray
of light between two mirrors is transverse to the earth’s motion
through ether, and it is then made parallel to the earth’s motion,
the path ought to be longer, we actually find no such lengthening.
According to Fitzgerald and Lorentz, _this is because the two mirrors
approached each other in the second part of the experiment_. To put
it differently, _the frame in which the mirrors were fixed contracted
in the direction of the earth’s motion, and the contraction was such in
magnitude as to compensate exactly for the lengthening of the path of
the ray of light which we ought to have detected_.
When we repeat the experiment with all kinds of different apparatus, we
find that the result is always the same (no displacement of the
fringes). It follows that the character of the material of which the
instrument is made—metal, glass, stone, wood, etc.—has nothing to
do with the result. Therefore all bodies undergo an equal and similar
contraction in the direction of their velocity relatively to the
ether. This contraction is such that it exactly compensates for the
lengthening of the path of the rays of light between two points of the
apparatus. In other words, the contraction is greater in proportion as
the velocity of bodies relatively to the ether becomes greater.
That is the explanation proposed by Fitzgerald. At first it seemed to
be very strange and arbitrary, yet there was, apparently, no other way
of explaining the result of Michelson’s experiment.
Moreover, when you reflect on it this contraction is found to be
less extraordinary, less startling, than one’s common sense at first
pronounces it. If we throw some non-rigid object, such as one of those
little balls with which children play, quickly against an obstacle,
we see that it is slightly pushed in at the surface by the obstacle,
precisely in the same sense as the Fitzgerald-Lorentz contraction.
The ball is no longer round. It is a little flattened, so that its
diameter is shortened in the direction of the obstacle. We have much
the same phenomenon, though in a more violent form, when a bullet
is flattened against a target. Therefore, if solid bodies are thus
capable of deformation—as they are, for cold is sufficient of itself
to concentrate their molecules more closely—there is nothing absurd or
impossible in supposing that a violent wind of ether may press them out
of shape.
But it is far less easy to admit that this alteration may be exactly
the same, in the given conditions, for all bodies, whatever be the
material of which they are composed. The little ball we referred to
would by no means be flattened so much if it were made of steel instead
of rubber.
Moreover, there is in this explanation something quite improbable,
something that shocks both our good sense and that caricature of
it which we call common sense. Is it possible to admit that the
contraction of bodies always exactly compensates for the optic effect
which we seek, whatever be the conditions of the experiment (and
they have been greatly varied)? Is it possible to admit that nature
acts as if it were playing hide-and-seek with us? By what mysterious
chance can there be a special circumstance, providentially and exactly
compensating for every phenomenon?
Clearly there must be some affinity, some hidden connection, between
this mysterious material contraction of Fitzgerald and the lengthening
of the light path for which it compensates. We shall see presently
how Einstein has illumined the mystery, revealed the mechanism which
connects the two phenomena, and thrown a broad and brilliant light upon
the whole subject. But we must not anticipate.
The contraction of the apparatus in Michelson’s experiment is extremely
slight. It is so slight that if the length of the instrument were equal
to the diameter of the earth—that is to say, 8,000 miles—it would be
shortened in the direction of the earth’s motion by only six and a half
centimetres! In other words, the contraction would be far too small to
be in any way measurable in the laboratory.
There is a further reason for this. Even if Michelson’s apparatus were
shortened by several inches—that is to say, if the earth travelled
thousands of times as rapidly as it does round the sun—we could not
detect and measure it. The measuring rods which we would use for the
purpose would contract in the same proportion. The deformation of any
object by a Fitzgerald-Lorentz contraction could not be established by
any observer on the earth. It could be discovered only by an observer
who did not share the movement of the earth: an observer on the sun,
for instance, or on a slow-moving planet like Jupiter or Saturn.
Micromegas would, before he left his planet to visit us, have been
able to discover, by optical means, that our globe is shortened by
several inches in the direction of its orbital movement; supposing
that Voltaire’s genial hero were provided with trigonometrical
apparatus infinitely more delicate than that used by our surveyors
and astronomers. But when he reached the earth, Micromegas, with
all his precise apparatus, would have found it impossible to detect
the contraction. He would have been greatly surprised—until he met
Einstein and heard, as we shall hear, the explanation of the mystery.
I have, unfortunately, neither the time nor the space—it is here,
especially, that space is relative, and is constantly shortened by the
flow of the pen—to give the dialogue which would have taken place
between Micromegas and Einstein. Perhaps, indeed, if we are to be
faithful to the Voltairean original, the dialogue would have been very
superficial, for—to speak confidentially—I believe that Voltaire
never quite understood Newton, though he wrote much about him, and
Newton was less difficult to understand than Einstein is. Neither did
Mme. du Châtelet, for all the praise that has been lavished upon her
translation of the immortal _Principia_. It swarms with meaningless
passages which show that, whether she knew Latin or no, she did not
understand Newton. But all this is another story, as Kipling would say.
The movement of the apparatus in the ether varies in speed according to
the hour and the month in which the Michelson and similar experiments
are made. As the compensation is always precise, we may try to
calculate the exact law which governs the contraction as a function
of velocities, and makes it, as we find, a precise compensation for
the latter. Lorentz has done this. Taking =V= as the velocity of
light and _v_ as the velocity of the body moving in ether, Lorentz
found that, in order to have compensation in all cases, the length of
the moving body must be shortened, in the plane of its progress, in the
proportion of
( _v_² )
1 to √(1 ———————— ).
( V² )
If we take by way of illustration the case of the orbital movement of
the earth, where v is equal to thirty kilometres, we find that the
earth contracts in the plane of its orbit in the proportion
( 1 )
√(1 ——————————— ).
( 100,000,000 )
The difference between these two numbers is ¹/₂₀₀,₀₀₀,₀₀₀, and
the two hundred millionth part of the earth’s diameter is equal to 6½
centimetres. It is the figure we had already found.
This formula, which gives the value of the contraction in all cases,
is elementary. Even the inexpert can easily see the meaning of it. It
enables us to calculate the extent of contraction for every rate of
velocity. We can easily deduce from it that if the earth’s orbital
motion were, not 30 kilometres, but 260,000 kilometres a second, it
would be shortened by one-half its diameter in the plane of its motion
(without any change in its dimensions in the perpendicular). At that
speed a sphere becomes a flattened ellipsoid, of which the small
axis is only half the length of the larger axis; a square becomes a
rectangle, of which the side parallel to the motion is twice as small
as the other.
These deformations would be visible to a stationary spectator, but they
would be imperceptible to an observer who shares the movement, for the
reason already given. The measuring rods and instruments, and even the
eye of the observer, would be equally and simultaneously altered.
Think of the distorting mirrors which one sees at times in places of
amusement. Some show you a greatly elongated picture of yourself,
without altering your breadth. Others show you of your normal height,
but grotesquely enlarged in width. Try, now, to measure your height and
breadth with a rule, as they are given in these deformed reflections in
the mirror. If your real height is 5 feet 6 inches, and your real width
2 feet, the rule will, when you apply it to the strange reflection of
yourself in the glass, merely tell you that this figure is 5 feet 6
inches in height and 2 feet in breadth. The rule as seen in the mirror
undergoes the same distortion as yourself.
Hence it is that, even if the globe of the earth had the fantastic
speed which we suggested above, its inhabitants would have no means
of discovering that they and it were shortened by one-half in the
plane east to west. A man 5 feet 6 inches in height, lying in a large
square bed in the direction north-south, then changing his position to
east-west, would, quite unknown to himself, have his length reduced
to 2 feet 9 inches. At the same time he would become twice as stout
as before, because previously his breadth was orientated from east to
west. But the earth travels at the rate of only thirty kilometres
a second, and its entire contraction is only a matter of a few
centimetres.
In contrast with the earth’s velocity, the speed of our most rapid
means of transport is only a small fraction of a kilometre a second.
An aeroplane going at 360 kilometres an hour has a speed of only 100
metres a second. Hence the maximum Fitzgerald-Lorentz contraction of
our speediest machines can only be such an infinitesimal fraction of an
inch that it is entirely imperceptible to us. That is why—that is the
only reason why—the solid objects with which we are familiar seem to
keep a constant shape, at whatever speed they pass before our eyes. It
would be quite otherwise if their speed were hundreds of thousands of
times greater.
All this is very strange, very surprising, very fantastic, very
difficult to admit. Yet it is a fact, if there really is this
Fitzgerald-Lorentz contraction, which has so far proved the only
possible explanation of the Michelson experiment. But we have already
seen some of the difficulties that we find in entertaining the
existence of this contraction.
There are others. If all that we have just said is true, only objects
which are stationary in the ether would retain their true shapes, for
the shape is altered as soon as there is movement through the ether.
Hence, amongst the objects which we think spherical in the material
world (planets, stars, projectiles, drops of water, and so on), there
would be some that really are spheres, whilst others would, on account
of the speed or slowness of their movements, be merely elongated or
flattened ellipsoids, altered in shape by their velocity. Amongst the
various square objects, some would be really square, while others,
travelling at different speeds relatively to the ether, would be rather
rectangles, shortened on their longer sides owing to their velocity.
And it is supposed that we would have no means of knowing which of
these objects moving at different speeds are really shaped as we think
and which are shaped otherwise, because, as the Michelson experiment
proves, we cannot detect a velocity relatively to the ether.
This we utterly decline to believe, say the Relativists. There are too
many difficulties about the matter. Why speak persistently, as Lorentz
does, of velocities in relation to the ether, when no experiment can
detect such a velocity, yet experiment is the sole source of scientific
truth? Why, on the other hand, admit that some of the objects we
perceive have the privilege of appearing to us in their real shape,
without alteration, while others do not? Why admit such a thing when it
is, of its very nature, repugnant to the spirit of science, which is
always opposed to exceptions in nature—science deals only with general
laws—especially when the exceptions are imperceptible?
That was the state of affairs—very advanced from the point of view of
the mathematical expression of phenomena, but very confused, deceptive,
contradictory, and troublesome from the physical point of view—when
“at length Malherbe arrived” ... I mean Einstein.