part leader of the Opposition. When the Act to constitute an
Australian High Commissionership was passed in 1909 Sir
George Reid became the first High Commissioner and was
created K.C.M.G. He represented his country in London in
genial fashion until 1916, and at the end of his term of office



REID, W. RELATIVITY



261



stood for the British House of Commons and was elected for the
St. George's Hanover Square division of London Jan. 1916.
He was created G.C.M.G. in 1911 and G.C.B. in 1916. He
published My Reminiscences (1917), as well as Five Free Trade
Essays (1875), and other economic papers. He died suddenly in
London, Sept. 12 1918.

REID, WHITELAW (1837-1912), American journalist and
diplomatist (see 23.52), died in London Dec. 15 1912. His last
public address was delivered before the students of the University
College of Wales, Aberystwyth, on " Thomas Jefferson." In
1912 appeared The Scot in America and the Ulster Scot and
posthumously, in 1913, American and English Studies.

See Royal Cortissoz, The Life of Whitelaw Reid (1921).

REINACH, JOSEPH (1856-1921), French author and politician
(see 23.55), was not reelected to the Chamber of Deputies in 1914.
During the World War his series of articles, " Les Commentaires
de Polybe," in the Figaro, were remarkable for their clear vision.
He died April 18 1921.

REJANE.GABRIELLE [CHARLOTTE REJU] (1857-1920), French
actress (see 23.58), died in Paris June 14 1920. During the
World War she visited England and appeared at the Court
theatre, London, in a patriotic play, Alsace, and at the Coliseum
in The Bet, when she played the part of a Frenchwoman visiting
the English battle-zone. She was made Chevalier of the Legion
of Honour for her war services.

RELATIVITY. The progress of physical science during the
decade 1910-20 was specially remarkable for the definite
emergence into general public discussion of the principle of
Relativity, as expounded by Prof. Albert Einstein, professor of
Physics in the Kaiser Wilhelm Institut, Berlin. Its meaning
and its history as part of present-day physical theory are
discussed below.

Introduction. The primary aim of the investigator in pure
science is the discovery of natural laws. As a secondary and
hardly less important aim, he tries to invent a mechanism which
shall account for the laws already known. The secondary aim
is forced upon him partly by the constitution of the human mind;
our intellects, unsatisfied with a mere accumulation of facts,
impel us ever to search for the causes underlying the facts:
Vere scire est per causas scire. But to the working scientist the
discovery of a mechanism has an additional and more practical
value. When he has found a mechanism which will account for
certain laws, he can proceed to examine the complete set of laws
which the mechanism demands. If his mechanism corresponds
with sufficient closeness to reality he may in this way be led to
the discovery of new natural laws. On the other hand, the
new laws deduced from the supposed mechanism may be false.
If the falsity of the new laws is not at once revealed science may
for a time be led into wrong paths. When more accurate experi-
menting or observation discloses that the laws are not true, a
recasting of ideas becomes necessary, and the branch of science
concerned may experience a time of revolution followed by a
period of rapid growth.

An obvious illustration of these general statements is provided
by the history of astronomy. The laws of the motions of the
planets, as observed from the earth, were tolerably well known
to the Greeks. They had also evolved an explanatory mechanism,
starting from the metaphysical premise that the paths of the
planets must necessarily be circles. The earth was the centre of
the universe and round this revolved spheres to which the
planets were attached. To explain the retrograde motion of the
outer planets, these were supposed attached to secondary
spheres revolving about points on the primary spheres which in
turn revolved about the earth. This mechanism of cycles and
epicycles held the field as an explanation of planetary motion
for eighteen centuries. Finally the observations of Tycho Brahe
provided a test which revealed the falsity of the whole structure.
The position of Mars was found to differ from that required by
the mechanism of epicycles by an amount as great as eight
minutes of arc. " Out of these eight minutes," said Kepler,
" we will construct a new theory that will explain the motions
of all the planets."



The history of the succeeding century of astronomy need not
be recapitulated here (see 2.811). The earth yielded its place as
the centre of the universe, and the structure of cycles and
epicycles crumbled away. The laws of planetary motion were
determined with a precision which for the time appeared to be
final. The mechanism underlying these laws was supposed to be
a " force " of gravitation. This force was supposed to act
between every pair of particles in the universe, its intensity
varying directly as the product of the masses of the particles
and inversely as the square of the distance separating them the
famous law of Newton.

In science, history repeats itself. Recent years have provided
a further instance of the general processes we have been con-
sidering. Under the Newtonian mechanism every planet would
describe a perfect ellipse about the sun as focus, and these
elliptic orbits would repeat themselves' indefinitely except in so
far as they were disturbed by the gravitational forces arising
from the other planets. But, after allowing for these disturbing
influences, Leverrier found that the orbit of the planet Mercury
was .rotating in its own plane at the rate of 43 seconds a century.
Various attempts have been made to reconcile this observed
motion with the Newtonian mechanism. The gravitational
forces arising from the known planets were demonstrably
unable to produce the motion in question, but it was possible
that Mercury's orbit was being disturbed by matter so far
unknown to us. Investigations were made as to the disturbance
to be expected from various hypothetical gravitating masses a
plajiet, or a ring of planets, between Mercury and the sun, a
ring of planets outside the orbit of Mercury, a belt of matter
extended in a flattened disc in a plane through the sun's centre,
an oblateness, greater than that suggested by the shape of the
sun's surface, in the arrangement of the internal layers of the
sun's mass. In every case the mass required to produce the
observed disturbance in the motion of Mercury would have
also produced disturbances not observed in the motions of the
other planets. The solution of the problem came only with the
theory of relativity. Just as Tycho's eight minutes of arc, in
the hands of Kepler and Newton, revolutionized mediaeval
conceptions of the mechanism of the universe, so Leverrier's
43 seconds of arc, in the hands of Einstein, has revolutionized
our igth-century conceptions, not only of purely astronomical
mechanism, but also of the nature of time and space and of the
fundamental ideas of science. The history of this revolution is
in effect the history of the theory of relativity. It falls naturally
into two chapters, the first narrating the building of an earlier
physical theory of relativity, and the second dealing with its
extension to gravitation.

The Physical Theory of Relativity. The earliest successful
attempt to formulate the laws governing the general motion of
matter is found in Newton's laws. The first law states that

" Every body perseveres in its state of rest or of uniform motion in a
right line unless it is compelled to change that state by forces impressed
tliereon."

In this law no distinction is made between rest and uniform
motion in a straight line, and the same is true of the remaining
laws. Hence follows the remarkable property to which Newton
draws explicit attention in his fifth corollary to the laws of
motion:

" The motions of bodies included in a given space are the same among
themselves, whether that space is at rest, or moves uniformly forwards
in a right line without any circular motion."

As a concrete application of this principle, Newton instances
" the experiment of a ship, where all motions happen after the
same manner whether the ship is at rest or is carried uniformly
forward in a right line." Just as a passenger on a ship in a still
sea could not determine, from the behaviour of bodies inside
the ship, whether the ship was at rest or moving uniformly
forward, so we cannot determine from the behaviour of bodies on
our earth whether the earth is at rest or not. We believe the
earth to be moving round the sun with a speed of about 30 km.
a second, so that there can be no question of the earth being
permanently at rest, but we are unable to determine whether



262



RELATIVITY



it is at rest at any specified point of its orbit, or, in the probable
event of its not being at rest, what its absolute velocity may be.
There is no more reason for thinking the sun, than the earth, to
be at rest. Newton wrote as follows:

" It is possible that in the remote regions of the fixed stars, or
perhaps far beyond them, there may be some body absolutely at
rest, but impossible to know, from the positions of bodies to one
another in our regions, whether any of these do keep the same posi-
tion to that remote body. It follows that absolute rest cannot be
determined from the position of bodies in our regions."

The above quotations are all from the first book of the
Principia Malhematica. Previous to them all Newton writes:
" I have no regard in this place to a medium, if any such there
is, that freely pervades the interstices between the parts of
bodies." The two centuries which elapsed after the publication
of the Principia witnessed a steady growth of the belief in the
reality of such an all-pervading medium. It was called the
aether, and by the end of these two centuries (1887) it was
almost universally believed that light and all electromagnetic
phenomena were evidence of actions taking place in this aether.
Light from the most distant stars was supposed to be transmitted
to us in the form of wave motions in the aether, and we could
see,the stars only because the sea of aether between us and these
stars was unbroken. It had been proved that if this sea of
aether existed it must be at rest, for the alternative hypothesis
that the aether was dragged about by ponderable bodies in
their motions had been shown to be incompatible with the
observed phenomenon of astronomical aberration and other
facts of nature (see 1.292). On this view it was no longer neces-
sary to go to Newton's " remote regions of the fixed stars, or
perhaps far beyond them," to find absolute rest. A standard of
absolute rest was provided by the aether which filled our
laboratories and pervaded all bodies. Owing to our motion it
would appear to be rushing past us, although without encounter-
ing any hindrance " like the wind through a grove of trees,"
to borrow the simile of Thomas Young. The determination of
the absolute velocity of the earth was reduced to the problem
of measuring the velocity of an aether current flowing past us
and through us.

In this same year (1887) the first experimental determination
of this velocity was attempted by the Chicago physicist A. A.
Michelson. The velocity of light was known to be, in round
numbers, 300,000 km. a second, a velocity which was believed
to represent the rate of progress of wave motion through the
aether. If the earth were moving through the aether with a
velocity of 1,000 km. a second, the velocity of light relative to
a terrestrial observer ought to be only 299,000 km. a second
when the light was sent in exactly the direction of the earth's
motion through the aether, but would be 301,000 km. a second
if the light was sent in the opposite direction. In more general
terms, if the earth were moving through the aether, the velocity
of light, as measured by a terrestrial observer, would depend
on the direction of the light, and the extent of this dependence
would give a measure of the earth's velocity. The velocity of
light along a single straight course does not permit of direct
experimental determination, but the same property of depend-
ence on direction ought to be true, although to a less extent,
of the average to-and-fro velocity of a beam of light sent along
any path and then reflected back along the same path.

It was through this property that Michelson attempted to
measure the earth's velocity through the aether.

The apparatus was simple in principle. A circular table ABCD
was arranged so as to be capable of slow rotation about its centre O.
Light sent along CO was divided up at O into two beams which
were made to travel along perpendicular radii OA, OB. The arms
OA, OB were made as equal as possible and mirrors were placed at
A and B to reflect the beams of light back to O. An extremely sensi-
tive optical method made it possible to detect even a very slight
difference in the times of the total paths of the two beams from O
back to O. There would in any case be a difference owing to the
necessarily imperfect equalization of the lengths of the arms OA, OB,
but if the earth is moving through the aether in some direction OP,
and if the table is made to rotate slowly about O, then this difference
ought itself to vary on account of the earth's motion through the
aether. Michelson, and afterwards Michelson and Money in
collaboration, attempted to estimate the amount of this variation.



No variation whatsoever could be detected, although their final
apparatus was so sensitive that the variation produced by a velocity
through the aether of even I km. a second ought to have shown itself
quite clearly.

Thus to the question " What is our velocity through the
aether ? " Nature appeared to give the answer " None." It
was never suggested that this answer should be accepted as
final; it would have brought us back to a geocentric universe.
Clearly either the question had been wrongly framed or the
answer wrongly interpreted. It was pointed out in 1893 by
Fitzgerald, and again, independently, in 1895, by Lorentz,
that the nidi result of the Michelson-Morley experiment could
be explained if it could be supposed that motion through the
aether altered the linear dimensions of bodies.




FIG. i.



FIG. 2.



To be explicit, it was found that the experiment would invariably
and of necessity give a null result if it was supposed that every
body moving through the aether with a velocity was contracted



in the direction of its motion in the ratio



u 2 , . - ,
f I ~, C being .the
c



velocity of light. The supposition that such a contraction occurred
was not only permissible it was almost demanded by electrical
theory. For Lorentz had already shown that if matter were a purely
electrical structure, the constituent parts would of necessity read-
just their relative positions when set in motion through the aether
and the final position of equilibrium would be one showing precisely
the contraction just mentioned.

On this view, there was no prima-facie necessity to abandon
the attempt to measure the earth's velocity through the aether.
The answer to the problem had merely been pushed one stage
farther back, and it now became necessary only to measure the
shrinkage of matter produced by motion. It was obvious from
the first that no direct material measurement could disclose the
amount of this shrinkage, since any measuring rod would shrink
in exactly the same ratio as the length to be measured; but
optical and electrical methods appeared to be available. Experi-
ments to this end were devised and performed by Rayleigh, Brace,
Trouton and Noble, Trouton and Rankine and others. In
every case a null result was obtained. It appeared then that if
the earth moved through the aether this motion was concealed
by a universal shrinkage of matter, and this shrinkage was in
turn concealed by some other agency or agencies whose wit, so
far, appeared to be greater than that of man.

At this time the word " conspiracy " found its way into the
technical language of science. There was supposed to be a
conspiracy on the part of the various agencies of nature to
prevent man from measuring his velocity of motion in space.
If this motion produced a direct effect x on any phenomenon,
the other agencies of nature seemed to be in league to produce a
countervailing effect x. A long train of experiments had not
revealed, as was intended, our velocity through the aether;
they had merely created a conviction that it was beyond the
power of man to measure this velocity. The conspiracy, if such
there was, appeared to have been perfectly organized.

A perfectly organized conspiracy of this kind differs only in
name from a law of nature. To the inventor who tries to devise
a perpetual-motion machine it may well appear that the forces
of nature have joined in a conspiracy to prevent his machine
from working, but wider knowledge shows that he is in conflict
not with a conspiracy, but with a law of nature the conservation
of energy. In 1905 Einstein, crystallizing an idea which must



RELATIVITY



263



have been vaguely present in many minds, propounded the
hypothesis that the apparent conspiracy might be in effect a
law of nature. He suggested, tentatively, that there might be
a true law to the effect that " it is of necessity impossible to
determine absolute motion by any experiment whatever."
This hypothetical law may again be put in the equivalent form :
" The phenomena of nature will be the same to two observers
who move with any uniform velocity whatever relative to one
another." This may be called the hypothesis of relativity.

The hypothesis in itself was not of a sensational character.
Indeed, from the quotations which have already been given
from Newton's works, it appears probable that Newton himself
would have accepted the hypothesis without hesitation: he
might even have regarded it as superfluous. The true significance
of the hypothesis can only be understood by a reference
to the scientific history of the two centuries which had elapsed
since Newton. The Newtonian view that absolute rest was to
be found only " in the remote regions of the fixed stars, or perhaps
far beyond them," had given place to a belief that absolute
rest was to be found all around us in an aether which permeated
all bodies. What was striking about the hypothesis was its
implication either that we could not measure the velocity
relative to ourselves of a medium which surrounded us on all
sides, or else that no such medium existed.

The hypothesis demanded detailed and exhaustive examina-
tion. It was for the mathematician to test whether the hypothe-
sis was in opposition to known and established laws of physics,
and to this task Einstein, Lorentz and others set themselves.
If a single firmly established law proved to be in opposition to
the hypothesis, then of course the hypothesis would require to
be abandoned. It was unlikely that such an event would occur
among the well-established laws, for if it did, the phenomena
governed by that law would enable direct measurement to be
made of the earth's velocity through the aether, a measurement
which had so far eluded all attempts of experimenters. It was
among the more obscure and less well-established laws, if any-
where, that discrepancies were to be looked for.

It is impossible here to give a complete account of the many
tests to which the relativity hypothesis has been subjected. The
result of all can be summed up in one concise and quite general
statement: Wherever the hypothesis of relativity has appeared
to be in conflict with known or suspected natural laws, further
experiment, where possible, has, without a single exception,
shown the laws to be erroneous, and has moreover shown the
alternative laws suggested by the hypothesis of relativity to be
accurate. It is only in somewhat exceptional cases that the
hypothesis of relativity of itself suffices to determine fully the
form of a natural law; these cases constitute the most striking
triumphs of the theory. As instances may be mentioned the
determination of the law connecting the mass of an electron with
its velocity; of the law expressing the velocity of light through
a transparent medium rn motion (Fizeau's water-tube experi-
ment); and of the formulae for the magnetic forces on moving
dielectric media (experiments of Eichenwald and H. A. Wilson). 1

Befo e passing on from the general statement which has been
made, particular mention must be made of one special case.
A natural law which was at an early stage seen to be in conflict
with the hypothesis of relativity was Newton's famous law of
gravitation namely, that every particle of matter attracts
every other particle with a force proportional to the product of
the two masses, and to the inverse square of their distance
apart. Either, then, Newton's great law had to be abandoned,
or els; the hypothesis of relativity had to be discarded, in which
case it would immediately become possible, in theory at least,
to determine the earth's velocity through space by gravitational
m~ans. It is the choice between these two alternatives that has
led to the most surprising developments of the theory of relativity;
and to these we shall return later.

1 For references to the original papers dealing with these and
other tests of the hypothesis of relativity see Cunningham, The
Principle of Relativity, or J. H. Jeans, Mathematical Theory of
Electricity and Magnetism (4th ed.).



Space and Time. The hypothesis of relativity, as has already
been explained, postulates that the phenomena of nature will
be the same to any two observers who move relative to one
another with any uniform velocity whatever. The hypothesis
has been so amply tested as regards all optical and electromag-
netic phenomena that no doubt is felt, or can rationally be felt,
as to its truth with respect to these phenomena. The hypothesis
can be examined and developed in two opposite directions. We
may, on the one hand, proceed from the general hypothesis to
the detailed laws implied in it; this has already been done, with
completely satisfactory results as regards confirmation of the
hypothesis. Or we may regard the hypothesis of relativity as
being itself a detailed law and attempt to generalize upward to
something still wider. It is this possibility which must for the
moment claim our attention.

In 1905 Einstein examined in full the consequences of the
hypothesis that one simple optical phenomenon namely, the
transmission of a ray of light in free space was, in accordance
with the hypothesis of relativity, independent of the velocity
of the observer. If an aether existed, and provided a fixed
framework of reference, then light set free at any instant would
obviously travel with a velocity which would appear to an
observer at rest in this aether to be the same in all directions,
and the wave front at any instant would be a sphere having the
observer as centre. On the hypothesis of relativity the phenom-
enon of light transmission must remain unaffected by the motion
of the observer, so that the light must appear to a moving observer
also, to travel with a uniform velocity in all directions, and-thus
to the moving observer also the wave front must appear to be a
sphere of which he will be the centre. It is, however, quite
obvious that the same spherical wave front cannot appear to
each of two observers who have moved some distance apart to
be centred round himself, unless the use either of the common
conceptions of science or of the ordinary words of language is
greatly changed. In fig. 2 it is not possible in ordinary language
that both O and P should at the same instant be at the centre of
the sphere ABC. The change to which Einstein was forced is
one which has an intimate bearing upon our fundamental
conceptions of the nature of space and time; this change it will
be necessary to explain in some detail.

Suppose that two observatories, say Greenwich and Paris,
wish to synchronize their clocks, with a view to, let us say, an
exact determination of their longitude difference. Paris will
send out a wireless signal at exact midnight as shown by the
Paris clock, and Greenwich will note the time shown by the
Greenwich clock at the instant of receipt of the signal. Green-
wich will not, however, adjust their clock so as to show exact
midnight when the signal is received; a correction of about -ooi
second must be made to allow for the time occupied by the