Lord Kelvin writing in 1893, in his preface to the English edition of
Hertz’s Researches on Electric Waves, says “many workers and many
thinkers have helped to build up the nineteenth century school of
_plenum_, one ether for light, heat, electricity, magnetism; and the
German and English volumes containing Hertz’s electrical papers, given
to the world in the last decade of the century, will be a permanent
monument of the splendid consummation now realised.”
Ten years later, in 1905, we find Einstein declaring that “the ether
will be proved to be superfluous.” At first sight the revolution in
scientific thought brought about in the course of a single decade
appears to be almost too violent. A more careful even though a rapid
review of the subject will, however, show how the Theory of Relativity
gradually became a historical necessity.
Towards the beginning of the nineteenth century, the luminiferous ether
came into prominence as a result of the brilliant successes of the wave
theory in the hands of Young and Fresnel. In its stationary aspect the
elastic solid ether was the outcome of the search for a medium in which
the light waves may “undulate.” This stationary ether, as shown by
Young, also afforded a satisfactory explanation of astronomical
aberration. But its very success gave rise to a host of new questions
all bearing on the central problem of relative motion of ether and
matter.
_Arago’s prism experiment._—The refractive index of a glass prism
depends on the incident velocity of light outside the prism and its
velocity inside the prism after refraction. On Fresnel’s fixed ether
hypothesis, the incident light waves are situated in the stationary
ether outside the prism and move with velocity _c_ with respect to the
ether. If the prism moves with a velocity _u_ with respect to this fixed
ether, then the incident velocity of light with respect to the prism
should be _c_ + _u_. Thus the refractive index of the glass prism should
depend on _u_ the absolute velocity of the prism, _i.e._, its velocity
with respect to the fixed ether. Arago performed the experiment in 1819,
but failed to detect the expected change.
_Airy-Boscovitch water-telescope experiment._—Boscovitch had still
earlier in 1766, raised the very important question of the dependence of
aberration on the refractive index of the medium filling the telescope.
Aberration depends on the difference in the velocity of light outside
the telescope and its velocity inside the telescope. If the latter
velocity changes owing to a change in the medium filling the telescope,
aberration itself should change, that is, aberration should depend on
the nature of the medium.
Airy, in 1871 filled up a telescope with water—but failed to detect any
change in the aberration. Thus we get both in the case of Arago prism
experiment and Airy-Boscovitch water-telescope experiment, the very
startling result that optical effects in a moving medium seem to be
quite independent of the velocity of the medium with respect to
Fresnel’s stationary ether.
_Fresnel’s convection coefficient k = 1 - 1/μ^2._—Possibly some form
of compensation is taking place. Working on this hypothesis, Fresnel
offered his famous ether convection theory. According to Fresnel, the
presence of matter implies a definite condensation of ether within the
region occupied by matter. This “condensed” or excess portion of ether
is supposed to be carried away with its own piece of moving matter. It
should be observed that only the “excess” portion is carried away,
while the rest remains as stagnant as ever. A complete convection of
the “excess” ether ρ′ with the full velocity _u_ is optically
equivalent to a partial convection of the total ether ρ, with only a
fraction of the velocity _k_. _u_. Fresnel showed that if this
convection coefficient _k_ is 1 - 1/μ^2 (μ being the refractive index
of the prism), then the velocity of light after refraction within the
moving prism would be altered to just such extent as would make the
refractive index of the moving prism quite independent of its
“absolute” velocity _u_. The non-dependence of aberration on the
“absolute” velocity _u_, is also very easily explained with the help
of this Fresnelian convection-coefficient _k_.
_Stokes’ viscous ether._—It should be remembered, however, that
Fresnel’s stationary ether is absolutely fixed and is not at all
disturbed by the motion of matter through it. In this respect Fresnelian
ether cannot be said to behave in any respectable physical fashion, and
this led Stokes, in 1845-46, to construct a more material type of
medium. Stokes assumed that viscous motion ensues near the surface of
separation of ether and moving matter, while at sufficiently distant
regions the ether remains wholly undisturbed. He showed how such a
viscous ether would explain aberration if all motion in it were
differentially irrotational. But in order to explain the null Arago
effect, Stokes was compelled to assume the convection hypothesis of
Fresnel with an identical numerical value for _k_, namely 1 - 1/μ^2.
Thus the prestige of the Fresnelian convection-coefficient was enhanced,
if anything, by the theoretical investigations of Stokes.
_Fizeau’s experiment._—Soon after, in 1851, it received direct
experimental confirmation in a brilliant piece of work by Fizeau.
If a divided beam of light is re-united after passing through two
adjacent cylinders filled with water, ordinary interference fringes will
be produced. If the water in one of the cylinders is now made to flow,
the “condensed” ether within the flowing water would be convected and
would produce a shift in the interference fringes. The shift actually
observed agreed very well with a value of k = 1 - 1/μ^2. The Fresnelian
convection-coefficient now became firmly established as a consequence of
a direct positive effect. On the other hand, the negative evidences in
favour of the convection-coefficient had also multiplied. Mascart, Hoek,
Maxwell and others sought for definite changes in different optical
effects induced by the motion of the earth relative to the stationary
ether. But all such attempts failed to reveal the slightest trace of any
optical disturbance due to the “absolute” velocity of the earth, thus
proving conclusively that all the different optical effects shared in
the general compensation arising out of the Fresnelian convection of the
excess ether. It must be carefully noted that the Fresnelian
convection-coefficient implicitly assumes the existence of a fixed ether
(Fresnel) or at least a wholly stagnant medium at sufficiently distant
regions (Stokes), with reference to which alone a convection velocity
can have any significance. Thus the convection-coefficient implying some
type of a stationary or viscous, yet nevertheless “absolute” ether,
succeeded in explaining satisfactorily all known optical facts down to
1880.
_Michelson-Morley Experiment._—In 1881, Michelson and Morley performed
their classical experiments which undermined the whole structure of the
old ether theory and thus served to introduce the new theory of
relativity. The fundamental idea underlying this experiment is quite
simple. In all old experiments the velocity of light situated in free
ether was compared with the velocity of waves actually situated in a
piece of moving matter and presumably carried away by it. The
compensatory effect of the Fresnelian convection of ether afforded a
satisfactory explanation of all negative results.
In the Michelson-Morley experiment the arrangement is quite different.
If there is a definite gap in a rigid body, light waves situated in free
ether will take a definite time in crossing the gap. If the rigid
platform carrying the gap is set in motion with respect to the ether in
the direction of light propagation, light waves (which are even now
situated in free ether) should presumably take a longer time to cross
the gap.
We cannot do better than quote Eddington’s description of this famous
experiment. “The principle of the experiment may be illustrated by
considering a swimmer in a river. It is easily realized that it takes
longer to swim to a point 50 yards up-stream and back than to a point 50
yards across-stream and back. If the earth is moving through the ether
there is a river of ether flowing through the laboratory, and a wave of
light may be compared to a swimmer travelling with constant velocity
relative to the current. If, then, we divide a beam of light into two
parts, and send one-half swimming up the stream for a certain distance
and then (by a mirror) back to the starting point, and send the other
half an equal distance across stream and back, the across-stream beam
should arrive back first.
——>_u_
O
A—————........
| _x_
|
|B
Let the ether be flowing relative to the apparatus with velocity _u_ in
the direction O_x_, and let OA, OB, be the two arms of the apparatus of
equal length _l_, OA being placed up-stream. Let _c_ be the velocity of
light. The time for the double journey along OA and back is
l l 2lc 2l
t₁ = ------ + ------ = -------- = --- β²
c - u c + u c² - u² c
where
$$ \beta = (1 - \frac {u^2}{c^2})^{-\frac {1}{2}} $$
a factor greater than unity.
For the transverse journey the light must have a component velocity _n_
up-stream (relative to the ether) in order to avoid being carried below
OB: and since its total velocity is _c_, its component across-stream
must be √(_c²_ - _u²_), the time for the double journey OB is
accordingly
$$ t_2 = \frac {2a}{\sqrt {c^2 - u^2}} = \frac {2a}{c} \beta $$
so that _t₁_ > _t₂_.
But when the experiment was tried, it was found that both parts of the
beam took the same time, as tested by the interference bands produced.”
After a most careful series of observations, Michelson and Morley failed
to detect the slightest trace of any effect due to earth’s motion
through ether.
The Michelson-Morley experiment seems to show that there is no relative
motion of ether and matter. Fresnel’s stagnant ether requires a relative
velocity of—_u_. Thus Michelson and Morley themselves thought at first
that their experiment confirmed Stokes’ viscous ether, in which no
relative motion can ensue on account of the absence of slipping of ether
at the surface of separation. But even on Stokes’ theory this viscous
flow of ether would fall off at a very rapid rate as we recede from the
surface of separation. Michelson and Morley repeated their experiment at
different heights from the surface of the earth, but invariably obtained
the same negative results, thus failing to confirm Stokes’ theory of
viscous flow.
_Lodge’s experiment._—Further, in 1893, Lodge performed his rotating
sphere experiment which showed complete absence of any viscous flow of
ether due to moving masses of matter. A divided beam of light, after
repeated reflections within a very narrow gap between two massive
hemispheres, was allowed to re-unite and thus produce interference
bands. When the two hemispheres are set rotating, it is conceivable that
the ether in the gap would be disturbed due to viscous flow, and any
such flow would be immediately detected by a disturbance of the
interference bands. But actual observation failed to detect the
slightest disturbance of the ether in the gap, due to the motion of the
hemispheres. Lodge’s experiment thus seems to show a complete absence of
any viscous flow of ether.
Apart from these experimental discrepancies, grave theoretical
objections were urged against a viscous ether. Stokes himself had shown
that his ether must be incompressible and all motion in it
differentially irrotational, at the same time there should be absolutely
no slipping at the surface of separation. Now all these conditions
cannot be simultaneously satisfied for any conceivable material medium
without certain very special and arbitrary assumptions. Thus Stokes’
ether failed to satisfy the very motive which had led Stokes to
formulate it, namely, the desirability of constructing a “physical”
medium. Planck offered modified forms of Stokes’ theory which seemed
capable of being reconciled with the Michelson-Morley experiment, but
required very special assumptions. The very complexity and the very
arbitrariness of these assumptions prevented Planck’s ether from
attaining any degree of practical importance in the further development
of the subject.
The sole criterion of the value of any scientific theory must ultimately
be its capacity for offering a simple, unified, coherent and fruitful
description of observed facts. In proportion as a theory becomes complex
it loses in usefulness—a theory which is obliged to requisition a whole
array of arbitrary assumptions in order to explain special facts is
practically worse than useless, as it serves to disjoin, rather than to
unite, the several groups of facts. The optical experiments of the last
quarter of the nineteenth century showed the impossibility of
constructing a simple ether theory, which would be amenable to analytic
treatment and would at the same time stimulate further progress. It
should be observed that it could scarcely be shown that no logically
consistent ether theory was possible; indeed in 1910, H. A. Wilson
offered a consistent ether theory which was at least quite neutral with
respect to all available optical data. But Wilson’s ether is almost
wholly negative—its only virtue being that it does not directly
contradict observed facts. Neither any direct confirmation nor a direct
refutation is possible and it does not throw any light on the various
optical phenomena. A theory like this being practically useless stands
self-condemned.
We must now consider the problem of relative motion of ether and matter
from the point of view of electrical theory. From 1860 the identity of
light as an electromagnetic vector became gradually established as a
result of the brilliant “displacement current” hypothesis of Clerk
Maxwell and his further analytical investigations. The elastic solid
ether became gradually transformed into the electromagnetic one. Maxwell
succeeded in giving a fairly satisfactory account of all ordinary
optical phenomena and little room was left for any serious doubts as
regards the general validity of Maxwell’s theory. Hertz’s researches on
electric waves, first carried out in 1886, succeeded in furnishing a
strong experimental confirmation of Maxwell’s theory. Electric waves
behaved generally like light waves of very large wave length.
The orthodox Maxwellian view located the dielectric polarisation in the
electromagnetic ether which was merely a transformation of Fresnel’s
stagnant ether. The magnetic polarisation was looked upon as wholly
secondary in origin, being due to the relative motion of the dielectric
tubes of polarisation. On this view the Fresnelian convection
coefficient comes out to be ½, as shown by J. J. Thomson in 1880,
instead of 1 - (1/μ²) as required by optical experiments. This obviously
implies a complete failure to account for all those optical experiments
which depend for their satisfactory explanation on the assumption of a
value for the convection coefficient equal to 1 - (1/μ²).
The modifications proposed independently by Hertz and Heaviside fare no
better.[1] They postulated the actual medium to be the seat of all
electric polarisation and further emphasised the reciprocal relation
subsisting between electricity and magnetism, thus making the field
equations more symmetrical. On this view the whole of the polarised
ether is carried away by the moving medium, and consequently, the
convection coefficient naturally becomes unity in this theory, a value
quite as discrepant as that obtained on the original Maxwellian
assumption.
Thus neither Maxwell’s original theory nor its subsequent modifications
as developed by Hertz and Heaviside succeeded in obtaining a value for
Fresnelian coefficient equal to 1 - (1/μ^2), and consequently stood
totally condemned from the optical point of view.
Certain direct electromagnetic experiments involving relative motion of
polarised dielectrics were no less conclusive against the generalised
theory of Hertz and Heaviside. According to Hertz a moving dielectric
would carry away the whole of its electric displacement with it. Hence
the electromagnetic effect near the moving dielectric would be
proportional to the total electric displacement, that is to K, the
specific inductive capacity of the dielectric. In 1901, Blondlot working
with a stream of moving gas could not detect any such effect. H. A.
Wilson repeated the experiment in an improved form in 1903 and working
with ebonite found that the observed effect was proportional to K - 1
instead of to K. For gases K is nearly equal to 1 and hence practically
no effect will be observed in their case. This gives a satisfactory
explanation of Blondlot’s negative results.
Rowland had shown in 1876 that the magnetic force due to a rotating
condenser (the dielectric remaining stationary) was proportional to K,
the sp. ind. cap. On the other hand, Röntgen found in 1888 the magnetic
effect due to a rotating dielectric (the condenser remaining stationary)
to be proportional to K - 1, and not to K. Finally Eichenwald in 1903
found that when both condenser and dielectric are rotated together, the
effect observed was quite independent of K, a result quite consistent
with the two previous experiments. The Rowland effect proportional to K,
together with the opposite Röntgen effect proportional to 1 - K, makes
the Eichenwald effect independent of K.
All these experiments together with those of Blondlot and Wilson made it
clear that the electromagnetic effect due to a moving dielectric was
proportional to K - 1, and not to K as required by Hertz’s theory. Thus
the above group of experiments with moving dielectrics directly
contradicted the Hertz-Heaviside theory. The internal discrepancies
inherent in the classic ether theory had now become too prominent. It
was clear that the ether concept had finally outgrown its usefulness.
The observed facts had become too contradictory and too heterogeneous to
be reduced to an organised whole with the help of the ether concept
alone. Radical departures from the classical theory had become
absolutely necessary.
There were several outstanding difficulties in connection with anomalous
dispersion, selective reflection and selective absorption which could
not be satisfactory explained in the classic electromagnetic theory. It
was evident that the assumption of some kind of discreteness in the
optical medium had become inevitable. Such an assumption naturally gave
rise to an atomic theory of electricity, namely, the modern electron
theory. Lorentz had postulated the existence of electrons so early as
1878, but it was not until some years later that the electron theory
became firmly established on a satisfactory basis.
Lorentz assumed that a moving dielectric merely carried away its own
“polarisation doublets,” which on his theory gave rise to the induced
field proportional to K - 1. The field near a moving dielectric is
naturally proportional to K - 1 and not to K. Lorentz’s theory thus gave
a satisfactory explanation of all those experiments with moving
dielectrics which required effects proportional to K - 1. Lorentz
further succeeded in obtaining a value for the Fresnelian convection
coefficient equal to 1 - 1/μ^2, the exact value required by all optical
experiments of the moving type.
We must now go back to Michelson and Morley’s experiment. We have seen
that both parts of the beam are situated in free ether; no material
medium is involved in any portion of the paths actually traversed by the
beam. Consequently no compensation due to Fresnelian convection of ether
by moving medium is possible. Thus Fresnelian convection compensation
can have no possible application in this case. Yet some marvellous
compensation has evidently taken place which has completely masked the
“absolute” velocity of the earth.
In Michelson and Morley’s experiment, the distance travelled by the beam
along OA (that is, in a direction parallel to the motion of the
platform) is 2_l_β², while the distance travelled by the beam along OB,
perpendicular to the direction of motion of the platform, is 2_l_β. Yet
the most careful experiments showed, as Eddington says, “that both parts
of the beam took the same time as tested by the interference bands
produced. It would seem that OA and OB could not really have been of the
same length; and if OB was of length _l_, OA must have been of length
_l_/β. The apparatus was now rotated through 90°, so that OB became the
up-stream. The time for the two journeys was again the same, so that 0B
must now be the shorter length. The plain meaning of the experiment is
that both arms have a length _l_ when placed along O_y_ (perpendicular
to the direction of motion), and automatically contract to a length
_l_/β, when placed along O_x_ (parallel to the direction of motion).
This explanation was first given by Fitz-Gerald.”
This Fitz-Gerald contraction, startling enough in itself, does not
suffice. Assuming this contraction to be a real one, the distance
travelled with respect to the ether is 2_l_β and the time taken for this
journey is 2_l_β/_c_. But the distance travelled with respect to the
platform is always 2_l_. Hence the velocity of light with respect to the
platform is
$$ \frac {2l}{\frac {2l\beta}{c}} = \frac {c}{\beta} $$
a variable quantity depending on the “absolute” velocity of the
platform. But no trace of such an effect has ever been found. The
velocity of light is always found to be quite independent of the
velocity of the platform. The present difficulty cannot be solved by any
further alteration in the measure of space. The only recourse left open
is to alter the measure of time as well, that is, to adopt the concept
of “local time.” If a moving clock goes slower so that one ‘real’ second
becomes 1/β second as measured in the moving system, the velocity of
light relative to the platform will always remain _c_. We must adopt two
very startling hypotheses, namely, the Fitz-Gerald contraction and the
concept of “local time,” in order to give a satisfactory explanation of
the Michelson-Morley experiment.
These results were already reached by Lorentz in the course of further
developments of his electron theory. Lorentz used a special set of
transformation equations[2] for time which implicitly introduced the
concept of local time. But he himself failed to attach any special
significance to it, and looked upon it rather as a mere mathematical
artifice like imaginary quantities in analysis or the circle at infinity
in projective geometry. The originality of Einstein at this stage
consists in his successful physical interpretation of these results, and
viewing them as the coherent organised consequences of a single general
principle. Lorentz established the Relativity Theorem[3] (consisting
merely of a set of transformation equations) while Einstein generalised
it into a Universal Principle. In addition Einstein introduced
fundamentally new concepts of space and time, which served to destroy
old fetishes and demanded a wholesale revision of scientific concepts
and thus opened up new possibilities in the synthetic unification of
natural processes.
Newton had framed his laws of motion in such a way as to make them quite
independent of the absolute velocity of the earth. Uniform relative
motion of ether and matter could not be detected with the help of
dynamical laws. According to Einstein neither could it be detected with
the help of optical or electromagnetic experiments. Thus the Einsteinian
Principle of Relativity asserts that all physical laws are independent
of the ‘absolute’ velocity of an observer.
For different systems, the _form_ of all physical laws is conserved. If
we chose the velocity of light[4] to be the fundamental unit of
measurement for all observers (that is, assume the constancy of the
velocity of light in all systems) we can establish a _metric_ “one-one”
correspondence between any two observed systems, such correspondence
depending only the _relative_ velocity of the two systems. Einstein’s
Relativity is thus merely the consistent logical application of the well
known physical principle that we can know nothing but _relative_ motion.
In this sense it is a further extension of Newtonian Relativity.
On this interpretation, the Lorentz-Fitzgerald contraction and “local
time” lose their arbitrary character. Space and time as measured by two
different observers are naturally diverse, and the difference depends
only on their relative motion. Both are equally valid; they are merely
different descriptions of the same physical reality. This is essentially
the point of view adopted by Minkowski. He considers time itself to be
one of the co-ordinate axes, and in his four-dimensional world, that is
in the space-time reality, relative motion is reduced to a rotation of
the axes of reference. Thus, the diversity in the measurement of lengths
and temporal rates is merely due to the static difference in the
“frame-work” of the different observers.
The above theory of Relativity absorbed practically the whole of the
electromagnetic theory based on the Maxwell-Lorentz system of field
equations. It combined all the advantages of classic Maxwellian theory
together with an electronic hypothesis. The Lorentz assumption of
polarisation doublets had furnished a satisfactory explanation of the
Fresnelian convection of ether, but in the new theory this is deduced
merely as a consequence of the altered concept of relative velocity. In
addition, the theory of Relativity accepted the results of Michelson and
Morley’s experiments as a definite principle, namely, the principle of
the constancy of the velocity of light, so that there was nothing left
for explanation in the Michelson-Morley experiment. But even more than
all this, it established a single general principle which served to
connect together in a simple coherent and fruitful manner the known
facts of Physics.
The theory of Relativity received direct experimental confirmation in
several directions. Repeated attempts were made to detect the
Lorentz-Fitzgerald contraction. Any ordinary physical contraction will
usually have observable physical results; for example, the total
electrical resistance of a conductor will diminish. Trouton and Noble,
Trouton and Rankine, Rayleigh and Brace, and others employed a variety
of different methods to detect the Lorentz-Fitzgerald contraction, but
invariably with the same negative results. _Whether there is an ether or
not, uniform velocity with respect to it can never be detected._ This
does not prove that there is no such thing as an ether but certainly
does render the ether entirely superfluous. Universal compensation is
due to a change in local units of length and time, or rather, being
merely different descriptions of the same reality, there is no
compensation at all.
There was another group of observed phenomena which could scarcely be
fitted into a Newtonian scheme of dynamics without doing violence to it.
The experimental work of Kaufmann, in 1901, made it abundantly clear
that the “mass” of an electron depended on its velocity. So early as
1881, J. J. Thomson had shown that the inertia of a charged particle
increased with its velocity. Abraham now deduced a formula for the
variation of mass with velocity, on the hypothesis that an electron
always remained a _rigid_ sphere. Lorentz proceeded on the assumption
that the electron shared in the Lorentz-Fitzgerald contraction and
obtained a totally different formula. A very careful series of
measurements carried out independently by Bücherer, Wolz, Hupka and
finally Neumann in 1913, decided conclusively in favour of the Lorentz
formula. This “contractile” formula follows immediately as a direct
consequence of the new Theory of Relativity, without any assumption as
regards the electrical origin of inertia. Thus the complete agreement of
experimental facts with the predictions of the new theory must be
considered as confirming it as a principle which goes even beyond the
electron itself. The greatest triumph of this new theory consists,
indeed, in the fact that a large number of results, which had formerly
required all kinds of special hypotheses for their explanation, are now
deduced very simply as inevitable consequences of one single general
principle.
We have now traced the history of the development of the restricted or
special theory of Relativity, which is mainly concerned with optical and
electrical phenomena. It was first offered by Einstein in 1905. Ten
years later, Einstein formulated his second theory, the Generalised
Principle of Relativity. This new theory is mainly a theory of
gravitation and has very little connection with optics and electricity.
In one sense, the second theory is indeed a further generalisation of
the restricted principle, but the former does not really contain the
latter as a special case.
Einstein’s first theory is restricted in the sense that it only refers
to uniform rectilinear motion and has no application to any kind of
accelerated movements. Einstein in his second theory extends the
Relativity Principle to cases of accelerated motion. If Relativity is to
be universally true, then even accelerated motion must be merely
_relative motion between matter and matter_. Hence the Generalised
Principle of Relativity asserts that “absolute” motion cannot be
detected even with the help of gravitational laws.
All movements must be referred to definite sets of co-ordinate axes. If
there is any change of axes, the numerical magnitude of the movements
will also change. But according to Newtonian dynamics, such alteration
in physical movements can only be due to the effect of certain forces in
the field.[5] Thus any change of axes will introduce new “geometrical”
forces in the field which are quite independent of the nature of the
body acted on. Gravitational forces also have this same remarkable
property, and gravitation itself may be of essentially the same nature
as these “geometrical” forces introduced by a change of axes. This leads
to Einstein’s famous Principle of Equivalence. _A gravitational field of
force is strictly equivalent to one introduced by a transformation of
co-ordinates and no possible experiment can distinguish between the
two._
Thus it may become possible to “transform away” gravitational effects,
at least for sufficiently small regions of space, by referring all
movements to a new set of axes. This new “framework” may of course have
all kinds of very complicated movements when referred to the old
Galilean or “rectangular unaccelerated system of co-ordinates.”
But there is no reason why we should look upon the Galilean system as
more fundamental than any other. If it is found simpler to refer all
motion in a gravitational field to a special set of co-ordinates, we may
certainly look upon this special “framework” (at least for the
particular region concerned), to be more fundamental and more natural.
We may, still more simply, identify this particular framework with the
special local properties of space in that region. That is, we can look
upon the effects of a gravitational field as simply due to the local
properties of space and time itself. The very presence of matter implies
a modification of the characteristics of space and time in its
neighbourhood. As Eddington says “matter does not cause the curvature of
space-time. It is the curvature. Just as light does not cause
electromagnetic oscillations; it is the oscillations.”
We may look upon this from a slightly different point of view. The
General Principle of Relativity asserts that all motion is merely
relative motion between matter and matter, and as all movements must be
referred to definite sets of co-ordinates, the ground of any possible
framework must ultimately be material in character. It _is_ convenient
to take the matter actually present in a field as the fundamental ground
of our framework. If this is done, the special characteristics of our
framework would naturally depend on the actual distribution of matter in
the field. But physical space and time is completely defined by the
“framework.” In other words the “framework” itself _is_ space and time.
Hence we see how _physical_ space and time is actually defined by the
local distribution of matter.
There are certain magnitudes which remain constant by any change of
axes. In ordinary geometry distance between two points is one such
magnitude; so that δ_x²_ + δ_y²_ + δ_z²_ is an invariant. In the
restricted theory of light, the principle of constancy of light velocity
demands that δ_x²_ + δ_y²_ + δ_z²_ - _c²_δ_t²_ should remain constant.
The _separation ds_ of adjacent events is defined by _ds²_ = -_dx²_ -
_dy²_ - _dz²_ + _c²dt²_. It is an extension of the notion of distance
and this is the new invariant. Now if _x_, _y_, _z_, _t_ are transformed
to any set of new variables _x₁_, _x₂_, _x₃_, _x₄_, we shall get a
quadratic expression for
$$ ds^2 = g_{1\;1}x_{1}^2 + 2g_{1\;2}x_{1}x_{2} + ... = \sum
g_{i\;j}x_{i}x_{j} $$
where the _g_’s are functions of _x₁_, _x₂_, _x₃_, _x₄_ depending on the
transformation.
The special properties of space and time in any region are defined by
these _g_’s which are themselves determined by the actual distribution
of matter in the locality. Thus from the Newtonian point of view, these
_g_’s represent the gravitational effect of matter while from the
Relativity stand-point, these merely define the non-Newtonian (and
incidentally non-Euclidean) space in the neighbourhood of matter.
We have seen that Einstein’s theory requires local curvature of
space-time in the neighbourhood of matter. Such altered characteristics
of space and time give a satisfactory explanation of an outstanding
discrepancy in the observed advance of perihelion of Mercury. The large
discordance is almost completely removed by Einstein’s theory.
Again, in an intense gravitational field, a beam of light will be
affected by the local curvature of space, so that to an observer who is
referring all phenomena to a Newtonian system, the beam of light will
appear to deviate from its path along an Euclidean straight line.
This famous prediction of Einstein about the deflection of a beam of
light by the sun’s gravitational field was tested during the total solar
eclipse of May, 1919. The observed deflection is decisively in favour of
the Generalised Theory of Relativity.
It should be noted however that the velocity of light itself would
decrease in a gravitational field. This may appear at first sight to be
a violation of the principle of constancy of light-velocity. But when we
remember that the Special Theory is explicitly _restricted_ to the case
of unaccelerated motion, the difficulty vanishes. In the absence of a
gravitational field, that is in any unaccelerated system, the velocity
of light will always remain constant. Thus the validity of the Special
Theory is completely preserved within its own _restricted_ field.
Einstein has proposed a third crucial test. He has predicted a shift of
spectral lines towards the red, due to an intense gravitational
potential. Experimental difficulties are very considerable here, as the
shift of spectral lines is a complex phenomenon. Evidence is conflicting
and nothing conclusive can yet be asserted. Einstein thought that a
gravitational displacement of the Fraunhofer lines is a necessary and
fundamental condition for the acceptance of his theory. But Eddington
has pointed out that even if this test fails, the logical conclusion
would seem to be that while Einstein’s law of gravitation is true for
matter in bulk, it is not true for such small material systems as atomic
oscillator.