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HeathEdgar
reach-PGIZJOOVWISRIV@cuhk.edu.hk
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<font color=3D"#fffff9"> Analogously, I seek in vain for a real somethi=
ng in classical mechanics (or in the special theory of relativity) to whic=
h I can attribute the different behaviour of bodies considered with respec=
t to the reference-systems K and K'. 1 Newton saw this objection and attem=
pted to invalidate it, but without success. But E. Mach recognised it most=
clearly of all, and because of this objection he claimed that mechanics m=
ust be placed on a new basis. It can only be got rid of by means of a phys=
ics which is conformable to the general principle of relativity, since the=
equations of such a theory hold for every body of reference, whatever may=
be its state of motion. 4=20 ct proportional to it. Under these condit=
ions, the natural laws satisfying the demands of the (special) theory of r=
elativity assume mathematical forms, in which the time co-ordinate plays e=
xactly the same r=F4le as the three space co-ordinates. Formally, these fo=
ur co-ordinates correspond exactly to the three space co-ordinates in Eucl=
idean geometry. It must be clear even to the non-mathematician that, as a =
consequence of this purely formal addition to our knowledge, the theory pe=
rforce gained clearness in no mean measure. 4=20 I am standing in fro=
nt of a gas range. Standing alongside of each other on the range are two p=
ans so much alike that one may be mistaken for the other. Both are half fu=
ll of water. I notice that steam is being emitted continuously from the on=
e pan, but not from the other. I am surprised at this, even if I have neve=
r seen either a gas range or a pan before. But if I now notice a luminous =
something of bluish colour under the first pan but not under the other, I =
cease to be astonished, even if I have never before seen a gas flame. For =
I can only say that this bluish something will cause the emission of the s=
team, or at least possibly it may do so. If, however, I notice the bluish =
something in neither case, and if I observe that the one continuously emit=
s steam whilst the other does not, then I shall remain astonished and diss=
atisfied until I have discovered some circumstance to which I can attribut=
e the different behaviour of the two pans. 3=20</font>
<font color=3D"#fffff4"> I am standing in front of a gas range. Standing =
alongside of each other on the range are two pans so much alike that one m=
ay be mistaken for the other. Both are half full of water. I notice that s=
team is being emitted continuously from the one pan, but not from the othe=
r. I am surprised at this, even if I have never seen either a gas range or=
a pan before. But if I now notice a luminous something of bluish colour u=
nder the first pan but not under the other, I cease to be astonished, even=
if I have never before seen a gas flame. For I can only say that this blu=
ish something will cause the emission of the steam, or at least possibly i=
t may do so. If, however, I notice the bluish something in neither case, a=
nd if I observe that the one continuously emits steam whilst the other doe=
s not, then I shall remain astonished and dissatisfied until I have discov=
ered some circumstance to which I can attribute the different behaviour of=
the two pans. 3=20 The theory of relativity leads to the same law of=
motion, without requiring any special hypothesis whatsoever as to the str=
ucture and the behaviour of the electron. We arrived at a similar conclusi=
on in Section XIII in connection with the experiment of Fizeau, the result=
of which is fore-told by the theory of relativity without the necessity o=
f drawing on hypotheses as to the physical nature of the liquid. 5=20 =
But this result comes into conflict with the principle of relativity set =
forth in Section V. For, like every other general law of nature, the law o=
f the transmission of light in vacuo must, according to the principle of r=
elativity, be the same for the railway carriage as reference-body as when =
the rails are the body of reference. But, from our above consideration, th=
is would appear to be impossible. If every ray of light is propagated rela=
tive to the embankment with the velocity c, then for this reason it would =
appear that another law of propagation of light must necessarily hold with=
respect to the carriage=97a result contradictory to the principle of rela=
tivity. 4=20</font>
<font color=3D"#fffff2"> These inadequate remarks can give the reader onl=
y a vague notion of the important idea contributed by Minkowski. Without i=
t the general theory of relativity, of which the fundamental ideas are dev=
eloped in the following pages, would perhaps have got no farther than its =
long clothes. Minkowski=92s work is doubtless difficult of access to anyon=
e inexperienced in mathematics, but since it is not necessary to have a ve=
ry exact grasp of this work in order to understand the fundamental ideas o=
f either the special or the general theory of relativity, I shall at prese=
nt leave it here, and shall revert to it only towards the end of Part II.=20=
We must note carefully that the possibility of this mode of interpretat=
ion rests on the fundamental property of the gravitational field of giving=
all bodies the same acceleration, or, what comes to the same thing, on th=
e law of the equality of inertial and gravitational mass. If this natural =
law did not exist, the man in the accelerated chest would not be able to i=
nterpret the behaviour of the bodies around him on the supposition of a gr=
avitational field, and he would not be justified on the grounds of experie=
nce in supposing his reference-body to be =93at rest.=94 6=20 TO what e=
xtent is the special theory of relativity supported by experience? This qu=
estion is not easily answered for the reason already mentioned in connecti=
on with the fundamental experiment of Fizeau. The special theory of relati=
vity has crystallised out from the Maxwell-Lorentz theory of electromagnet=
ic phenomena. Thus all facts of experience which support the electromagnet=
ic theory also support the theory of relativity. As being of particular im=
portance, I mention here the fact that the theory of relativity enables us=
to predict the effects produced on the light reaching us from the fixed s=
tars. These results are obtained in an exceedingly simple manner, and the =
effects indicated, which are due to the relative motion of the earth with =
reference to those fixed stars, are found to be in accord with experience.=
We refer to the yearly movement of the apparent position of the fixed sta=
rs resulting from the motion of the earth round the sun (aberration), and =
to the influence of the radial components of the relative motions of the f=
ixed stars with respect to the earth on the colour of the light reaching u=
s from them. The latter effect manifests itself in a slight displacement o=
f the spectral lines of the light transmitted to us from a fixed star, as =
compared with the position of the same spectral lines when they are produc=
ed by a terrestrial source of light (Doppler principle). The experimental =
arguments in favour of the Maxwell-Lorentz theory, which are at the same t=
ime arguments in favour of the theory of relativity, are too numerous to b=
e set forth here. In reality they limit the theoretical possibilities to s=
uch an extent, that no other theory than that of Maxwell and Lorentz has b=
een able to hold its own when tested by experience. 1=20</font>
<font color=3D"#fffff9"> The second class of facts to which we have allud=
ed has reference to the question whether or not the motion of the earth in=
space can be made perceptible in terrestrial experiments. We have already=
remarked in Section V that all attempts of this nature led to a negative =
result. Before the theory of relativity was put forward, it was difficult =
to become reconciled to this negative result, for reasons now to be discus=
sed. The inherited prejudices about time and space did not allow any doubt=
to arise as to the prime importance of the Galilei transformation for cha=
nging over from one body of reference to another. Now assuming that the Ma=
xwell-Lorentz equations hold for a reference-body K, we then find that the=
y do not hold for a reference-body K' moving uniformly with respect to K, =
if we assume that the relations of the Galileian transformation exist betw=
een the co-ordinates of K and K'. It thus appears that of all Galileian co=
-ordinate systems one (K) corresponding to a particular state of motion is=
physically unique. This result was interpreted physically by regarding K =
as at rest with respect to a hypothetical =E6ther of space. On the other h=
and, all co-ordinate systems K' moving relatively to K were to be regarded=
as in motion with respect to the =E6ther. To this motion of K' against th=
e =E6ther (=93=E6ther-drift=94 relative to K') were assigned the more comp=
licated laws which were supposed to hold relative to K'. Strictly speaking=
, such an =E6ther-drift ought also to be assumed relative to the earth, an=
d for a long time the efforts of physicists were devoted to attempts to de=
tect the existence of an =E6ther-drift at the earth=92s surface. 6=20 =
But no person whose mode of thought is logical can rest satisfied with th=
is condition of things. He asks: =93How does it come that certain referenc=
e-bodies (or their states of motion) are given priority over other referen=
ce-bodies (or their states of motion)? What is the reason for this prefere=
nce? In order to show clearly what I mean by this question, I shall make u=
se of a comparison. 2=20 In one of the most notable of these attempts=
Michelson devised a method which appears as though it must be decisive. I=
magine two mirrors so arranged on a rigid body that the reflecting surface=
s face each other. A ray of light requires a perfectly definite time T to =
pass from one mirror to the other and back again, if the whole system be a=
t rest with respect to the =E6ther. It is found by calculation, however, t=
hat a slightly different time T' is required for this process, if the body=
, together with the mirrors, be moving relatively to the =E6ther. And yet =
another point: it is shown by calculation that for a given velocity v with=
reference to the =E6ther, this time T' is different when the body is movi=
ng perpendicularly to the planes of the mirrors from that resulting when t=
he motion is parallel to these planes. Although the estimated difference b=
etween these two times is exceedingly small, Michelson and Morley performe=
d an experiment involving interference in which this difference should hav=
e been clearly detectable. But the experiment gave a negative result=97a f=
act very perplexing to physicists. Lorentz and FitzGerald rescued the theo=
ry from this difficulty by assuming that the motion of the body relative t=
o the =E6ther produces a contraction of the body=20</font>
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