Relativity: The Special and General Theory
In What Respects are the Foundations of Classical
Mechanics and of the Special Theory of Relativity
We have already stated several times that classical mechanics starts out from the
following law: Material particles sufficiently far removed from other material particles
continue to move uniformly in a straight line or continue in a state of rest. We have also
repeatedly emphasised that this fundamental law can only be valid for bodies of reference
K which possess certain unique states of motion, and which are in uniform translational
motion relative to each other. Relative to other reference-bodies K the law is not valid.
Both in classical mechanics and in the special theory of relativity we therefore
differentiate between reference-bodies K relative to which the recognised " laws of nature
" can be said to hold, and reference-bodies K relative to which these laws do not hold.
But no person whose mode of thought is logical can rest satisfied with this condition of
things. He asks : " How does it come that certain reference-bodies (or their states of
motion) are given priority over other reference-bodies (or their states of motion) ? What
is the reason for this Preference? In order to show clearly what I mean by this question, I
shall make use of a comparison.
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 may be mistaken for the other. Both are half full of
water. I notice that steam is being emitted continuously from the one pan, but not from
the other. 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 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 steam, 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 emits steam whilst the other does not, then I shall
remain astonished and dissatisfied until I have discovered some circumstance to which I
can attribute the different behaviour of the two pans.
Analogously, I seek in vain for a real something in classical mechanics (or in the special
theory of relativity) to which I can attribute the different behaviour of bodies considered
with respect to the reference systems K and K1.1) Newton saw this objection and
attempted to invalidate it, but without success. But E. Mach recognsed it most clearly of
all, and because of this objection he claimed that mechanics must be placed on a new
basis. It can only be got rid of by means of a physics 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.
1) The objection is of importance more especially when the state of motion of the
reference-body is of such a nature that it does not require any external agency for its
maintenance, e.g. in the case when the reference-body is rotating uniformly.