21. IN WHAT RESPECTS ARE THE FOUNDATIONS OF CLASSICAL MECHANICS AND OF THE
SPECIAL THEORY OF RELATIVITY UNSATISFACTORY?
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
K'.
* 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.
[*]
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.