The logic of modern physicsBridgman, P. W. (Percy Williams)
Philosophy
The logic of modern physics
Bridgman, P. W. (Percy Williams)
Physics -- Philosophy
An examination of what Einstein actually did in deriving his results
will show, I believe, that the situation is really different from that
suggested above. In the first place, the requirement that the laws of
nature be of invariant form actually places no restriction, as any one
can see by setting himself the task of expressing, for example, an
inverse cube law for gravitation in terms of generalized coordinates.
The work of expressing such a law can be attacked in a perfectly routine
way. (The essential difference between the invariability requirements of
the special and general theories is to be noted; the special theory
requires that the velocity of light, for instance, have the same
_numerical_ value in all allowed systems: the general theory merely that
all laws have the same _literal_ form, but with variable numerical
coefficients.) But, as Einstein says, if any one actually attempts to
carry through the work of expressing an inverse cube law in generalized
coordinates, he will find the task prohibitively complicated, and will
seek for some simpler formulation. What Einstein actually did,
therefore, was to require that the laws of nature be _simple_ in
generalized form. Now we know that the law of gravitation as formerly
expressed in ordinary coordinates as an inverse square law was
approximately exact, and was also simple. Any deviations from this law
are small, and all experience leads us to expect that to the first order
of small quantities the deviations can be taken care of mathematically
in the form of small correction terms to this law. This by itself gives
nothing, however, because a small correction term can be added to our
equations in an infinite number of ways. If, however, we know that the
equation must be of a certain type after the correction terms have been
added, the possibilities are so much restricted that the form of the
correction term may be determined. In arguing as to the probable type of
the equation, Einstein advanced the considerations by which physics gets
into the situation.
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