Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000Bird, J. Malcolm (James Malcolm)
Philosophy
Einstein's Theories of Relativity and Gravitation: A selection of material from the essays submitted in the competition for the Eugene Higgins prize of $5,000
Bird, J. Malcolm (James Malcolm)
Relativity (Physics)
in playing it for himself.
SOME FURTHER CONSEQUENCES
I need not trespass upon the subject matter of those essays which
appear in full by going here into any details with regard to the
manner in which time and space are finally found to depend upon one
another and to form the parts of a single universal whole. But I
may appropriately point out that if time and space are found to be
relative, we may surely expect some of the less fundamental concepts
that depend upon them to be relative also. In this expectation we are
not disappointed. For one thing,]* [mass has always been assumed to
be a constant, independent of any motion or energy which it might
possess. Just as lengths and times depend upon relative motion,
however, it is found that mass, which is the remaining factor in
the expression for energy due to motion, also depends upon relative
velocities. The dependence is such that if a body takes up an amount
of energy $E$ with respect to a certain system, the body behaves,
to measurements made from that system, as though its mass had been
increased by an amount $E/C^2$, where $C$ is as usual the velocity
of light.]194
[This should not startle us. The key to the situation lies in the
italicized words above, which indicate that the answer to the query
whether a body has taken up energy or not depends upon the seat of
observation. If I take up my location on the system $S$, and you
on the system $S'$, and if we find that we are in relative motion,
we must make some assumption about the energy which was necessary,
initially, to get us into this condition. Suppose we are on two
passing trains.]* [The chances are that either of us will assume that
he is at rest and that it is the other train which moves, although
if sufficiently sophisticated one of us may assume that he is moving
and that the other train is at rest.]272 [Whatever our assumption,
whatever the system, the localization of the energy that is carried
in latent form by our systems depends upon this assumption. Indeed,
if our systems are of differing mass, our assumptions will even govern
our ideas of the amount of energy which is represented by our relative
motion; if your system be the more massive, more energy would have to
be localized in it than in mine to produce our relative motion. If
we did not have the universal principle of relativity to forbid,
we might make an arbitrary assumption about our motions and hence
about our respective latent energies; in the presence of this veto,
the only chance of adjustment lies in our masses, which must differ
according to whether you or I observe them.]*
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