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 1915 Einstein brought out an extension of his first principle. This
he calls the "general theory of relativity." It states that in our
choice of coordinate systems we "should not be limited in any way
so far as their state of motion is concerned."1 This leads to the
three astronomical consequences mentioned later in this paper, two
of which have been more or less confirmed, and the third practically
contradicted as far as quantitative measures are concerned.5
As is well known the kinetic energy of a moving body may be
expressed as $e = 1/2mv^2$, but if the body is charged electrically,
the fraction becomes $1/2(m + m')v^2$, where $m'$ is a quantity
dependent on the square of the electrical charge. That is to say,
we have the normal mass of the body, and also what we may call its
electrical mass. If when in this condition a portion of the mass is
electrical, the question at once occurs to us, why may not the whole
mass be electrical, in other words, a form of energy? Although this
has not been satisfactorily proved hitherto, yet such is the general
belief among physicists. As Einstein puts it "inert mass is nothing
else than latent energy."1 The same idea is sometimes expressed as
"the mass of ordinary matter is due to the electromagnetic energy of
its ultimate particles, and electromagnetic energy wherever found
must possess mass, i.e., inertia."6 If that is so, since a ray of
light on the undulatory theory is a form of electromagnetic energy,
it too must possess mass. Since all mass with which we are familiar is
subject to the attraction of gravitation, it seemed likely that a ray
of light would be bent out of its course in passing near the sun, and
this as we have seen was proved to be true at the recent solar eclipse.
That portion of the mass of a body due to its electrical charge can
be readily shown experimentally to vary with the velocity of the
body. Einstein has shown the same to be true of the normal mass,
as is illustrated in the advance of the perihelion of the orbit
of Mercury. He has also pointed out that gravitation, inertia and
centrifugal force are all closely related, and obey similar laws. Thus
if we rise from the earth with accelerated velocity, we apparently
increase our weight. Again if the velocity of rotation of the earth on
its axis should be increased, our weight would be diminished. These
facts are suggestive when we come to consider the ultimate cause
of gravitation.
Another fact which must be rather startling to the older school
of scientists is that momentum is no longer simply $mv$, mass times
velocity, but that the velocity of light $c$, comes into the question,
and the formula for momentum now assumes the form of
$$\frac{m v}{\sqrt{1 - \frac{v^2}{c^2}}}$$
For ordinary velocities this correction is extremely small, but it
has been shown to be necessary, both theoretically and experimentally,
when dealing with the high velocities with which we are now familiar.
Public-domain text, read in full here on John Shaqi.
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