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)
[For most of the velocities with which we are familiar $E/C^2$ is,
like the difference between $K$ and unity, such an extremely small
quantity that the most delicate measurements fail to detect it. But
the electrons in a highly evacuated tube and the particles shot
out from radioactive materials attain in some cases velocities as
high as eight-tenths that of light. When we measure the mass of such
particles at different velocities we find that it actually increases
with the velocity, and in accordance with the foregoing law.]194
[This observation, in fact, antedates Einstein's explanation, which
is far more satisfactory than the earlier differentiation between
"normal mass" and "electrical mass" which was called upon to account
for the increase.]*
[But if the quantity $E/C^2$ is to be considered as an actual increase
in mass, may it not be possible that all mass is energy? This would
lead to the conclusion that the energy stored up in any mass is
$mC^2$. The value is very great, since $C$ is so large; but it is in
good agreement with the internal energy of the atom as calculated
from other considerations. It is obvious that conservation of mass
and of momentum cannot both hold good under a theory that translates
the one into the other. Mass is then not considered by Einstein as
conservative in the ordinary sense, but it is the total quantity of
mass plus energy in any closed system that remains constant. Small
amounts of energy may be transformed into mass, and vice versa.]194
[Other features of the theory which are often displayed as consequences
are really more in the nature of assumptions. It will be recalled that
when we had agreed upon the necessity of employing signals of some
sort, we selected as the means of signalling the speediest messenger
with which we happened to be acquainted. Our subsequent difficulties
were largely due to the impossibility of making a proper allowance
for this messenger's speed, even though we knew its numerical value;
and as a consequence, this speed enters into our formulae. Now we have
not said in so many words that $C$ is the greatest speed attainable,
but we have tacitly assumed that it is. We need not, therefore, be
surprised if our formulae give us absurd results for speeds higher than
$C$, and indicate the impossibility of ever attaining these. Whatever
we put into a problem the algebra is bound to give us back. If we look
at our formula for $K$, we see that in the event of $v$ equalling $C$,
lengths become zero and times infinite. The light messenger itself,
then, has no dimension; and for it time stands still.
If we suppose $v$ to be greater than $C$, we get even more bizarre
results, for then the factor $K$ is the square root of a negative
number, or as the mathematician calls it an "imaginary" quantity;
and with it, lengths and times become imaginary too.
Public-domain text, read in full here on John Shaqi.
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