| IT is clear from our previous considerations that
the (special) theory of relativity has grown out of electrodynamics and
optics. In these fields it has not appreciably altered the predictions
of theory, but it has considerably simplified the theoretical structure,
i.e. the derivation of laws, and—what is incomparably more important—it
has considerably reduced the number of independent hypotheses forming the
basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz
theory so plausible, that the latter would have been generally accepted
by physicists even if experiment had decided less unequivocally in its
favour. |
1 |
| Classical mechanics required to be modified before it could
come into line with the demands of the special theory of relativity. For
the main part, however, this modification affects only the laws for rapid
motions, in which the velocities of matter v are not very small
as compared with the velocity of light. We have experience of such rapid
motions only in the case of electrons and ions;
for other motions the variations from the laws of classical mechanics are
too small to make themselves evident in practice. We shall not consider
the motion of stars until we come to speak of the general theory of relativity.
In accordance with the theory of relativity the kinetic energy of a material
point of mass m is no longer given by the well-known expression
but by the expression
This expression approaches infinity as the velocity v approaches
the velocity of light c. The velocity must therefore always remain
less than c, however great may be the energies used to produce the
acceleration. If we develop the expression for the kinetic energy in the
form of a series, we obtain
|
2 |
| When
is small compared with unity, the third of these terms is always
small in comparison with the second, which last is alone considered in
classical mechanics. The first term mc2 does not contain
the velocity, and requires no consideration if we are
only dealing with the question as to how the energy of a point-mass depends
on the velocity. We shall speak of its essential significance later.
|
3 |
| The most important result of a general character to which the
special theory of relativity has led is concerned with the conception of
mass. Before the advent of relativity, physics recognised two conservation
laws of fundamental importance, namely, the law of the conservation of
energy and the law of the conservation of mass; these two fundamental laws
appeared to be quite independent of each other. By means of the theory
of relativity they have been united into one law. We shall now briefly
consider how this unification came about, and what meaning is to be attached
to it. |
4 |
| The principle of relativity requires that the law of the conservation
of energy should hold not only with reference to a co-ordinate system K,
but also with respect to every co-ordinate system K' which is in
a state of uniform motion of translation relative to K, or, briefly,
relative to every “Galileian” system of co-ordinates. In contrast to classical
mechanics, the Lorentz transformation is the deciding factor in the transition
from one such system to another. |
5 |
| By means of comparatively simple considerations we are led to draw
the following conclusion from these premises, in conjunction with the
fundamental equations of the electrodynamics of Maxwell: A body moving with
the velocity v, which absorbs 1 an amount of energy
E0 in the form of radiation without suffering an alteration in
velocity in the process, has, as a consequence, its energy increased by
an amount |
6 |
| In consideration of the expression given above for the kinetic
energy of the body, the required energy of the body comes out to be |
7 |
| Thus the body has the same energy as a body of mass
moving with the velocity v. Hence we can say: If a body takes
up an amount of energy E0, then its inertial mass increases
by an amount
the inertial mass of a body is not a constant, but varies according
to the change in the energy of the body. The inertial mass of a system
of bodies can even be regarded as a measure of
its energy. The law of the conservation of the mass of a system becomes
identical with the law of the conservation of energy, and is only valid
provided that the system neither takes up nor sends out energy. Writing
the expression for the energy in the form
we see that the term mc2, which has hitherto attracted our
attention, is nothing else than the energy possessed by the body
1 before it absorbed the energy E0.
|
8 |
| A direct comparison of this relation with experiment is not
possible at the present time, owing to the fact that the changes in energy
E0 to which we can subject a system are not large enough
to make themselves perceptible as a change in the inertial mass of the
system.
is too small in comparison with the mass m, which was present
before the alteration of the energy. It is owing to this circumstance that
classical mechanics was able to establish successfully the conservation
of mass as a law of independent validity.
|
9 |
| Let me add a final remark of a fundamental nature. The success
of the Faraday-Maxwell interpretation of electromagnetic
action at a distance resulted in physicists becoming convinced that there
are no such things as instantaneous actions at a distance (not involving
an intermediary medium) of the type of Newton’s law of gravitation. According
to the theory of relativity, action at a distance with the velocity of
light always takes the place of instantaneous action at a distance or of
action at a distance with an infinite velocity of transmission. This is
connected with the fact that the velocity c plays a fundamental rôle
in this theory. In Part II we shall see in what way this result becomes
modified in the general theory of relativity. |
10 |