HKB
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.
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[11] 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
image024
[11] E0 is the energy taken up, as judged from a co-ordinate system moving with the body.
In consideration of the expression given above for the kinetic energy of the body, the required energy of the body comes out to be
image025
Thus the body has the same energy as a body of mass
image026
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
image027
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
image028
we see that the term mc2, which has hitherto attracted our attention, is nothing else than the energy possessed by the body[12] before it absorbed the energy E0.
[12] As judged from a co-ordinate system moving with the body.
A direct comparison of this relation with experiment is not possible at the present time (1920; see[Note], p. 48), 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.
image027
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.
[Note] The equation E = mc2 has been thoroughly proved time and again since this time.
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 role in this theory. In Part II we shall see in what way this result becomes modified in the general theory of relativity.
XVI.
EXPERIENCE AND THE SPECIAL THEORY OF RELATIVITY