UPON ITS ENERGY-CONTENT?

September 27, 1905

The results of the previous investigation lead to a very interesting conclusion, which is here to be deduced.

I based that investigation on the Maxwell-Hertz equations for empty space, together with the Maxwellian expression for the electromagnetic energy of space, and in addition the principle that:—

*
The laws by which the states of physical systems alter are
independent of the alternative, to which of two systems of
coordinates, in uniform motion of parallel translation
relatively to each other, these alterations of state are
referred (principle of relativity).
*

With these principles^{*} as my
basis I deduced *inter alia* the
following result (§ 8):—

Let a system of plane waves of light, referred to the system
of co-ordinates (*x, y, z*), possess the energy *l*; let the
direction of the ray (the wave-normal) make an angle
with the axis of *x* of the system. If we introduce a new system
of co-ordinates () moving in uniform parallel translation
with respect to the system (*x, y, z*), and having its origin
of co-ordinates in motion along the axis of *x* with the
velocity *v*, then this quantity of light—measured in the
system ()—possesses the energy

where *c* denotes the velocity of light. We shall make use of this
result in what follows.

Let there be a stationary body in the system (*x, y, z*),
and let its energy—referred to the system (*x, y, z*) be E_{0}.
Let the energy of the body relative to the system ()
moving as above with the velocity *v*, be H_{0}.

Let this body send out, in a direction making an angle
with the axis of *x*, plane waves of light, of energy ½L measured
relatively to (*x, y, z*), and simultaneously an equal quantity
of light in the opposite direction. Meanwhile the body remains at
rest with respect to the system (*x, y, z*). The principle of
energy must apply to this process, and in fact (by the principle of
relativity) with respect to both systems of co-ordinates. If we call
the energy of the body after the emission of light E_{1} or
H_{1} respectively, measured relatively to
the system (*x, y, z*) or
() respectively, then by employing
the relation given above we obtain

By subtraction we obtain from these equations

The two differences of the form H − E occurring in this expression
have simple physical significations. H and E are
energy values of the same body referred to two systems of
co-ordinates which are in motion relatively to each other, the
body being at rest in one of the two systems (system (*x, y, z*)).
Thus it is clear that the difference H − E can differ from the
kinetic energy K of the body, with respect to the other
system
(),
only by an additive constant C, which depends on the
choice of the arbitrary additive constants of the energies H and E. Thus we may place

since C does not change during the emission of light. So we have

The kinetic energy of the body with respect to () diminishes as a
result of the emission of light, and the amount of diminution is
independent of the properties of the body. Moreover, the difference
K_{0} − K_{1}, like the kinetic energy of the electron
(§ 10),
depends on the velocity.

Neglecting magnitudes of fourth and higher orders we may place

From this equation it directly follows that:—

*If a body gives off the energy L in the form of radiation, its mass
diminishes by L/c²*.
The fact that the energy withdrawn from the body
becomes energy of radiation evidently makes no difference, so that we
are led to the more general conclusion that

The mass of a body is a measure of its energy-content; if the energy
changes by L, the mass changes in the same sense by
L/9 × 10^{20}, the energy being measured
in ergs, and the mass in grammes.

It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.

If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies.

* The principle of the constancy of the velocity of light is of course contained in Maxwell's equations.

## About this Edition
This edition of Einstein's
The footnote is as it appeared in the 1923 edition. The 1923 English
translation modified the notation used in Einstein's 1905 paper to
conform to that in use by the 1920's; for example, This electronic edition was prepared by John Walker in March 2001. You can download a ready-to-print PostScript file of this document or the LaTeX source code used to create it from this site; both are supplied as Zipped archives. An Adobe Acrobat PDF edition of this document is also available.
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