
"Does
the
Inertia of a Body depend upon its EnergyContent?"
Albert
Einstein (1905)
Translated
from
"Ist die Trägheit eines Körpes von seinem Energiegehalt abhänging?", in
Das Relativitätsprincip, 4th edition
Originally from Annalen der Physik 18 p.639641
THE
results of the
previous
investigation
lead to a very interesting conclusion, which is here to be deduced.
I based that investigation on the MaxwellHertz
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 ^{[note]}
as my basis
I deduced inter alia the following result
(Section
8):
–
Let a system of
plane waves
of
light, referred
to the
system of
coordinates (x, y, z),
possess the energy l; let the
direction of the ray (the wavenormal)
make an
angle φ
with the axis
of x of the system. If we
introduce
a new system of coordinates (ξ, η,
ζ) moving in
uniform parallel translation with respect to the system
(x, y, z),
and having its origin of coordinates in motion along the axis
of z with the velocity v,
then this quantity of light – measured in the system (ξ,
η, ζ)
– 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
( ξ, η, ζ),
moving as above with the velocity v,
be H_{0}.
Let this body send out, in a
direction making an angle φ
with
the axis of z, plane waves of
light,
of energy ½ L
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
coordinates.
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
(ξ, η, ζ)
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
coordinates 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 ( ξ, η,
ζ),
only by an additive constant C,
which
depends on the choice of
the arbitrary 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 (ξ, η,
ζ)
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 (Section
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 energycontent;
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
energycontent 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.
Bern,
September 1905
(received 27th September 1905)
original
footnotes:
footnote 1 
The
principle of the constancy of the
velocity of light is of course contained in Maxwell's
equations. 
EB
2007

