200
MOTION OF CENTER OF GRAVITY
Doc. 35
THE
PRINCIPLE
OF
CONSERVATION OF MOTION OF THE CENTER
OF GRAVITY
AND
THE
INERTIA
OF ENERGY
by
A.
Einstein
[Annalen
der
Physik 20
(1906):
627-633]
In
a
paper
published
last
year1
I
showed
that Maxwell's
electromagnetic
equations
in
conjunction
with the principle of
relativity
and the principle of
energy
conservation led
to
the conclusion that the
mass
of
a body
changes
with
the
change
in its
energy
content,
no
matter
what
kind
of
change
of
energy
this
may
be.
It turned
out
that
to
an
energy change
of
magnitude
AE
there
must
correspond
a
change
of
mass
of the
same
sign and
of
magnitude
AE/V2,
where
V
denotes the
velocity
of light.
In
the
present
paper
I
want
to
show
that the
above theorem
is the
necessary
and
sufficient condition for the
law
of the conservation
of
motion
of
the
center
of gravity
to
be
valid
(at least
in
first
approximation)
also
for
systems
in
which not
only
mechanical, but also
electromagnetic
processes
take place.
Although
the
simple
formal considerations that
have
to
be
carried
out to
prove
this
statement
are
in the
contained in
a
work
by
H.
Poincare2,
for
the sake of
clarity
I
shall
not
base
myself
upon
that
work.
§1.
A
special
case
Let
K
be
a
stationary
rigid
hollow
cylinder
freely
floating in
space.
Let
there
be
in
A
an
arrangement
for
sending
a
certain
amount S
ing energy
through
the
cavity to
B. During
the emission of this
quantity of
a
pressure
acts
upon
the left interior wall of
the tube
K,
imparting to
the latter
a
certain
velocity
that is directed
to
the left.
If the
hollow cylinder's
mass
is
M,
then this
velocity
equals
1/V

S/M
,
as can
be
proved
easily from
the
laws of
pressure,
where
V
denotes the
1A.
Einstein,
Ann.
d.
Phys. 18
(1905):
639.
2H.
Poincare, in Lorentz-Festschrift
(1900):
252-278.
[1]
[2]
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