50 DOC.
1
MANUSCRIPT ON
SPECIAL RELATIVITY
quence-if the
theory
of
relativity
is
correct-must
really
hold.
[p. 40]
§14.
The
Inertia of
Energy[74]
Suppose
that
a rectangular parallelepiped-shaped plate
is
at
rest
relative
to
E',
and that its
two
lateral
surfaces,
of
surface
area
f,
are
oriented
perpendicularly
to
the x'-axis.
Let these
two
lateral surfaces
send
out
simultaneously
in
the
positive
x' direction and the
negative
x'
direction
completely identically
constituted
wave
trains,
whose
cross–
section
is
f
and
whose
(spatial) lengths,
measured in
E',
are
equal
to
l'1
=
l'2
=
l'.
We
imagine
that the
plate
floats
freely
in
space.
As
a
result of the
wave
emission,
the
plate
will
experience completely symmetrical
forces
owing
to the
radiation
pressure
and hence
remain
at rest.
We wish
to
determine the
energy
law and the
momentum
law for this
system,
both
with
respect
to
E'
as
well
as
with
respect
to
a
system
E,
which
is
always
related
to
E'
in the
same
way
as
heretofore. To this
end,
we
must
first
investigate
the
dimensions and the intensities of the
two
wave
trains
with
respect
to
E.
To
begin
with,
it
is
obvious
that
f is
also the
cross
section of the
two
wave
trains with
respect
to
E.
By
contrast,
the
lengths
l1
and
l2
of the
wave
trains with
respect
to
E
are
different from
l'.
For
the front
plane
and
rear
plane
of the
one wave
train
we
have,
respectively,
x'
=
ct'
+
a'
+
l'
and
x'
=
ct'
+
a'.
If
one
transforms
by
means
of
equations
(IIb),
one
obtains
x
=
ct
+ a
+
l'
611
+
I
and
x
=
ct
+
a,
where, again,
we
have
set
N
i
-
=
b,
and
a
denotes another
constant.
Thus,
we
obtain for the first
wave
train
with
respect
to
E
1
-
Üv
Zj
=
I'
c
N
i
+
-ÜV
c
x
}
~-.1
l:_::..:~_:.:::::_;_:.:.:_:.:.:.:::.:..~__::..~~..
I,
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