DOC. 71 PRINCETON LECTURES
SPECIAL RELATIVITY
There
is,
therefore,
a
four-dimensional
vector
of force
per
unit
volume, whose first
three
components,
k1, k2, k3,
are
the
ponderomotive
force
components per
unit
volume,
and
whose
fourth
component is
the
rate
of
working
of the field
per
unit
volume, multiplied
by
V-1.
Fig.
2.
A
comparison
of
(36)
and
(35)
shows
that
the
theory
of
relativity
formally
unites the
ponderomotive
force of
the
electric
field, pe,
and
the
Biot-Savart
or
Lorentz
force
i X
h.
Mass and
Energy.
An
important
conclusion
can
be
drawn
from
the
existence
and
significance
of
the 4-vector
K".
Let
us
imagine
a
body upon
which
the electro-
magnetic
field
acts
for
a
time. In the
symbolic figure
(Fig.
2)
Ox1
designates
the
x1-axis,
and
is at
the
same
time
a
substitute
for
the three
space
axes
Ox1,
Ox2,
Ox3;
Ol
designates
the real
time axis.
In
this
diagram
a
body
of finite
extent
is
represented, at
a
definite
time
l, by
the
interval
AB;
the
whole
space-time
existence of the
body
is represented
by
a
strip
whose
boundary
is
everywhere
[43]
303
[47]
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