DOC. 71 PRINCETON LECTURES
301
SPECIAL
RELATIVITY
as one
can easily verify by
substituting
from
(30a)
and
(31). Equations (32)
and
(33)
have
a
tensor
character,
and
are
therefore co-variant
with
respect
to
Lorentz
transformations, if
the
/M"
and the jm
have
a
tensor character,
which
we assume.
Consequently,
the
laws
for
transforming
these
quantities
from
one
to
another allowable
(inertial)
system
of co-ordinates
are
uniquely
determined. The
progress
in
method which
electro-dynamics
owes
to
the
theory
of
special
relativity
lies
principally
in
this,
that
the number
of
independent
hypotheses is
diminished. If
we
consider,
for
example, equations (19a)
only
from the
standpoint
of
relativity
of
direction,
as we
have done
above,
we see
that
they
have three
logically
independent terms.
The
way
in
which the electric
intensity enters
these
equa-
tions
appears to
be
wholly
independent
of the
way
in which
the
magnetic
intensity
enters
them; it
would
not
be
sur-
prising
if instead of
0l/0l
we
had,
say,
~qJT,
or
if
this term
were
[43]
absent. On
the
other
hand,
only
two independent terms
appear
in
equation (32).
The
electromagnetic
field
appears
as a
formal
unit;
the
way
in which
the
electric
field
enters
this
equation
is
determined
by
the
way
in
which the
magnetic
field
enters
it.
Besides
the
electromagnetic
field, only
the electric
current
density
appears
as an
inde-
pendent entity.
This advance
in
method
arises from
the
fact
that the
electric
and
magnetic
fields lose
their
separate
existences
through
the
relativity
of
motion.
A field
which
appears to
be
purely
an
electric
field,
judged
from
one
system,
has also
magnetic
field
components
when
judged
from
another
inertial
system.
When
applied to
an
electromagnetic
field,
the
general
law of
transformation
furnishes,
for the
special
case
of
the
special
Lorentz
trans-
formation,
the
equations
[41]