384 CONSTITUTION
OF
RADIATION
We
will
call this
proposition
the
principle of
the
constancy
of the
velocity
of light.
According
to
the addition
theorem
of
velocities,
this
same
ray
of
light will
not
also
propagate
with the
velocity
c
with
respect
to
a
coordi-
nate
system
K'
that is in translatory
motion
relative
to
the ether.
The
laws
of
propagation
of light thus
seem
to be
different relative
to
the
two
coordinate
systems,
and from
this it
seems
to
follow that the
principle of
relativity
is
incompatible
with the
laws of
propagation
of
light.
However,
the addition
theorem of
velocities is
based
on
the arbitrary
assumptions
that
statements concerning
time
as
well
as
those
concerning
the
shape
of
moving
bodies
have
a
meaning
that is
independent
of
the
state
of
motion of
the coordinate
system
used.
One
can
see,
however,
that
a
definition
of
time
and
of
the
shape
of
moving
bodies necessitates
the introduction
of
clocks that
are
at rest
with respect
to
the coordinate
system
used.
The
above
concepts
must
therefore
be
defined separately for each coordinate
system,
and
it is
not
a
foregone
conclusion that for
two
coordinate
systems
K
and
K'
moving
relative
to
each other these
definitions
yield the
same
time values
t
and
t' for
the
individual
events;
it is
equally impossible
to say
a
priori
that
every statement
about the
shape
of
the
bodies valid
with respect
to
the
coordinate
system
K
shall
also
be
valid
with
respect
to
the coordinate
system
K'
that is
moving
relative
to K.
From
this it follows that the currently
used
transformation
equations
for the transition
from
one
coordinate
system
to
another
one moving
uniformly
relative
to
it
are
based
on
arbitrary
assumptions.
If these
are dropped,
then
the foundations of the Lorentz
theory,
or,
more
generally,
the
principle of
the
constancy of
the velocity
of
light,
turn
out
to
be
reconcilable with the
principle of
relativity.
One
thus arrives
at
new
equations
for the transfor-
mation of
coordinates,
which
are
uniquely
determined
by
the
two
principles,
and which, given
the
appropriate
choice
of
the
origins
of
coordinates
and
times,
are
characterized
by
the fact that
through
them
the
equation
x2
+
y2
+
z2
-
c2t2
=
x'2
+
y'2
+
z'2
-
c2t'2
becomes
an
identity.
Here
c
denotes the
velocity of
light in
vacuum;
x,
y,
z,
t
are
space-time
coordinates with reference
to
K,
and
x', y',
z',
t'
with reference
to K'.