254 DOC.
21
THEORY OF RELATIVITY
t1
-
t0 =
t0'
-
t1'
will be satisfied.
Now
we can
set
up
such clocks
at
arbitrary points
of
the
coordinate
system
K and
regulate
all of them
according
to
the clock
U0
in
conformity
to
the
given
rule. Then
we can
evaluate the times of
events at all
of these
points.
Relativity
of Time
As
regards
the
given
definition,
one
has
to be
careful about
one thing
in
particular.
We
use
for the definition of time
a
system
of clocks that
are
at rest
relative
to the
system
K.
Hence this definition has
meaning
only
with
respect
to
a
coordinate
system
K
in
a
specific
state
of motion. If in addition
to
the coordinate
system
K
we
introduce
another
system
K'
that
is
in uniform translational motion relative
to
K,
then
we can
define
a
time with
respect
to
K'
just
as
well
as we
have done
previously
with
respect
to
K.
But it is
not
a
priori
evident that
agreement
can
be
produced
between the
readings
of these
two
systems
of clocks. There
is
no reason a
priori why
two events
that
are
simultaneous with
respect
to
K
must
also be simultaneous with
respect
to
K'.
This is what
one
understands
by
the
"relativity
of time."
Spacetime Transformation
Thus
it turns out
that the
principle
of
constancy
of the
velocity
of
light
and the
relativity principle
are
incompatible
with each other
only as
long
as one
holds
to
the
postulate
of absolute
time, i.e., to
the absolute
meaning
of
simultaneity.
But if
one
admits the
relativity
of
time,
then the
two
principles
turn out to
be
compatible
with
each
other; proceeding
from these
two
principles,
one
arrives then
at
the
theory
designated
as
the
"theory
of
relativity."
The fundamental
problem
connected with this
conception
is
the
following:
We
are
given
two
coordinate
systems
K
and K'. Let K' be in
a
state
of uniform translation with
respect
to
K,
and
let
v
be
the
velocity
of this
motion. We
are
given
the location and time of
an
arbitrary
event
(i.e.,
the coordinates
x,
y,
z,
and the time
t)
with
respect
to
K.
One
has
to determine location and time
(x'
y', z',
t')
with
respect
to
K'. For the sake of
simplicity,
the
position
of
the
coordinate
axes
of both
systems
shall
be
chosen
as
shown
in
the
accompanying figure.
Fig.
3.