DOC.
21
THEORY OF RELATIVITY
255
Conventional kinematics solves this
problem
by
means
of the
following
equations:
x'
=
x
-
vt
y'
=
y
z'
=
z
t'
=
t.
The last
of
these
equations
expresses
the
assumption
that
temporal
determinations
have
a meaning
independent
of the
state
of motion
(assumption
of "absolute
time").
But these
equations
also have hidden
in
them
an
implicit assumption,
with which
we
must
get acquainted.
The
diagram represents
the
position
and the
state
of
motion of
the
two
systems
K
and
K',
as
these
appear
when observed from
K.
Let
us
now
consider
a
point
P'
on
the x'-axis whose distance from O'
is
equal
to
l'. That
means:
an
observer
moving
with K'
must
lay
his
meter
stick
l'
times
along
the x'-axis in
order
to
get
from O'
to
P'.
But observers who
are
at rest in
system
K will have
to
proceed differently
in
order
to
evaluate the distance
O'P'.
They
determine
those
spatial points
in the
system
K
at
which O' and
P'
are
located
at
a specified
time
(of
the
system K).
The distance
l
between these
two
points, subsequently
determined
by
laying
the
meter
stick
along
the x-axis of
K,
is
the
length
we are seeking.
One
sees
that the
two
procedures
are
fundamentally different,
so
that
it is
a
priori possible
that
their numerical results l and l' differ from each other. This shows that
one
cannot
reject a priori
the
possibility
that the
concept
of
spatial
distance
might
also
possess
only
a
relative
meaning.
Thus,
in
addition
to
the
"relativity
of
time,"
we
must also
admit
a
"relativity
of
lengths."
This shatters the foundation
on
which the indicated transformation
equations
for
spatial
coordinates and time
values
are
based. In the
theory
of
relativity,
the
place
of
these
equations
is
taken
by
equations
that
simultaneously
satisfy
the
principle
of
relativity
and the
principle
of
constancy
of the
velocity
of
light.
One finds the
new
equations by formulating mathematically
the
requirement
that
every light ray
should
propagate
with the
same
velocity
c
in
both
systems
K and K'.
In
this
way
one
arrives
at
the
transformation
equations