258
THE
RELATIVITY PRINCIPLE
occupies
a
certain
position
in
S,
i.e., coincides with
a
certain
point
II
that is
at rest
relative to
S. The
totality
of positions of points
II
relative
to
the coordinate
system S
we
call position,
and
the
totality
of
the interrelations
of positions of
points
P
we
call
the
kinematic
shape
of
the
body
with
respect to
S
for the time
t.
If the
body
is
at
rest
relative
to
S,
its kinematic
shape
is identical with the
geometric
one.
It is clear
that observers
who
are
at rest
relative
to
a
reference
system S
can
ascertain
only
the kinematic
shape
with
respect
to
S
of
a
body
that is in
motion
relative
to
S,
but
not
its
geometric shape.
In the
following,
we
will
usually
not
distinguish
explicitly
between
geometric
and
kinematic
shape;
a
statement of geometric nature
refers
to
kinematic
or
geometric
shape,
respectively,
depending
on
whether
the latter
refers
to
a
reference
system S
or
not.
§3.
Transformation of
coordinates
and
time
Let
S
and S' be equivalent
reference
systems,
i.e.,
these
systems
shall
have
unit
measuring
rods
of
the
same
length
and
clocks
running
at
the
same
rate
when
these
objects
are
compared
with
each
other
in
a
state
of
relative
rest.
It is then
obvious
that all
physical
laws that hold with
respect
to S
will
hold in
exactly
the
same
form
for
S' too,
if
S and
S'
are
at
rest
relative
to
each
other.
The
principle
of
relativity requires
such
total
equivalence
also if
S'
is in
uniform
translational
motion
with
respect
to S. Hence,
specifically, the
velocity of
light
in
vacuum
must
have
the
same
numerical value
with
respect
to
both
systems.
Let
a
point
event
be
determined
by
the variables
x, y, z,
t
with
respect to
S,
and
by
the variables
x',
y',
z',
t' with
respect to
S',
where
S
and S'
are moving
without acceleration
and
relative
to
each
other.
We
seek
the
equations
that relate the former
to
the latter variables.
Right
off,
we
can
state
about these
equations
that
they must
be
linear
with
respect to
these variables
because
this is
required
by
the
homogeneity
properties
of
space
and
time.
Specifically, from
this it follows that the
coordinate
planes
of S'
are
uniformly
moving
planes
with respect
to
S;
yet
in
general
these
planes
will
not be
perpendicular
to
each other.
However,
if
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