302
THE
RELATIVITY PRINCIPLE
While
this is
not
the
place
for
a
detailed discussion
of this
question,
it will
occur
to anybody who
has been following
the applications of the
principle of
relativity.
Therefore I
will
not
refrain
from
taking
a
stand
on
this question
here.
We
consider
two systems
E1
and
E2
in
motion. Let
E1
be
accelerated
[93]
in the
direction
of its X-axis, and
let
r
be
the
(temporally constant)
magnitude
of
that
acceleration.
E2
shall
be
at
rest,
but it shall
be
located
in
a homogeneous
gravitational field that
imparts
to
all
objects
an
acceleration
-r
in the direction
of
the X-axis.
[94] As
far
as we
know,
the
physical
laws
with
respect
to
E1
do
not
differ
from
those with respect
to
E2;
this
is
based
on
the
fact that all bodies
are
equally
accelerated in the
gravitational
field.
At
our
present state
of
experience
we
have
thus
no reason
to
assume
that the
systems E1
and
E2
differ
from each
other in
any
respect, and
in the discussion that
follows,
we
shall therefore
assume
the
complete
physical equivalence of
a
gravitational
field
and
a
corresponding
acceleration
of
the reference
system.
This
assumption
extends the
principle of
relativity
to
the
uniformly
accelerated translational
motion of
the reference
system. The
heuristic value
of this
assumption rests
on
the
fact that it
permits
the
replacement
of
a
homogeneous
gravitational
field
by a
uniformly
accelerated reference
system,
the latter
case
being to
some
extent
accessible
to
theoretical
treatment.
§18.
Space
and time in
a
uniformly
accelerated
reference
system
We
first consider
a body
whose
individual material
points,
at
a
given
time
t
of the nonaccelerated reference
system
S,
possess
no
velocity
relative
to
S,
but
a
certain acceleration.
What
is the influence
of
this
acceleration
r
on
the
shape
of
the
body
with respect
to S?
If
such
an
influence is
present,
it will consist
of
a
constant-ratio
dilatation in the direction
of
acceleration
and possibly
in
the two
directions
perpendicular
to
it,
since
an
effect of
another kind is
impossible
for
reasons
of
symmetry.
The
acceleration-caused dilatations (if
such
exist
at
all)
must
be
even
functions of
r;
hence
they
can
be neglected
if
one
restricts oneself
to
the
case
in
which
r
is
so
small that
terms
of
the
second
or
higher
power
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