DOC.
71
PRINCETON LECTURES 319
THE
GENERAL THEORY
without
acceleration,
and
in
which the
laws of the
special
theory
of
relativity,
which
have been
developed above,
hold
with remarkable
accuracy.
Such
regions
we
shall
call
“Galilean
regions.”
We
shall
proceed
from the
consideration of
such
regions
as a
special
case
of
known
properties.
The
principle
of
equivalence
demands
that in
dealing
with Galilean
regions
we
may equally
well
make
use
of
non-inertial
systems,
that
is,
such
co-ordinate
systems as,
relatively to
inertial
systems,
are
not
free
from accelera-
tion and rotation.
If,
further,
we are
going to
do
away
completely
with
the
vexing question
as
to
the
objective
reason
for the
preference
of certain
systems
of co-ordinates,
then
we
must
allow
the
use
of
arbitrarily moving
systems
of
co-ordinates.
As
soon as we
make
this
attempt
seriously
we come
into
conflict
with that
physical
interpretation
of
space
and
time
to
which
we were
led
by
the
special
theory
of
relativity.
For
let K'
be
a
system
of
co-ordinates
whose
z'-axis coincides
with the
z-axis
of
K,
and which
rotates
about the latter
axis
with
constant angular
velocity.
Are
the
configurations
of
rigid bodies, at
rest
relatively to
K',
in
accordance with the
laws of
Euclidean
geometry?
Since
K'
is
not
an
inertial
system,
we
do
not
know
directly
[79]
the
laws of
configuration
of
rigid
bodies
with
respect to
K',
nor
the
laws of nature,
in
general.
But
we
do
know
these laws
with
respect to
the inertial
system
K,
and
we can
therefore infer their form with
respect to
K'.
Imagine
a
circle
drawn about the
origin
in
the
x'y'
plane
of
K',
and
a
diameter
of this circle.
Imagine,
further,
that
we
have
given
a
large
number
of
rigid rods,
all
equal to
each
other.
We
suppose
these
laid
in series
along
the
periphery
and
the diameter
of
the
circle, at rest
relatively
to
K'. If
U
is
the number
of these rods
along
the
periphery,
D
the
number
[59]