DOC.
30 FOUNDATION OF GENERAL RELATIVITY 151
recognize
that
the
path of
a
ray
of light
with
respect
to K'
must in
general
be curvilinear,
if with
respect
to K
light
is
propagated
in
a
straight
line with
a
definite
constant
velocity.
§
3.
The
Space-Time Continuum. Requirement
of
General
Co-Variance for the
Equations Expressing General
Laws
of
Nature
In
classical
mechanics,
as
well
as
in
the
special
theory
of
relativity,
the
co-ordinates
of
space
and time have
a
direct
physical meaning.
To
say
that
a
point-event
has
the
X1
co-
ordinate
x1
means
that the
projection
of
the
point-event
on
the
axis
of Xl,
determined
by rigid
rods
and
in accordance with the.
rules of
Euclidean
geometry,
is
obtained
by
measuring off
a
given
rod
(the
unit
of length)
x1
times
from
the
origin
of
co-
ordinates
along
the
axis of
X1.
To
say
that
a
point-event
has
the
X4
co-ordinate
x4
=
t, means
that
a
standard
clock,
made to
measure
time in
a
definite
unit
period,
and which is
stationary
relatively
to
the
system
of co-ordinates and
practic-
ally
coincident
in
space
with the
point-event,*
will
have
measured
off
x4
=
t
periods
at
the
occurrence
of
the
event.
This
view
of
space
and
time has
always
been
in the
minds
of
physicists,
even
if,
as a
rule, they
have been
unconscious
of it.
This
is
clear
from
the
part
which these
concepts
play
in
physical
measurements;
it
must also have
underlain the
reader's
reflexions
on
the
preceding paragraph
(§
2)
for
him
to
connect
any
meaning
with what he there
read.
But
we
shall
now
show
that
we
must
put
it
aside
and
replace
it
by
a
more
general
view,
in
order to be able to
carry through
the
postulate
of
general
relativity, if
the
special
theory
of
relativity
applies
to
the
special case
of
the
absence
of
a
gravi-
tational
field.
In
a space
which
is free of
gravitational
fields
we
introduce
a
Galilean
system
of
reference
K
(x,
y, z, t),
and also
a
system
of
co-ordinates
K'
(x',
y',
z',
t')
in uniform rotation
relatively
to
K. Let
the
origins
of
both
systems,
as
well
as
their
axes
*
We
assume
the
possibility of verifying "simultaneity"
for
events im-
mediately proximate
in
space,
or-to
speak more
precisely-for
immediate
proximity or
coincidence in
space-time,
without
giving a
definition
of
this
fundamental
concept.