DOC. 42 SPECIAL AND GENERAL RELATIVITY
353
Exact Formulation
of
the
General
Principle
of
Relativity
109
principle
of
relativity.
According
to
the
special theory
of
rel-
ativity,
the
equations
which
express
the
general
laws
of
nature
pass
over
into
equations
of
the
same
form
when,
by making
use
of the
Lorentz
transformation,
we
replace
the
space-time
variables
x,
y,
z, t,
of
a
(Galileian)
reference-body
K
by
the
space-time
variables
x',
y',
z',
t'
of
a new
reference-body
K'.
According to
the
general theory
of
relativity,
on
the
other
hand, by application
of
arbitrary
substitutions
of the Gauss
vari-
ables
x1, x2, x3, x4,
the
equations
must
pass over
into
equations
of
the
same form;
for
every
transformation
(not
only
the
Lorentz
transformation)
corresponds to
the transition of
one
Gauss co-ordinate
system
into another.
If
we
desire
to
adhere
to
our
"old-time"
three-dimensional
view
of
things,
then
we
can
characterise the
development
which
is
being undergone by
the
fundamental idea of the
general theory
of
relativity
as
follows:
The
special theory
of
relativity
has
reference
to
Galileian
domains, i.e. to
those in
which
no
gravitational
field exists. In this connection
a
Gal-
ileian
reference-body
serves as body
of
reference, i.e.
a
rigid
body
the
state
of motion
of
which
is
so
chosen
that the
Gal-
ileian
law
of the uniform rectilinear motion of
"isolated"
ma-
terial
points
holds
relatively to
it.
Certain considerations
suggest
that
we
should refer
the
same
Galileian domains
to
non-Galileian
reference-bodies
also.
A
gravitational
field
of
a
special
kind
is
then
present
with
respect
to
these
bodies
(cf.
Sections
20
and
23).
In
gravitational
fields
there
are no
such
things
as
rigid
bodies with Euclidean
properties;
thus
the
fictitious
rigid