352
DOC. 42 SPECIAL AND GENERAL RELATIVITY
TWENTY-EIGHT
Exact Formulation
of
the
General
Principle
of
Relativity
We
are
now
in
a
position to replace
the
provisional
formulation of the
general principle
of
relativity
given
in
Section
18
by
an
exact
formulation.
The
form
there
used, "All
bodies of reference
K,
K',
etc.,
are
equivalent
for
the
description
of natural
phenomena
(formu-
lation of the
general
laws
of
nature),
whatever
may
be their
state
of
motion," cannot
be
maintained,
because the
use
of
rigid
reference-bodies, in
the
sense
of the method followed
in the
special theory
of
relativity, is
in
general
not
possible
in
space-time description.
The
Gauss
co-ordinate
system
has
to
take the
place
of the
body
of reference. The
following
statement
corresponds to
the fundamental idea of the
gen-
eral
principle
of
relativity: "All
Gaussian co-ordinate
systems
are essentially
equivalent
for the
formulation
of
the general
laws
of
nature."
We
can
state
this
general principle
of
relativity
in still
an-
other
form,
which
renders it
yet
more
clearly intelligible
than
it
is
when in the
form
of
the natural extension of the
special
108