354 DOC. 42 SPECIAL AND GENERAL RELATIVITY
110
Relativity
body
of
reference
is
of
no
avail
in the
general theory
of rel-
ativity.
The
motion of clocks
is also
influenced
by gravita-
tional
fields,
and
in
such
a way
that
a physical
definition
of
time which
is
made
directly
with
the
aid
of
clocks has
by
no
means
the
same
degree
of
plausibility
as
in
the
special
the-
ory
of
relativity.
For this
reason
non-rigid
reference-bodies
are
used,
which
are as
a
whole
not only moving
in
any
way
whatsoever,
but
which
also
suffer alterations
in form
ad
lib.
during
their
motion.
Clocks,
for
which the
law
of motion
is
of
any
kind,
however
irregular,
serve
for
the definition of time. We
have
to imagine
each of these
clocks fixed
at
a
point on
the
non-rigid reference-body.
These
clocks
satisfy
only
the
one
condition,
that the
"readings"
which
are
observed simulta-
neously
on
adjacent
clocks
(in
space)
differ
from
each other
by
an
indefinitely
small
amount.
This
non-rigid
reference-
body,
which
might appropriately
be termed
a
"reference-
mollusc," is
in the
main
equivalent to
a
Gaussian
four-
dimensional co-ordinate
system
chosen
arbitrarily.
That
which
gives
the "mollusc"
a
certain
comprehensibility
as
compared
with the Gauss co-ordinate
system is
the
(really
unjustified)
formal
retention of the
separate
existence of the
space
co-ordinates
as
opposed to
the time co-ordinate.
Every
point
on
the mollusc
is
treated
as
a
space-point,
and
every
material
point
which
is at rest
relatively
to
it
as
at rest,
so
long as
the
mollusc
is
considered
as reference-body.
The
general principle
of
relativity requires
that
all
these molluscs
can
be used
as
reference-bodies with
equal right
and
equal
success
in the formulation of the
general
laws
of
nature;
the