402
DOC.
42
SPECIAL AND GENERAL
RELATIVITY
Relativity
and
the
Problem of
Space
163
was
the
development
of Euclidean
geometry,
whose axiom-
atic formulation
must
not
be allowed
to
blind
us
to
its
empir-
ical
origin
(the
possibilities
of
laying out
or
juxtaposing
solid
bodies).
In
particular,
the three-dimensional
nature
of
space
as
well
as
its
Euclidean character
are
of
empirical
origin
(it
can
be
wholly
filled
by
like constituted
"cubes").
The
subtlety
of
the
concept
of
space
was
enhanced
by
the
discovery
that there exist
no
completely
rigid
bodies.
All
bodies
are
elastically
deformable and alter
in
volume with
change
in
temperature.
The
structures,
whose
possible congruences
are
to
be described
by
Euclidean
geometry, cannot
therefore be
represented
apart
from
physical concepts.
But since
physics
af-
ter
all
must
make
use
of
geometry
in
the establishment of
its
concepts,
the
empirical content
of
geometry
can
be stated and
tested
only
in the framework of the whole
of
physics.
In this connection atomistics
must
also
be borne
in mind,
and
its
conception
of finite
divisibility;
for
spaces
of sub-
atomic extension
cannot
be measured
up.
Atomistics
also
com-
pels
us
to give up,
in
principle,
the idea of
sharply
and
statically
defined
bounding
surfaces of
solid
bodies.
Strictly
speaking,
there
are no precise
laws,
even
in
the
macro-region,
for
the
possible configurations
of
solid
bodies
touching
each
other.
In
spite
of
this,
no one
thought
of
giving
up
the
concept
of
space,
for
it
appeared indispensable
in
the
eminently
satisfac-
tory
whole
system
of natural science.
Mach,
in
the
nineteenth
century,
was
the
only
one
who
thought seriously
of
an
elimi-
nation of the
concept
of
space,
in
that
he
sought to replace
it
by
the notion of the
totality
of the instantaneous distances