DOC. 52 GEOMETRY AND EXPERIENCE 213
GEOMETRY
AND
EXPERIENCE
237
physics.
But
it
is
my
conviction
that in the
present
stage
of
development
of theoretical
physics
these
concepts
must
still be
employed
as
independent
concepts;
for
we are
still far from
[16]
possessing
such certain
knowledge
of the
theoretical
principles
of atomic
structure
as
to
be able
to construct
solid bodies and
clocks
theoretically
from
elementary
concepts.
[17]
Further,
as
to
the
objection
that there
are no
really
rigid
bodies
in
nature,
and that therefore the
properties predicated
of
rigid
bodies do
not apply
to
physical
reality-this
objection
is
by no means so
radical
as
might
appear
from
a
hasty
examina-
tion.
For
it
is not
a
difficult task
to
determine the
physical
state
of
a
measuring-body
so
accurately
that its
behavior
relative
to
other
measuring-bodies
shall be
sufficiently
free from
ambiguity
to
allow
it
to
be
substituted
for the
“rigid”
body.
It
is to
meas-
uring-bodies
of this
kind
that
statements
about
rigid
bodies
must
be
referred.
All
practical geometry
is
based
upon
a
principle
which
is
[18]
accessible
to experience,
and which
we
will
now try
to
realize.
Suppose
two
marks have been
put
upon
a
practically-rigid
body.
A
pair
of
two
such marks
we
shall call
a
tract.
We
imagine
two
practically-rigid
bodies,
each with
a
tract
marked
out
on
it.
These
two tracts
are
said
to
be
“equal to
one
another” if the
marks of the
one
tract
can
be
brought
to
coincide
permanently
with
the marks of the other. We
now assume
that:
If
two tracts
are
found
to
be
equal
once
and
anywhere, they
are
equal always
and
everywhere.
[19]
Not
only
the
practical geometry
of
Euclid,
but also its
nearest
generalization,
the
practical
geometry
of Riemann, and there-
with the
general
theory
of
relativity, rest upon
this
assumption.
[20]
Of the
experimental
reasons
which
warrant
this
assumption
I
will
mention
only one.
The
phenomenon
of the
propagation
of
[p.
128]
light
in
empty space
assigns
a
tract, namely,
the
appropriate path
of
light, to
each
interval
of local
time,
and
conversely.
Thence it
follows that the above
assumption
for
tracts must
also
hold
good
for
intervals
of clock-time in the
theory
of
relativity.
Conse-
quently
it
may
be
formulated
as
follows: if
two
ideal
clocks
are
going at
the
same
rate at any
time and
at any
place
(being