28
DOC.
1
MANUSCRIPT ON SPECIAL RELATIVITY
[p.
21][54]
§8.
The
Physical Meaning
of
Spatial
and
Temporal
Determinations
Prompted by
the difficulties described in the
previous
§,
we now
seek
to
solve the
dilemma
that consists in the
incompatibility
of
postulates
(a),
(b),
and
(c)
of
the
previous
§
by
relinquishing (c)
but
keeping
the
empirically supported postulates (a)
and
(b).
We realize that the
postulate
(c) can
be
given up, i.e.,
that it is
not
logically
necessary, by investigating
the
meaning
that the
spatial
and
temporal
determinations
have in
physics.
Physical meaning
of
spatial
determinations. The
propositions
of
Euclidean
geometry
acquire a physical
content
through our assumption
that there exist
objects
that
possess
the
properties
of
the
basic
structures
of Euclidean
geometry.
We
assume
that
appropriately
constructed
edges
of solid bodies
not
subjected
to
external influences
have the
definitional
properties
that
straight
lines have
(material
straight line),
and
that the
part
of
a
material
straight
line
between
two
marked material
points
has the
properties
of
a
segment.
Then the
propositions
of
geometry
turn
into
propositions
concerning
the
arrangements
of material
straight
lines and
segments
that
are
possible[57]
when these
structures
are
at
relative
rest.[56]
By
virtue of its
properties,
every
material
straight
line
can
be extended.
By repeatedly laying
a
shorter
segment
on a longer
one
and
counting
these
operations,
one can measure
the latter
by
means
of
the
former; i.e.,
the
length
of
the
latter
can
be
expressed by
a
number
if
the former
(the
measuring rod)
is
regarded
as being given once
and for
all.
The
position
of
a
material
point
on a
material
straight
line
on
which
a
fundamental
point
is
given
once
and for all
can
be
defined
by
its
distance from the
latter,
that
is,
by
a
number
(coordinate).
[p.
22]
From
among
all the material
straight
lines
at rest
relative
to
one
another,
we
think
of three that
are
perpendicular to
one
another and intersect in
one
point
as
being
distinguished,
and from
among
all the material
straight
line
segments
we
likewise
imagine a (transportable) segment,
which
we
will think of
as
being
used for
measuring
all
lengths
(measuring
rod).
We call
these
structures,
taken
together,
"the
coordinate
system." Geometry
teaches how
we can
express
the
position
of
every
material
point
with
respect
to
such
a
coordinate
system
K
by means
of three numbers
(coordinates).
The
shape
and
position
of
a
material structure at
rest
relative
to
K
are
given by
the
totality
of
the
positions (coordinates)
of
all
of
its
material
points
with
respect
to K.
The
physical
meaning
of
temporal
determinations. If
we
consider what
happens
physically
with
respect
to
the coordinate
system K,
then
we
know that
spatial
coordinates
x, y, z
do
not
suffice
for
the
determination of the
physical
variables. The
specification
of
a
fourth basic
variable,
the
temporal coordinate,
is
also needed. This
coordinate
as
well
we
will define in such
a
way
that each
temporal
determination
shall
appear
as
the result of
a precisely
defined
measurement
procedure.