344
DOC.
17
THE THEORY
OF
RELATIVITY
vacuum
with
the
universal
velocity c.
This
ought
to
hold
independently
of whether the
light-emitting
body
is
in
motion
or
at
rest.
We
shall
designate
this
proposition
as
the
principle
of
constancy
of
the
velocity
of
light.
Thus,
the
question we
have
just
asked
can
also
be formulated
as
follows: Is it
impossible
to
reconcile the
principle
of
relativity,
which
seems
to
be
satisfied
without
exception,
with this
principle
of
constancy
of the
velocity
of
light?
[5]
To
begin
with,
the
following
obvious
consideration
argues against
this
possibility:
If
every ray
of
light
propagates
with
the
velocity c
relative
to
the reference
system k,
then
the
same
cannot be true with
respect
to
the reference
system
k', if k'
is in
motion
relative
to k.
For
if
k'
is
moving
with
velocity v
in
the direction of the
propagation
of
a
light ray,
then the
propagation
velocity
of the
light ray
relative to
k'
would have
to
be
set
equal
to
c
-
v
according
to
our
customary
views.
The
laws
of
propagation
of
light
with
respect
to
k'
would
then
differ
from those
with
respect
to
k,
which would
mean a
violation of
the
principle
of
relativity.
That
is
a frightful
dilemma. But it
turned
out
that
nature
is
not
responsible
for
this
dilemma;
rather,
this
dilemma
stems from
the
fact
that
we
have
been
making
tacit
and
arbitrary
assumptions
in
our
arguments,
and
thus
also in
the
argument just
given,
and
that these
have to
be
dropped
in
order
to arrive at
a
consistent and
simple
interpretation
of
things.
Let
me
try
to
analyze
these
arbitrary
assumptions,
which
permeated
the foundations
of
our thinking
in
physics.
The
first
and
most
important
of these
arbitrary
assumptions
concerned the
concept
of
time,
and
I will
try
to
explain
in what this
arbitrariness
consists.
To be
able to do this
well,
I will start
by discussing space,
in
order
to draw
a
parallel
between
space
and
time.
If
we
wish to
describe the
position
of
a
point
in
space,
i.e.,
the
position
of
a
point
relative
to
a
coordinate
system
k,
we specify
the
point's orthogonal
coordinates
x, y,
z.
The
meaning
of these coordinates
is
as
follows:
According
to
familiar
rules,
we
construct
perpendiculars
to
the coordinate
planes,
and
check
how
many
times
a
given
unit
measuring
rod
can
be
laid
along
these
perpendiculars.
The coordinates
are
the results of
this
counting. Thus,
the
specifying
of
spatial
position
by means
of
coordinates
is
the result of
specific
manipulations.
Accordingly,
the coordinates
I
specify
have
a
completely
determinate
physical meaning; one can
verify
whether
a specific, given
point
really
has
the indicated coordinates
or
not.
Where
do
we
stand
with time in this
respect?
As
we
shall
see, we are
not
so
well
off
when it
comes
to time.
Up
to
now,
people
always
contented themselves
with
saying:
Time
is
the
independent
variable
of
events.
The
measurement
of the time
value
of
an
actually
occurring
event
can never
be
based
on
such
a
definition.
Hence
we
must
try
to
define time
in
a way
that
will make it
possible
to
measure
time
on
the
basis
of
this
definition.
Let
us imagine a
clock
(a
balance
wheel
clock,
for
example)
at
the
origin
of
a
coordinate
system
k.
Using
this clock
we can
evaluate the
time
of
events
occurring
directly
at this
point
or
in its
immediate
vicinity.
However,
events
occurring
at
another
point
of k
cannot
be evaluated
directly
with this clock. If
an
observer
standing
next to