DOC.
71
PRINCETON LECTURES
285
SPECIAL
RELATIVITY
to
which
the laws of
mechanics
(more generally
the
laws
of
physics) are expressed
in
the
simplest
form. We
may
surmise
the
validity
of the
following
proposition:
If
K
is
an
inertial
system,
then
every
other
system
K'
which
moves
uniformly
and without rotation
relatively
to
K,
is
also
an
inertial
system;
the laws of
nature are
in concordance
for
all
inertial
systems.
This
statement
we
shall call
the
“principle
of
special
relativity.”
We shall
draw certain
conclusions from this
principle
of
“relativity
of
translation”
just
as we
have
already
done
for
relativity
of
direction.
In order
to
be
able
to
do
this,
we
must
first solve
the
following
problem.
If
we are given
the
Cartesian
co-ordi-
nates,
xv,
and
the time
t,
of
an
event
relatively
to
one
inertial
system, K,
how
can we
calculate
the
co-ordinates,
x'v,
and the
time,
t',
of
the
same
event relatively to
an
inertial
system
K' which
moves
with
uniform translation
relatively
to
K?
In
the
pre-relativity
physics
this
problem
was
solved
by making
unconsciously
two
hypotheses:-
1.
Time
is absolute;
the time of
an
event, t',
relatively
to
K'
is
the
same as
the
time
relatively to K.
If
instanta-
neous
signals
could
be
sent to
a
distance,
and
if
one
knew
that the
state
of
motion
of
a
clock
had
no
influence
on
its
rate,
then
this
assumption
would be
physically
validated.
For then
clocks,
similar
to
one
another,
and
regulated
alike,
could
be
distributed
over
the
systems
K and
K',
at
rest
relatively
to
them,
and
their
indications would
be
independent
of the
state
of motion
of the
systems;
the time
of
an
event
would
then
be
given
by
the
clock
in
its
immedi-
ate neighbourhood.
2.
Length is
absolute;
if
an
interval,
at rest
relatively
to K,
has
a
length
s,
then
it has the
same
length
s,
relatively
to
a
system
K'
which
is
in motion
relatively
to
K.
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