DOC.
21
THEORY OF RELATIVITY 249
describe the
position
of
a thing
relative
to
a glass
pipe,
a
wooden
framework,
the
walls of
a
room,
the surface of the
earth, etc. In
a
theory,
the coordinate
system
is
the
representative
of this solid
body.
This
is
an
imaginary rigid
framework that
is to
be
replaced
by
a
real
solid
body
whenever
one
has
to
test
the
correctness
of
a
theoretical
result
in
which
spatial
determinations
appear.
Thus,
the
physicist's
coordinate
system
represents a
real
rigid body
to
which the
phenomena
to
be
studied
are
to
be referred.
Let
us
take
some
simple empirical
law in which
spatial
determinations
appear,
e.g.,
Galileo's familiar law of inertia:
a
material
point
not
acted
upon
by
external
forces
moves uniformly
in
a straight
line. It is clear
that
this
law cannot
hold
true
if
the motion is referred
to
an
arbitrarily
moving
coordinate
system (e.g., one
undergoing arbitrary rotation).
We
must
therefore formulate Galileo's fundamental
law in the
following
way:
It is
possible
to
choose
a
coordinate
system
K that
is in
such
a
state
of
motion that
every freely moving
material
point
moves
rectilinearly
and
uniformly
relative
to
it.
Naturally,
the law also holds then for
all
other coordinate
systems
at rest
with with
respect
to
K.
If Galileo's fundamental law
were
not
valid for
any
coordinate
system
that
is in
motion relative
to
K,
then the
state
of motion of
K
would be
privileged
with
respect
to
all other
states
of motion. We could then
designate
this
state
of
motion,
appropriately, as
that of absolute
rest. However,
a simple argument
shows that
every
freely moving
material
point
satisfies Galileo's fundamental law
not
only
with
respect
to
K but also with
respect
to
every
coordinate
system
K' in
uniform translational
motion relative
to
K.
The laws of
mechanics
are just as
valid
relative
to
such
systems
K'
as they are
relative
to
K.
There exists
a
whole
class of
coordinate
systems moving
uniformly
relative
to
one
another that
are
strictly equivalent
when
it
comes
to
formulating
the laws of mechanics. But this
equivalence
of the
systems
K and K' that
are
moving uniformly
relative
to
each other
is not
limited
to
mechanics.
So
far
as our
experience extends,
this
equivalence
holds
generally.
The
assumption
of the
equivalence
of
all such
systems
K,
K',
which rules
out the
privileging
of
one
state of
motion
over
all
others,
we
will
designate
as
the
"relativity principle."
H.
A.
Lorentz's
Theory
and
the
Relativity
Principle.
The
Principle
of the
Constancy
of the
Velocity
of
Light
Lorentz's
theory
arouses our
mistrust in that
it
seems
to
contradict
the
relativity
principle.
The
following argument
shows
this.
According
to
Lorentz's
theory,
the
motion of
matter
does
not
result
in
any
motion of
the
luminiferous
ether.
Instead,
the
parts
of the latter
are
at rest
relative
to
each other. If
we
choose
a
coordinate
system
K
that
is at rest
relative
to
the
ether,
then this coordinate
system
K is
privileged
with