DOC.
2
RELATIVITY AND
ITS CONSEQUENCES
133
These transformation
equations
have
been introduced into
electrodynamics
in
a
very
[17]
felicitous
manner by
Mr.
Lorentz. We
will call
them
Lorentz
transformations.
If
we
solve
these
equations
with
respect
to
t, x, y,
z
we
obtain
equations
of the
same form, except
that the
primed
letters
are
replaced
by
nonprimed ones,
and
v
is
replaced
by
-v.
Moreover, this
result
is
an
obvious
consequence
of the
principle
of
relativity:
relative
to S',
S
is
moving
with
velocity -v
parallel
to
the
x
and x'
axes.
By combining
the
transformation
equations
with the
equations
expressing
the
rotation
of
one system
with
respect
to
another
one,
we can
obtain the
most
general
transforma-
tions
of
coordinates.
§7.
Physical Interpretations
of
the
Transformation Equations
1.
Consider
a
body
attached
to
S'. Let x'1,
y'1,
z'1 and x'2,
y'2,
z'2
be
coordinates
of
two
points
of
the
body.
At
any
instant
t
of the
system
S
we
will have
the
following
relations between these coordinates:
(6)
X2
~X1 =
c22
y
2
-yi
T-1
1
CO
II
22
~zx
= Zx
r
-
z'
2
^
1
(*'2
This shows
us
that the kinematic
configuration
of
a body
in
uniform translational
motion
with
respect
to
a
coordinate
system
depends on
the
velocity
v
of
the
translation.
Furthermore,
the
kinematic
configuration
differs from
the
geometric
configuration solely
by a
contraction
in
the direction of the
motion,
a
contraction
which
is
in
the ratio
V2
1 :
1
-
- .
A
relative
motion of
two
reference
systems
with
a velocity
v
that
exceeds
c2
the
velocity
of
light
in
vacuum
is incompatible
with
the
principle
here
assumed.
One
recognizes
at
once
in
these
equations
the
hypothesis
of
Messrs.
Lorentz and
FitzGerald
(§3).
This
is
the
hypothesis
that looked
so
strange
to
us
and
that had
to be
introduced
to
explain
the
negative
results of the
experiment
of
Michelson
and
Morley.
Here
this
hypothesis
appears naturally
as an
immediate
consequence
of the
principles
assumed.
2.
Let
us
consider
a
clock
H'
which
is at
rest at the
origin
of
S',
and
which
runs
p0
times
faster
than
one
of
the clocks
used for the determination of
physical
time
in
the
systems
S
or
S'. In other
words,
when
the
two
clocks
are compared
while
at
relative
rest, clock
H'
will indicate
p0
periods during
the unit
time
indicated
by
the other
clock.