DOC.
2
RELATIVITY AND
ITS CONSEQUENCES
129
connecting
the
two
points
P1
and
P2
by successively applying
the
measuring
rod
along
the
line
P1P2,
which
is
assumed
to be
a
material
line.
As
one can see,
it
is
with
some
justification
that the results obtained
in
the
first
and
in
the second
case are
designated
as
the
"length
of the bar."
But in
no way
does
this
mean
a priori
that these
two
operations
must
necessarily
lead to
the
same
numerical value
for the
length
of the
bar. All
that
one can
deduce
from
the
principle
of
relativity-and
this
is
easy
to
demonstrate-is that the
two
methods lead
to
the
same
numerical
value
for the
length only
when
the bar
AB
is
at rest
relative
to
the
system
S.
But
in
no way
is
it
possible
to assert
that the
second
method
yields a
numerical
value
for the
length
independently
of the
velocity v
of the bar.
More
generally,
if
the
configuration
of
a body
in
uniform translational motion
with
respect
to S
is
determined
by
ordinary geometric
methods,
by means
of
measuring
rods
or
other
solid
bodies
moving
in
exactly
the
same way
the results of
measurement
turn out
to
be
independent
of
the
velocity v
of
the
translation: these results
give us
what
we
will
call
the
geometric configuration
of the
body. By
contrast,
if
one
marks in
the
system
S
the
positions
of various
points
of the
body
at
a
given
instant,
and determines the
configuration
formed
by
these
points
by
geometric
measurements
using
measuring
rods
at rest with
respect
to
S,
one
obtains
as a
result
what
we
will call
the
kinematic
configuration
of the
body
with
respect
to
S.
[13]
The second
hypothesis
used
unconsciously
in kinematics
can
thus be
expressed
as
follows:
The
kinematic
configuration
and
the
geometric configuration are
identical.
[Continued
in
the
15
February
issue
of
Archives,
pp. 125-144]
§6.
The New
Transformation Equations
(the
Lorentz
Transformation)
[14]
and
Their
Physical Meaning
To
emphasize
the considerations
discussed in
the
preceding
section,
it is
easy
to
see
that
the
rule
of
the
parallelogram
of
velocities,
which
made
one
think that Lorentz's
theory
cannot
be reconciled
with
the
theory
of
relativity,
is
based
on unacceptable arbitrary
hypotheses.
In
fact,
this
rule
leads
to
the
following
transformation
equations,
t'
=
t,
x'
=
x
-
vt,
y'
=
y,
z'
=
z,
or more generally,
t'
=
t,
x'
= x
-
vxt,
y'
=
y
-vyt,
z'
=
z
-
vzt.
The first of these
equations
expresses, as we
have
seen,
an
ill-founded
hypothesis
about the
time
coordinates of
an
elementary
event
taken
with
respect
to
two
systems
S
and
S' that
are
in
uniform translational motion
with
respect
to
each
other. The other
three
equations
express
the
hypothesis
that the kinematic
configuration
of
the
system
S'