D O C . 3 1 I D E A S A N D M E T H O D S 1 2 1
are also simultaneous in reference to a second inertial system when is in mo-
tion relative to . Indeed, a simple analysis shows that according to our principle
this is not at all the case.
Let the rod be moving with con-
stant velocity in the direction relative
to the inertial system. The rod is then at rest
relative to its own inertial system (the
co-moving system). If now, again, a light
signal is sent from , then—from what has
been said above—the events of arrival in and are simultaneous when seen
from (i.e., from the rod). Due to the movement of the rod when seen from the
(not co-moving) system , the light ray has to traverse a longer path.
Therefore, it takes longer than the light ray . The arrival in occurs—when
judged from —later than the arrival in , while—when judged from —they
arrive simultaneously.
In this consideration, the validity of the principle of the constancy of the speed
of light has been assumed—in agreement with the principle of special relativity—
for both systems and
When there are identical clocks on the rod, resting in and , respectively, i.e.,
at rest relative to , then let them be adjusted such that their hands show simulta-
neity relative to . Clocks arranged in this manner and at rest relative to shall
be called “synchronous” (i.e., identically adjusted) relative to . The totality of
identically constructed and identically adjusted clocks, at rest relative to , shows
the “time of system .” According to this, every admissible coordinate system
(inertial system) has its own time.
8. The Relativity of Length
For the length of a rod , moving uniformly relative to and at rest relative to
, one can give the following two definitions:
a. Direct measurement of length by repeated laying off of a unit measuring rod,
at rest relative to , along .
b. Determination of those points and of system , where the ends and
of the rod are located at a certain time of system ; where the measurement
of the distance is achieved by the repeated laying off of a unit
K′ K′
K
Fig. 1
• • •
A
B M
A B –
A B –
K′
M
[p. 8]
A B
K′
K M B –
M A – B
K A K′
K K′ .
A B
K′
K′ K′
K′
K′
K′
AB K
K′
K′ AB
A*
B*
K A
B t K
A*
B*