1 2 6 D O C . 3 1 I D E A S A N D M E T H O D S

. This is the shortening of moving bodies introduced by Lorentz and

Fitzgerald in their explanation of the Michelson experiment.

Here it follows as a consequence of our general postulates. According to the

principle of relativity, this shortening cannot happen only with the movement of

rigid bodies relative to , but must rather occur with the movement relative to any

admissible coordinate system. Thus, it is easily shown from (5), or the inversion of

(5), that a rod oriented in the -direction and relatively at rest in , with length

in , has, when seen from , the length . Therefore, one can say that

either one of these two rods moving lengthwise relative to the other is—when seen

from the other one—shortened.

Next, we consider a unit clock permanently at rest in the origin of , when its

periods are characterized by the values

( = integer)

From the first and fourth equation in (5) one finds

Since is larger than 1 whenever v is nonzero, it follows that a clock mov-

ing relative to a coordinate system—when viewed from this coordinate system—

runs more slowly than if it were not moving.

These two consequences concerning the behavior of moving bodies and clocks

are, in principle, testable by experiment. Because of considerable practical difficul-

ties, none of these consequences has so far been tested experimentally, the reason

being that in nearly all practically accessible cases is a practically vanishing

quantity compared to the unit.

Considering the fundamental importance of the Lorentz transformation for the

theory of relativity, we have to add that the principle of the constancy of the speed

of light and the principle of relativity alone are not yet sufficient to derive the trans-

l 1

v2

c2

---- - –

K

x K l

K K′ l 1

v2

c2

---- - –

[p. 12]

K′

t′ 0 t′ ; n = = n

{2}

t

1

v2-

c2

---- –

------------------n

=

1

1

v2

c2

----- –

------------------

v2-

c2

----