142 RELATIVITY, THE SPECIAL THEORYB's, and B's with that of a third observer C, then A's is synchronous with C's.
Synchronicity is therefore fully defined within any one inertial frame. Because of
the second postulate, the use of light signals remains a valid tool for the compar-
ison of the A and B clocks even if, after initial synchronization in the common
inertial frame, B and his clock start moving with uniform velocity relative to A,
that is, if B joins another inertial frame.
[Remark. In an unpublished manuscript,f written in 1921, Einstein spells out
three additional assumptions which are made in this reasoning: (1) Homogeneity:
the properties of rods and clocks depend neither on their position nor on the time
at which they move, but only on the way in which they move. (2) Isotropy: the
properties of rods and clocks are independent of direction. (3) These properties
are also independent of their history.]
The time of an event is defined as the reading of a clock coincident with the
event and at rest relative to it. Events which are simultaneous in one inertial frame
are not simultaneous in another. Einstein's example: two identical rods R, and R 2
are coincident in a given inertial frame in which two observers O, and O 2 have
synchronized their respective clocks. Observer O, stays with R, in this frame, O 2
moves with R 2 into another inertial frame. Three durations are measured: Oj
measures the time i, for a light ray to move from one end of R, to the other and
back, and O 2 does the same for R 2 , finding a time / 2. Observer O, also measures
the duration t\ for light to move from one end of R 2 to the other and back. Then
i, = t 2 , in accordance with the first postulate, but £, ¥= t(: 'We see that we cannot
attach absolute meaning to the concept of simultaneity.'
The two postulates of special relativity have physical content only if the exper-
imental prescriptions for measuring position and time (and, therefore, for velocity)
are added. The postulates together with these prescriptions fully specify Einstein's
theory of special relativity.
- From the Postulates to the Lorentz Transformations. Let us continue with
the example of the two rods. Physics would be incomplete if the inequality £, ^
t\ could not be sharpened into a specific relation between these two durations.
Einstein obtained this relation by deriving the Lorentz transformation from his
postulates. In essence, his argument runs as follows. Consider two inertial frames,
(x,y,z,t) and (x',y',z',tr), the second moving with a velocity v in the x direction
relative to the first. At t = t' = 0, the two frames coincide. At that moment a
spherical light wave is emitted from the joint origin, t seconds later the wave is
spread over the sphere
The compatibility of the two postulates demands that the wave be equivalently
spread over
t This is the Morgan manuscript, the origins of which are described in Chapter 9.