The most ingenious idea was that of local time. Imagine two observers
who wish to adjust their timepieces by optical signals; they exchange
signals, but as they know that the transmission of light is not
instantaneous, they are careful to cross them. When station B perceives
the signal from station A, its clock should not mark the same hour as
that of station A at the moment of sending the signal, but this hour
augmented by a constant representing the duration of the transmission.
Suppose, for example, that station A sends its signal when its clock
marks the hour _O_, and that station B perceives it when its clock marks
the hour _t_. The clocks are adjusted if the slowness equal to _t_
represents the duration of the transmission, and to verify it, station B
sends in its turn a signal when its clock marks _O_; then station A
should perceive it when its clock marks _t_. The timepieces are then
adjusted.
And in fact they mark the same hour at the same physical instant, but on
the one condition, that the two stations are fixed. Otherwise the
duration of the transmission will not be the same in the two senses,
since the station A, for example, moves forward to meet the optical
perturbation emanating from B, whereas the station B flees before the
perturbation emanating from A. The watches adjusted in that way will not
mark, therefore, the true time; they will mark what may be called the
_local time_, so that one of them will be slow of the other. It matters
little, since we have no means of perceiving it. All the phenomena which
happen at A, for example, will be late, but all will be equally so, and
the observer will not perceive it, since his watch is slow; so, as the
principle of relativity requires, he will have no means of knowing
whether he is at rest or in absolute motion.
Public-domain text, read in full here on John Shaqi.
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