If an observer be stationed at A with a clock, he can estimate the time
of events occurring in the immediate neighbourhood of A, by looking for
the position of the hands of the clock, which are synchronous with the
event. If an observer be stationed at B with a clock,—we should add that
the clock is of the same nature as the one at A,—he can estimate the
time of events occurring about B. But without further premises, it is
not possible to compare, as far as time is concerned, the events at B
with the events at A. We have hitherto an A-time, and a B-time, but no
time common to A and B. This last time (_i.e._, common time) can be
defined, if we establish by definition that the time which light
requires in travelling from A to B is equivalent to the time which light
requires in travelling from B to A. For example, a ray of light proceeds
from A at A-time t_{A} towards B, arrives and is reflected from B at
B-time t_{B}, and returns to A at A-time t′_{A}. According to the
definition, both clocks are synchronous, if
t_{B} - t_{A} = t′_{A} - t_{B}.
We assume that this definition of synchronism is possible without
involving any inconsistency, for any number of points, therefore the
following relations hold:—
1. If the clock at B be synchronous with the clock at A, then the clock
at A is synchronous with the clock at B.
2. If the clock at A as well as the clock at B are both synchronous with
the clock at C, then the clocks at A and B are synchronous.
Thus with the help of certain physical experiences, we have established
what we understand when we speak of clocks at rest at different
stations, and synchronous with one another; and thereby we have arrived
at a definition of synchronism and time.
In accordance with experience we shall assume that the magnitude
$$ \frac {2 \overline{AB}}{t'_{A} - t_{A}} = c $$
where _c_ is a universal constant.
We have defined time essentially with a clock at rest in a stationary
system. On account of its adaptability to the stationary system, we call
the time defined in this way as “time of the stationary system.”
§ 2. On the Relativity of Length and Time.
The following reflections are based on the Principle of Relativity and
on the Principle of Constancy of the velocity of light, both of which we
define in the following way:—
1. The laws according to which the nature of physical systems alter are
independent of the manner in which these changes are referred to two
co-ordinate systems which have a uniform translators motion relative to
each other.
2. Every ray of light moves in the “stationary co-ordinate system” with
the same velocity _c_, the velocity being independent of the condition
whether this ray of light is emitted by a body at rest or in motion.[6]
Therefore
velocity = Path of Light/Interval of time,
where, by ‘interval of time’ we mean time as defined in §1.
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