VI
Until the beginning of the present century it was
universally assumed that time is like a moving knife-
edge covering all places in the universe simultaneously
and that the only arbitrary elements in its determi-
nation were our choice of time unit and time zero.
It therefore came as a great shock when, in 1905,
Einstein discovered a previously unsuspected gap in
the theory of time-measurement. For, in his analysis
of the nature of the velocity of light it occurred to
him that time-measurement depends on simultaneity,
and that although this idea is perfectly clear when two
events occur at the same place it was not equally clear
for events in different places. Einstein realized that the
concept of simultaneity for a distant event and one
in close proximity to the observer is an inferred con-
cept depending on the relative position of the distant
event and the mode of connection between it and the
observer's perception of it. If the distance of an exter-
nal event is known and also the velocity of the signal
that connects it and the resulting percept, the observer
can calculate the epoch at which the event occurred
and can correlate this with some previous instant in
his own experience. This calculation will be a distinct
operation for each observer, but until Einstein raised
the question it had been tacitly assumed that, when
we have found the rules according to which the time
of perception is determined by the time of the event,
all perceived events can be brought into a single ob-
jective time-sequence the same for all observers. Ein-
stein not only realized that it was a hypothesis to
assume that, if they calculate correctly, all observers
must assign the same time to a given event, but he
produced cogent reasons why, in general, this hypoth-
esis should be rejected.
Einstein assumed that there are no instantaneous
connections between external events and the observer.
The classical theory of time, with its assumption of
worldwide simultaneity for all observers, in effect
presupposed that there were such connections. Instead,
Einstein postulated that the most rapid form of com-
munication is by means of electromagnetic signals (in
vacuo), including light rays, and that their speed is the
same for all observers at relative rest or in uniform
relative motion. He regarded this assumption as a
consequence of the principle of special relativity (as
it is now called) which asserts that the laws of physics
are the same for all such observers. He found that,
although the invariance of the velocity of light is com-
patible with the idea of worldwide simultaneity for
all observers at relative rest, those in uniform relative
motion would, in general, be led to assign different
times to the same event and that a moving clock would
appear to run slow compared with an identical clock
at rest with respect to the observer.
It is well known that Einstein's theory automatically
explained the failure of the Michelson-Morley experi-
ment for measuring the Earth's velocity through the
luminiferous aether and has been successful in explain-
ing many other results that could not be accounted
for in the classical theory of time. The phenomenon
of the apparent slowing down of a clock in motion
relative to the observer is called “time dilatation.” It
is essentially a phenomenon of measurement applicable
to all forms of matter and is a reciprocal effect: if A
and B are two observers in uniform relative motion,
B's clock seems to A to run slow and equally A's clock
seems to run slow according to B. This reciprocity no
longer holds, however, if forces are applied to change
the motion of one of the observers. In particular, if
A and B are together at some instant and at a later
instant the motion of B is suddenly reversed so that
he eventually comes back to A with the same speed,
the time that elapses between the instant at which B
left A and the instant when he returns to A will be
shorter according to B's clock than according to A's.
Consequently, although we accept Isaac Barrow's view
that “Time is the continuance of anything in its own
being,” the special theory of relativity prevents our
agreeing with him unconditionally when he went on
to say “nor do I believe there is anyone but allows
that those things existed equal times which rose and
perished together.”
Empirical evidence that can only be understood in
terms of time dilatation has come from the study of
cosmic-ray phenomena. Elementary particles known
as mu-mesons, found in cosmic-ray showers, disinte-
grate spontaneously, their average “proper lifetime”
(that is time from production to disintegration accord-
ing to an observer travelling with a meson) being about
two micro-seconds (two millionths of a second). These
particles are mainly produced at heights of about ten
kilometers above the Earth's surface. Consequently,
those observed in the laboratory on photographic
plates must have travelled that distance. But in two
micro-seconds a particle that travelled with the veloc-
ity of light would cover less than a kilometer, and
according to the theory of relativity all material parti-
cles travel with speeds less than that of light. However,
the velocity of these particles has been found to be
so close to that of light that the time-dilatation factor
is about ten, which is the amount required to explain
why it is that to the observer in the laboratory these
particles appear to travel about ten times as far as they
could in the absence of this effect.
Although the theory of relativity has undermined the
classical concept of universal time, the same for all
observers, it has led to time-measurement's becoming
even more significant than before in physics, since time
standards are now tending to be regarded as primary
standards for spatial as well as for temporal measure-
ment. This is because the theory leads us to reject the
classical rigid body concept, since it implies the in-
stantaneous transmission of a disturbance through the
body from one end to the other, and this is incom-
patible with the basic assumption that no signal can
travel faster than light. Instead of spatial measurement
depending on the idea of the rigid body, it can be based
on the radar principle. According to this, distance is
measured in terms of the time taken by light (or other
electromagnetic signals) to traverse it. This technique
is now being used by radio astronomers to redetermine
the scale of the solar system.
Although the laws of nature do not enable us to
define a local standard of rest, in principle this can
be determined by the bulk distribution of matter in
the universe. According to most current cosmological
theories, there is at each place in the universe a prefer-
ential time-scale for the description of the universe,
being that associated with the local standard of rest,
and these local time-scales all fit together to form one
worldwide cosmic time. It is with reference to this that
we can give objective meaning to such concepts as the
age of the Earth, the age of the solar system, the age
of our Galaxy, and the age of the universe. Thus,
despite the theory of relativity, we can still retain the
concept of a unique cosmic time-scale for our descrip-
tion of the physical universe and the dating of events.
