There is one matter of great theoretical importance, which is not very
clear in the usual accounts of relativity. How do we know whether
two events are to be regarded as happening to the same piece of
matter? An electron or a proton is supposed to preserve its identity
throughout time; but our fundamental continuum is a continuum of
events. One must therefore suppose that one unit of matter is a
series of events, or a series of sets of events. It is not clear what
is the theoretical criterion for determining whether two events both
belong to one such series. We may assume, I suppose, that two events
which overlap—i.e. which are both present at some point of
space-time—must belong to one unit of matter. (It is not to be assumed
that an event which belongs to one unit of matter belongs to no other.)
We may also assume that two events which have a space-like interval,
or have a zero interval without overlapping, do not belong to one unit
of[Pg 81] matter. But when two events have a time-like interval, there is no
obvious criterion. Any two such events can be connected by a geodesic
in which any two points have a time-like separation; therefore, so far
as the laws of dynamics are concerned, they might both belong to
the same material unit. Yet sometimes we think they do, and sometimes
we think they do not. It is evidently part of the business of physics
to tell us how we are to decide this question in a given case. What can
we say about it?[26]
The decision must depend upon intermediate history—i.e. upon
the existence of some series of intermediate events (or sets of events)
following each other according to some law. If there exists any law
which is in fact obeyed by strings of events, such a law can be used
to define what we mean by one material unit. We know that there are
such laws, but their importance in this connection is not emphasized,
because it has hardly been realized that there is a problem owing to
the substitution of events for bits of matter as the fundamental stuff
of physics. For common sense, there is a more or less vague law of what
may be called qualitative continuity. If you look persistently in a
given direction, what you see, as a rule, alters gradually; there are
exceptions, such as explosions, but they are rare. (I am not talking
of a theoretical gradualness, but of one that is obvious to untrained
perception.) If you see, say, a well-defined red patch, whose shape
and tint do not alter greatly while you are looking, you conclude
that there is a material object there, especially if you can touch it
whenever you choose. Common sense achieves in this way a considerable
measure of constancy in its objects. More is achieved by reducing
matter to molecules, more still by reducing it to atoms, and yet more
by reducing it to protons and electrons. But physicists would not feel
pleased with[Pg 82] electrons and protons but for the fact that their tables
and chairs, their laboratories and their books, consist, on the whole,
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