|
Bertrand Russell
Philosophical Consequences Of Relativity
Of the consequences in philosophy which may be supposed to follow from the
theory of relativity, some are fairly certain, while others are open to
question. There has been a tendency, not uncommon in the case of a new
scientific theory, for every philosopher to interpret the work of Einstein in
accordance with his own metaphysical system, and to suggest that the outcome is
a great accession of strength to the views which the philosopher in question
previously held. This cannot be true in all cases; and it may be hoped that it
is true in none. It would be disappointing if so fundamental a change as
Einstein has introduced involved no philosophical novelty.
Space-Time
For philosophy, the most important novelty was present already in the special
theory of relativity; that is, the substitution of space-time for space and
time. In Newtonian dynamics, two events were separated by two kinds of
interval, one being distance in space, the other lapse of time. As soon as it
was realised that all motion is relative (which happened long before Einstein),
distance in space became ambiguous except in the case of simultaneous events,
but it was still thought that there was no ambiguity about simultaneity in
different places. The special theory of relativity showed, by experimental
arguments which were new, and by logical arguments which could have been
discovered any time after it became known that light travels with a finite
velocity, that simultaneity is only definite when it applies to events in the
same place, and becomes more and more ambiguous as the events are more widely
removed from each other in space.
This statement is not quite correct, since it still uses the notion of
"space." The correct statement is this: Events have a
four-dimensional order, by means of which we can say that an event A is nearer
to an event B than to an event C; this is a purely ordinal matter, not
involving anything quantitative. But, in addition, there is between
neighbouring events a quantitative relation called "interval," which
fulfils the functions both of distance in space and of lapse of time in the
traditional dynamics, but fulfils them with a difference. If a body can move so
as to be present at both events, the interval is time-like. If a ray of light
can move so as to be present at both events, the interval is zero. If neither
can happen, the interval is space-like. When we speak of a body being present
"at" an event, we mean that the event occurs in the same place in
space-time as one of the events which make up the history of the body; and when
we say that two events occur at the same place in space-time, we mean that
there is no event between them in the four-dimensional space-time order. All
the events which happen to a man at a given moment (in his own time) are, in
this sense, in one place; for example, if we hear a noise and see a colour
simultaneously, our two perceptions are both in one place in space-time.
When one body can be present at two events which are not in one place in
space-time, the time-order of the two events is not ambiguous, though the
magnitude of the time-interval will be different in different systems of
measurement. But whenever the interval between two events is space-like, their
time-order will be different in different equally legitimate systems of
measurement; in this case, therefore, the time-order does not represent a
physical fact. It follows that, when two bodies are in relative motion, like
the sun and a planet, there is no such physical fact as "the distance
between the bodies at a given time"; this alone shows that Newton's law of
gravitation is logically faulty. Fortunately, Einstein has not only pointed out
the defect, but remedied it. His arguments against Newton, however, would have
remained valid even if his own law of gravitation had not proved right.
Time not a Single Cosmic Order
The fact that time is private to each body, not a single cosmic order, involves
changes in the notions of substance and cause, and suggests the substitution of
a series of events for a substance with changing states. The controversy about
the aether thus becomes rather unreal. Undoubtedly, when light-waves travel,
events occur, and it used to be thought that these events must be
"in" something; the something in which they were was called the
aether. But there seems no reason except a logical prejudice to suppose that
the events are "in" anything. Matter, also, may be reduced to a law
according to which events succeed each other and spread out from centres; but
here we enter upon more speculative considerations.
Physical Laws
Prof. Eddington has emphasised an aspect of relativity theory which is of great
philosophical importance, but difficult to make clear without somewhat abstruse
mathematics. The aspect in question is the reduction of what used to be
regarded as physical laws to the status of truisms or definitions. Prof.
Eddington, in a profoundly interesting essay on "The Domain of Physical
Science," [Footnote 1] states the matter as follows:--
In the present stage of science the laws of physics appear to be divisible into
three classes--the identical, the statistical and the transcendental. The
"identical laws" include the great field-laws which are commonly
quoted as typical instances of natural law--the law of gravitation, the law of
conservation of mass and energy, the laws of electric and magnetic force and
the conservation of electric charge. These are seen to be identities, when we
refer to the cycle so as to understand the constitution of the entities obeying
them; and unless we have misunderstood this constitution, violation of these
laws is inconceivable. They do not in any way limit the actual basal structure
of the world, and are not laws of governance (op. cit., pp. 214-5).
It is these identical laws that form the subject-matter of relativity theory;
the other laws of physics, the statistical and transcendental, lie outside its
scope. Thus the net result of relativity theory is to show that the traditional
laws of physics, rightly understood, tell us almost nothing about the course of
nature, being rather of the nature of logical truisms.
This surprising result is an outcome of increased mathematical skill. As the
same author [Footnote 2] says elsewhere:--
In one sense deductive theory is the enemy of experimental physics. The latter
is always striving to settle by crucial tests the nature of the fundamental
things; the former strives to minimise the successes obtained by showing how
wide a nature of things is compatible with all experimental results.
The suggestion is that, in almost any conceivable world, something will be
conserved; mathematics gives us the means of constructing a variety of
mathematical expressions having this property of conservation. It is natural to
suppose that it is useful to have senses which notice these conserved entities;
hence mass, energy, and so on seem to have a basis in our experience, but are
in fact merely certain quantities which are conserved and which we are adapted
for noticing. If this view is correct, physics tells us much less about the
real world than was formerly supposed.
Force and Gravitation
An important aspect of relativity is the elimination of "force." This
is not new in idea; indeed, it was already accepted in rational dynamics. But
there remained the outstanding difficulty of gravitation, which Einstein has
overcome. The sun is, so to speak, at the summit of a hill, and the planets are
on the slopes. They move as they do because of the slope where they are, not
because of some mysterious influence emanating from the summit. Bodies move as
they do because that is the easiest possible movement in the region of
space-time in which they find themselves, not because "forces"
operate upon them. The apparent need of forces to account for observed motions
arises from mistaken insistence upon Euclidean geometry; when once we have
overcome this prejudice, we find that observed motions, instead of showing the
presence of forces, show the nature of the geometry applicable to the region
concerned. Bodies thus become far more independent of each other than they were
in Newtonian physics: there is an increase of individualism and a diminution of
central government, if one may be permitted such metaphorical language. This
may, in time, considerably modify the ordinary educated man's picture of the
universe, possibly with far-reaching results.
Realism in Relativity
It is a mistake to suppose that relativity adopts an idealistic picture of the
world--using "idealism" in the technical sense, in which it implies
that there can be nothing which is not experience. The "observer" who
is often mentioned in expositions of relativity need not be a mind, but may be
a photographic plate or any kind of recording instrument. The fundamental
assumption of relativity is realistic, namely, that those respects in which all
observers agree when they record a given phenomenon may be regarded as
objective, and not as contributed by the observers. This assumption is made by
common sense. The apparent sizes and shapes of objects differ according to the
point of view, but common sense discounts these differences. Relativity theory
merely extends this process. By taking into account not only human observers,
who all share the motion of the earth, but also possible "observers"
in very rapid motion relatively to the earth, it is found that much more
depends upon the point of view of the observer than was formerly thought. But
there is found to be a residue which is not so dependent; this is the part
which can be expressed by the method of "tensors." The importance of
this method can hardly be exaggerated; it is, however, quite impossible to
explain it in non-mathematical terms.
Relativity Physics
Relativity physics is, of course, concerned only with the quantitative aspects
of the world. The picture which it suggests is somewhat as follows:--In the
four-dimensional space-time frame there are events everywhere, usually many
events in a single place in space-time. The abstract mathematical relations of
these events proceed according to the laws of physics, but the intrinsic nature
of the events is wholly and inevitably unknown except when they occur in a
region where there is the sort of structure we call a brain. Then they become
the familiar sights and sounds and so on of our daily life. We know what it is
like to see a star, but we do not know the nature of the events which
constitute the ray of light that travels from the star to our eye. And the
space-time frame itself is known only in its abstract mathematical properties;
there is no reason to suppose it similar in intrinsic character to the spatial
and temporal relations of our perceptions as known in experience. There does
not seem any possible way of overcoming this ignorance, since the very nature
of physical reasoning allows only the most abstract inferences, and only the
most abstract properties of our perceptions can be regarded as having objective
validity. Whether any other science than physics can tell us more, does not
fall within the scope of the present article.
Meanwhile, it is a curious fact that this meagre kind of knowledge is
sufficient for the practical uses of physics. From a practical point of view,
the physical world only matters in so far as it affects us, and the intrinsic
nature of what goes on in our absence is irrelevant, provided we can predict
the effects upon ourselves. This we can do, just as a person can use a
telephone without understanding electricity. Only the most abstract knowledge
is required for practical manipulation of matter. But there is a grave danger
when this habit of manipulation based upon mathematical laws is carried over
into our dealings with human beings, since they, unlike the telephone wire, are
capable of happiness and misery, desire and aversion. It would therefore be
unfortunate if the habits of mind which are appropriate and right in dealing
with material mechanisms were allowed to dominate the administrator's attempts
at social constructiveness.
Bibliography A. S. Eddington, Space, Time,
and Gravitation (Cambridge, 1921); Bertrand A. W. Russell, The A. B. C. of
Relativity (1925).
Footnote 1: In Science, Religion and Reality, ed. by Joseph Needham (1925).
Footnote 2: A. S. Eddington, Mathematical Theory of Relativity, p. 238
(Cambridge, 1924)
|