The reader may say: What then is left of physics? What do we really
know about the world of matter? Here we may distinguish three
departments of physics. There is first what is included within the
theory of relativity, generalized as widely as possible. Next, there
are laws which cannot be brought within the scope of relativity.
Thirdly, there is what may be called geography. Let us consider each of
these in turn.
The theory of relativity, apart from convention, tells us that the
events in the universe have a four-dimensional order, and that,
between any two events which are near together in this order, there
is a relation called “interval,” which is capable of being measured
if suitable precautions are taken. We make also an assumption as to
what happens when a little measuring rod is carried round a closed
circuit in a certain manner; the consequences of this assumption are
such as to make it highly probable that it is true. Beyond this, there
is little in the theory of relativity that can be regarded as physical
laws. There is a great deal of mathematics, showing that certain
mathematically-constructed quantities must behave like the things we
perceive; and there is a suggestion of a bridge between psychology and
physics in the theory that these mathematically-constructed quantities
are what our senses are adapted for perceiving. But neither of these
things is physics in the strict sense.
The part of physics which cannot, at present, be brought within
the scope of relativity is large and important. There is nothing
in relativity to show why there should be electrons and protons;
relativity cannot give any reason why matter should exist in little
lumps. With this goes the whole theory of the structure of the atom.
The theory of quanta also is quite outside the scope of relativity.
Relativity is, in a sense, the most extreme application of what may
be called next-to-next methods. Gravitation is no longer regarded
as due to the effect of the sun upon a planet, but as expressing
characteristics of the region in which the planet happens to be.
Distance, which used to be thought to have a definite meaning however
far apart two points might be, is now only definite for neighboring
points. The distance between widely separated places depends upon the
route chosen. We may, it is true, define _the_ distance as the geodesic
distance, but that can only be estimated by adding up little bits,
that is to say, by the method we use in estimating the length of a
curve. What applies to distance applies equally to the straight line.
There is nothing in the actual world having exactly the properties
that straight lines were supposed to have; the nearest approach is the
track of a light ray. Straight lines have to be replaced by geodesics,
which are defined by what they do at each point, not all at once,
like Euclidean straight lines. Measurement, in Weyl’s theory, suffers
the same fate. We can only use a measuring rod to give lengths in one
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