FROM THE PREFACE TO THE FIRST EDITION
The methods of progress in theoretical physics have undergone a vast
change during the present century. The classical tradition has been to con-
sider the world to be association of observable objects (particles, fluids,
fields, etc.) moving about according to definite laws of force, so that one
could form a mental picture in space and time of the whole scheme. This
led to a physics whose aim was to make assumptions about the mecha-
nism and forces connecting these observable objects, to account for their
behavior in the simplest possible way. It has become increasingly evident
in recent times, however, that nature works on a different plan. Her fun-
damental laws do not govern the world as it appears in our mental picture
in any very direct way, but instead they control a substratum of which we
cannot form a mental picture without introducing irrelevancies. The for-
mulation of these laws requires the use of the mathematics of transforma-
tions. The important things in the world appear as the invariants (or more
generally the nearly invariants, or quantities with simple transformation
properties) of these transformations. The things we are immediately aware
of are the relations of these nearly invariant to be a certain frame of ref-
erence, usually one chosen so as to introduce special simplifying features
which are unimportant from the point of view of general theory.
The growth of the use of transformation theory, as applied first to rel-
ativity and later to the quantum theory, is the essence of the new method
in theoretical physics. Further progress lies in the direction of making
our equations invariant under wider and still wider transformations. This
state of affairs is very satisfactory from a philosophical point of view, as
implying an increasing recognition of the part played by the observer in
himself introducing the regularities that appear in his observations, and a
lack of arbitrariness in the ways of nature, but in makes things less easy
for the learner of physics. The new theories, if one looks apart from their
mathematical setting, are built up from physical concepts which cannot
be explained in terms of things previously known to the student, which
cannot even be explained adequately in words at all. Like the fundamen-
tal concepts (e.g. proximity, identity) which every one must learn on his
arrival into the world, the newer concepts of physics can be mastered only
by long familiarity with their properties and uses.
From the mathematical side the approach to the new theories presents
no difficulties, as the mathematics required(at any rate that which is re-
quired for the development of physics up to the present) is not essentially
different from what has been current for a considerable time. Mathemat-
ics is the tool specially suited for dealing with abstract concepts of any
kind and there is no limit to its power in this field. For this reason a book
on the new physics, if not purely descriptive of experimental work, must
be essentially mathematical. All the same the mathematics is only a tool
and one should learn to hold the physical ideas in one’s mind without
reference to the mathematical form. In this book I have tried to keep the
iii
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