Cyclic Method of Physics. I must explain this reference to an
endless cycle of physical terms. I will refer again to Einstein’s law of
gravitation. I have already expounded it to you more than once and
I hope you gained some idea of it from the explanation. This time I
am going to expound it in a way so complete that there is not much
likelihood that any one will understand it. Never mind. We are not
now seeking further light on the cause of gravitation; we are
interested in seeing what would really be involved in a complete
explanation of anything physical.
Einstein’s law in its analytical form is a statement that in empty
space certain quantities called potentials obey certain lengthy
differential equations. We make a memorandum of the word
‘potential’ to remind us that we must later on explain what it means.
We might conceive a world in which the potentials at every moment
and every place had quite arbitrary values. The actual world is not
so unlimited, the potentials being restricted to those values which
conform to Einstein’s equations. The next question is, What are
potentials? They can be defined as quantities derived by quite
simple mathematical calculations from certain fundamental
quantities called intervals. (MEM. Explain ‘interval.’) If we know the
values of the various intervals throughout the world definite rules
can be given for deriving the values of the potentials. What are
intervals? They are relations between pairs of events which can be
measured with a scale or a clock or with both. (MEM. Explain ‘scale’
and ‘clock’.) Instructions can be given for the correct use of the
scale and clock so that the interval is given by a prescribed
combination of their readings. What are scales and clocks? A scale
is a graduated strip of matter which …. (MEM. Explain ‘matter.’) On
second thoughts I will leave the rest of the description as ‘an
exercise to the reader’ since it would take rather a long time to
enumerate all the properties and niceties of behaviour of the
material standard which a physicist would accept as a perfect scale
or a perfect clock. We pass on to the next question, What is
matter? We have dismissed the metaphysical conception of
substance. We might perhaps here describe the atomic and
electrical structure of matter, but that leads to the microscopic
aspects of the world, whereas we are here taking the macroscopic
outlook. Confining ourselves to mechanics, which is the subject in
which the law of gravitation arises, matter may be defined as the
embodiment of three related physical quantities, mass (or energy),
momentum, and stress. What are ‘mass,’ ‘momentum,’ and
‘stress’? It is one of the most far-reaching achievements of
Einstein’s theory that it has given an exact answer to this question.
They are rather formidable-looking expressions containing the
potentials and their first and second derivatives with respect to the
co-ordinates. What are the potentials? Why, that is just what I have
been explaining to you!
The definitions of physics proceed according to the method
immortalized in ‘The House that Jack built’: This is the potential,
that was derived from the interval, that was measured by the scale,
that was made from the matter, that embodied the stress, that….
But instead of finishing with Jack, whom of course every youngster
must know without need for an introduction, we make a circuit back
to the beginning of the rhyme: …that worried the cat, that killed the
rat, that ate the malt, that lay in the house, that was built by the
priest all shaven and shorn, that married the man…. Now we can
go round and round for ever.
But perhaps you have already cut short my explanation of
gravitation. When we reached matter you had had enough of it.
‘Please do not explain any more, I happen to know what matter is.’
Very well; matter is something that Mr. X knows. Let us see how it
goes: This is the potential that was derived from the interval that
was measured by the scale that was made from the matter that Mr.
X knows. Next question, What is Mr. X?
Well, it happens that physics is not at all anxious to pursue the
question, What is Mr. X? It is not disposed to admit that its
elaborate structure of a physical universe is ‘The House that Mr. X
built.’ It looks upon Mr. X – and more particularly the part of Mr. X
that knows – as a rather troublesome tenant who at a late stage of
the world’s history has come to inhabit a structure which inorganic
Nature has by slow evolutionary progress contrived to build. And
so it turns aside from the avenue leading to Mr. X – and beyond –
and closes its cycle leaving him out in the cold.
From its own point of view physics is entirely justified. That matter
in some indirect way comes within the purview of Mr. X’s mind is
not a fact of any utility for a theoretical scheme of physics. We
cannot embody it in a differential equation. It is ignored; and the
physical properties of matter and other entities are expressed by
their linkages in the cycle. And you can see how by the ingenious
device of the cycle physics secures for itself a self-contained
domain for study with no loose ends projecting into the unknown.
All other physical definitions have the same kind of interlocking.
Electric force is defined as something which causes motion of an
electric charge; an electric charge is something which exerts
electric force. So that an electric charge is something that exerts
something that produces motion of something that exerts
something that produces…. ad infinitum.
Arthur S. Eddington, THE NATURE OF THE PHYSICAL WORLD