The nature of the physical world

by Sir Arthur Stanley Eddington

By adding together certain of the measures of structure in a symmetrical manner and by ignoring others we reduce the really important measures to 16.[37] These can be divided into 10 forming a symmetrical scheme and 6 forming an antisymmetrical scheme. This is the great point of bifurcation of the world.

Symmetrical coefficients (10). Out of these we find it possible to construct Geometry and Mechanics. They are the ten potentials of Einstein (

). We derive from them space, time, and the world-curvatures representing the mechanical properties of matter, viz. momentum, energy, stress, etc.

Antisymmetrical coefficients (6). Out of these we construct Electromagnetism. They are the three components of electric intensity and three components of magnetic force. We derive electric and magnetic potential, electric charge and current, light and other electric waves.

We do not derive the laws and phenomena of atomicity. Our building operation has somehow been too coarse to furnish the microscopic structure of the world, so that atoms, electrons and quanta are at present beyond our skill.

But in regard to what is called field-physics the construction is reasonably complete. The metrical, gravitational and electromagnetic fields are all included. We build the quantities enumerated above; and they obey the great laws of field-physics in virtue of the way in which they have been built. That is the special feature; the field laws—conservation of energy, mass, momentum and of electric charge, the law of gravitation, Maxwell’s equations—are not controlling laws.[38] They are truisms. Not truisms when approached in the way the mind looks out on the world, but truisms when we encounter them in a building up of the world from a basal structure. I must try to make clear our new attitude to these laws.

Identical Laws. Energy momentum and stress, which we have identified with the ten principal curvatures of the world, are the subject of the famous laws of conservation of energy and momentum. Granting that the identification is correct, these laws are mathematical identities. Violation of them is unthinkable. Perhaps I can best indicate their nature by an analogy.

An aged college Bursar once dwelt secluded in his rooms devoting himself entirely to accounts. He realised the intellectual and other activities of the college only as they presented themselves in the bills. He vaguely conjectured an objective reality at the back of it all—some sort of parallel to the real college—though he could only picture it in terms of the pounds, shillings and pence which made up what he would call “the commonsense college of everyday experience”. The method of account-keeping had become inveterate habit handed down from generations of hermit-like bursars; he accepted the form of accounts as being part of the nature of things. But he was of a scientific turn and he wanted to learn more about the college. One day in looking over his books he discovered a remarkable law. For every item on the credit side an equal item appeared somewhere else on the debit side. “Ha!” said the Bursar, “I have discovered one of the great laws controlling the college. It is a perfect and exact law of the real world. Credit must be called plus and debit minus; and so we have the law of conservation of £ s. d. This is the true way to find out things, and there is no limit to what may ultimately be discovered by this scientific method. I will pay no more heed to the superstitions held by some of the Fellows as to a beneficent spirit called the King or evil spirits called the University Commissioners. I have only to go on in this way and I shall succeed in understanding why prices are always going up.”

I have no quarrel with the Bursar for believing that scientific investigation of the accounts is a road to exact (though necessarily partial) knowledge of the reality behind them. Things may be discovered by this method which go deeper than the mere truism revealed by his first effort. In any case his life is especially concerned with accounts and it is proper that he should discover the laws of accounts whatever their nature. But I would point out to him that a discovery of the overlapping of the different aspects in which the realities of the college present themselves in the world of accounts, is not a discovery of the laws controlling the college; that he has not even begun to find the controlling laws. The college may totter but the Bursar’s accounts still balance.