This paper presents Chapter XI (section 2) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.
The paragraphs of original material are accompanied by brief comments in color, based on the present understanding. Feedback on these comments is appreciated.
The heading below links to the original materials.
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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.
The underlying law is the conservation of substance (force).
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 I” 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.
The law of conservation of momentum and energy results from the overlapping of the different aspects in which the “non-emptiness of space” presents itself to our practical experience. Once again we find that a fundamental law of physics is no controlling law but a “put-up job” as soon as we have ascertained the nature of that which is obeying it. We can measure certain forms of energy with a thermometer, momentum with a ballistic pendulum, stress with a manometer. Commonly we picture these as separate physical entities whose behaviour towards each other is controlled by a law. But now the theory is that the three instruments measure different but slightly overlapping aspects of a single physical condition, and a law connecting their measurements is of the same tautological type as a “law” connecting measurements with a metre-rule and a foot-rule.
I have said that violation of these laws of conservation is unthinkable. Have we then found physical laws which will endure for all time unshaken by any future revolution? But the proviso must be remembered, “granting that the identification [of their subject matter] is correct”. The law itself will endure as long as two and two make four; but its practical importance depends on our knowing that which obeys it. We think we have this knowledge, but do not claim infallibility in this respect. From a practical point of view the law would be upset, if it turned out that the thing conserved was not that which we are accustomed to measure with the above-mentioned instruments but something slightly different.
Field-substance arises as cyclic motion, which then quantizes into atomic structure as material-substance.
Motion makes up the kinetic energy. Structure makes up the potential energy. Energy is, therefore, an aspect of substance.
Momentum involves motion of structure. Stress arises from twisting of structure. Both momentum and stress are aspects of substance.
Thus, all conservation laws boils down to the conservation of substance. We perceive substance through its aspect of force. This is what Faraday meant by CONSERVATION OF FORCE.
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