This paper presents Chapter XII (section 4) 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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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 anyone 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 \t 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 coordinates. What are the potentials? Why, that is just what I have been explaining to you!
Einstein’s potentials are derived from relationships between space and time that is referenced from material-space and material-time. These potentials actually exist in field substance whose key property is quantization. Material-substance is limiting form of field-substance that is quantized. So potentials are same as quantization but from referenced from opposite ends.
The definitions of physics proceed according to the method immortalised 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 forever.
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 up 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.
But I am not now writing of pure physics, and from a broader standpoint I do not see how we can leave out Mr. X. The fact that matter is “knowable to Mr. X” must be set down as one of the fundamental attributes of matter. I do not say that it is very distinctive, since other entities of physics are also knowable to him; but the potentiality of the whole physical world for awaking impressions in consciousness is an attribute not to be ignored when we compare the actual world with worlds which, we fancy, might have been created. There seems to be a prevalent disposition to minimise the importance of this. The attitude is that “knowableness to Mr. X” is a negligible attribute, because Mr. X is so clever that he could know pretty much anything that there was to know. I have already urged the contrary view—that there is a definitely selective action of the mind; and since physics treats of what is knowable to mind * its subject-matter has undergone, and indeed retains evidences of, this process of selection.
* This is obviously true of all experimental physics, and must be true of theoretical physics if it is (as it professes to be) based on experiment.
In general, the explanations pf physics are circular, and we need to break through this circle. We do this by investigating every inconsistency, disharmony and discontinuity.
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