Eddington 1927: Is the Fitzgerald Contraction Real

Rocket Contracted

This paper presents Chapter II (section 5 and Summary) 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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Is the Fitzgerald Contraction Real

I am often asked whether the FitzGerald contraction really occurs. It was introduced in the first chapter before the idea of relativity was mentioned, and perhaps it is not quite clear what has become of it now that the theory of relativity has given us a new conception of what is going on in the world. Naturally my first chapter, which describes the phenomena according to the ideas of classical physics in order to show the need for a new theory, contains many statements which we should express differently in relativity physics.

Is it really true that a moving rod becomes shortened in the direction of its motion? It is not altogether easy to give a plain answer. I think we often draw a distinction between what is true and what is really true. A statement which does not profess to deal with anything except appearances may be true; a statement which is not only true but deals with the realities beneath the appearances is really true.

The FitzGerald contraction was postulated to explain the null results from Michelson-Morley experiment. Therefore, it was not something observed directly in an experiment. The truth factor must be determined by consistency with experimental observation.

You receive a balance-sheet from a public company and observe that the assets amount to such and such a figure. Is this true? Certainly; it is certified by a chartered accountant. But is it really true? Many questions arise; the real values of items are often very different from those which figure in the balance-sheet. I am not especially referring to fraudulent companies. There is a blessed phrase “hidden reserves”; and generally speaking the more respectable the company the more widely does its balance-sheet deviate from reality. This is called sound finance. But apart from deliberate use of the balance-sheet to conceal the actual situation, it is not well adapted for exhibiting realities, because the main function of a balance-sheet is to balance and everything else has to be subordinated to that end.

The physicist who uses a frame of space has to account for every millimeter of space—in fact to draw up a balance-sheet, and make it balance. Usually there is not much difficulty. But suppose that he happens to be concerned with a man travelling at 161,000 miles a second. The man is an ordinary 6-foot man. So far as reality is concerned the proper entry in the balance-sheet would appear to be 6 feet. But then the balance sheet would not balance. In accounting for the rest of space there is left only 3 feet between the crown of his head and the soles of his boots. His balance-sheet length is therefore “written down” to 3 feet.

Statements, such as, “a man travelling at 161,000 miles a second”, are self-contradictory because a man’s inertia is inconsistent with the inertial characteristics of an object traveling naturally at 161,000 miles a second. Such statements have created a lot of confusion. They represent the speculative element in the theory of relativity.

The writing-down of lengths for balance-sheet purposes is the FitzGerald contraction. The shortening of the moving rod is true, but it is not really true. It is not a statement about reality (the absolute) but it is a true statement about appearances in our frame of reference.  (The proper-length is unaltered; but the relative length is shortened. We have already seen that the word “length” as currently used refers to relative length, and in confirming the statement that the moving rod changes its length we are, of course, assuming that the word is used with its current meaning.) An object has different lengths in the different spaceframes, and any 6-foot man will have a length 3 feet in some frame or other. The statement that the length of the rapid traveler is 3 feet is true, but it does not indicate any special peculiarity about the man; it only indicates that our adopted frame is the one in which his length is 3 feet. If it hadn’t been ours, it would have been someone else’s.

Perhaps you will think we ought to alter our method of keeping the accounts of space so as to make them directly represent the realities. That would be going to a lot of trouble to provide for what are after all rather rare transactions. But as a matter of fact we have managed to meet your desire. Thanks to Minkowski a way of keeping accounts has been found which exhibits realities (absolute things) and balances. There has been no great rush to adopt it for ordinary purposes because it is a four-dimensional balance-sheet.

The FitzGerald contraction is not real because an object made up of material-substance is already in its most contracted form. One cannot increase the natural speed of a material object without decreasing its inertia. Whenever a material object is accelerated, such as a rocket, its inertia shall decrease. But for the accelerations possible for material objects, the corresponding decrease in inertia is infinitesimal.  

The field-substance contracts as it becomes increasingly substantial with increasing quantization. The highest contraction takes place as the substance transitions from field to material phase with the formation of atom. In the material phase the contraction is infinitesimal with increasing inertia.

The contraction may be visualized by looking at the decrease in wave length of the substance with increasing quantization. For material-substance the de Broglie’s wavelength is infinitesimal. Therefore, any contraction is infinitesimal too.

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Summary

Let us take a last glance back before we plunge into four dimensions. We have been confronted with something not contemplated in classical physics—a multiplicity of frames of space, each one as good as any other. And in place of a distance, magnetic force, acceleration, etc., which according to classical ideas must necessarily be definite and unique, we are confronted with different distances, etc., corresponding to the different frames, with no ground for making a choice between them. Our simple solution has been to give up the idea that one of these is right and that the others are spurious imitations, and to accept them en bloc; so that distance, magnetic force, acceleration, etc., are relative quantities, comparable with other relative quantities already known to us such as direction or velocity. In the main this leaves the structure of our physical knowledge unaltered; only we must give up certain expectations as to the behaviour of these quantities, and certain tacit assumptions which were based on the belief that they are absolute. In particular a law of Nature which seemed simple and appropriate for absolute quantities may be quite inapplicable to relative quantities and therefore require some tinkering. Whilst the structure of our physical knowledge is not much affected, the change in the underlying conceptions is radical. We have travelled far from the old standpoint which demanded mechanical models of everything in Nature, seeing that we do not now admit even a definite unique distance between two points. The relativity of the current scheme of physics invites us to search deeper and find the absolute scheme underlying it, so that we may see the world in a truer perspective.

The frames of space address the range of motion for material-substance. This range extends from absolute rest for an object of infinite inertia to a natural speed commensurate with the inertia of a hydrogen atom. This upper limit of motion is insignificant compared to the speed of light.

Within this range of motion the variation in material properties are almost negligible. This is the reason for the success of Newtonian mechanics. The higher motion, which is a significant ratio of speed of light, is applicable to field-substance only.

Thus, we do not really have to give up our faith in standard values. We simply have to be aware of the conditions under which the values are standard. Such standards may change under different conditions. We now know that different conditions apply to material-substance and field-substance.

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