Reference: The Book of Physics
Note: The original text is provided below.
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Summary
This section considers the reality of the Fitzgerald contraction. Eddington doesn’t commit to a definite answer. He believes Fitzgerald contraction to be relative and not absolute. Its value is based on the relative frame of space. It is not an absolute value that is real.
The absolute frame of space was mathematically introduced by Einstein in his general theory of relativity by using a four-dimensional co-ordinate system that included time.
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Comments
The frame of space is based on the relative velocity of the observer, therefore, it is not real. It is only part of a mathematical process. In reality, the Fitzgerald contraction will occur only when the rod accelerates, because that would be an absolute framework.
According to the theory of Substance, matter is already in a very accelerated state compared to energy because, as a substance, it is much more condensed than energy. It may be accelerated further to become as condensed as the black hole, but not much beyond that.
The opposite of contraction is expansion. It will occur when the force being applied to accelerate the object is taken away. If acceleration is taken away from matter, it would expand into energy. Further taking away of acceleration may expand energy into aether.
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Original Text
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.
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.
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.
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