It is brought out that special relativity is afflicted with an inconsistency which can be removed only by postulating that light is not an electromagnetic phenomenon but is associated in an identical manner with all phenomena. A clue to the nature of this association is given by an analysis of length contraction which shows that light is necessarily involved in the operations of measuring length and that these operations are the same for all inertial observers. This entails a new definition of the term "measurement."

Einstein’s special theory of relativity is based on the following two assumptions¹:

A. All inertial frames are equivalent with respect to all the laws of physics.

B. The speed of light in empty space has the same value c in all inertial frames.

The theoretical consequences of these assumptions, like length contraction, time dilation, mass-energy equivalence, etc., were worked out virtually in one go. And they were strongly indicative of something revolutionary about special relativity. But that "something" remains as mysterious today as it was at the birth of the theory. Here we begin a reappraisal of this situation.

Considering the assumptions (A) and (B), it is brought out that they are inconsistent with each other and can be made consistent only by introducing the postulate that light is associated with each and every law of physics as intimately as with Maxwell’s electromagnetic theory. This leads us to inquire into the nature of this association of light with the whole of physics. In answer, we undertake an analysis of a particular prediction of special relativity, namely, length contraction. This analysis reveals that the operations of measuring length are the same for all inertial observers and further that light is necessarily involved in these operations. Like most consequences of special relativity, this one also reflects the theory’s revolutionary character as it clashes with the common belief among the physicists that there are many different ways of measuring length, most of them having no formal involvement of light. This, in turn, implies that special relativity prescribes a new definition of the term "measurement". This term being so basic to physics, its new definition would seem to be at the root of the revolutionary character of this theory. The problem of finding the new definition, i.e., identifying the operations of measuring length and the role of light in these operations, will be taken up in the next instalment of this series.

One of the worst misconceptions afflicting the 20^th century physics concerns the status of special relativity. Because of its assumption (A), this theory is a LAW for the laws of physics. It is neither a part of classical physics, nor a part of quantum physics; rather it rules over both of them. It is the anchor for the ship of physics.

Strangely, however, as recorded by Margenau, it is customary among the physicists to regard relativity as a part of classical physics.² This custom has proved harmful in two ways. Firstly, those tackling the interpretational problems of quantum mechanics never sought any help from special relativity. Secondly, and this is our main concern here, the physicists remained oblivious of a serious problem facing special relativity itself. To see this, note that due to the alleged electromagnetic nature of light, assumption (B) renders special relativity subservient to Maxwell’s electromagnetic theory. Those who follow the above custom find nothing wrong with this; for example, Bunge considers it entirely normal to say that special relativity makes little if any sense without Maxwell’s theory.³

Avoidance of this wrong custom is, however, necessary for a clear view of special relativity. And this view reveals an inconsistency in the theory. Thus, while assumption (A) requires this theory to be a LAW for the laws of physics, assumption (B) forces it into subservience to Maxwell’s theory which is merely a candidate for being a law of physics. There are at least two ways to retrieve the theory from this dangerous confrontation between its basic assumptions. Though looking quite different in the beginning, they lead to the same result. One starts by reconciling assumptions (A) and (B) and the other by replacing assumption (B). Here, only the former will be considered.

Thus, one way to eliminate the above inconsistency in special relativity is to introduce the postulate that light is associated with each and every law of physics in the same manner in which it is associated with Maxwell’s theory. Looking from another angle, one can say that in combining assumptions (A) and (B), special relativity presupposes that light is associated with each and every law of physics in exactly the same manner; it is just this implicit presupposition of the theory which is appearing here explicitly as a postulate. And this postulate firstly implies that light is not an electromagnetic phenomenon and secondly poses the question as to the nature of the postulated association of light with physics as a whole. In answer to this question, we undertake an analysis of a specific prediction of special relativity, viz., length contraction.

Consider a rod R moving parallel to its length with a speed v in an inertial frame S. According to special relativity, its length l as measured by the observer in S is given by⁴

l = l_o (1 - v²/c²)^½ , (1)

where l_o is the length of the rod in an inertial frame S_o in which it is at rest and, of course, c is the speed of light in empty space. This result is known as length contraction, with (1 - v²/c²)^½ as the contraction factor.

Now, just like special relativity (Sec. 2 ), length contraction has also got some misconceptions attached to it which must be cleared away in order to see its real significance. Let us have a brief view of these wrong attachments.

The situation represented by the rod R and the inertial frames S and S_o in Sec. 3.1 is the replication of the one considered by Einstein in his main paper on special relativity (except that he does not use the symbols R, S and S_o.). Now, Eq.(1) is what special relativity says about this situation. But Einstein says something more also. He contends that the observers in frames S_o and S use essentially different procedures, designated by him (a) and (b), respectively, for measuring the length of the rod, and further that special relativity predicts that the results obtained by these procedures must be different, whereas "Current kinematics tacitly assumes that the lengths determined by these two operations are precisely equal."⁵

Einstein repeated all this in his main book on relativity.⁶ Bridgman sought to bring out the allegedly wider significance of the situation. First he states the position clearly. Thus, taking Einstein and himself as the observers in frames S and S_o, respectively, he writes, "Since Einstein’s operations [viz., procedure (b)] were different from our operations[viz., procedure (a)] above, his "length" does not mean the same as our "length." We must accordingly be prepared to find that the length of a moving body measured by the procedure of Einstein is not the same as that [measured by our procedure] above; this of course is the fact, and the transformation formulas of relativity give the precise connection[viz., Eq.(1)] between the two lengths."⁷

And then he draws the moral, namely: "We must always be prepared some day to find that an increase in experimental accuracy may show that the two different sets of operations which give same results in the more ordinary part of the domain of experience [for example, the procedures (a) and (b) for low speeds of the rod], lead to measurably different results in the more unfamiliar part of the domain [ high speeds of the rod]. We must remain aware of these joints in our conceptual structure if we hope to render unnecessary the services of the unborn Einsteins."⁸

Now, there are a few points which make the link alleged by Einstein (and accepted ex cathedra by Bridgman and others) between length contraction and his procedures (a) and (b) look suspicious. For example, consider another inertial frame S’ in which also the rod R is moving parallel to its length but with a speed v’ which is different from its speed v in S. According to special relativity, its length l’ as measured by the observer in S’ is given by⁴

l’ = l_o (1 - v’²/c²)^½ . (2)

This observer has to necessarily use the same procedure for the measurement of l’ as that used by the observer in S for the measurement of l because the rod is moving relative to both of them . So we have the observers in frames S and S’ measuring the length of the rod using identical procedures and yet obtaining different results, l and l’, respectively. Now, special relativity has the same explanation for the difference of l and l’ as that for the difference of l and l_o; thus, l is different from l’ because v is different from v’, and l is different from l_o because v is different from zero. But the explanation which Einstein^5,6, Bridgman⁷ and others concerned give for the difference of l and l_o, namely, in terms of different procedures (a) and (b), is not valid for the difference of l and l’, and is therefore wrong.

This mistake of Einstein not only went undetected but was also made the launching pad of a new philosophy of physics called operationism. And the builders of this philosophy also made many more mistakes on their own. One of these concerns length contraction. To bring it out, let us read Frank’s rendering of the operational meaning of concepts. He writes, "A concept (e.g., "length") has an operational meaning if we can give an "operational definition" of that concept. This means that we have to describe a set of physical operations, which we must carry out, in order to assign in every individual case a uniquely determinate value to the concept (e.g., to the length of an individual piece of iron). We know that the "length" depends on temperature, pressure, electric charge, and other physical properties. Since Einstein’s theory of relativity, we know that the length of a body will "alter" with its speed [this is length contraction]. Hence the description of the operation by which we measure a length contains also the operation by which we keep temperature, pressure, speed, etc., constant. Or, in other words, the operational definition of length contains, strictly speaking, also the operational definitions of temperature, pressure, speed, etc."⁹

Before coming to the mistake in question, note that there is a circularity implicit in the last sentence of this quotation; this is because the operational definition of each of temperature, pressure and speed, in turn, contains the operational definition of length. Popper has just this in mind when he writes that "it can be shown quite easily that all so-called operational definitions will be circular."¹⁰

But neither Popper nor any other critic of operationism has noticed another extremely serious mistake made by the operationists and exhibited in the above quotation.⁹ The mistake consists in not seeing the fundamental difference between the dependence of the length of a rod on its speed, on the one hand, and its all other dependences, such as on temperature, pressure, etc., on the other. The difference is that the former dependence remains unaffected if we change the material or the structure of the rod, whereas the latter dependences are all affected by this change. This, in turn, implies that the origin of the dependence of the length of a rod on its speed is located outside the rod, whereas its all other dependences concern the inside of the rod. By mixing these two fundamentally different categories, the operationists inadvertently locked themselves away from the origin of length contraction, i.e., from at least a part of the revolutionary message of special relativity. Anyway, let us now see how length contraction looks when freed from these two mistakes.

As mentioned just above, a remarkable characteristic of the result represented by Eq.(1) is that the contraction factor, (1 - v²/c²)^½, does not depend on the material or the structure of the rod R. It is clear, therefore, that the origin of this factor, and hence of the quantities v and c appearing in it, lies outside the rod. Now, all that lies outside the rod and is also connected with the above result comprises the inertial frame S and the operations used by the observer in this frame to measure the length of the rod. Accordingly, we can conclude that the quantities v and c together represent the inertial frame S and the operations of meassuring length carried out by the observer in S.

Now, c cannot represent the inertial frame S because, according to assumption (B), it is same for all inertial frames. Also, v cannot represent the operations of measuring length because the latter are discrete entities incapable of varying continuously while the forrmer can vary only continuously. Consequently, the conclusion appearing at the end of the last paragraph can be restated in a more specific form, namely, that the quantity v represents the inertial frame S and the quantity c is the signature of the operations of measuring length. This relation of c to the operations of measuring length implies that light is necessarily involved in the operations of measuring length and that these operations are the same for all inertial observers.¹¹

We have just seen that according to special relativity the operations of measuring length necessarily involve light and are the same for all inertial observers. As against this, the common belief in physics is that length can be measured in many different ways,¹² most of them having no formal involvement of light which is believed to be an electromagnetic phenomenon. It is clear, therefore, that what the physicist normally means by "measurement" is fundamentally different from the meaning which he has himself (inadvertently and through the person of Einstein) assigned to this term in special relativity. This new definition of measuremennt is at the root of the revolutionary character of this theory. Through this theory, Einstein has, so to speak, released light from its illegal confinement in Maxwell’s electromagnetic cage into the skies of physics where it flies along a path called "measurement."

A few words of explanation are in order here. We said in Sec. 2 that the custom of regarding special relativity as a part of classical physics is wrong. But this does not mean that special relativity has nothing to do with classical physics; in fact the former rules over the latter. Similarly, when we say that light is not an electromagnetic phenomenon, there is no implication here that it has nothing to do with electromagnetic phenomena. It is actually associated with all phenomena, including the electromagnetic ones, since it reveals them by being necessarily involved in the operations of measurement. Finally, to say that the procedures which the physicist regards as different ways of measuring length are not really so, is not to say that they have no place in physics. These procedures are legitimate, extensively and usefully employed in experimental physics, etc. Of all their titles, only one is being denied here, namely, that they are not ways of measuring length. And this occasions a brief remark about operationism. Founded on Einstein’s idea that the concepts in physics be defined in terms of the operations of measurement, operationism has essentially two components, namely: Einstein’s idea, a recipe for defining concepts in physics, and the operations of measurement which represent the material to be used in the recipe. Since the second component is, as shown above, defective (in the sense that what are considered as the operations of measurement are not really so), operationism cannot but be, to use Bunge’s expression, "a phony philosophy of physics."¹³ But the opponents of this philosophy are not aware of the defect in its second component. Therefore, they hold its first component, i.e., Einstein’s idea, responsible for its phoniness. Thus, Bunge declares that "there are no operational definitions."¹⁴ And Popper reports that Einstein went so far as to repent over having advanced this idea.¹⁵ As will be shown elsewhere, Bunge, Popper, Einstein, etc., are all wrong in their judgements of Einstein’s idea; this idea, which is a refined version of the cardinal Galilean principle of relating concepts to experience, is at least as seminal a contribution of Einstein as his special theory of relativity.

Finally, our conclusion that special relativity, a LAW for the laws of (classical as well as quantum) physics, is the carrier of a new definition of measurement, implies that this definition will be the appropriate starting point to find a replacement for what Jammer describes as "the immense diversity of opinion and the endless variety of theories concerning quantum measurements"¹⁶ as well as to get away from Bunge’s crippling thesis that "no adequate general theory of measurement is available, either in classical or in quantum physics, and moreover it is doubtful that any can be developed ... . "¹⁷

References

1. A.P.French, Special Relativity (Nelson, London, 1968) p. 72

2. H.Margenau, The Nature of Physical Reality (McGraw-Hill, London, 1950) p. 39, note 2

3. M.Bunge, Philosophy of Physics (D. Riedel, Boston,1973) p. 132

4. Ref. 1, pp. 96-7

5. A.Einstein, ‘On the Electrodynamics of Moving Bodies’ in A.Einstein and Others, The Principle of Relativity (Dover, New York, 1923) pp. 41-2

6. A.Einstein, Relativity (Methuen, London, 1922) pp. 28-9

7. P.W.Bridgman, The Logic of Modern Physics (MacMillan, New York, 1927) p. 12

8. Ref. 7, p. 24

9. P.Frank, Philosophy of Science (Prentice-Hall, N.J., 1957) pp. 311-2

10. K.R.Popper, The Logic of Scientific Discovery (Hutchinson, London, 1959) p. 440

11. Parallel treatments of two other predictions of special relativity, namely, time dilation and the increase of the mass of a particle with its speed, lead to the results that light is also involved in the operations of measuring time and mass, respectively, and that these operations are the same for all inertial observers.

12. Ref. 7, pp. 9-23

13. Ref. 3, p. 3

14. Ref. 3, pp. 10-11

15. K.R.Popper, Conjectures and Refutations (Routledge and Kegan Paul, London, 1963) p. 114

16. M.Jammer, The Philosophy of Quantum Mechanics (John Wiley, N.Y., 1974) p. 521

17. Ref. 3, p. 72