The Critical Rationalist                       Vol. 01  No. 03
ISSN: 1393-3809                                    30-Dec-1996

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Part I

(4) Einstein's theory of relativity is a striking example for this observation. Most of you will know of Popper's admiration for Einstein, and how he was inspired by the theory of relativity (and by its high refutability in contrast to the irrefutability of psychoanalysis) more than by anything else to develop the criterion of falsifiability as a demarcation between science and metaphysics (Popper 1976, pp. 37-38). And in connection with this criterion he often quoted--and amplified--Einstein's words from Geometrie und Erfahrung (Einstein 1921):

Insofar as the expressions of mathematics refer to reality they are not certain, and insofar as they are certain they do not refer to reality.

(5) Going by this sentence it would appear that there could hardly have been a more perfect understanding on methodology than that between Einstein and Popper. And they even agreed in this, that they both believed the theory of relativity not to be the final truth. Einstein spent the last thirty years of his life in search of a general field theory. And from Popper's Realism and the Aim of Science (Popper 1983, p. xxviii) it can be seen that he considered the issue between Einstein and Lorentz, which is none other than the issue between relativistic physics and non-relativistic physics, to be still open.

(6) Most amazing about this is that they both held the key to the problem in their hands. Let us take a look at the general theory of relativity and at Einstein's concept of "curved space". It is reputed to be a difficult concept, but Einstein's deduction is simple enough to be understood by everybody. In one of his famous Gedankenexperimente he assumes a large box, or lift, being accelerated through space at a constant rate outside any other field of gravitation. He then first discusses the situation of a generation of physicists being born and living in that box, without being able to "look out of the window", and finds that, due to the constant rate of acceleration, they will be under the impression of living in a gravitational field. Permanent acceleration will permanently press them to the floor of the box. He then lets a ray of light travelling horizontally (parallel to the bottom, or x-axis) fall into the box through a hole in its side, and finds that, due to the finite velocity of light, and, again, due to the constant rate of acceleration of the box, this ray, which had been travelling in a straight line outside the box, will assume the shape of a parabolic curve inside the box. From the combination of these two considerations he infers that the scientists living in that box will ascribe the deflection of light to the influence of the gravitational field. And his further inference is that, since we, the human race, are living in the gravitational field of the earth, and the sun, without being able to "look out of the window", we must also assume that the lines of light will be curved in this field. Going by his own explanation, this, and nothing else, lies at the bottom of his famous concept of "curved space".

(7) Now, I fear that some of you may not believe this. The lift-example is taken from the book "Über die spezielle und die allgemeine Relativitätstheorie" in which Einstein tried to explain the theory of relativity to non-physicists in a popular way (Einstein 1917, chapter 20). It seems unfair to hold this attempt at a simple visualisation of a difficult scientific theory against him. But I assure you that I have looked through Einstein's papers very carefully, especially through the early ones, and I have found many complicated discussions of the implications resulting from curved space, and also many adaptations of the theory to empirical results which surprised me because the experiments in question might well have been taken as refutations of the theory. I have also found the arguments used in the lift-example formulated in a more scientific shape, referring not to lifts, or boxes, but to systems of coordinates, and planets, and ellipses (Einstein 1916). But the gist of the argument always remained the same. And nowhere have I found anything like a critical discussion of the fundamental premise that light will be deflected in the gravitational field. The discussion of this premise did not take place in Einstein's papers; nor have I found it anywhere else.

(8) You may still not feel reassured because I am only a lawyer, and admittedly know very little about physics, and even less about mathematics. But perhaps a quotation from Einstein's own text will convince you. In "Die Grundlage der allgemeinen Relativitätstheorie" (Einstein 1916)--and this is not a simplified book, but one of his original publications in Annalen der Physik--he explicitly says (the translation is mine, but the words are his):

For it is possible `to create' [he puts this in quotation marks] a gravitational field by merely changing the system of coordinates ... it is easy to see that the way of light relative to K' [K' is the system of coordinates that is being accelerated, i.e. the "lift"] will generally be curved if light moves in a straight line and with constant velocity relative to K.

(9) This, I believe, shows quite clearly that, at that time, he considered the deflection of light as a necessary implication of acceleration, resulting from a purely mathematical operation, viz. the "changing of the system of coordinates". To him it was the result of a mathematical equation. In fact he inferred this deflection from two very simple premises: (1) the constant velocity of light, and (2) an identification of acceleration with gravitation[2].

(10) Let us now look at this argument with Karl Popper's eyes.

(11) According to Popper's "Logic of Scientific Discovery" Einstein's reasoning is not only very strong, but in fact too strong. For it is, of course, true that the ray of light falling into the accelerating box will form a parabolic curve. But this is true not only for light, but also for any other ray travelling at constant speed, and entering the box at an angle of tex2html_wrap_inline620 . The shape of the parabolic curve will, of course, vary depending on the velocity of the ray and the acceleration of the box, but if one of two intersecting systems of coordinates is moving at constant velocity while the other is being accelerated the function of the intersection must necessarily be a parabolic curve. This is not only true for rays of light; it is even true for rays, or lines, that exist only in our imagination, or for a box without top or bottom, and therefore without gravitational field. It is independent of any physical properties of those rays, and has nothing to do with gravitation, but simply consists of a geometrical description of two bodies, or systems of coordinates, moving at speeds relative to each other, when one of them is being accelerated and the other is not. It is the result of a valid mathematical inference which can therefore never be refuted. It is a simple truism of analytical geometry and therefore belongs to mathematics, but not to physics. So it falls victim to Einstein's own criterion: because it is certain it does not refer to reality. And if it does not refer to reality, then it does not describe a physical property of light, or of space. And in Popper's terminology the theory of curved space is non-empirical because it cannot be refuted by any conceivable experiment, or physical property of light[3]. Therefore we may not infer from this theory that space is curved in reality, and that light will be deflected in the gravitational field.

(12) I wonder if any of you will accept this. If you do not, I would be eager to hear a counter argument because I know of none. I have discussed this argument with physicists of my acquaintance without being contradicted. I have tried to get a public discussion by publication in serious periodicals of science, but was rejected. I then tried to get support, or contradiction, from experts and sent a paper containing this argument--and other arguments which I consider even more important, but which are not directly related to Karl Popper's theories--to well known physicists in England, France, the U.S.A. and Germany without being deemed worthy of a reply[4]. So I have never been able to put on trial my case Popper v. Einstein. Nobody seems to be willing to believe that a practising lawyer can have anything sensible to say on the theory of relativity; nor is anybody willing to discuss the argument on its own merits. All I can do, therefore, is take advantage of a defenseless audience and present my view at the Annual Popper Conference, and via The Critical Rationalist, and I am grateful to be able to do so. To me it appears clear that some aspects of Einstein's general theory of relativity and Popper's "Logic of Scientific Discovery" contradict each other flatly and cannot, therefore, both be right.

(13) I could end my article at this point because this was what I wanted to say. But you may ask: What about the empirical confirmations? Was not the general theory of relativity almost miraculously confirmed in Eddington's famous experiments, made during the eclipses of 1919 and 1922? Did he not observe that the light coming from distant stars was in fact deflected in the gravitational field of the sun?--And did not Einstein predict that the spectrum of light coming from other stars would be shifted towards the lower frequencies, which has since been confirmed by observation many times, in particular by the American astronomer Edwin Hubble?--Was it not even observed that there is a time shift if we circumnavigate the earth in fast aeroplanes, which was predicted, and can only be explained, by the special theory of relativity?

(14) I have tried to look into all these empirical confirmations. Some of them require more knowledge of mathematics than I have. This does not worry me too much because, as an admirer of Karl Popper, I am more interested in refutations than in confirmations, and to refute an empirical theory you do not necessarily need mathematics. It may be sufficient to discuss the premises on which it relies. According to the Logic of Scientific Discovery (Popper 1980) one refutation will bring down the theory of relativity, and so many confirmations will not set it up again if this refutation is valid and can be repeated. But as far as my understanding goes I can say that all the "confirmations" of the theory of relativity are extremely dubious. I will explain this for the three most important ones, trying to be as brief as possible.

(15) Eddington's experiment is justly famous, not only for its results but also for its magnanimity because, while the First World War was still going on, a team of British scientists meticulously designed an experiment to put to the test the theory of a German scientist. Anti-Semitism was not so important in 1919, and Einstein was still considered to be a German citizen. Eddington believed in the theory of relativity and tried to confirm it. His experiment was carried out during the eclipse of 1919, and repeated in 1922, and Eddington was able to show that, as Einstein had predicted, the light coming from distant galaxies was in fact deflected, as by a convex lens, in the gravitational field of the sun. It seems that this was the point when all resistance against the theory of relativity which had previously existed ultimately broke down. My impression is that the theory of relativity was never again seriously challenged after that.

(16) But looking into the publications of that time will produce some surprising results. As mentioned, Eddington's experiment was carried out in 1919/1922. But Einstein had already read, in 1915, a paper before the Royal Prussian Academy of Science in which he stated that the deflection of light passing the sun was 1.7 sec. of arc relative to the passing distance from the sun (Einstein 1915). And he adapted his general theory of relativity to this value. Therefore the value cannot have been predicted by the theory, but must have been known before, and independent of it. The theory was designed, and adapted, so as to explain this particular value.

(17) After the publication of Eddington's experiment Einstein still spoke of a deflection of 1.7 sec. of arc. So the outcome of the experiment seems to have been exactly what he expected. But he now explained this value as having been caused "one half by the (Newtonian) attractive field of the sun, the other half by the geometric modification ("curving") of space caused by the sun" (Einstein 1917, p. 84f, my translation of his words).

(18) At least this last explanation can certainly not be valid. For, as I have tried to show before, the concept of "curved space" had been based, by Einstein, exclusively on the deflection of light in the gravitational field. If (only) one half of the deflection actually observed can be explained by the curving of space, which had, in turn, been explained by the gravitational field, then the other half cannot be explained by the same gravitational field, this time in the "Newtonian" sense. You cannot arbitrarily "split" the effect of gravitation into one half causing curved space, and the other half causing attraction[5]. This seems to indicate that the deflection actually observed by Eddington must have been much stronger than Einstein's equations would permit[6].

(19) Nevertheless there remains the indisputable fact that the theory of relativity predicts a deflection of light by gravitation and that a deflection was actually observed. The inconsistency in Einstein's explanation does not affect this coincidence; it only puts a question mark behind the alleged correspondence of the exact values of theory and observation. But it gives additional weight to the question whether the theory of relativity can be a true explanation of this observation.

(20) Almost equally famous is Einstein's explanation of the redshift of light coming from distant galaxies which can be observed by the shift of the characteristic spectral lines. In special relativity Einstein explains that a clock which is being moved in a straight line will go more slowly than one that is stationary (Einstein 1917, p. 25). In general relativity he infers from this that a clock fastened on the periphery of a rotating disc will permanently work more slowly than one at rest (Einstein 1917, p. 53). And finally he reaches the general conclusion that any oscillating process, as which he regards the atom emitting light, will be decelerated in the vicinity of inert mass[7]. This implies that the spectrum of light coming from stars with great inert mass will be shifted towards the lower frequencies. That was Einstein's explanation of the redshift which had also already been observed when he wrote.

(21) But the American astronomer Edwin Hubble discovered in or before 1937 that the redshift of light coming from distant galaxies is proportional to their distance from earth (Hubble 1938, p. 35). According to Einstein's theory the extent of the redshift, being caused by gravitation, would be a function of inert mass. It should therefore vary in proportion to the inert mass of the object from which light is coming. So we should expect to observe different redshifts in heavier or less heavy bodies. But the Hubble effect--in its common interpretation by the Doppler principle[8]--shows that the extent of the redshift is in fact graduated not in proportion to mass, but to distance. This would only conform with general relativity if we assume the stars, or galaxies, to be arranged precisely in the order of their size (mass), which conflicts with observation.

(22) So here we have a serious clash. We can either accept the general theory of relativity or Hubble's explanation of the redshift in the light coming from distant galaxies. And in view of the strong, and repeated, empirical confirmation of Hubble's observation I think we must decide in favour of Hubble.

(23) Another famous experiment is usually discussed in terms of the special theory of relativity[9]. The special theory of relativity rests on two fundamental premises. One is the constant vacuum spreading velocity of light, which Einstein accepted as the result of various experiments, and the other is the equivalence of all inertial systems, which he assumed because we have no reason to believe the laws of physics to be different on other stars from those here on earth. From these two premises Einstein inferred, in faultless mathematical deduction, that, if the velocity of light is constant, time itself must be variable. And he predicted that, therefore, a body in motion will age more slowly than one that is stationary.

(24) To test this theory a most interesting experiment was carried out in October 1971 by two American physicists, Hafele & Keating (1972b, 1972a). Four caesium beam atomic clocks were flown on regularly scheduled commercial jet flights around the world twice, once eastward and once westward. It was observed that the flying clocks lost time (aged more slowly) during the eastward trip, and gained time (aged faster) during the westward trip relative to the corresponding time recorded by the reference atomic time scale at the U.S. Naval Observatory, MEAN (USNO). Hafele & Keating explained this as a prediction of the theory of relativity in the following words:

... consider a view of the (rotating) earth as it would be perceived by an inertial observer looking down on the North Pole from a great distance. A clock that is stationary on the surface at the equator has a speed tex2html_wrap_inline622 relative to nonrotating space, and hence runs slow relative to hypothetical co-ordinate clocks of this space in the ratio...

(25) I will not continue this quotation because I think the pivot of criticism is obvious: the clock of comparison actually used in the experiment was not in the hands of "an inertial observer looking down on the North Pole from a great distance"; it was at U.S. Naval Observatory, which is, to my knowledge, situated at Richmond, Florida, and therefore close to the equator. So it was itself rotating with the equator. If there is no preferred inertial system, as Einstein claims, then relative to this clock the velocity of both flying clocks, eastward and westward, was equal, and therefore, if the theory of relativity had been right, the time dilatation should have been equal too[10]. But in fact the flying clocks lost time during the eastward trip and gained time during the westward trip. So we have another clash, this time between observation and special relativity. We can either believe in Einstein's theory of special relativity or in the observations made by Hafele & Keating. But we cannot believe in both.

(26) And the worst is yet to come: As Hafele & Keating explain, special relativity predicts a time difference for the clock coming back to its starting point after having circumnavigated the earth. But what is a "time difference"? This clearly depends on what meaning we give to the concept of "time".

(27) There have been endless discussions of this concept. Being a firm believer in Popper's methodological nominalism, and in his view that any discussion of "concepts" will inevitably end in "empty verbiage and barren scholasticism"[11], I have no intention of joining them. I will therefore try to cut short any discussion on the "true", or "real" meaning of the concept of "time" by stating explicitly that, in this article, I am not discussing the "existence" of time, or of the "reversibility" of natural events connected with the concept of the "arrow of time", or anything of that sort, but will simply use the term "time" in the everyday sense which we employ when we ask somebody: "What time is it?" We then expect an answer expressed in units of time, i.e. in terms of "days", "hours", "minutes", "seconds" etc.

(28) The advantage of using the concept of "time" in this everyday sense is that we ourselves can define its meaning, for example by setting clocks. This is an implication of Popper's methodological nominalism[12]. And if, as a matter of expedience, we define "time" as a unique coordinate of singular events, meaning that no set of space coordinates may have more than one time function, then there can never be two different "times" for any singular physical location. Let me explain this by an example. We could, quite arbitrarily, define noon time as the point when the sun reaches its zenith at, say, Greenwich. If our plane now starts from Greenwich and returns to Greenwich when the sun is in its zenith there, and the clock on board does not show 12.00 h sharp at its arrival then we do not have two different times at Greenwich but, according to our definition, the clock is wrong. And we should not blame the sun for this either, nor would it be wise to alter our definition of "time" so that it will now permit two "times" at Greenwich because this would create an awful muddle. Our problem is, rather, to find out what happened to the clock, which is an empirical problem.

(29) But relativity will, even starting from this premise of time defined by the course of the sun, predict a time difference for the plane surrounding the equator[13]. It is, as I understand it, a necessary theoretical implication of relativity that the clock starting and arriving exactly when the sun has reached its zenith at Greenwich will not show 12.00 h sharp at its arrival, but some fractions of a second less, and this although we have defined 12.00 h as being the moment when the sun reaches its zenith at Greenwich. So, in spite of our nominalistic definition of time permitting no more than one time function for one location, and assuming only that we can circumnavigate the earth, we can infer from relativity that,

  1. time will be 12.00 h when the sun reaches its zenith at Greenwich, and
  2. time will not be 12.00 h when the sun reaches its zenith at Greenwich.

(30) Assuming that a circumnavigation of the earth is possible, the theory is therefore contradictory.

(31) If this inference is correct, then special relativity must be wrong. And if the inference is not correct it must still be wrong because, if it does not predict a time difference, it cannot account for the time difference observed by Hafele & Keating in their experiment.

(32) So we are faced with a truly enigmatic situation. And since the mathematical formulae of special relativity are faultless this implies that one of its empirical premises must be given up. But special relativity rests on only two empirical premises. One of them is the assumption that the laws of nature (physics) are universal; giving up this would be the end of all explanation. And the other is the hypothesis of the constant spreading velocity of light. Therefore it must be this second premise which has to be given up. In other words: Special relativity does not explain, or establish, the relativity of space and time; but it does refute the empirical hypothesis of the constant spreading velocity of light[14]. If we can travel around the world and come back to our starting point, then the velocity of light, if it is finite, cannot be constant. And since the constancy of the spreading velocity of light is the fundamental premise both of special and of general relativity this all boils down to the thesis:

If the earth is round then the theory of relativity must be wrong.

(33) It also follows from this that the time dilatation observed by Hafele & Keating was not an effect of special or of general relativity, but must have been an effect of something else, at any rate something empirical. My conjecture is that it was an effect of ether[15], though of a somewhat different kind than that expected by Michelson/Morley in their famous experiment (1887).

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The Critical Rationalist                       Vol. 01  No. 03
ISSN: 1393-3809                                    30-Dec-1996

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TCR Issue Timestamp: Mon Dec 30 17:41:04 GMT 1996