A QUESTION OF TIMETHE MICHELSON-MORLEY EXPERIMENTThe prevalent belief in the nineteenth century was that light is a wave, carried by a subtle medium, the aether, which is at rest in the universe. The sun is at rest, in the center of the universe, and the earth moves through the aether and around the sun at about 30 km/sec. The Michelson-Morley (M&M) experiment was designed to verify this belief. If light is sent back and forth on earth, in the direction of the earth’s movement, then the round trip should take longer than it would if there were no aether. It should also take longer than it would for light moving back and forth in the direction perpendicular to the earth’s movement. The M&M experiment used two identical rods perpendicular to each other along which the light moved back and forth. This experiment, first performed in 1881, repeated in 1887, and often thereafter, could find no indication of a difference. But the belief could not be shaken, and Hendrik Lorentz, in 1895 and again in 1904, thought the explanation could possibly be that the rod placed in the direction of the earth’s movement might contract due to the earth’s movement, just enough to make the round trip time equal to the case when there is no movement, of when the movement is in the perpendicular direction. The equation he developed came to be known as the Lorentz transformation (LT). All of the texts dealing with mathematical physics and quantum physics published in recent years develop the Lorentz Transform, of 1904, and the associated gamma factor, as a logical, mathematical consequence of Einstein’s Special Theory of Relativity (SRT) proposed in 1905. There is no mention in many of these texts of the M&M experiment; no mention of Lorentz’s attempt to show that contraction of matter, or distance, for the round trip of light in the M&M experiment, could possibly account for the null result of that experiment; no mention of the fact that Einstein appropriated Lorentz’s math in order to rationalize his SRT. The historical development is opposite to that currently delivered as the gospel. 1. Michelson Morley and Lorentz The Michelson-Morley (M&M) experiment is the key to understanding the development of physics early in the 20 the century. There is still a lot of confusion about its character and implications. It is worth noting that the theory does not anticipate or support Einstein’s Special Theory of Relativity (SRT). Einstein did not believe in the existence of the aether. To give some indication of the historical setting in which the M&M experiment was conducted I quote some sentences from the paper which H.A. Lorentz wrote in 1895. “As Maxwell first remarked and as follows from a very simple calculation, the time required by a ray of light to travel from a point A to a point B and back to A must vary when the two points together undergo a displacement without carrying the aether with them…. The experiment was carried out by Michelson in 1881 {and repeated with Morley in 1887}. His apparatus, a kind of interferometer, had two horizontal arms, P and Q, of equal length and at right angles one to the other….two positions come especially under consideration in which the arm P, or the arm Q lay as nearly as possible in the direction of the Earth’s motion…it was anticipated that when the apparatus was revolved from one of these principle positions into the other there would be a displacement of the interference fringes….But of such a displacement…no trace was discovered. “If we assume the arm which lies in the direction of the Earth’s motion to be shorter than the other… then the result of the Michelson experiment is explained completely.” Lorentz thought that perhaps the molecules of a solid might be compressed in the direction of motion, and this could explain why the time of travel is the same in both directions. His transformation attempted to quantify this contraction of matter. Lorentz conjectured as early as 1895 that perhaps the rod parallel to the earth’s movement might shrink because ‘electrons would lose their spherical shape due to the earth’s motion’. ‘Electron’ at that time was a word denoting some elementary particle that is the ultimate constituent of matter. Lorentz quantified his conjecture in a paper in 1904. He showed how much shorter the round trip, in the direction parallel to the earth’s motion, needed to be so that the effect of the earth’s motion would be counteracted. He then tried to find how much shorter the rod would have to be on each leg of the roundtrip in the direction parallel to the earth’s motion. Here is where he got into trouble that no one, to date, has appreciated. The formula he ended up with, called the gamma factor, is one of the most widely used expressions in astronomy and particle physics. It is also the basis of Einstein’s SRT – and it is wrong. To understand the challenge, and the significance, of the Michelson-Morley (M&M) experiment we can look at an analogous situation. We know that the velocity of a plane is measured with respect to the air stream through which it moves. If we fly from, say, San Francisco to New York and back and the air is still, it will take six hours each way, at 500 miles per hour. If the air is moving at 100 miles an hour, from west to east, and the plane flies at 500 miles per hour, with respect to the air stream, the distance of about 3000 miles is covered in five hours (at 500+100 miles per hour) and the return trip takes 7.5 hours (at 500-100 miles per hour). So the total time is not 12 hours but 12.5 hours! The gain and loss, due to the movement of the air, don’t quite balance out. Analogously, that would be the situation if the velocity of light is measured with respect to the aether, and the earth moves through the aether. It is easy to show that if the round trip time distance is reduced by 240 miles, or the distance between SF and NY by 120 miles, that is, by one-half this amount, it takes 4.7 hours going, 7.3 hours returning, and the total time will be 12 hours – the same as it would be if the earth were at rest in the aether. We cannot reduce the distance between NY and SF by the square root of 240 or about 16 miles, since that would not be enough to bring the time back to 12 hours. BUT THAT IS EXACTLY WHAT THE LORENTZ TRANSFORM PROPOSES TO DO. All derivations of the Lorentz Transformation (LT) are based, like the Michelson-Morley experiment, on two-way travel. An additional assumption is that the same length contraction applies to both paths, coming and going. In the analogy, if we call s the velocity of the plane, and v the velocity of the jet stream, we can calculate the shortening required as a function of s and v. The formula is [1 – v*2/s*2], as the fraction by which we have to shrink the total length. In reality we need to reduce the distance between the end points by one-half this amount for each leg of the journey, in the direction parallel to the earth’s motion. A quick review of how we get this formula should be helpful. We can let L be the distance from SF to NY, and s the speed of the plane (to distinguish it from the speed of light c). We can then write: L = sT, L = (s-v)T’, and L = (s+v)T’’; where T is the time when the air is still, T’ the time flying against the jet stream, and T” the time flying with the jet stream. The fractional increase in time due to the jet stream is then given by the ratio (T”+ T’)/2T which is easily seen to be [s/(s-v) + s/(s+v)]/2. It takes a little algebra to arrive at the formula: T”+T’ = 2T/[1 – v*2/s*2]. This formula holds true for light by substituting c for s. Since the denominator is always less than one, this formula shows that the round trip time is always increased due to the result of a jet stream, or the aether in the case of light. Whatever mechanism we want to invent, this formula shows how much we need to shrink the total path to get the M&M result under these assumptions. But there is a subtle point that must be noted. If we want to deal with a single direct path, that is in some sense the ‘average’ of coming and going, we could, mathematically, take the square root of the total path reduction that is needed. This produces the Lorentz factor (often called the ‘gamma’ factor), that appears in the denominator in many important equations in particle physics as well as in astronomy. It applies only to a fictitious one-way path that has no basis in reality. The problem with this step lies in the relationship between mathematics and physics: Taking a square root, a geometric mean, is appropriate, ONLY if a second factor follows and acts on a first factor, that is to say, if the factors multiply. For example in the case of the Doppler factor, a stretch of a time interval on one leg of a journey is followed by second stretch on the return path – the Doppler factors (not the Doppler shifts) multiply (see the chapter on Doppler). Similarly if I stretch a rubber band by a factor 2, and then do a second stretch, by a factor 8, the total is 2x8 = 16 (and not 2 + 8 = 10). The ‘average’, in the sense of a geometric mean, is then the square root of 16 or 4 (since 4x4=16). In the case of addition we would not take the square root of 10 to get the average of 2 + 8. But that, in essence, is what Lorentz did! Apparently he did not realize that time of travel, unlike the Doppler factor, did not involve stretching or shrinking. The shorter time on one leg of a journey is not further modified on the return leg. We simply get a longer time of transit, and the two times add – they do not multiply. If we use the case v = c/2 we find that the total distance must be reduced by the factor (1 - .25) = .75 on each path – which in the case of the plane flying between SF and NY, requires a distance of 2250 miles on each leg. But if we tried to reduce each path by the square root of .75 we would only reduce the distance to about 2600 miles - not enough to reduce the round trip to 12 hours. We can conclude that if in fact matter shrinks when in motion (and I doubt very much that this is true) then the Lorentz transformation badly underestimates the reduction in time that is required to reach the result of the Michelson-Morley experiment. If a trip should take six hours in each direction but in fact takes 3 hours going and 9 hours returning (after shortening the distance to reduce the total time from 16 hours to 12), then taking the correct arithmetic average is not much of an improvement over the incorrect geometric average – the average time has no physical significance in either case. The point is that the LT is meaningless on both physical and mathematical grounds. In the case of a multiplicative process, for example stretching a rubber band by a factor of 2 and then a factor of 8, there is a conceivable physical alternative where we stretch it twice by a factor of 4. That is not the case where one trip takes 3 hours and the return trip 9 hours, and the model is that of a carrying airflow or aether. There is no average airflow and no average time that makes sense. Simply put, the mathematics of the Lorentz transformation, the last step of taking the square root as pertaining to the time for one leg of the journey, is pure fantasy, with no connection to reality – it ignores the physics of two way travel. There can be no physical significance to the square root, or to any concepts or quantities containing this factor. Incidentally, Lorentz made this mistake because he took an expression made up of squared quantities, c*2/(c*2 – v*2), and introduced for this expression a new variable, called beta-squared. That made it natural and tempting to take the square root – without bothering to ask about the sense or legitimacy of this operation. This is equation 3 in section 4 of his 1904 paper. The reader may recognize beta-squared as the fraction by which the total time must be shortened, and half of the shortening should pertain to each leg of the round trip – not the square root. The Lorentz transformation is a science fiction fantasy, but it has captured 20th century physics and cosmology. Einstein maintained that he developed the Lorentz transformation independently. He does not cite Lorentz in his 1905 paper. It is most curious, therefore, that he made the same mathematical mistake of taking the square root at the same point in the development of the transform as his predecessor. The defect in the LT does not show up because in all down-to-earth experiments we are dealing with velocities one hundred thousand to one million times smaller than the velocity of light. The defect becomes readily apparent only when the velocity is about one tenth the velocity of light, or greater. This happens in cosmology and in particle physics and requires a rethinking of much of 20th century physical theory. In cosmology, we encounter large red shifts, especially with type 1A supernovae. Using a revised formula for the Doppler factor, we are led to a radically different view of the origin and destiny of the universe. 2. Michelson-Morley and Einstein Einstein’s thinking, in terms of analogies to the M&M experiment was confused. Had his thinking been clear he would have said of the M&M experiment: The null effect is clearly explained by the fact that, according to the principle of relativity (the first principle of SRT), the speed of light is c in the inertial system of earth. There is no aether, and since the observer is also in that system there is zero relative motion, v, and therefore no distortion of time or space. The light travels at velocity c in all directions. The experiment should have a null result, but can say nothing about the second principle (that the speed of light is independent of the movement of the source). But Einstein was confused about the meaning of the M&M experiment. Some examples can help illustrate the situation. Suppose I row a boat downstream for two hours, and then, using the same strokes row back up stream for two hours. It is clear that if the stream has any velocity, v, I will not come back to the same place I started. I either need to row longer or stronger, on the way back, or by some trick, make the distance shorter on the return trip. Now for a similar argument based on a train trip: The train is moving with velocity, v and I am taking a walk from the back of the train to the front and then back again. How does the speed of the train affect the time it takes for this round trip? Notice that this really defines a different problem. I haven't asked whether I will come back to the same place on "shore", I am only interested in my walk on the train. So the answer to the second experiment will not be the same as the answer to the first. In the second example, as we know from experience, it really doesn't matter how fast the train is moving, I walk at a certain speed and that gets me to the front of the train and back again in the same time, whether the train is standing still or travelling at 100 miles an hour. The second example is the appropriate analogy to the M-M experiment - seen from Einstein's point of view. The first is appealing since the light is seen to be struggling against, or being aided by the aether, similar to the relation of the rower and the stream. But in fact the earth corresponds to the train, the sun to the embankment, and the light moves a fixed distance to a mirror and then back to the starting point, just like the walker on the train, whereas the rower does not move with respect to the boat. So as seen here on earth, it doesn't matter if the round trip of the light is parallel or perpendicular to the movement of the earth around the sun. The time back is the time forward in either case - provided we forget about the 'aether' - as Einstein did. Einstein also used the parallel example to the M-M experiment involving a train and embankment. But he was not consistent in his use of the parallel and therefore drew the wrong conclusion. In section 7 of his 1917 book he lets the light beam originate on the embankment and from there deduces that the speed of light as measured on the train would have to be less than c because of the motion of the train, but that is an improper use of the analogy, and an incorrect inference. If the train corresponds to the earth then that is where the light in the M-M experiment originates and is measured. It is found to have velocity c, as would be predicted by the classical view. To make this error clear I quote from section 7: "Along the embankment we will send a ray of light with velocity c in the direction of the moving train. On the track a train moves with velocity v in the same direction as the ray of light, but of course more slowly. We ask, what is the velocity of the light relative to the train? We can apply the discussion of the preceding paragraph, because the man walking on the train plays the role of the ray of light. So with respect to the train the light must move at a slower speed, w, and is given by w = c - v which would make the velocity of light with respect to the train be less than c. This result violates the principle that all natural laws must be the same in all reference systems." [Note that the light moves along the embankment whereas the man moves on the train – we can’t equate these!] Einstein concludes that the light moves with velocity c - v 'relative to the train' for an observer ON the train. In fact it moves with velocity c when the source is on the train. This is a mistake due to the ambiguity of the phrase 'relative to the train'. This phrase can mean that we evaluate the motion along the ground as experienced on the train, or it can mean that it is the motion of an object that is on the train. The two should not be used interchangeably. It is hard to believe that this ambiguity was not caught by Einstein or any of his followers - but there is no other way to interpret his own words - and subsequent statements. As appears clear from Einstein's references to the M-M experiment, he was of the opinion that it proved something about what an observer on the sun, (that is, on the embankment), would experience, and that the experiment confirmed SRT. His confusion becomes clear through a citation in his second book on relativity. Einstein published this second book on Relativity in 1922 and found it necessary to defend himself against unnamed critics. An analysis of that defense is revealing. Early in the chapter on Special Relativity there occurs the following: "We should note in particular, that a ray of light, which in one coordinate system K has velocity c, would have, according to equation 21, a different velocity in a moving system K', which depends on the velocity of that system (with respect to K). This would give K a unique place, which would distinguish it from other coordinate systems in relative motion to K. But all experiments have shown that electromagnetic and optical phenomena, relative to the earth as coordinate system, do not depend on the motion of the earth with respect to the sun. In particular this was the case with the Michelson-Morley experiment. Consequently the relativity principle of Special Relativity is beyond question." Everything is true in the above except the final statement that intends to justify SRT. In particular it is true that every coordinate system in which an experiment is conducted is "special" with respect to other coordinate systems that are in motion relative to the first. But this statement must be carefully interpreted. Quantities which are relative to a system K, will have a different value with respect to another system K', so K is special, in that sense. Let's look in detail at his statement: 'But all experiments have shown that electromagnetic and optical phenomena, relative to the earth as coordinate system, do not depend on the motion of the earth with respect to the sun'. This statement is a direct consequence of the first principle but says nothing about the second. In effect, it says that motion is relative to the earth, so it should not be surprising that this was the observed result. An observer on the ground can use a stop watch to time a round trip walk that takes place on the train, and will get the same result as an observer on the train. He can't conclude that the walker travels at the same speed with respect to the ground as with respect to the train. He can't conclude that the distances walked in the forward and backward directions, as measured on the ground, are equal; all he discovers is that the duration of the experiment is the same measured in different coordinate systems, the time of the trip does not go to infinity as the speed of the train approaches the speed of the walker, as would be required by the Lorentz Transformation - and by analogy the same is true for light. Time is invariant, not speed. Based on the logic of the analogy, the M-M experiment shows the same thing. The speed of the walker on the train does not depend on the velocity of the train, and the speed of light, originating and measured here on earth, does not depend on the movement of the earth with respect to the sun. All this is just another way of saying that the speed of light is constant relative to the body from which it originates - measured at a fixed distance with respect to the time and place of the origin of the light! This truth is embodied in Einstein’s first principle. It is important to see the difference between Einstein's and Lorentz's point of view. For Lorentz and the scientists of the nineteenth century, the issue was whether the motion of the earth with respect to the aether, or what was seen as the same thing, the motion with respect to the sun, would show an effect on the speed of light. It was not a question of looking at the problem as though the source of light or the observer is on the sun. Looking at the problem from the point of view of an observer on the embankment (which in the case of the M-M experiment is an observer on the sun), was Einstein's contribution - but it was unclear, even to Einstein, how this changed the entire question of what the M-M experiment could prove. Einstein constantly shifted his point of view. Sometimes he was concerned with what an observer in a system in relative motion would experience (in this case the observer would be on the sun); sometimes he was concerned with what is happening to the light beam as it travels along in the ‘chosen’ system. Lorentz, on the other hand took only the position of an observer on earth – that is the train. The essence of what M&M can teach us is that light and sound must be treated differently – that there is no carrier for light as there is for sound. The Lorentz Transformation is an attempt to avoid this conclusion, in order to conform to 19th century thinking, by inventing a contraction of matter based on speed. Einstein makes incorrect use of Lorentz’s device (which works only for a round trip of light). He also uses a geometric mean where he should have used an arithmetic mean. The negative result of the M&M experiment, together with the failure of SRT, impacts the derivation of the Doppler factor for light. This, in turn, impacts conclusions about the nature and age of the universe. Cosmologists are drawing false inferences about the character of the universe from the erroneous Doppler formula based on Einstein’s SRT. TABLE OF CONTENTS SIMULTANEITY AND SYNCHRONIZATION THE MICHELSON-MORLEY EXPERIMENT APPENDIX I: TYPE 1A SUPERNOVAE APPENDIX II: A EUCLIDEAN MODEL OF THE UNIVERSE APPENDIX III: MASS AND ENERGY
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