Can special relativity be transformed into a coherent theory?

The common sense analysis of the M-M experiment

Or how to change the century-long-overdue relativistic paradigm which is still constricting the evolution of physics

I said earlier that one of the reasons for my preferring Asimov's description of the Michelson-Morley experiment was what I believe to have been a “slip of the tongue” on the part of that author. Now is a good time to reveal it.

By and large, Asimov's description of the experiment is right at the end of his book (Asimov's new guide to science is almost 1000 pages long). A summary of the main points of the experiment, however, is presented on page 350. And in that summary I read the following:

If the earth is moving through a motionless ether, Albert Michelson had reasoned [before conducting the experiment], then a beam of light sent in the direction of its motion and reflected back should travel a shorter distance than one sent out at right angles and reflected back. (My italics.)

Michelson's initial reasoning was clearly the common sense reasoning. Need I explain why? No, I don't think so. This reasoning is so common that just about anyone should easily arrive at the same conclusion. After analysing the experiment mathematically, however, the conventional conclusion was that exactly the opposite is the case! Why? What could possibly change the initial reasoning so dramatically? Asimov says nothing about that in his book, and (as far as I know) neither does anybody else. Of course, the relativists will immediately remind you of certain assumptions (the laws of physics in inertial frames of reference, principle of relativity applied, etc.), but a solid line of reasoning proving that those assumptions are warranted and indispensable... I have never seen anywhere. And that's not all. Even with those assumptions employed, I challenge any physicist to prove that the conventional mathematical analysis is superior to the common sense analysis. Come on, you physicists out there, show me the error in the common sense reasoning below.

• The experiment was designed to establish if there is a frame of reference at absolute rest (call it ether, call it space, call it what you will).
• The initial assumption was that there is such a frame of reference.
• Therefore, all measurements involved should be performed relative to that assumption.

Now, in the case where the beam of light was sent out in a direction perpendicular to that of the earth's motion, the conventional analysis does measure the distance travelled by the light relative to that assumed frame of reference. (“In the time it takes light to reach the mirror the motion of the earth has carried the mirror from...”, remember?) In the parallel case, however, the distance travelled by the beam of light is not measured relative to the assumed frame of reference—even though the same reasoning should categorically be employed. (That's simply because in the time it takes light to reach that mirror, the motion of the earth has carried it from its original point—relative to the assumed frame of reference at absolute rest—to another point, relative to the assumed frame of reference at absolute rest!) A visual description of the common sense reasoning in the Michelson-Morley experiment is shown in the animation below.

In natural language, then, the common sense analysis of the parallel journey says: In the time it takes light to travel from its source to the mirror at its velocity c plus earth's velocity v, the mirror has moved in space a certain distance—which I shall denote z. The distance travelled by the light in the first leg of the parallel journey is, therefore, in mathematical language: (d+z)/(c+v). In the return leg, on the other hand, in the time it takes light to travel back from the mirror to the source the motion of the earth has carried the source a certain distance in space in the direction of the earth's motion. Mathematically this leg of the journey is expressed thus: (d-z)/(c-v). A visual depiction of this common sense analysis of the parallel journey completed by the light is shown in the animation below.

Now, the total time taken by the light to complete the journey in the direction parallel to the earth's direction of motion is:

So how does the common sense result compare to the conventional result of the parallel case? Let's put them side by side and see:

Now we can extract the final conclusion in the common sense analysis of the Michelson-Morley experiment by comparing the two results above. And since I am only interested in a qualitative analysis of the experiment I can easily derive the final conclusion I have been seeking:

Thus, if there is a need of me to say this, for any value of v greater than zero the time taken by the light to cover the distance from its source to the mirror and back is shorter than the time taken by the light to complete the perpendicular journey! And, of course, this conclusion is exactly the same to Michelson's original one (the one put forward by the common sense), and is the exact opposite of the conventional conclusion. Surprised? You shouldn't be. When between the rational analysis of a phenomenon and its formal (mathematical) interpretation there are conditions (assumptions) imposed by the dogma, chances are that the general sense will no longer be common and that the common will no longer make sense. The history of physics is littered with such examples, and more often than not one idea is replaced by its exact opposite.

So the common sense analysis of the Michelson-Morley experiment leads to a completely different conclusion than the conventional analysis employed by the establishment since 1887. Nonetheless, the two different approaches have something in common: They both conclude that there ought to be a difference between the times taken by the light to complete the two return journeys. The experiment, however, did not detect the difference predicted. Now, we have seen how the conventional establishment dealt with that most unexpected result. Through the propositions of people like Lorentz and Fitzgerald, and with the theoretical contributions of others, the undesirable result of the Michelson-Morley experiment was assimilated in the conventional understanding by being "explained-away" by the special theory of relativity. One might argue (quite rightly) that the undesirable result of the MM experiment was assimilated and “explained away” by the Lorentz-Fitzgerald proposition, but that argument would be unacceptable to the conventional establishment. “Sure”, they would say, “the proposition that objects in motion contract in the direction of their motion by an amount proportional to the motion's rate does, somehow, explain the findings of Michelson and Morley—but that is not enough”. “Why not?”, you might dare to ask. “Because the Lorentz-Fitzgerald proposition does not eliminate the classic idea of a luminiferous ether. The special theory of relativity does that, and that's ultimately what the result of the M-M experiment tells us ”. Hmmm... At this point I shall resist the temptation to contest the validity of the last remark, and I shall proceed instead to explain the result of the M-M experiment by using the common sense version of the Lorentz-Fitzgerald method.

The Lorentz-Fitzgerald contraction could be seen as a desperate and unwarranted act, whose sole reason for creation was to provide some explanation for the inconvenient result of the M-M experiment. Now, to provide an explanation for the negative result of the M-M experiment I will also put forward a proposition. A proposition much more plausible than the conventional Lorentz-Fitzgerald contraction, I should say. And I say that simply because the common sense proposition I will use to explain the result of the M-M experiment is not only able to do that; it is also logically coherent—and, therefore, mentally comprehensible.

The common sense proposition says that all objects in motion extend (in the direction of their motion) and contract (in the direction at right angles to the direction of motion) by an amount determined by their intrinsic velocity.

I believe that some of you have expected to eventually see my proposing that objects in motion extend in the direction of motion, rather than contract, for that proposition was certainly “on the cards”. After all, how better to resolve a line of reasoning that ultimately led to a conclusion diametrically contradictory to the conventional one. But how many of you have anticipated the other half of my proposition—that objects in motion do also contract (along the direction perpendicular to that of motion)? Not many, I'm sure. I am quite firm in my belief, however, that there is an absolute necessity for a two-fold extension-contraction process to explain the result of the M-M experiment in a logically consistent, and physically sensible, manner. In fact one of my many arguments against the special theory of relativity is concerned with the purported manner in which the contraction experienced by objects in motion takes place. After all, what physical object could contract (by an amount that, theoretically, could be anywhere from near zero to 99.9999999999999999999999% infinite) in one direction without experiencing an automatic extension along its perpendicular axis? How could a material object of this Universe, which has contracted in the direction of its motion from its length of (say) many kilometres to a fraction of a millimetre, and which has consequently suffered an increase in its density that is very close to infinite, remain unchanged in shape along the axis perpendicular to the direction of its motion? The special theory of relativity is silent on this issue, and so are the works of Lorentz, Fitzgerald, and others who concerned themselves with writing about the conventional understanding over the years. But if the professed contraction is a real phenomenon, as it is asserted, then the physical changes I've just mentioned should definitely come into play. It is primarily for these reasons that my common sense proposition had to consist of a two-fold transformational process.

That is all I need to say about my common sense analysis of the M-M experiment, as far as I'm concerned. Naturally, my next step is concerned with a review of the special theory of relativity from the perspective created by this analysis. It is time to see if the "fruits" of my labour are tastier than those offered by the conventional establishment, and, indeed, if they are also easier to digest.

The Michelson-Morley experiment

Or how the current dark ages in physics have been drawn by the flawed conventional analysis of that infamous experiment

The Michelson-Morley experiment was conducted in 1887 with the definitive scope of detecting the (rather ill-thought) concept of ether wind. But the experiment was more apt at establishing if there are such things as absolute motion and absolute space, in fact. For those with a limited knowledge of the main aspects related to the experiment the paragraphs below may be helpful.

Physics theories of the late 19th century postulated that, just as water waves must have a medium to move across (water), and audible sound waves require a medium to move through (such as air or water), so also light waves require a medium, the "luminiferous aether". Because light can travel through a vacuum, it was assumed that the vacuum must contain the medium of light. Because the speed of light is so great, designing an experiment to detect the presence and properties of this aether took considerable ingenuity.

Earth travels a tremendous distance in its orbit around the sun, at a speed of around 30 km/s or over 108,000 km per hour. The sun itself is travelling about the Galactic Center at even greater speeds, and there are other motions at higher levels of the structure of the universe. Since the Earth is in motion, it was expected that the flow of aether across the Earth should produce a detectable "aether wind". Although it would be possible, in theory, for the Earth's motion to match that of the aether at one moment in time, it was not possible for the Earth to remain at rest with respect to the aether at all times, because of the variation in both the direction and the speed of the motion.

At any given point on the Earth's surface, the magnitude and direction of the wind would vary with time of day and season. By analysing the return speed of light in different directions at various different times, it was thought to be possible to measure the motion of the Earth relative to the aether.

Michelson had a solution to the problem of how to construct a device sufficiently accurate to detect aether flow. The device he designed, later known as an interferometer, sent a single source of white light through a half-silvered mirror that was used to split it into two beams travelling at right angles to one another. After leaving the splitter, the beams travelled out to the ends of long arms where they were reflected back into the middle on small mirrors. They then recombined on the far side of the splitter in an eyepiece, producing a pattern of constructive and destructive interference based on the spent time to transit the arms. If the Earth is traveling through an ether medium, a beam reflecting back and forth parallel to the flow of ether would take longer than a beam reflecting perpendicular to the ether because the time gained from traveling downwind is less than that lost traveling upwind. The result would be a delay in one of the light beams that could be detected when the beams were recombined through interference. Any slight change in the spent time would then be observed as a shift in the positions of the interference fringes.

The paragraphs above are from Wikipedia, where you can also find a detailed conventional analysis of the experiment. In what follows I will also use a conventional analysis of the Michelson-Morley experiment, written by Isaac Asimov. The reason I'm using that particular description is two-fold: Firstly, because Asimov's description is better suited to my purpose (which is looking for absolute space and motion); secondly, because in Asimov's description I found a beautiful “slip of tongue” about how common sense has been stripped of its sense by a silly assumption, a dogmatic view, and a terrible mathematical translation. Before getting to that, however, I want to show you below an animation with a basic image of the interferometer used in the experiment. (My interferometer may look different than Michelson's, but it nevertheless contains all the relevant features of the original interferometer. In the animation below S is the source of light, the two M are the two mirrors, and the two d represent the lengths of the interferometer's arms. The rest of the animation is pretty much self explanatory, so I'll say no more about that.)

In analysing the experiment we shall assess individually the two paths travelled by the beams of light. Thus, in the case where light is sent out in the direction of earth's motion, from the source S to the mirror M over the distance d, the light travels at its velocity c + the velocity of the earth v. This is the first leg of the journey, and mathematically this is expressed thus: d / (c + v). The second leg of this (parallel) journey takes place from the mirror M back to the source S, over the distance d. In this case, however, the light travels at its velocity c minus earth's velocity v. Mathematically this second leg of the journey is expressed thus: d / (c – v). In Asimov's words, from this point on:

The total time for the round trip is:

Combining the terms algebraically, we get:

Now suppose that the light-beam is sent out to a mirror at the same distance in a direction at right angles to the earth's motion through the ether. The beam of light is aimed from S (the source) to M (the mirror) over the distance d. However, during the time it takes the light to reach the mirror, the earth's motion has carried the mirror from M to M ', so that the actual path travelled by the light beam is from S to M '.

This distance we call x, and the distance from M to M ' we call y (see diagram above). While the light is moving the distance x at its velocity c, the mirror is moving the distance y at the velocity of the earth's motion v. Since both the light and the mirror arrive at M ' simultaneously, the distances travelled must be exactly proportional to the respective velocities. Therefore:

Now we can solve for the value of x by use of the Pythagorean theorem... In the right triangle S M M ' then, substituting vx/c for y:

The light is reflected from the mirror at M ' to the source, which meanwhile has travelled on to S '. Since the distance S ' S '' is equal to S S ', the distance M ' S '' is equal to x. The total path travelled by the light beam is therefore:

The time taken by the light beam to cover this distance at its velocity c is:

How does this compare with the time that light takes for the round trip in the direction of the earth's motion? Let us divide the time in the parallel case by the time in the perpendicular case...:

Now any number divided by its square root gives the same square root as a quotient... So the last equation simplifies to:

This expression can be further simplified if we multiply both the numerator and the denominator [like below]:

And there you are. That is the ratio of the time that light should take to travel in the direction of the earth's motion as compared with the time it should take in the direction perpendicular to the earth's motion. For any value of v greater than zero, the [last] expression above is greater than 1. Therefore, if the earth is moving through a motionless ether, it should take longer for light to travel in the direction of the earth's motion than in the perpendicular direction. (In fact, the parallel motion should take the maximum time and the perpendicular motion the minimum time.) Michelson and Morley set up their experiment to try to detect the directional difference in the travel time of light. By trying their beam of light in all directions, and measuring the time of return by their incredibly delicate interferometer, they felt they ought to get differences in apparent velocity...

They found no differences at all in the velocity of light with changing direction! To put it another way, the velocity of light was always equal to c, regardless of the motion of the source—a clear contradiction of the Newtonian laws of motion. In attempting to measure the absolute motion of the earth, Michelson and Morley had thus managed to cast doubt not only on the existence of the ether, but on the whole concept of absolute rest and absolute motion, and upon the very basis of the Newtonian system of the universe. (I. Asimov—Asimov's new guide to science, pp. 811-814)

The results of the experiment generated a subsequent linear reasoning and theoretical development which eventually reached a climax with Einstein's creation of the relativistic philosophy. Thus, following the path opened by the Michelson-Morley experiment, in 1893...

...the Irish physicist George Francis FitzGerald came up with a novel explanation to account for the negative results of the M-M experiment. He suggested that all matter contracts in the direction of its motion and that the amount of contraction increases with the rate of motion. According to this interpretation, the interferometer is always shortened in the direction of the earth's “true” motion by an amount that exactly compensates for the difference in distance that the light beam has to travel. Moreover, all possible measuring devices, including human sense organs, would be “foreshortened” in just the same way, so that the foreshortening could, in no possible way, be measured.

Then:

The Dutch physicist Hendrik Antoon Lorentz soon carried FitzGerald's idea one step further. Thinkink about cathode rays, on which Lorentz was working at the time, he reasoned that if the charge of a charged particle were compressed into a smaller volume, the mass of the particle should increase. Therefore, a flying particle foreshortened in the direction of its travel by the FitzGerald contraction would have to increase in mass.

Until, finally:

Einstein introduced a second important idea in his special theory of relativity: that the speed of light in a vacuum never varies, regardless of the motion of its source. In Newton's view of the universe, a light beam from a source moving toward an observer should seem to travel more quickly than one from a source moving in any other direction. In Einstein's view, this would not seem to happen, and from that assumption he was able to derive the Lorentz-FitzGerald equations. He showed that the increase of mass with velocity, which Lorentz had applied only to charged particles, can be applied to all objects of any sort. Einstein reasoned further that increases in velocity would not only foreshorten length and increase mass but also slow the pace of time; in other words, clocks would slow down along with the shortening of the yardsticks. (I. Asimov—Asimov's new guide to science, pp. 352-357)

And there it is—the theoretical development following the Michelson-Morley experiment. According to the conventional establishment, the road from the Michelson-Morley experiment to the creation of relativity was a natural and sensible progression that culminated with Einstein's vision. The special theory of relativity became one of the most precious jewels in the crown of physics, and as such it has been reigning absolutely now for just over a century. Most conventional physicists, who are die-hard relativists, no longer question the special theory of relativity—in spite of its many apparent vagaries. But, in the last four or five years, a small number of conventional physicists have found the need (and courage) to question the absolute validity of Einstein's first theory of relativity. One of them, Lee Smolin, believes for instance that the special theory of relativity needs to be changed, somehow, (although he doesn't seem to know how exactly that could be done, or what exactly needs to be changed). However, the cold fact is that physicists like Lee Smolin are so very few at this point in time that the special theory of relativity should still enjoy its absolute status for quite a while yet.

The special theory of relativity has been—nevertheless—opposed by many people since its inception, and that reality is still manifest today. The conventional physicists may scream all they want about the “irrefutable” validity of the theory; the fact is that more and more people are no longer fascinated by the bombastic picture painted by relativists. Instead, they are increasingly asking: “What on earth are you saying, Messrs. Physicists?” To which, of course, the relativists of today can only reply with the same arguments and the same mental pictures used by the relativists at the very beginning of the twentieth century. Not much has changed in the relativity saga, with the exception of some new “patching up” being required. For instance, Einstein assumed that the known velocity of light could never be superseded. That assumption had to hold, for otherwise things could be sent backwards in time. But the fact of the matter is that the speed of light has been superseded (and in the worst of all possible scenarios, in the form of an undeniable signal)! So, our relativists had no choice but to “patch up” the theory, somehow. In the end no one is quite sure if that particular hole in the special theory of relativity has been “patched-up”, although you can bet your last dollar that no relativist would accept that the “hole” is still there for all to see! In fact, no one is quite sure how relativists could claim that other “holes” in the special theory of relativity (in the form of the twin and the clock paradoxes) do not exist. I will come back to these issues a little later. Next, however, we'll reassess the Michelson-Morley experiment from the “common sense” perspective.