Absolutely!
There is no other theory in physics that has been met with more opposition than Einstein's special theory of relativity. From dissident physicists, to professional philosophers, to common thinkers, the special theory has been relentlessly attacked by a continuously increasing number of apparently ill-dedicated opponents ever since its inception, more than a century ago. Needless to say, the conventional establishment of physicists (which is by and large formed by die-hard relativists) has fought back with all its might, taking full advantage of its powers, its influence, and its resources. And, sure enough, for many years there was hardly any voice of discontent with Einstein's theory that reached the general public. Today, however, those opposing the teachings of the special theory of relativity have access to the uncensored medium of the Internet, and their voices can not only be heard by those living in the present—they will also be heard by those in the future.
Relativists pretend that they're not really troubled by the opposition. That's because, according to them, those who oppose special relativity are all "crackpots" and “cranks”, an inferior breed of people, driven by megalomanic visions and delusions, who are incapable of understanding either the deep insights or the physical truisms revealed by the special theory of relativity. It matters little, if at all, to relativists that the theory's claims and descriptions are manifestly incomprehensible and illogical; indeed they keep repeating them with such unyielding faith and nonchalance that one could rightfully attribute them to... crackpots. Let's look at a few examples of how conventional relativists describe, in natural language, the physical reality of our Universe. Firstly, let's see how they have dealt with a well known argument presented half a century ago.
University of London Professor Herbert Dingle showed why special relativity will always conflict with logic, no matter when we first learn it. According to the theory, if two observers are equipped with clocks, and one moves in relation to the other, the moving clock runs slower than the non-moving clock. But the relativity principle itself (an integral part of the theory) makes the claim that if one thing is moving in a straight line in relation to another, either one is entitled to be regarded as moving. It follows that if there are two clocks, A and B, and one of them is moved, clock A runs slower than B, and clock B runs slower than A. Which is absurd.
Dingle's Question was this: Which clock runs slow? Physicists could not agree on an answer. As the debate raged on, a Canadian physicist wrote to Nature in July 1973: "Maybe the time has come for all of those who want to answer to get together and to come up with one official answer. Otherwise the plain man, when he hears of this matter, may exercise his right to remark that when the experts disagree they cannot all be right, but they can all be wrong." (My emphasis.)
The problem has not gone away. Alan Lightman of MIT offers an unsatisfactory solution in his Great Ideas in Physics (1992). "[T]he fact that each observer sees the other clock ticking more slowly than his own clock does not lead to a contradiction. A contradiction could arise only if the two clocks could be put back together side by side at two different times." But clocks in constant relative motion in a straight line "can be brought together only once, at the moment they pass." So the theory is protected from its own internal logic by the impossibility of putting it to a test. Can such a theory be said to be scientific? --TB
Professor Dingle has been, for almost fifty years now, a favourite target for those relativists who have taken the role of "popularising" physics. With vitriolic sarcasm and self-assumed superiority, a good number of them have chosen to expose to the general public the "fallacious" arguments raised by the now departed Herbert Dingle. And the way they've done that was by providing 'explanations' similar to the one offered in the example I cited above.
However, I say it should be obvious in a thinker's mind that Lightman's 'solution' is just another malicious and hollow, pontifical declaration, whose sole purpose was to shut up the masses. Indeed, for a rational mind the last two sentences in the cited example should be enough to thoroughly dispel any shadow of confusion that might have been created by Lightman's declaration. It shouldn't be too difficult, either, to realise that one's claim that "a contradiction could arise only if the two clocks..." is merely a stipulation made by fiat: it is unwarranted, it cannot be demonstrated in any way, and it is therefore of no value. In fact, a sound reasoning should lead one to the following conclusion: It suffices to have two clocks anywhere in the Universe and to declare that each of them is running slower than the other, in order to have a contradiction. If a conventional relativist can't see that one could prove mathematically that what I've just said is correct, then nothing will emancipate his shackled brain.
The argument raised by Professor Dingle has been dubbed "the clock paradox", and although vehemently rejected as a real paradox by the conventional relativists, it continues to remain a thorny subject for Einstein's disciples. Regardless of one's personal view of the special theory of relativity, though, the most important question is this: How can a theory that has been so reach in predictions, and so apparently successful in its numerous testing, lead to logical inconsistencies like "the clock paradox"? The answer to that question is surprisingly simple (if one is willing to confront the conventional tenets of the special theory of relativity with a healthy dose of scepticism, and with an objective and rational mind). Before proceeding to answer that question, however, I have to mention (at least) some of the other shortcomings of Einstein's special relativity.
Another famous paradox that has been duly resolved by the conventional relativists is "the twin paradox". This paradox—non-paradox is...
...a thought experiment in special relativity, in which a twin who makes a journey into space in a high-speed rocket will return home to find he has aged less than his identical twin who stayed on Earth. This result appears puzzling on this basis: Each twin sees the other twin as traveling; so, according to the theory of special relativity, each should see the other age more slowly. How can an absolute effect (one twin really does age less) result from a relative motion? Hence it is called a paradox. In fact, there is no contradiction and the thought experiment can be explained within the standard framework of special relativity.
The twin paradox is, in principle, a variation of the clock paradox—although, in this case, the apparent paradox is conventionally resolved by a referential asymmetry the twins experience. Specifically, the paradox is not a paradox (we're told) because the twin in the high-speed rocket must accelerate when leaving the earth, and must decelerate when returning (which means that the travelling twin finds himself in a non-inertial frame of reference). The twin staying on earth, on the other hand, does not have to change his inertial frame—hence the mentioned asymmetry. And thus, since there is no symmetry, there is nothing paradoxical if one twin is younger than the other. (This is a very brief outline of the manner in which the twin paradox is conventionally resolved. A detailed explanation is much more complicated, involving world lines, Minkovski diagrams, relativistic Doppler shifts, and other concepts created by the special theory. For my purpose, though, no detailed explanation of any of the many paradoxes in special relativity is necessary—as you will realise later.)
Beside the two paradoxes I have discussed, there are others I'll not even mention. That's simply because all of them are direct consequences of either the two postulates upon which the special relativity was built, or of some conceptual interpretations extracted from others' proposals and principles. The paradoxes I don't want to mention, however, can be easily found online. But, as far as I'm concerned, they are not really important. To my mind there are other things far more important in SR. For instance, the experimental evidence on the basis of which SR has been granted an almost invincible status is certainly more important, and one of the more celebrated examples of that evidence is provided by the muon phenomenon.
The twin paradox is, in principle, a variation of the clock paradox—although, in this case, the apparent paradox is conventionally resolved by a referential asymmetry the twins experience. Specifically, the paradox is not a paradox (we're told) because the twin in the high-speed rocket must accelerate when leaving the earth, and must decelerate when returning (which means that the travelling twin finds himself in a non-inertial frame of reference). The twin staying on earth, on the other hand, does not have to change his inertial frame—hence the mentioned asymmetry. And thus, since there is no symmetry, there is nothing paradoxical if one twin is younger than the other. (This is a very brief outline of the manner in which the twin paradox is conventionally resolved. A detailed explanation is much more complicated, involving world lines, Minkovski diagrams, relativistic Doppler shifts, and other concepts created by the special theory. For my purpose, though, no detailed explanation of any of the many paradoxes in special relativity is necessary—as you will realise later.)
Beside the two paradoxes I have discussed, there are others I'll not even mention. That's simply because all of them are direct consequences of either the two postulates upon which the special relativity was built, or of some conceptual interpretations extracted from others' proposals and principles. The paradoxes I don't want to mention, however, can be easily found online. But, as far as I'm concerned, they are not really important. To my mind there are other things far more important in SR. For instance, the experimental evidence on the basis of which SR has been granted an almost invincible status is certainly more important, and one of the more celebrated examples of that evidence is provided by the muon phenomenon.
On the phenomenon of the "long-living" muons (in two descriptions)
One undeniable proof that confirms (according to the conventional understanding) the validity of the special relativity is the so-called phenomenon of the "long-living" muons. The muon is a particle with an average lifetime of about two microseconds, and it is produced by the collision of cosmic rays with atoms in Earth's atmosphere. Although muons travel at speeds close to that of light, in two microseconds they could travel less than a kilometre. Yet despite of being produced at some twenty kilometres above the Earth, muons are detected at the surface of our planet. (This is a summary of how John Gribbin begins his description of the "long-living" muons in his book for the general public called "Schrodinger's kittens".) How do muons manage to reach the surface of the Earth?
The explanation is that because muons are moving so fast relative to the Earth, time is running more slowly for them. To be precise, the special theory of relativity says that the lifetime of the muon is extended by a factor of 9—they live 9 times longer, according to our clocks, than they would if they were sitting still. But remember that the special theory of relativity also says that the muons are entitled to regard themselves as sitting still. In their own frame of reference, surely they should still decay before reaching the ground? Not at all! If the muons are regarded as being at rest, which is indeed allowed, then we have to regard the Earth as rushing past the muons at a sizeable fraction of the speed of light! This, of course, will cause the Earth to shrink, from the point of view of the muons, by the amount calculated from the Lorentz transformations. Because the speed involved is the same, and because of the symmetry between space and time in those equations, the amount of contraction is the same as the amount of dilation—a factor of 9. But because of the opposite sign in front of the time part of those equations, the thickness of the Earth's atmosphere shrinks by a factor of 9. From the muons' point of view, the distance they have to cover is only one-ninth of the distance we measure for the thickness of the Earth's atmosphere, and they have ample time to complete such a short journey before they decay.
So, that is how John Gribbin (a conventional relativist) describes the phenomenon of the "long-living" muons. J. G. is one of the most prolific popularisers of physics, and the description above is clearly written for laypeople. Alas, there are no polls conducted in the world to see what those who have read the book would have to say about the conventional explanation of the muon phenomenon. Nevertheless, I do know what I have to say about that, and later I will share my view with you. For now, however, I will cite below a little more detailed description of the same phenomenon—this one written for first year physics students, I believe, by one Michael Fowler from University of Virginia.
The first clear example of time dilation was provided over fifty years ago by an experiment detecting muons. (David H. Frisch and James A. Smith, Measurement of the Relativistic Time Dilation Using Muons, American Journal of Physics, 31, 342, 1963). These particles are produced at the outer edge of our atmosphere by incoming cosmic rays hitting the first traces of air. They are unstable particles, with a “half-life” of 1.5 microseconds (1.5 millionths of a second), which means that if at a given time you have 100 of them, 1.5 microseconds later you will have about 50, 1.5 microseconds after that 25, and so on. Anyway, they are constantly being produced many miles up, and there is a constant rain of them towards the surface of the earth, moving at very close to the speed of light. In 1941, a detector placed near the top of Mount Washington (at 6000 feet above sea level) measured about 570 muons per hour coming in. Now these muons are raining down from above, but dying as they fall, so if we move the detector to a lower altitude we expect it to detect fewer muons because a fraction of those that came down past the 6000 foot level will die before they get to a lower altitude detector. Approximating their speed by that of light, they are raining down at 186,300 miles per second, which turns out to be, conveniently, about 1,000 feet per microsecond. Thus they should reach the 4500 foot level 1.5 microseconds after passing the 6000 foot level, so, if half of them die off in 1.5 microseconds, as claimed above, we should only expect to register about 570/2 = 285 per hour with the same detector at this level. Dropping another 1500 feet, to the 3000 foot level, we expect about 280/2 = 140 per hour, at 1500 feet about 70 per hour, and at ground level about 35 per hour. (We have rounded off some figures a bit, but this is reasonably close to the expected value.)
To summarize: given the known rate at which these raining-down unstable muons decay, and given that 570 per hour hit a detector near the top of Mount Washington, we only expect about 35 per hour to survive down to sea level. In fact, when the detector was brought down to sea level, it detected about 400 per hour! How did they survive? The reason they didn’t decay is that in their frame of reference, much less time had passed. Their actual speed is about 0.994c, corresponding to a time dilation factor of about 9, so in the 6 microsecond trip from the top of Mount Washington to sea level, their clocks register only 6/9 = 0.67 microseconds. In this period of time, only about one-quarter of them decay. What does this look like from the muon’s point of view? How do they manage to get so far in so little time? To them, Mount Washington and the earth’s surface are approaching at 0.994c, or about 1,000 feet per microsecond. But in the 0.67 microseconds it takes them to get to sea level, it would seem that to them sea level could only get 670 feet closer, so how could they travel the whole 6000 feet from the top of Mount Washington? The answer is the Fitzgerald contraction. To them, Mount Washington is squashed in a vertical direction (the direction of motion) by a factor of the same as the time dilation factor, which for the muons is about 9. So, to the muons, Mount Washington is only 670 feet high—this is why they can get down it so fast!
I know that the majority of people do not contest what physicists are saying for the simple reason that they do not understand them. Indeed that is the only reason why most people tacitly accept whatever physicists are saying. That's not to say that they don't try to think about what they're reading, or hearing, but the vast majority of them very soon realise that, regardless of how much they know about the subject, some things they just cannot make any sense of. Alas, when these things happen they readily believe that they're not capable of understanding because they're just not smart enough. But there are also, nonetheless, other people out there who do not so easily accept what they read, or hear—not before scrutinising, at least, everything and every thing that appears to elude their ability to understand. Now, those people will not hesitate to doubt the things they are told, if those things do not make sense to them. That's because those people are well aware that every thing that's truly understood is also coherently described. And, ultimately, regardless of how complex that thing may be, if it is really understood and coherently described it should also be comprehended by the common thinker.
The conventional explanation of the "long-living" muons, however, can only find some sort of acceptance in a common thinker's mind by bullying his or her brain into submission.
Nevertheless, the phenomenon of the “long-living” muons can be described in a coherent language that everyone will understand, and later I will do just that. Before that, however, I want to invite you to look at SR from another perspective. A perspective you should not be aware of unless your understanding of SR is concordant with mine, which is highly unlikely (but not impossible).
A new perspective from which to contemplate the conventional relativistic understanding
There was a time when I believed that Einstein did a con job with his SR. I thought I had good reasons to believe that, too. Reasons extending from his social factors at the time to his enormous desire to succeed in convincing the world that he is not only a real physicist, but one worthy of leading the world into a new era of intellectual progress.
I imagined the brash and irreverent Albert telling himself something like this: “The world of physics is going through a tough period these days. But this period is also one of commensurate opportunity. Physics is in dire need of a new and radical theory, and the paper I am currently writing will deliver that theory. And that's not all. The theory I'm offering the world cannot be either rejected or ignored, because it unifies a few tentative proposals from important figures in the business, and because it has the great advantage of being nigh impossible to test for a very long time. Moreover, since I have been able to arrive at the solutions offered previously by people who had definitely thought long and hard about what we know and what we don't, my theory instantly acquires significantly more weight. Yeah, for those main reasons I'm convinced that my theory will be embraced by physicists, and also because the only arguments that could be raised against it would mainly be of a philosophical nature (and thus they'll matter little for this generation of positivists). Should I continue to be troubled, then, by those doubts that my own mind keeps torturing me with? I think not. After all, physics is no longer based on philosophical arguments, and philosophers' logic is heavily tainted by the human handicaps anyway. Ultimately, the modern physics is based on mathematics, and my theory is mathematically healthy and strong. Besides, the doubts I have only raise their heads when I begin to question the validity of the assumptions upon which my theory is based. Once my own mind accepts that my assumptions are warranted, though, those doubts no longer exist”.
I haven't really stopped thinking about SR ever since I first became acquainted with it, many years ago. In the meantime I have gotten older, I have had ample time to 'chew' on SR's more subtle points, and I have also changed that old belief of mine. In time I have come to find interesting and new angles from which to contemplate what SR is suggesting, and I have even learnt to construct a quite solid case in its defence. But all that has not managed to transform me into a believer. On the contrary, the more arguments I developed for defending SR, the clearer I could see how silly the theory basically was! And this has remained my firm conviction, in spite of knowing that (if I wanted to) I could argue for the validity of SR better than most conventional relativists. Indeed, nowadays I am amazed at what a poor job conventional relativists have done in trying to 'sell' to the masses Einstein's first theory of relativity. They have invariably insisted on the empirical testing and on the theoretical predictions of SR that have consistently appeared to have been confirmed by increasingly more complex experiments. Alas, physicists have totally failed to see that, in its conventional form, SR remains incoherent—and, therefore, incomprehensible. In some ways SR is like a modern version of Zeno's paradoxes. The general public listens to the quite complex analyses used by mathematicians to 'explain away' those famous paradoxes, but deep down people instinctively know that mathematics is much too sensitive to the less than perfect quantitative dissections of the physical realm to accept its solutions as perfect descriptions of reality. And that's not all. People have also realised that, in most cases, the exclusive use of mathematical reasoning in fact reveals the lack of a thorough understanding of the issues at stake.
One of my most enjoyable pastimes of late is to lay in bed in darkness and think about ways of exposing the theoretical weaknesses of SR and the reasons why it should be rejected in its conventional form. When I find one I do not rush to write it down. I never do that. Instead, I proceed to subject it to the best scrutiny my mind can develop. There are quite a few advantages to my method, but there is also one dangerous side effect. There have been times when I have forgotten some beautiful examples by the next day. Nevertheless, I have always believed that I would rediscover them at some stage—although I must confess that that belief has remained only approximately true. A couple of nights ago, however, I took a very rare step and I put on paper a short description of my thoughts. I'd like to share now that little sample of my thoughts with you.
Albert, a conventional relativist, is assigned the role of the observer in a new experiment designed to test the effects of SR. He is placed into a laboratory which is launched in space at a uniform velocity very close to that of light. After a while Albert writes in his logbook: “We (the laboratory and myself) are travelling uniformly relative to all celestial bodies. Having been informed that our velocity is very close to c, we are contracted in the direction of motion by a substantial amount. Nonetheless, at the same time I have invoked my right to regard our inertial frame of reference as being at rest. Therefore we suffer no contraction at all. Conclusion number 1: We contract and we do not contract, at the same time, in our frame of reference. Conclusion number 2: We increase and we do not increase, at the same time, in mass. Conclusion number 3: We experience and we do not experience, at the same time, a time dilation. Conclusion number 4: I believe and I do not believe, at the same time, in what SR has taught me”.
I said a moment ago that I no longer believe that Einstein had dubious reasons for creating the special theory of relativity. Indeed, today I believe that he was fair-dinkum (as we say in this part of the world) when he wrote his paper. Based on my experience accumulated over the years I think that my current belief makes more sense. After all, we humans are far more inclined in our younger days to become convinced that some idea is the only one that could be right. Not only that, we are willing to take a definite and uncompromising stand on some issue we believe in also when we're usually young—being ready to go as far as sacrificing even our life for one cause or another. That's why I believe today that the young Albert Einstein was driven by a genuine belief that his SR was correct. As he grew older, though, there is enough evidence to suggest that Einstein began to be haunted by certain doubts about what SR was really teaching and predicting (especially about the declared non-existence of a frame of reference at absolute rest). And this last point shows that as Einstein grew older he had more time (and perhaps more wisdom) to keep 'chewing' at what his theory meant. Now this is a reasonable proof that a strictly literal translation of SR's equations can trouble even the theory's creator. We do need to understand what we're saying, after all. (In fact it is absolutely imperious that we do, for otherwise we create unhealthy possibilities for undesirable legacies. History is rife with concrete examples of the kind.)
A century of relativistic thinking should have given the many thousands of people who have worked hard in that field ample time to polish every imaginable rough corner SR has carried with it since 1905, I say. But that is not the case at all. The SR of today is just as abrasive as it has ever been. The theory is riddled with inconsistencies, and it is still being promoted (if not enforced) on the basis of some surprisingly weak arguments and some dubiously conducted, and interpreted, observations. Now this is my own personal assessment, and it is based on issues I have never seen discussed anywhere. Which is a fact that continues to bother me—for, as you'll see, the issues I'll discuss on these pages (and the arguments I'll raise against SR) are neither ambiguous, nor easily refutable. But perhaps I should give you one such example right now.
SR predicts that time runs slower for an observer in motion than for one at rest. Einstein arrived to this conclusion very shortly before writing his paper, and he jubilantly told his friend Michele Besso: “I've completely solved the problem. An analysis of the concept of time was my solution. Time cannot be absolutely defined, and there is an inseparable relation between time and signal velocity.” For Einstein time was what is measured with a clock, and through his own process of reasoning he had come to that most famous prediction that time is variant. Now, since time is what we measure with clocks, he was forced to declare (for obvious reasons) that all conceivable clocks are affected alike. Of course, then, that meant that the flow of time experienced by the biological clocks we are, will likewise be affected. Nonetheless, since light has a finite velocity, and since Einstein had chosen to relate everything to the speed of light, I find it curious that he had to agonise for a long time before realising that “there is an inseparable relation between time and signal velocity”.
Now, when conventional relativists talk about how the variant nature of time has been proven beyond any doubt, they like to explain why clocks in motion run slower than stationary ones. I'm sure you know the official explanation, so I'll resist the urge to draw some diagram of it. I'll only mention the two vertically oriented mirrors that are facing each other, and between which there is a beam of light keeping track of time as it bounces up and down between the mirrors. A setup like that formed, in principle, the architecture of the atomic clocks used by Hafele and Keating (and it indeed remains the basic principle of all atomic clocks).
A very, very brief interlude
After I finished typing the above paragraph I took a short break, and in that time I changed my mind about not showing a diagram of the official understanding, which shows why travelling clocks do really run slower than their counterparts at rest. I won't explain what made me change my mind.
Above is a diagram of what we're talking about. This conventionally accepted explanation is easy music to the 'common sense' ears—no explanation required. Surprisingly, though, no one grabbed this opportunity to confront the accepted explanation with a rather obvious move: “What happens if I do this?” (See drawing below, in which I simply changed the orientation of the clocks).
I have never seen discussed anywhere if a travelling clock, oriented as in the drawing above, could run slower than a stationary one. (In the drawing above I have changed the orientation of both clocks, although only the orientation of the clock in motion is really of relevance to our current topic. But you have probably already realised this.) Nonetheless, running slower it must, for SR is categorical: All clocks are affected by motion, and all in the manner asserted. A clock in motion with the orientation above, however, could not run slower than an identical stationary clock—it could only run faster ! (Since objects travelling uniformly contract in the direction of their motion, the distance travelled by the beam of light between the two mirrors becomes shorter than that covered by the light in the stationary clock—which ultimately results in a clock in motion that runs faster than its counterpart at rest). As I said, I have never seen this issue discussed anywhere, although I'd love to hear how a conventional relativist could tackle this problem.
The above scenario is not only questioning the prediction of time dilation in SR. It also questions the claim that, within an inertial frame of reference, there is no possible way of establishing if that frame of reference is in motion or is at rest. Indeed, it appears immediately clear that if two identical clocks (with a make-up based on the same principles as those above) are oriented at right angles relative to each other, they should readily indicate if their inertial frame of reference is in motion. I'm sure you don't need me to spell out all the details in order to see that, when all things are considered, there doesn't seem to exist any argument a conventional relativist might resort to in order to deny that my observations are valid. (And there is neither any empirical evidence that could be used to that end—for no pertinent experiment has ever been conducted.) I believe I have good reasons to say that, but if you know better feel free to hit me with all the might of your evidence.
It is hard to believe that such a successful theory as SR is purported to be could be flawed. But, then again, it is probably even harder to believe that so many brilliant minds could have erred in the mathematical analysis of the M-M experiment, as I contended in my 'common sense' analysis of that experiment. As hard as it may be to believe my assessment, however, there always comes a time of reckoning for any human invention or claim—and the outcome of such inevitable event is not determined by either followers or fame, as you surely know. The decisive tests for any theory lie in its capacity to provide a coherent explanation for the phenomenon it was created, in its capacity to cohesively integrate and cooperate with the other theories of the time, and in its capacity to predict the behaviour of related phenomena. SR, in its conventional format and understanding, does not meet all required criteria, and this fact suggests that the theory is lacking something. But what is that something that is missing from SR?
One of the things that is wrong in SR is the Lorentz-Fitzgerald contraction, which is supposed to affect all objects in uniform motion. I believe, on the basis of my analysis of the M-M experiment, that objects in motion extend in that direction—rather than contract. (I have specified before that according to my understanding objects in motion extend in that direction and contract along the axis perpendicular to the direction of motion. From this point onwards, however, I will not mention the contracting part of that two-fold transformation. Thus when I say that objects in motion extend in that direction, I mean that objects in motion experience the two-fold transformation I have specified.)
But I have reasons to believe that the Lorentz-Fitzgerald contraction is not the only thing that is wrong in the conventional SR. There are other things that have made SR incomprehensible and irrational, things that have been incorporated into the theory from either the dogmatic canons of the establishment, or from the philosophical views prevalent in the relatively modern physics.
For instance, when the M-M experiment announced their null result a number of conceptual ideas found immediate shelter in physicists' thinking. Let me give you a couple of examples. Since the experiment failed to detect the so-called “ether wind”, a new belief became the predominant paradigm—namely that there was no privileged frame of reference in the Universe (i.e. no reference at rest). Now, the jump from the result of the M-M experiment to the belief that there was no such thing as a frame of reference at rest in the Universe was very much a leap of faith, rather than a valid conclusion. Alas, the things did not stop even there. In a dubious act of extrapolation, another idea found a place in the conventional reasoning: Objects in uniform motion can rightfully be also regarded as being at rest! Naturally, such an ambivalent idea was likely to eventually fester confusion, contradiction, and abuse. And that's exactly what has happened: The ill-begotten legacy of that idea has expanded into an epidemic view that has remained in physics ever since. So much so that no conventional physicist today is asking himself: “How could an object be in motion and at rest at the same time?” (Sure, one can always concoct some explanation even for such a silly idea, but you can bet your last dollar for a dime that the concocted explanation will make as much sense as the idea itself.)
Now, to illustrate the damaging effects of that silly idea (still employed in conventional physics) I will use a similar approach to those Einstein was so fond of. Imagine thus that you are a passenger in a night train that travels uniformly. Since there is complete darkness (in your car, as well as outside) the fact that you are sitting next to the window does not help you at all to establish if the train is moving, or if it is stationary. As you ponder in thought about that, suddenly you notice a well lit train station that seems to rapidly advance towards you. A few moments later the station appears to rush past your window, and then it disappears in a direction opposite to the one you are facing. At this point your mind begins to wonder if what you saw was a consequence of either your train being in motion, or of the train station itself speeding past you. Eventually you realise that you cannot give a definite answer to that question, and this fact bothers you. Moreover, you also realise that there could even be a third possibility—that both your train and the station were moving in opposite directions, and this bothers you even more. However strange it may all sound, the thought that all three possibilities may be true almost manages to convert your mind to the idea. A short while later, however, your mind is peaceful again (and that brings a smile on your face).
The thing that pacified your mind was your eventual realisation that your inability to establish the truth bears no consequence whatsoever to the physical reality you're a part of. "Clearly", your mind had reasoned, "in reality only one of the three possibilities is correct, and regardless of either my ability or inability to determine which possibility is the correct one, the physical reality I am a part of is unambiguously defined and established. Ultimately, the physical reality I am a part of is the truth I can merely speculate about at this point in time".
Let me repeat something here, for it is most important: One of the crucial tenets of SR is the Lorentz-Fitzgerald contraction, which is believed to affect all objects in uniform motion. It is worth keeping in mind, at all times, that the Lorentz-Fitzgerald contraction is a real effect, not merely some figure of speech (or some conceptual artefact designed to be used merely in symbolic logic). It is also worth remembering, at all times, that the Lorentz-Fitzgerald contraction is the only thing that explains the null result of the M-M experiment. Finally, it is just as important remembering that the amount of contraction suffered by an object in uniform motion is directly determined by its intrinsic velocity. Keeping these three things in mind goes a long way in helping to discern between what could be real, and what could not.
Now, with the three things above firmly planted in mind, consider the following: Had the silly idea discussed earlier been a real possibility, the Lorentz-Fitzgerald contraction would have been completely unnecessary; furthermore, had that silly idea been a real possibility the null result of the MM experiment would not have raised an eyebrow in the physics community! (I should mention here that my claims in this paragraph—and a couple of others before it—are opening avenues for conventional relativists to let either their ire or sarcasm flow freely and forcefully in response. Somehow I doubt, however, that most will take that chance.)
Ever since Galileo physicists have confidently affirmed that the book of Nature is written in the language of mathematics. But that is only partially correct. The book of Nature (or the book of the Universe, really) is also written in spoken language. After all, the spoken language is not only the medium invented by the mind and reason—it is also the medium used by the mind to reason. In fact not even mathematics itself could exist without the spoken language, and this truth should have been paid the attention it rightfully deserves.
Now, just like the book of the Universe, SR must be written in the spoken language as well, not only in the language of mathematics. And if SR is indeed as eloquent in its mathematical language as it is claimed, it ought to be just as eloquent in its spoken language. This ought to be so, since mathematics itself is basically a more efficient, more condensed, spoken language! Indeed, that undoubtedly must be so, since everything expressed in mathematical language can be equally well expressed in spoken language (if time and space is not a constraint).
But the truth is that SR is far from eloquent in spoken language. Why? is the question. The answer is simple: Because SR is just as far from being eloquent in its mathematical language. At the beginning of this page I said that, in some ways, SR is like a modern version of Zeno's paradoxes. I want to conclude this page, which I hope is slowly introducing you to that new perspective from which to contemplate SR (remember?), by showing you why I said that.
Zeno is the author of a number of paradoxes that have tortured many a mind for almost 2500 years. Only four of his paradoxes have survived since his time, and of those I will use only one. (The four paradoxes are logically related, anyway.) The paradox I'll use is called the Dichotomy, but popularly it is usually called The paradox of the motionless runner. Below I have cited this paradox exactly as it is described in a Maths Forum page online.
A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters.
Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal.
There is a more modern version of this paradox, which I also found online, and which is described as below.
Zeno stands eight feet from a tree, holding a rock. He throws his rock at the tree. Before the rock can reach the tree, it must traverse half the eight feet. It will take some finite time for the rock to fly four feet. After that time, it will still have four feet to go, and to traverse that distance must first cover half of it: two feet, and more time. After it travels two feet, it must travel one foot, then half a foot, then a quarter foot, and so on ad infinitum. Therefore, Zeno concludes, the rock can never hit the tree.
Now, Zeno's four paradoxes are “explained away” on a web page called Interactive Real Analysis (which is part of MathCS.org). Below I will cite the concluding paragraph from that particular web page.
Though all four arguments seem illogical, not to mention confusing, they are not that simple to explain away and lead to some very serious problems for mathematics. To the Greek mathematicians, who had no real concept of convergence or infinity, these reasonings were incomprehensible. Aristotle discarded them as "fallacies" without really showing why and Zeno's paradoxes were hidden away in the mathematical closet for the next 2500 years. For that time, they were reduced mainly as novelties of philosophy. However, they were revived mathematically in the twentieth century by the efforts of people like Bertrand Russell and Lewis Carroll. Today, armed with the tools of converging series and Cantor's theories on infinite sets, these paradoxes can be explained to some satisfaction. However, even today the debate continues on the validity of both the paradoxes and the rationalizations.
The paradox of the motionless runner, as well as its more modern version, are thus resolved ("to some satisfaction") by using the modern mathematical tools of converging series and Cantor's theories on infinite sets. Specifically, in modern mathematics it is understood that 1/2 + 1/4 + 1/8 + 1/16 +.......= 1. This is in stark contrast to the maths known before the 19th Century (Cantor discovered his theory of infinite sets in the 1860s), when the understanding was that 1/2 + 1/4 + 1/8 + 1/16 +.......< 1 (would always give a total smaller than 1). In effect, then, the Dichotomy paradox (or The paradox of the motionless runner) is dispelled by the modern mathematical understanding because it asserts that 50m+25m+12.5m+6.25m........= 100m. (And, of course, the paradox of the rock and the tree is resolved in the same mathematical manner.)
Now, although the modern mathematical analysis of the paradox we're discussing appears to satisfactorily “explain it away”, the last sentence in the paragraph above reveals that the debate of Zeno's paradoxes continues even today. This fact is rather unsettling, and one surely must wonder why a debate is still deemed necessary. (Interestingly, a google search of Zeno displays a vast number of mathematical and physical theories used to explain certain aspects of his four paradoxes. Indeed, even SR is mentioned in some of the pages displayed!)
From my point of view, however, the paradox of the motionless runner is easily and fully resolved by using nothing else but common sense and careful reasoning. Moreover, I contend that there is not only one way of resolving the paradox—that there are two of them. Let's then begin by discussing the first one, which is (somewhat) more complicated than the second. Before revealing it to you, however, please read once again the description of the original paradox—the one of the motionless runner.
OK. Now please consider carefully what the word reach means! Think carefully, and—most importantly—think in the context of the topical subject of the paradox: A runner wants to run a distance of 100m. Alas, the word reach is a very poor choice—considering its vital importance in what should be an unambiguous description of the essence of the apparent paradox in question. That fact should become manifestly evident as soon as the following question is asked: What exactly does the statement “to reach the 100m mark” mean? For those who may find it difficult to realise how paramountly important this question is, I will supplement my verbal explanation with the picture below.
Now, let the 100m mark be a line as in the picture above, and let the footprint be the leading “part” of the runner. Let me ask again, at this point: What exactly does it mean “to reach the 100m mark”? More specifically, if it's necessary: Where should the tip of the footprint be, in order “to reach the 100m mark”? This question one might answer thus: In order to satisfy the requirement (“to reach the 100m mark”) the tip of the footprint should be in contact with the line (i.e. it should be touching the line). Why this should be so, one might continue, is quite obvious. Anywhere less than that would result in a distance less than 100m, which would then automatically eliminate Zeno's line of reasoning—which is “the heart” of the paradox.
But that argument is unsatisfactory. Careful reasoning should compel one to realise that the sentence “the footprint should be touching the line” doesn't clarify the issue at all. (Do I need to explain why? I hope not. Just think about the other variables that are absolutely essential to the issue—like the thickness of the line and its precise position relative to the 100m point, for instance.) Careful reasoning should compel one to ultimately realise that, in order to truly satisfy the quintessential aspect of the paradox, the footprint should step over the line (which, incidentally, should be an imaginary line—meaning of zero thickness). Think about it, and you should indeed realise that in the physical realm there can only be two possibilities: either the footprint has some part beyond the line, or behind it! There is no infinite precision in the Universe, and therefore one can never say—for example—that the footprint should be right on the line. (In fact I'm not sure that such claim should be even mathematically considered valid.) That this line of reasoning is indeed the correct one is even better emphasised by the 'modern' version of the paradox. Just think about what it means to hit the tree.
And now, finally, it should become absolutely clear that the paradox is resolved even if Zeno's own reasoning is used. How? Like this. In order to reach the 100m mark the runner must cover a distance of 101m (the 101m figure is for argument's sake only; the real figure could be 100.0000000000000000000001m, for the solution to stand). Using Zeno's own line of reasoning, then, the runner will reach the 100m mark because 50.5m+25.25m+12.625m+.....=100m.
Zeno's so-called paradoxes have managed to remain controversial for so long because they have not only been superficially and ambiguously described, but also because they have been poorly understood. Of course, the unsatisfactory descriptions of the 'paradoxes' have, to a quite significant degree, negatively influenced their understanding as well. This is a situation rather common in our historical and social evolution, and it is highly likely that it will continue to march with us into the future. We have always been aware that the spoken language lacks the precision of mathematics, and that's why mathematics is the chosen language in science—a physicist might argue at this point. But the truth is that any mathematical solution or description is developed as an extension of a line of reasoning, and a line of reasoning is expressed—by and large—in spoken language. And that's not all. It is overwhelmingly the case that a mathematical solution that is an extension of a flawed line of reasoning, will also be flawed. But no one will find that surprising, isn't it?
Like Zeno's so-called paradoxes, SR is poorly expressed in spoken language, and it is just as poorly understood. Furthermore, since it is poorly understood, the mathematical description of SR is commensurately deficient as well. An eloquent example of this becomes evident when the conventional explanation of the “long living” muons is scrutinised in a manner similar to the one I used in my analysis of Zeno's Dichotomy paradox. Let me re-cite below a portion of the 'popular' description of that phenomenon I showed you earlier:
The explanation is that because muons are moving so fast relative to the Earth, time is running more slowly for them. To be precise, the special theory of relativity says that the lifetime of the muon is extended by a factor of 9—they live 9 times longer, according to our clocks, than they would if they were sitting still. But remember that the special theory of relativity also says that the muons are entitled to regard themselves as sitting still. In their own frame of reference, surely they should still decay before reaching the ground? Not at all! If the muons are regarded as being at rest, which is indeed allowed, then we have to regard the Earth as rushing past the muons at a sizeable fraction of the speed of light! This, of course, will cause the Earth to shrink, from the point of view of the muons, by the amount calculated from the Lorentz transformations.
What exactly is it meant when it is said “that muons are entitled to regard themselves as sitting still”? Why these ambiguous descriptions in 'spoken language' (“...muons are entitled to regard themselves as sitting still”, "...then we have to regard the Earth as rushing past the muons..."), when in their mathematical translation there is no ambiguity at all? What is the reason for not saying "muons are sitting still and the Earth is rushing past the muons"? After all, that is exactly what SR states in mathematical language. Instead of that, however, there is an ambivalence in the conventional presentation of SR which makes you wonder (or, which at least makes me wonder) if it is a consequence of infantilism, or of perversity. And it would have been bad enough if that ambivalence would have been used only as the descriptive perceptions of two observers in different frames of reference who, oblivious of a third possibility, may each feel entitled to state: "From my point of view it looks equally probable that either I'm moving towards you, or that you are moving towards me". As it stands, though, the ambivalence in the conventional description and understanding of SR is even worse augmented by the paradoxical manner in which the precisely defined transformation suffered by an object travelling at a particular speed can suddenly be imparted to another object, which is travelling at a totally different velocity!
The ambiguity and ambivalence in SR have been a consequence of the combined belief that there is no frame of reference at absolute rest in the Universe and that the speed of light is the fundamental yardstick in the physical realm. The belief that there is no frame of reference at absolute rest is nowadays claimed to have been proven by the null result of the M-M experiment, although that is more of a rather tenuous inference than a fact. Alas, the general understanding at the time was equating the idea of an absolute frame of reference with the idea of the luminiferous ether, and that certainly did not help. In spite of the null result of the M-M experiment, and contrary to the modern claim, most physicists at the time were not ready to give up on the existence of a frame of reference at absolute rest. With the creation of SR, however, Einstein declared the ether redundant, and with that declaration the idea of an absolute frame of reference was also deemed unnecessary. Interestingly, though, even Einstein himself came to have second thoughts about ether later in life, and his words below reveal a description of the ether remarkably similar to how one would describe absolute space.
More careful reflection teaches us, however, that the special theory of relativity does not compel us to deny ether. We may assume the existence of an ether; only we must give up ascribing a definite state of motion to it, i.e. we must by abstraction take from it the last mechanical characteristic which Lorentz had still left it.
Unfortunately, Einstein did not go any further with this (rather late) acknowledgement, and neither did anyone else. This is a most unfortunate fact, for if we can assume the existence of an ether without a state of motion (as the creator of SR assures us that we should), then most of what the theory of special relativity is saying should instantly be seen as being, at the least, questionable.
Let us assume, for argument's sake, that there is in the Universe an ether as that described by Einstein. That ether, then, becomes (first and foremost) the frame of reference at absolute rest relative to which all motions may be measured. And that highly desirable state of affairs brings with it many other benefits. For instance, in regards to what we have discussed above, the ambiguity and ambivalence in the conventional description and understanding of SR will instantly be eliminated. That's naturally because since there is now a frame of reference at rest, no object in the Universe is any longer entitled to regard itself as sitting still. Instead, each object's motion is then measured relative to space (which is really the ether described by Einstein), and whatever transformation may be then affecting it (be it either in the form of the conventional contraction, or of the common sense extension), it will be directly determined by, and proportional to, the object's intrinsic velocity.
Finally, on this page, some food for thought.
It is quite strange that no one seems to have questioned if SR should have actually been used to explain the muon phenomenon. The reason I'm saying this is rather obvious. SR is a theory that deals strictly with objects in uniform motion, and muons surely do not meet that criterion. Muons are massive particles, about 207 times heavier than electrons, and since they are in the gravitational field of the Earth they should be accelerating towards the centre of our planet. Think about it.
It's been some 6-7 years since I had written the above, and although I had meant for that long to mention my second solution to Zeno's Dichotomy paradox, I must confess that to this day I failed to do so. In my defence, though, I can tell you that for a long time I had hoped that someone (anyone) would raise that issue to me in one form or another, or--even better--that some one (any one) would try to outguess it on their own. Unfortunately neither of those hopes of mine has happened to become a reality until this point in time, which to my tripartite RAG mind means that I ought to, finally, atone for that shortcoming of mine without any auxiliary expectations.
Nonetheless, with that confession being now out in the open I have just decided a moment ago to extend one last invitation to some one (to any one) to try to as I said outguess that second solution to Zeno's paradox above. This final invitation of mine, however, shall be extended only for a period of exactly two weeks from this 25th day of March 2016 onwards. So, let's wait and see what--if anything--happens until then.
That's all for now. Thank you for your attention.
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