To Alexander et al,
First of all, I do not believe in authority! If I can not figure something out for myself, I will say "I do not know!" I certainly will not believe anyone else unless they can show me specifically how they "figured it out". I have a Ph.D. in theoretical physics I received from Vanderbilt University over 30 years ago. I went into physics because physics seemed to be the only field (math doesn't really count) not chock full of bullshit! By the time I got my degree, my faith in physicists was gone - at the upper level it is nothing but one big circle jerk, just a bullshit party. We all know "Knowledge is Power!", the problem is, the most popular use of that power is to hide stupidity; they get away with it because no one knows what they are doing, not even the members themselves. The more they know, the less they think.
Likewise, I do not suggest that you consider me an authority. I will tell you my conclusions if you ask, but I have made many mistakes on many occasions and any of my deductions may very well be in error. It is up to you to follow and check those deductions. If that is beyond your capabilities, then I am sorry. In my opinion, you appear to be out of your depth.
You apparently take the position that the authorities are correct. If you believe that, then use their model to calculate the result, but you will have to do it right: i.e., blind yourself to the correct collection of errors because the conventional model is chock full of them.
I present my model (which I think is error free - but I could certainly be wrong) in my "Foundations of Physical Reality" which I have been trying to get someone competent to read for almost 20 years.
I apologize to all for the poor performance of that server but it is free. Usually a decent download can be obtained if the server is not too overloaded. If you cannot follow it all, see if you can follow Chapter 3; it points out the single most significant error in modern physics. With regard to that error, I believe I have clearly demonstrated that Einstein's assertion of Minkowski space-time is in no way necessary to explain the validity of either the Lorentz transformations or the so called tests of general relativity. At least at the minimum, a rational person must declare the question open.
When one is presented with a choice between two different representations of a given phenomena, there exists only a limited number of criteria on which a rational decision between the two can be made. Experiment is the first and foremost of those criteria (do both attacks provide equally accurate descriptions of reality). Here, only experiment can choose.
If experiment cannot separate two pictures of reality, then one must rely on other points of issue. Over 50 years of effort by our "best minds" has been totally unable to reconcile Einstein's general theory and quantum mechanics. My presentation, on the other hand, is fully compatible with classical quantum mechanics from the very beginning. It is, in fact, the proper derivation of classical quantum mechanics which provides the mechanism to resolve the difficulties brought on by the success of Maxwell's equations.
But, before we discuss the deeper problems with Einstein's approach, we should recognize that his theory is incompatible with quantum theory even on the introductory level. Einstein's picture does not allow definition of simultaneity and yet simultaneous collapse of the wave function is a basic tenet of classical quantum mechanics. This problem is generally avoided by misdirection of attention: we are told that, as the wave functions themselves are not observable, the instantaneous collapse has no physical consequences and thus, as the conflict cannot be examined it does not really exist. This is misdirection because it avoids the central issue: if I attempt to discuss something which I cannot define, then I am speaking of something meaningless by definition. If one accepts Einstein's picture of the universe as a valid representation, then one can no more discuss instantaneous collapse of a wave function than one can discuss how many angels can dance on the head of a pin. The issue is extremely significant as it drives an irreconcilable conceptual wedge between the two theories.
Then there is the difficulty with infinite uncertainty in tau. Again we find the magic of misdirection coming to Einstein's aid: the common explanation of the necessary infinite uncertainty in tau required by quantized mass is that it implies the half life of a stable particle is infinite. This may be totally true (as it clearly is in my model); yet it is complete and blatant misdirection of attention. Return for a moment to Einstein's relativity: tau is the time-like invariant interval between two events of interest. That these events are defined by stable particles is of no significance to Einstein, tau is a value directly calculable from changes in position and time, neither of which need have infinite uncertainty even if the mass is quantized. It was actually nothing more than a trick to keep the student from questioning Einstein's representation of the universe: Minkowski space-time.
In my picture, the infinite uncertainty in tau isn't just an ad hoc meaningless consequence of mass quantization, it is part and parcel of the very structure of reality. The very fact that most all our endeavors concern us with massive entities leads to tau being a special coordinate; an asymmetry of the universe otherwise totally nonexistent.
These complaints could be increased by bringing in some of the ugly problems of standard relativistic quantum mechanics and the extreme machinations which are brought to bear to cover those difficulties. Of issue is the fact that even opening attempts to bring Einstein's space-time continuum to quantum mechanics is not a straight forward issue. At any rate, my presentation, being nothing more than a simple change in the geometry of representation, provides each and every conclusion which may be deduced from Einstein's theory and yet totally eliminates all conflict with quantum mechanics.
Beyond the conflicts with quantum mechanics, there are significant shortcomings in common sense interpretations of reality forced by the adoption of Minkowski space-time. Notice that there exist paths in Einstein's space which cannot be followed by any real object (any path which contains a segment, the metric of which is real). What is clear is that Einstein's picture requires constraints outside the geometry itself. Again, the issue has been avoided for years by misdirection of attention: the answer usually given is that objects cannot travel faster than the speed of light. The fact that that answer really amounts to circular reasoning is fundamentally pointed out by those who search for Tachions. It is also interesting to note that the above constraint is actually quite simple: no object can follow a path where proper time is imaginary. If that is true, why include the possibility of imaginary tau in your geometry? In my geometry, tau is a real coordinate; imaginary tau is no more meaningful than is imaginary x and carries exactly the same philosophical weight.
In the same vein, the light cone is a mathematical singularity of Minkowski space; this together with the fact that all of our information about the universe is obtained via electromagnetic phenomena, puts us on the wrong side of the singularity! It is this fact that makes Minkowski space so difficult to visualize. For any rational person, the pervasiveness of singularity alone should be sufficient reason to throw out Minkowski geometry as a useable representation of the universe: at least if they wish to use mathematics to relate events.
Finally, who in their right mind would set up a geometry to describe the universe which would require for one of its coordinates something which is impossible to measure (I am of course, again referring to time): clearly, in a general frame of reference, time is not a measurable variable even in Einstein's picture. Furthermore, why set up a geometry such that path lengths are directly measured quantities (Einstein's invariant interval along any path is proper time). As I pointed out in my original presentation, on the face of it, such a geometry should be expected to lead to unnecessarily complex problems in analyzing one's data.
Thus it is that I feel Einstein's solution is just a magician's trick to satisfy the Lorentz transformations and does not actually provide a useable solution to the problem Maxwell presented to us. My answer, on the other hand, solves every problem Einstein solves and, in addition, generates no conflicts with either classical quantum mechanics or common sense interpretation of the geometry itself.
However, even if both Einstein's explanation and mine were equally capable of explaining observation, there are other reasons to reject Einstein. Given that two attacks on a problem are equally successful, we should be moved to place more faith in the simpler (Occam's razor). The sheer complexity of Riemann geometry should place the judgement of history against Einstein. Kenneth Ford, who has written an extremely complete introduction to physics says of Einstein's general theory that "the mathematics of the theory is too formidable to present, even sketchily, and we shall have to be content with pointing out a few interesting features of the theory". In many respects, what Einstein really did was to convince the world that general relativity was far to complex for ordinary mortals to comprehend. Einstein's solution is so difficult that it is not even taught to most physics majors much less scientists in other fields. The explanation I have presented, on the other hand, is so simple and straight forward as to be understood by most high-school science students.
If we have exhausted correctness and simplicity, we still have the issue of symmetry and beauty. Is a space with one imaginary axis symmetric or beautiful? The only answer I can give is that beauty is in the eye of the beholder and is certainly not a required law of physics. I myself find certain symmetry and beauty in my attack: for example, negative mass generates positive energy since energy is nothing more than the magnitude of the four dimensional momentum. Negative mass merely indicates the entity is going in the opposite direction in tau, not backwards in time. Dirac's concept that antiparticles are bubbles in an infinite sea of filled states is totally unnecessary mental machination. Particles can no more emit energy by dropping into a negative mass state than they can emit energy by "dropping" into a negative momentum state.
The Galilean transformations are wrong and the Lorentz transformations are right. That is an experimental fact, it is a statement about the forces which make up the structure of our universe, not the geometry. The geometry is the way we choose to display the experimental facts. What I have pointed out is that the truth of the Lorentz transformations does not require we resort to Einstein's space-time continuum. A four dimensional Euclidean universe subject to the rules of quantum theory is entirely consistent with the Lorentz transformations.
Fundamentally, we have here an argument between two different views of the universe. These views are founded in the respective geometries used to represent reality. Is it really a question of who is right? Once, when asked which geometry was right, Poincaré stated that "one geometry can not be more true than another; it can only be more convenient."
In the final analysis, I believe it will be determined that it is Einstein's concept of a space-time continuum and the resultant notation which is in conflict with quantum theory, not the relationships supposedly defending those concepts. If the Lorentz transformations do not require Einstein's space-time continuum, then just exactly what does? Is the concept really helpful or is it, as I believe, just a complex exercise in Riemann geometry serving no purpose other than to confuse and misdirect the scientific community for almost 90 years?
In defense of the statement that the scientific community is confused and misdirected I point out that failure of a proposition to be Lorentz covariant is today accepted as proof of error in the same way that failure of velocity addition was taken as proof of error a hundred years ago.
The Emperor has been wearing no clothes!