Dear Edwin

Thank you

Ok I had hoped or assumed that your correlating clock cycle counts to consideration of energy value, resulted in our works having an equivalence. The only difference being you speak in terms of a variation of energy as clocks increase or decrease their cycle count, while I relate the same principle with term of force dilation.

However, when you convey to me that you don't know if mechanical clocks can measure relativistic effects near massive gravitating bodies, then I realize I have misunderstood something within your work. That you must have divorced Theory of General Relativity in preference of original concept. For the answer to my question within scope of GR is a trivial one. "This is not a criticism, as I value original opinion, especially yours"

I take your point concerning qualitative research for exploratory purposes. That a predictive solution is not worth more than mere curiosity, if it can't be related to a reasoning whether conventional or not. You offered a good example of a hypothesis which stands alone as an island, detached from conventional theory or unique justifications. However that example entirely neglects two points of my essay.

1. That I anchor my hypothesis to an observation and measure I term "force Dilation". It is incontestable within scope of GR, although you might argue beyond its bounds.

2. And I follow through with metaphysics within context of why nature would behave this way. That atomic force dilation occurs because space contains the substance which provides atoms with the capacity for force. That Baryonic systems are evolved to harvest this energy potential, and all the agencies of matter are directed towards an optimised structural theme.

I wont revisit these arguments now because that's what the assay was for. But for your example of qualitative exploration to stand comparative to my work, well it would seem to dismiss all of my crafted arguments and justifications.

To me at least, the complex systems of this world serve as a glaringly obvious clue. A clue that nature is serviced by an organisational principle, the types of which we are only aware of one. It surprises me that others are so blind to this evidence, even when I can articulate a scenario which rationalizes universal agencies and structures within its context.

What I believe my work is deserving of at the very least, is curiosity, on the mere basis that such a rationale can be crafted at all. Surely a relatively simple task would be to test such an idea, attempt to pull a card out from under the house, see if and where it might break down? I feel my ideas are well prepared for such a challenge, but it is not forthcoming so far. I would hope this much might occur at an international science essay contest questioning the fundamentals of universal existence. Even on the basis of it being a novelty theory.

Anyway, I'm off sailing now. I'm going to find a quiet little cove, dive for lobsters and scallops, and spend the rest of my time reading and rating essays. You are destined to do well in this contest, and probably all future contests to come. You're an asset to this event.

Steve

Edwin,

Seems to be sparse reviewing and rating in this essay contest. I am revisiting those I have reviewed and see if I have scored them before the deadline approaches. I find that I have rated yours on 1/19. Thanks for reviewing mine.

Jim Hoover

Ed,

There is something that always bothered me about SR and relative motion being the same irrespective of whose frame of reference was used. Specifically, let's say that I jump up from the ground. My vertical leap is ... well, not much. But I do get a few inches off the ground. Knowing this, I can calculate the force needed for the jump and the amount of energy needed for the jump. Surely the amount of force and energy needed to move me by 6 inches is less than the amount of force and energy needed to move the Earth by 6 inches. So, it seems to me that part of your preferred reference frame is the result of a minimum energy principle associated with action.

Best Regards and Good Luck,

Gary Simpson

    Edwin,

    That was a bit of fun but I felt I needed a drink listening to those three. I also felt a bit sorry for Einstein not getting much of a word in. It seemed a bit 'scripted' somehow.

    Your different views were interesting to read but I must say I could't get me head round the concept or point of 'deriving SR with just one frame'. Surely the wholw point of SR is that it handles transitions BETWEEN states of motion. You may not recall my 2012 essy but I showed that can be done with CSL with solid evidence. Our conceptions of 'frame transitions' must be very different. I still need that drink!

    A nice refresher of Hertz's views anyway.

    Best of luck.

    Richard

      Dear Steven,

      This essay contest provides a forum for us to showcase our theories and explanations of nature. Almost by definition, everyone who publishes his essay has faith in his idea and wants to share it with the world, but the author always understands more about his theory than anyone else, for obvious reasons.

      One may or may not assign the same meaning to keywords as others, and may or may not be aware of all competing theories and how they stack up. This list could go on and on, but with 200 contestants, all of whom believe in their approach, it is tough to recognize the truth immediately. In my case, I focus on fundamentals, which to me means fields, photons, electrons, etc. A mechanical clock is to me so complex that I make almost no assumptions about it. Even if I understood your theory exactly, I would hesitate to apply it to such a macro, mechanical, system.

      You are blessed to be able to find a quiet little cove, dive for lobsters and scallops, and relax in that way. I do see that your essay has shot to the very top, so congratulations!

      Thanks again for your kind words about my essay.

      Edwin Eugene Klingman

      Dear Jouko Harri Tiainen,

      By equating i to the speed of light (i=c) you suggest that the speed of light is a "constant of motion" if "the laws of physics (or the equations) are the same in all inertial reference frames."

      If one believes as Einstein, that "space does not exist absent of field" and that the gravitational field fills space, then the Galilean invariance of the Maxwell-Hertz equations implies only one time dimension, and this is consistent with constant speed of light in a local gravity frame. Coordinates fixed in the gravity frame see constant c. But for other objects moving in the frame with velocity v, the constant local c appears as c+v from the perspective of elapsed time. This preserves the geometry of the Minkowski differential, without implying different time frames.

      You then postulate that the mathematical definition of +i and -i can be associated with GR (c=i) and QM (h=i). That is truly fascinating. My own interpretation of the relativity of a self-interacting field (such as gravity) leads to unidirectional time. I will try to see how to understand this in terms of your postulate. The Minkowski geometry does not imply multiple time dimensions. It is compatible with 'same time' Lorentz formulations in one inertial frame.

      You interpret h=i in Schrödinger's equation to satisfy 'Planck's quanta is constant' and "all time is equal for all observers", compatible with time as universal simultaneity. As I mention above, my own interpretation of the 'imaginary' i is as represented in geometric algebra, i.e., i is the duality operator that transforms one element of geometric algebra into its dual.

      I think your essay is very deep and requires much thought. I plan to give it much thought and will score it accordingly. Congratulations on writing an essay deserving much thought.

      Best regards,

      Edwin Eugene Klingman

      Dear Jouko Harri Tiainen,

      After reading Armin's comments on your page, I want to expand on my remarks. I admire Armin's work very very much, but I don't think I agree with all of his statements, perhaps because I ignored your use of bra and ket, and also your treatment of entanglement. I pretty much ignore everyone's treatment of entanglement, for reasons I have already published, but as it is a common belief today, I do not generally downgrade essays for expressing this belief, or even a novel way of trying to make sense of it. Armin makes some good points, such as E=-m if i=c. Perhaps i~c would be more appropriate? You do use +i and -i so one might get E=m. Or perhaps this can relate to the negative energy of the gravitational field. I simply need more thought on this matter.

      Nevertheless, my perspective here is that you are simply letting the speed of light take on a unit value and similarly Planck's constant take on unit value and you are trying to make sense of the imaginary i in key physics equations.

      Why is that i there?

      I have concluded, with many others, that geometric algebra is the most powerful tool available for physicists today. In geometric algebra the function of i is that of a duality operator, which transforms the element it is operating on into its dual. That is how I'm interpreting your work. As I say below, your essay (for me) requires more study, but I do not dismiss it out of hand. Perhaps because physicists are so comfortable with complex analysis and so used to using the imaginary i in Minkowski geometry and Schrödinger's equation they see no need to think further. For pure geometry this is probably reasonable, but physicists tend to treat the i in quantum mechanics as somewhat mystical. Again, I want to spend more time thinking about this, and I will do so in the framework of the geometric algebra duality operator.

      By equating i to the speed of light (i=c) you suggest that the speed of light is a "constant of motion" if "the laws of physics (or the equations) are the same in all inertial reference frames."

      If one believes as Einstein, that "space does not exist absent of field" and that the gravitational field fills space, then the Galilean invariance of the Maxwell-Hertz equations implies only one time dimension, and this is consistent with constant speed of light in a local gravity frame. Coordinates fixed in the gravity frame see constant c. But for other objects moving in the frame with velocity v, the constant local c appears as c+v from the perspective of elapsed time. This preserves the geometry of the Minkowski differential, without implying different time frames.

      You then postulate that the mathematical definition of +i and -i can be associated with GR (c=i) and QM (h=i). That is truly fascinating, and may relate to the energy-time conjugation I develop in my essay. My own interpretation of the relativity of a self-interacting field (such as gravity) leads to unidirectional time. I will try to see how to understand this in terms of your postulate. The Minkowski geometry does not imply multiple time dimensions. It is compatible with 'same time' Lorentz formulations in one inertial frame.

      You interpret h=i in Schrödinger's equation to satisfy 'Planck's quanta is constant' and "all time is equal for all observers", compatible with time as universal simultaneity. As I mention above, my own interpretation of the 'imaginary' i is as represented in geometric algebra, i.e., i is the duality operator that transforms one element of geometric algebra into its dual.

      I think this part of your essay is potentially very deep and requires thought. I plan to give it more thought and will score it accordingly. Congratulations.

      Best regards,

      Edwin Eugene Klingman

      Dear Richard,

      Thanks much for reading and commenting. Didn't mean to give you a headache, or a need for a drink. You're right, Einstein didn't get to say much. Most physicists can (and probably do) fill in his arguments as they are standard special relativity explanations, while Hertz's, Heaviside's, and the Tavernkeeper's arguments are not as well known. And I plead nine pages!

      The reason to derive Lorentz with 'just one frame' is to show that the Lorentz transformation can be derived with only one time dimension. All SR derivations are based on two inertial frames, each with its own universal time dimension, and leads to the 'relativity of simultaneity', which is nonintuitive and leads to nonsense: "your clock runs slower, while my clock runs slower", etc. And many seem to think that the very existence of the Lorentz transformation implies two inertial frames with two time dimensions. My derivation still handles transitions between states of motion, but not between different time dimensions. There is a very big difference. The focus is on the difference in energy of the 'states of motion' not the difference between different 'space-times'.

      Probably our conceptions are very different. I've found that the more a physicist is comfortable with special relativity, the harder it is for him to understand my point. That's probably to be expected.

      Come back to the Tavern. The drinks will be on the house!

      Best regards,

      Edwin Eugene Klingman

      Dear Richard J Benish,

      As you note elsewhere, we both have high regard for Tom Phipps' contributions to physics, despite certain disagreements with his approach. You further point out something I believe often goes unnoticed:

      "...understanding a theory about gravity (i.e. GR) is often confused for understanding the physical phenomenon of gravity itself."

      As you say with reference to "matter tells space time how to curve, and space-time tells matter how to move", no academic physicist bothers to point out that we have no idea how these orders are carried out. You extend this line of criteria to "quantum gravity", and to how "gravitons" work, in that they make no physical sense. Just part of quantum field theorists attempt to force the universe into a bookkeeping scheme.

      With respect to your comments above, your first paragraphs effectively summarize the situation. I agree that one-way measurements are hard, perhaps impossible, hence the average back-and-fourth measurements predominate. I have designed an experiment that should be capable of measuring the velocity of the local frame from within the context of the local frame with no outside information. This should establish whether my approach is valid or invalid.

      The experiment you discuss has never been done, yet, like other 'gedanken' experiments, it is typically accepted as reality. It's not quite clear to me why achievable experiments that question the status quo are not performed. I hope both of our experiments will be performed.

      You then discuss maximum geodesics and accelerometers. My own perspective is that "curved space-time" outside matter is equivalent to energy density distributions in flat space. As you probably know, Weinberg, Feynman, and others have shown that iterated flat space approaches lead to Einstein's field equations in "curved space" so my inclination is to reject "curved space-time" (incapable of dealing with "density" or with "self-interaction energy") and this bias extends to rejecting higher dimensional theories of physics. You identify the motion as not through space, but of space, and view this as curvature in (4+1)D. My perspective on the gravito-magnetic ('C') field is analogous to electro-magnetic circulation, i.e., circulation of the field with characteristic angular momentum. Circa 2006 Martin Tajmar used accelerometers to measure gravito-magnetic field circulation. I reject higher dimensions of space, from 4 to 11, however it might be possible to interpret circulation in space as a fourth dimension. This is more a mathematical representation, like the Minkowski representation, than a true description of the physics. Clearly n-dimensional representations are of utility in physics. Having read your essay several times I'm still not exactly clear on how your (4+1)D model is to be interpreted. My 3D mind, operating in time, works well with n-dimensional math, but does not grasp spatial models greater than 3D.

      As for the accelerometer questions (ignoring gravito-magnetic issues) it is probably not purple-winged horsies, but the gravity gradient dG/dt that imparts momentum and induces local gravito-magnetic circulation. How this registers or not on an accelerometer is not clear to me, having not studied accelerometers in ages. The equivalence principle that falling 'cancels' gravity, does not prevent the accumulation of kinetic energy.

      In summary, I do not intuitively grasp how a gravitation field 'pulls' and I don't think 'gravitions' is the answer, nor do I accept 'curved space' explains anything physical. 'Pushing' seems to bring with it another set of problems, and might work for a universe with only one central body, but I can't envision a many-body dynamics in such a case. Gravity to me is the great mystery, acceptance of which seems to unlock other doors big time. Neither gravitons, curved space-time, 'dynamic space' nor (4+1)D do it for me, yet I feel the field as I just sit here typing. It's real, and when I accept the reality, and play with the equations, lots of the universe falls out. I know this doesn't answer your questions, but it's a mystery to me.

      I appreciate your many comments. If we ever meet, let's drink to Tom Phipps.

      Edwin Eugene Klingman

      Gary,

      Not sure I understand the question. Since energy = work = force x distance, the distance the earth moves, for the reaction force, will be much less than 6 inches. When you reach the height, and fall back, presumably the earth is falling back to you. Don't try to measure it.

      I live on the coast, and to get to Silicon Valley I cross a reservoir/lake which is on a fault line. On my side the ground is moving north, on the other side of the lake the ground is moving south (if one believes plate tectonics). I never experience a jolt, and I've never seen them repair the bridge. Some things we almost have to take on faith?

      Best regards, Edwin Eugene Klingman

      Ed,

      If I move 6" away from the Earth, doesn't relativity say that is the same thing as the Earth moving 6" away from me? Wouldn't it take more energy to move the Earth than to simply move me?

      Best Regards and Good Luck,

      Gary Simpson

      Dear Gary,

      You're correct of course that if you move 6 inches away from Earth, the earth is now 6 inches away from you. But the movement is measured from the ground you stand on. You move 6 inches away from the initial ground surface, while the earth moves an infinitesimal distance away from the initial origin. Since initially there was zero linear momentum in the system, the momentum of you moving up is theoretically canceled by the momentum of the Earth moving away from you. Since momentum is mass times velocity, the velocity of the Earth moving away is infinitesimally small, which means it will not have moved very far by the time you reach 6 inches (ignoring gravity). This is essentially in the frame of the earth. Special relativity is not concerned with this, only with your velocity relative to the Earth (and the speed of light c, relative to each of your inertial frames).

      The classical relativistic system in which you are the rest frame and the Earth is moving away from you, or the Earth is the rest frame and you are moving away from Earth is not a very useful formalism here; in the 'space-time' perspective the energy is ignored. In theory, from the Earth's rest frame perspective, your clock will run slower, whereas if you are the rest frame, a clock on the Earth will run slower. Similarly, in the special relativistic formulation where you are one inertial frame and the earth is the other inertial frame then the speed of light with respect to you is c, where your velocity is the equal zero. At the same time when the Earth is viewed as the rest frame then the speed of light with respect to the Earth is c and the velocity of the Earth is considered equal to zero. This makes about as much sense as Einstein's railway based gedanken experiments.

      In special relativity the energy that got you moving or got the Earth moving is not really the issue. What is at issue is your velocity and the speed of light. If you are at rest it is the velocity of the Earth and the speed of light that is the issue. The relative energies (and gravity) are ignored. Particle physics treats relativistic energies in terms of the Lorentz transformation, but doesn't treat where that energy came from -- for example how long one had to accelerate a particle in a collider to reach that energy. Similarly, as I interpret what you're asking, if you wish to say that you are at rest and the Earth is moving away from you at a certain velocity, the energy required to move the Earth away from you is not part of the problem. Special relativity assumes that one frame is at rest and the other is moving. It does not ask what it took to get the other frame moving. It's assumed moving when one formulates the problem.

      What my essay focuses on is 'time dilation' and I claim that you and the Earth share one universal time. In this case your atomic clock will run 'slower' than the clock in the rest frame of the Earth, but that is an energy-time effect, not a space-time effect. In special relativity the view is symmetric however in reality, for example in the GPS system, the symmetry is not found. The clock on earth is always the fastest clock. This is because you were initially at rest and then your energy changed, in such a way that your atomic clock measures a different frequency, or energy, which special relativity falsely interprets as measuring your 'time dimension'.

      That's probably enough answer for a comment. Is this more what you had in mind?

      Best regards,

      Edwin Eugene Klingman

      I had to make a new post sorry I oouldn't reply to your first comments.

      Thank you and a big thanks to Armin as well (he sent me a reply that made clear what he meant by his comments).

      Your comments have been wonderful and I really do appreciate your time and effort in responding. Since I cannot work how to put equations and images into this post I have attached a PDF it contains Peter Jackson's red/green sock trick and a "two slit" diagram as well. Also if you have more question see the first post in my thread there is a FAQ rejoinder. Your and Armin's remarks and deep intuitions have been very very helpfulAttachment #1: Edwin.pdf

      Ed,

      That is an excellent answer. I believe I owe you a few beers:-)

      Very Best Regards and Good Luck,

      Gary Simpson

      Dear Mr. Klingman,

      your essay is interesting indeed.

      I would be glad if you find a moment to go through my essay, and to have a discussion about convergences and differences between our works.

      Best of luck,

      Flavio

        Dear Flavio,

        Thank you for reading my essay and commenting. Your invited me to read your essay and compare and contrast. It's difficult for me to summarize in a few words. My last essay, The Nature of Mind, offers nine pages that address the issue of intuition, which you appear down on. You seem to lump determinism and absolute simultaneity, local realism and conservation laws into the same category of 'prejudice'. My current essay argues for absolute simultaneity, and I elsewhere argue for local realism, while I have a more nuanced view of determinism, and I have argued against conservation as a consequence of symmetry, as all symmetries I am aware of are approximate.

        I recently watched a YouTube discussion between Jordan Peterson and Camille Paglia, a goodly portion of which dealt with Derrida, Foucault, and other deconstructionists and radical relativists. For a number of reasons I feel this nonsense is beginning to infect physics, probably because physics is chaotic in the extreme, based (in my opinion) on fundamental false assumptions and prejudices that have endured for about a century, both in relativity and QM.

        Once one discards intuition, one is left with 'word hash', combining words/equations in 'narratives' [see Gibbs] and having no idea how to discriminate reality from story. My current essay focuses on one non-intuitive narrative, while previous essays address other such instances. As you spend quite a bit of time on Bell I will address Bell.

        You refer to Bell's theorem as "momentous no-go theorem" and spend a couple of pages on his logic. If you look at his first paper, his first equation determines the outcome: A = +/-1, B = +/-1, where A and B are measurements on Stern-Gerlach. This is based on the (prejudiced) assumption of quantum qubits. You clearly state that QM provides only probabilistic predictions. Many-body experiments on spin yield qubit outcomes, as should be expected. Stern-Gerlach does not yield qubit outcomes but smeared results that match 3D spin dynamics in an inhomogeneous field. However Pauli's mathematical projection of qubit mechanics: O|+> = +|+>, O|-> = -|-> is Bell's prejudiced assumption of reality. In other words Bell claims to look for a classical (local variable) description of Stern-Gerlach, but then constrains the problem to quantum results based on the mathematical projection of Pauli, not on the empirical results of Stern-Gerlach.

        Feynman later put the final nail in this coffin by assuming that his favorite two-slit photon experiment could be carried over directly to a two-slit spin analog (the SG experiment). Of course the same equations apply, because he's making the same mathematical projection, but the actual physics of the photon in two-slits is vastly different from the physics of atoms in a homogeneous magnetic field, and Feynman's extended SG model has never been tested.

        Since Feynman and Bell's math and logic have been accepted as gospel, local realism has been excluded from physics. A no-go theorem based on atoms in a magnetic field, constrained to never-tested single-qubit spin results, is then "proved" by photon-based experiments which actually do produce two-state results: on/off detections.

        I repeat - the entire industry is based on the erroneous assumption that the results of the Stern-Gerlach atomic experiments are +1 and -1 deflections, "tested" by photonic experiments that use +1 and 0 detections. The atomic data produced by Stern-Gerlach clearly conflicts with Bell's initial assumption, but instead of trying sophisticated tests of Stern-Gerlach using modern technology the whole entanglement industry is based on 1922 experiments that clearly do not yield +1 and -1 results. The confusion of 1920s quantum mechanics is locked in. Here is your fundamental 'prejudice'.

        My suggestion is if one wishes to 'deconstruct' physics, look for the basic assumptions that violate intuition and that lead to nonsense. Of course that is dangerous for those toiling in the establishment, so generalizations are preferred.

        This is how I would contrast your approach with my approach.

        Good luck in the contest and in your careers.

        Edwin Eugene Klingman

        Thank you for the answer. I accept your point about not being able to represent Einstein given the space limitation. I also agree that Poincare's conventionalism has long-since been surpassed by Einstein's relativity. In fact a lot of people fail to understand the difference in Poincare's philosophical view and therefore claim he discovered relativity before Einstein. He was almost there but not quite. It is easy for us to see the right idea now but at that time conventionalism must have seemed like a reasonable alternative to some.

        Dear Peter,

        Special relativity means different things to different people (I know this from a year of discussions). In your opinion light is to define a 'preferred' reference frame. I cannot believe this makes sense in reality, and as I point out, the nonsense flows from space-time symmetry [i.e., light as 'preferred' frame] and vanishes with energy-time asymmetry.

        You're also of the opinion that one needs to understand quantum gravity to appreciate your point. You claim to understand quantum gravity; I have an understanding that I'm sure differs from yours.

        For many I talked with last year, the first statement that they disagree with tends to shut them down, rather than try to understand how their belief may be reinterpreted. Although quantum mechanics has probably a dozen interpretations, almost all of which yield the same calculations, there is surprising resistance to an interpretation of special relativity that makes sense, but differs from the received wisdom. I'm disappointed that you "didn't dig into the remainder of the paper" but with 200 essays, it's hard to study them all.

        I'm fairly knowledgeable about GA and I do not see an E8-type assignment of GA product terms to the standard model as meaningful, so we do agree on the significance of GA, but not on all physics. On your thread you were happy to hear about Arthur's "Understanding geometric algebra for electromagnetic theory". I suggest after you read this book you may wish to reread my essay.

        Best regards,

        Edwin Eugene Klingman

        Dear Bashir,

        Thank you for your kind remarks.

        You cover many aspects of physics in your essay. I interpret your "indivisible atom" to be the fundamental "substance", which you seem to postulate to be the photon. You say all other composite particles have two key categories, "charge and neutral". My suggestion would be to focus on mass and charge, in terms of gravitational fields in electromagnetic fields, as described in equations (1) in my essay. Since gravitation interacts with itself, while the electromagnetic field does not have charge so does not interact with itself, we have a linear field and an interacting non-linear field. I do not believe this situation has been sufficiently explored, but mine is a minority view. Your intuition seems to be good, but I do not believe your basic model will take you as far as you wish to go. I encourage you in your efforts to understand nature.

        My best regards,

        Edwin Eugene Klingman

        Dear Avtar,

        I hope you will read my essay again, as I do not believe you have understood its potential significance for your work. You say your photon model depends on special relativity, as it matches the observed universe expansion data. But that is not based on the relativity of simultaneity as you imply. Cosmic microwave background on which all cosmology models are based is essentially Machian, and time is considered absolute with respect to this background. So contradicting "the relativity of simultaneity" does not seem relevant, as it is not involved in cosmological 'universe expansion' models. My impression is that you reached this point and decided not to go further. This is unfortunate, as Hertz's extension of Maxwell's equations address the problem you address, but as "disturbances in the ether", with implied local energy density. Moreover, the recent observation of colliding neutron stars has demonstrated that gravitational disturbances propagate at the same speed as electromagnetic disturbances in the field. There is no "acceleration time" involved!

        This Hertzian extension of Maxwell's theory envisions energy flow in a body, while Maxwell/Einstein envisions energy flow between systems. It seems de facto true that cosmology 'universe expansion' observations concern energy flows within the cosmological frame, not simultaneous flows between frames. (When one frame is the universe, what is the other frame?)

        The problem here for your model, is that there is no acceleration. As soon as a disturbance occurs in the field, it immediately propagates at the speed of sound (the generic term for perfect fluid models) - no acceleration.

        The significance for you is that this lack of acceleration required to reach speed c implies that light never has value v < c. Of course you refer to recent experiments in which light impinges on a semiconductor material and is absorbed, whence it photons become 'excitons'. In my opinion, such interactions are phonon-like, not pure photons, and are more likely explained as many-body phenomena, rather than pure photons. Of course I may be wrong, there is not enough information to determine this yet. If the phenomenon is essentially one of absorption and re-emission then formulas with the inverse square root of (1-(v/c)**2) are undefined. These are in most of your equations, since you seem to conceive of local 'photon' mass density as a material body, instead of the equivalent mass density of the disturbance in the field. The v-based equations for the photon are inappropriate in the Hertzian framework, which you seem not to have understood in my essay. In spite of this, and for reasons too long to include in a comment, I do find your Postulate 1 on page 5 to be is very astute and appropriate to the problem. It is that which first excited me about your essay.

        My best regards,

        Edwin Eugene Klingman