Peter,

Thanks for having a read and the comments. FYI, I read and commented upon your essay fairly early although I did not score it until yesterday.

Regarding the copy paste in the first of your posts, I suppose it could be true ut my thinking regarding quaternions is not really based upon toroids or similar structures. Rather, a quaternion is exactly what Hamilton said it was ... the ratio between two non-linear vectors. That can then be applied in any number of ways with your description being one.

Regarding absolute velocities. Equation 2 is a testable hypothesis. Its truth or lack of truth requires experimentation. It is possible that the 6*pi^5 value is coincidence. If it is not a coincidence, then there must be a way to get from 6*pi^5 to the observed Mp/Me ratio. Motion was the easiest thing that came to my mind and since the equations need to contain the Lorentz Transform, Equation 2 seemed like a good bet. I'm sure there are other corrections possible.

Your present essay uses quaternions quite well although perhaps you don't realize it. All of the vector rotations you present can be represented by quaternions ... i.e., what do I multiply vector a by to get vector b (Q = b/a).

Regarding 3-D extensions of the Pythagoras Theorem, I do not understand your question. You can build a theorem with as many dimensions as desired, you simply do it two terms at a time. Going beyond three dimensions simply does not make physical sense. Whether or not ct can serve as a 4'th term, it is not something you can measure with a yardstick. That means either c or t can be whatever you want it to be to make the four square sum be correct.

Best Regards and Good Luck,

Gary Simpson

Hi Gary,

When Kaluza-Klein theory came up, Einstein acknowledged that a five dimensional theory was a promising direction to field unity. But he cautioned that extra dimensions (beyond the 4 of Minkowski space-time) should be entertained "only when there are good physical reasons to do so."

Lisa Randall's "warped spacetime" has five spacetime dimensions (the fifth may be infinite). The "good physical reason" she supplies is that K-K particles are not distinguishable from particles of 4-dimension origin--gravitons.

Your good physical reason is different, but in principle the same as Randall's. You both aim to solve the mass hierarchy problem. While she solves that with string theory branes to form the boundary of a complete field theory, you introduce a scalar term that as I understand it, varies in mass value with the evolution of the (time-dependent) field.

If I understood properly, I agree. There must be an absolute limit on the mass, however, living on an absolute interval [0,oo) ... and this would create a paradox, if but for the mathematical proof by Perelman that the interval is reversible on a three-manifold. (See https://terrytao.files.wordpress.com/2009/09/poincare.pdf.)

So in my mind, there's no harm in confusing scalar time and complex (imaginary) time. They have same root, i. Where a pair of lines of positive trajectory meet, on a positively curved manifold, they continue in the imaginary part of the complex plane "... north of the North Pole ... " as Hawking said. The point is, the trajectory is continuous, whether one maps it onto a 2-dimension plane, c , or onto a Riemann sphere. In principle, it's possible to calculate a position in imaginary time 'backward' to the point where it joins its pair origin - possible, but unimaginably difficult. It brings to mind Einstein's remark, "I think of a quantum as a singularity, surrounded by a large vector field."

A countable infinity of quanta in four dimensions does not differ - using Einstein's definition for quantum - from the assumption of curved spacetime. A finite number of coordinates with the metric signature - or - - - (Minkowski space-time), sufficiently bounds a countable infinity of quanta interacting by Mach's principle.

It is of interest that the symmetry of Ramanujan's function (http://home.iiserbhopal.ac.in/~kashyap/tau.pdf) that results in the sum of all positive and negative integers, -1/12 suggests that natural numbers are holistic; i.e., forming a holomorphic map to every neighborhood of the complex plane. Every neighborhood is complex differentiable. So the domain of classical theory is complex, though all measurement results are on the positive side of the real line.

While I'm not entirely satisfied with this answer, one has to stop somewhere.

All best,

Tom

    Dear Gary,

    Thank you very much for a very large and interesting comment in my forum thread. I do not think that now there is time for lengthy discussions, time will come in the middle of April.

    Nevertheless, I will try to briefly answer the questions that have arisen with you.

    With "tired light" is associated one of my recommended research principles is associated with the impossibility of abstract and ideal properties of matter and fields. I can imagine that photons move exactly at the speed of light, hence, they interact with the physical vacuum. This interaction is necessarily associated with energy dissipation. But how photons carry real energy for many billions of years without losses, I can not imagine it. And this question is individual and connected with subjectivity. Whether the researcher allows supernatural properties of matter and fields or not, everyone should answer this question himself. I do not insist, but it is always necessary to think, but are there analogs to this phenomenons?

    «I too am a believer that the vacuum is some type of medium ... I'm simply less clear regarding what its properties must be.»

    In my essay I tried to show that the medium is multilevel, fractal, nonlinear and consists of electron-positron pairs and their de Broglie waves, including waves formed on the harmonics of the Compton waves of an electron, (analogous in structure to the electron), from pairs of d quarks and their de Broglie waves, from pairs of preons and their de Broglie waves, etc.

    The de Broglie waves have energy, mass, and they are connected with their Compton waves. They are designed to create conditions for the stability of Compton waves. The waves of de Broglie form other waves of de Broglie, etc. If Compton waves are limiting elements and are stable, then de Broglie waves are dynamic and much more often change their parameters by means of quantum parametric resonance.

    Thus, the medium of the physical vacuum, first of all, is a dynamic nonlinear medium that easily changes phase state of its elements.

    The Mathieu equation is used to solve parametric resonance problems in classical mechanics, the energy dissipation function is always involved in it and nonlinear properties of elements or medium participate.

    In radio engineering, using the Mathieu equation, a parametric generator is calculated. The values of the Mathieu equation can be obtained by substituting the solution in the form of an expansion in the Fourier series. I.e. the elements of the medium, in the form of de Broglie waves, are deterministic elements.

    The condition for the formation of self-organizing solitons is the nonlinear properties of the medium of a physical vacuum with high-Q elements. Solitons can interact through their de Broglie waves only if the frequencies coincide or are close to the harmonics and subharmonics of quantum parametric resonance. Therefore, chemical bonds are so selective, and self-organizing structures of matter are repeated.

    Another very important property is the high rigidity of the medium of the physical vacuum and the speed of propagation of interaction in each level of matter. For example, photons are spiral elements from quarks. A pair of spiral elements of the quark matter level is screwed into the medium of the physical vacuum and moves in equilibrium in the de Broglie's own wave of elasticity, like a warp motor. This is analogous to the pairs of Cooper electrons moving in eddy currents in equilibrium in the state of superconductivity, but 43.6 times slower than the speed of light, because they are elements of a higher level of matter and have 137 times the cross section of interaction.

    «I have never thought about the speed of gravity as you describe. I do not think gravity propagates at light speed»

    My statements about the speed of gravity are based on my own experiment. At the end of my essay, I gave the results of an experiment on recording the orbital toroidal gravitational wave of the Earth. The signal of the gravitational wave is very distorted, but, nevertheless, the period of 52 minutes of the action of the Earth's orbital gravitational wave is viewed. This means that the speed of propagation of the main gravitational wave of the quark matter level, along the Earth's orbit, is equal to the speed of light.

    In addition, at the maximum intensity of the variations, often, the lines become wide. If the scale is stretched, then an oscillatory process is observed with a period of about 72 seconds. In my work «Deterministic gravitational waves» , reference [20] gives the corresponding spectra of these oscillatory processes. From these my experiments it follows that there is a second gravitational wave in the Earth's orbit of the preon level of matter, which has a propagation velocity 43.6 times faster of the speed of light. I have no doubt that in this way it is possible to register gravitational waves of many levels of the fractal matter.

    I'm sorry that I can not explain briefly.

    I found a strange phenomenon, as soon as my rating rises, then immediately it falls sharply. Therefore, I am convinced that it is necessary to give grades at the last moment.

    I wish you success in the contest.

    Kind regards,

    Vladimir

    4 days later

    Tom,

    Thanks for reading and commenting. Also, my apologies for my tardiness. I've been distracted by small things of late plus I'm annoyed by all the one-bombers.

    It looks like you've got the main ideas that I present. I can only hope that Einstein would judge my motivation positively.

    What I find interesting in almost all of the comments to my essay is that only one commenter has noted any value in my proton diameter calculation. Perhaps I should take this as a hint that the approach is false and that folks are merely too polite to state such. Or perhaps the implication is more than anyone wishes to consider. Nonetheless, I consider it to be a significant piece of circumstantial evidence that requires refutation by an objective party. If it is not possible to refute, then the implications of the methodology need to be seriously considered.

    Best Regards and Good Luck,

    Gary Simpson

    Dear Gary,

    I read your essay, but I don't have much in terms of pertinent comments, since I have no clue what your ideas about this year's essay topic are.

    As for quaternions, I am not a specialist so I cannot evaluate if your extended 5-dimensional system is an interesting avenue to explore. I also did not understand why it is useful to introduce such a system. You do jump abruptly on page 8 to speculations about the proton radius, and I suppose somehow they are related. You say that you "place the burden upon the reader" to read all your references and figure it out... With 200 essays that compete for attention, it is quite an hopeful attitude!

    I suspect your hypothesis of the ratio Mp/Me depending on absolute velocity can easily be falsified by astronomical observation. For instance, the fact that hydrogen atoms in fast moving astrophysical jets (or the ejected matter around supernova remnants) seem to continue to behave as regular hydrogen atoms probably puts limits to the hypothesized variation of the ratio.

    Since I cannot compare your essay to the other essays in the contest that I rated (and that try to deal at least a little to this year's essay topic), I will not score it. But I do wish you good luck in your further research!

    Marc

      Marc,

      Thanks for having a read and attempting to comment.

      You suggest using hydrogen jets as a method to falsify Equation 2. The problem with your suggestion is that the observation would be taken from the Earth's reference frame. The Mp/Me ratio must be determined in another reference frame that is moving with respect to the Earth.

      My comment regarding placing the burden upon the reader was not intended in the way you interpret. Rather, it should be interpreted as follows ... if 6*pi^5 is a coincidence, then how is it possible that this coincidence leads to an accurate calculation of the proton diameter? That would require two successive coincidences with the second coincidence being truly amazing. Basically, I offer the proton diameter calculation as circumstantial evidence.

      Why have 5 dimensions? Simple. Lots of smart people have been trying to combine QM and GR for almost 100 years without success. The two models are each 4-D, but they each treat time differently. If the two different times are each viewed as "dimensions", then the result is a 5-D model. Then comes the trick of making time scalar and then multiplying it by Euler's Equation to get the time for GR and the time for QM.

      It is clear that you see no connection between my essay and the essay topic. You admit yourself that your essay is non-falsifiable meta-physics. I was faced with essentially the same choice. Rather than going down that path, I chose to focus on the time-evolution aspect in a way that is empirically testable. I state this very early in the essay. Essentially, I argue time to be a scalar only with no direction. This should remove a restriction on other peoples' thinking.

      Don't worry about scoring, although now I am suspicious that perhaps you already have scored my essay and are one of my 8 one-bombers to-date.

      In any event, I have one request of you. Keep Equation 2 in the back of your head. The scalar portion is obviously the Lorentz Transform. The complex portion is the obvious choice to add to the LT to produce Euler's Equation. I think that the complex portion accounts for motion induced stellar aberration.

      Best Regards and Good Luck,

      Gary Simpson

      Dear Gary,

      My apologies for this late reply. I read your article several times, needing to step back.

      Well, I entirely agree that the transformation of a n-D space over real numbers into a space over complex numbers gives at least a n-D+1 space. Each high-school student discovering complex numbers knows that this stage of her/his mathematical life implies an extension from the real line to the complex plan having a real and an imaginary dimension. This point is generalizable to any passage from a real vector space to a complex one.

      Personally I always thought that current formulations like "The passage from Newtonian physics to SR is a passage from 3-D physics to 4-D physics" are not really exact, and that the correct formulation is "The passage from Newtonian physics to SR is a passage from 4-D physics to 5-D physics." Obviously, Newtonian physics needing 3 space coordinates and one time coordinates operates over a real 4-D vector space. The essential difference between Newtonian physics and SR is that in Newtonian physics the 3 spatial coordinates and the time coordinate are mathematically speaking identical, whereas in SR, spatial coordinates and the time coordinate are equivalent but not identical. Within Newtonian physics, there is no mean to distinguish mathematically the real time coordinate from the in turn real space coordinates. In SR, the intervention of i say in time intrinsically distinguishes the latter from space. Well, but because of its respectively real and imaginary dimensions, time is a plan. So SR operates over 5 dimensions.

      Now, "historically" speaking, if your approach leads to a "coincidence" with the result of the Paul Scherrer Institute experience rectifying the diameter of the proton, it is not simply a "coincidence." Thanks to symmetry in prediction and retrodiction, a theoretical result going with something already known, but obtained on a different basis, is equivalent to a confirmed prediction.

      But for obvious heuristic reasons, the confirmation of a prediction about something for the moment absolutely hypothetical would be more striking.

      Do you think that your approach implies such possibilities?

      Once again, all the best;

      Yours sincerely

      Peter

        Peter,

        Many thanks for reading and commenting upon my essay. I am flattered that you would read it several times and consider it so carefully. Also, many thanks for your vote of support. It appears that you have offset one of the 8 one-bombs I have received.

        It is clear to me that you understand exactly what I intended with this essay. In answer to the question at the end of your post, the answer is YES! In fact, this is why my essay only loosely fits the essay topic. I have no other means of reaching a technical audience.

        The coincidences here are several. First, is the value of 6*pi^5 itself. I think the exponent five corresponds to the system dimensions and I think the value 6 corresponds to the 3 real dimensions plus the 3 complex dimensions.

        The second coincidence involves the calculated values for diameter and velocity. The calculated proton size is accurate. However, the calculated velocity appears not to be accurate. But this could be a matter of interpretation.

        In a post above, Colin Walker states that the velocity associated with the Cosmic Microwave Background is much smaller than the value that I state and he gives a numerical value. The value I present is exactly 5 times the value that he states. You might be able to assist here. I remember from either math or statistics that there is a type of average where a value is divided by the number of degrees of freedom that a system has. So, in this case, that would be 5. So, if the problem is formulated correctly, the velocity associated with the CMB would be the velocity I calculate divided by 5. That makes a third interesting coincidence.

        The question is exactly as you state it ... Is 3-D space curved within 4-D space-time, or is 4-D space-time curved within 5-D space (quantum-space-time?)?

        Your statement regarding time being a plane is correct in my opinion. I think that we experience a scalar time that then operates upon the complex plane to produce two time values. One is used by GR and the other is used by QM. Dr. Crowell commented in a post above that I have presented a bi-quaternion. That makes sense since it is the sum of a real and a complex quaternion. That also means that there are only 5 dimensions needed vs the 8 dimensions of the complete octonion group. Equation 2 seems natural to produce these two time values since it adds a term to the Lorentz Transform to produce a form of Euler's Equation.

        There is a rather subtle point that I should also mention. When applying the Lorentz Transform to mass for example, we would normally apply it to the entire mass of the atom ... meaning the nucleus and the electrons. What I propose differs from this in that the LT is only applied to the nucleus. The electrons of a neutral atom are taken to be stationary vibrations that arise from the vacuum. They do not move with the nucleus but rather are pulled from the vacuum as the nucleus passes through space. This provides a tangible medium for light and for action at a distance. Since all particle accelerators use charged particles rather than neutral atoms, I am not sure how to falsify this by experiment. Perhaps there is some way to apply the photo-electric effect to something moving at high speed. Or perhaps there is some way of modifying the Stern-Gerlach experiment.

        Best Regards and Good Luck,

        Gary Simpson

        Hi Gary,

        You have reviewed my theory some times ago. But in my new essay I have more interesting developments. I derive Newtons gravitation(long distance) law from the SAME system that generate all the quantum mechanical results. Moreover, the simulations that predict the electron and the proton now I find an analog of it in the standard physics via Helmann potential which is a combination of Coulomb and Yukawa potentials. The proton radius that I get in my simulation is close to .815 fm, maybe there is some link between our theories but I don't see it. Thanks for your attention.

        last year essay

        this year essay

        for gravity the particle "p" has the correct energy

        [link:www.reality-theory.net/gravity.htmlgravity[/link]

          Gary, Phil, Jonathan,

          I communicated with Fischbach, suggesting that the neutrino output of the sun, assumed constant, would be denser when the earth is closest to the sun and vice versa. If, as I believe, radioactive nuclei may be triggered by neutrinos this could account for their observed variation in radioactivity as a function of orbital position. I think they either bought this argument or were unaware of a better argument.

          What a powerhouse of ideas FQXi brings together annually.

          Best regards to all,

          Edwin Eugene Klingman

          Dear Gary,

          We have each reviewed the other's essays, so this is just a personal note. In reading comments on essays I generally find your comments and Stefan Weckbach's comments to be friendly, sincere, original, informed, and interesting.

          Those are very good qualities.

          With best regards,

          Edwin Eugene Klingman

          Adel,

          Thanks for having a read and commenting. We might be working the same problem from a slightly different perspective. I will read your essay, comment, and score ASAP. The contest is winding down so we must all act quickly near the end.

          Bets Regards and Good Luck,

          Gary Simpson

          Dear Gary

          Your work is amazing! And promising!

          To fully understand its interest, I will have to analyze your papers, but I cannot do it now, I have to do it with time for fully seeing how your 5D geometry and my own ideas can couple. A purely mathematical theory needs some physical support besides fitting data and I am interested in seeing what kind of concepts about the nature of particles can be compatible with your analysis.

          My essay, as yours, has behind it a much deeper work. The model of Earth's past climate I present is built from data but I already knew that it had to be so because I have discovered something about the expansion of space that implies it. What I discovered is the one hypothesis no one considered, as I mention in the essay: it is not the space that expands but matter that decays. Space expansion is as apparent as the rotation of the skies, a consequence of the decrease of standard units, established from matter properties. You can see the similarities with Ptolemy model, with dark energy dragging stars away as celestial spheres dragged them around and dark matter in the role of epicycles (explaining the motion of galaxies instead of planets). And other similarities, like a distant universe made of stuff not available locally and that changes (rotates / expands) while locally it is invariant. Note that I do not think that these models are "mistakes"; they are models of data as obtained and are a necessary first step in the discovery process - without Ptolemy model, Copernicus could not have made his work, nor me without the space expansion model. I have a draft paper presenting my solution for the cosmological problem and apparently almost everybody quickly understands that it has to be the correct solution, judging by the emails I received and by the number of downloads (over 900) (vixra.org/abs/1107.0016).

          Now, how can this decay of matter, a very slow exponential decrease of size, mass and charge, be expressed by your exponential function? Possibly it is just a question of defining the proper units, as I do in the above paper. I think that field and mass or charge or just aspects of the same kind of entity, which is decreasing in intensity while expanding through space.

          You are right that if life becomes extinct it will never recover in Earth; but it's worse than that - if endotherms disappear, life evolution will be blocked at the reptile level.

          In relation to the "bombs" (five or six) in my essay, I know that there are groups of persons that see my work as a threat; and I know it because they emailed me saying it when I put the paper in vixra! However, I was not expecting it in this contest. Curiously, mathematicians have contacted me with supporting words, advices and even an invitation to submit to a journal in mathematics. The fact is that this is a very delicate matter, I understand the problem this change of paradigm represents and I worked out a solution; but it requires cooperation instead of "bombs". To publish my work in a journal of mathematics or in a non-occidental scientific system would be a disaster for occidental physics and I want to avoid it. My presence in this contest is a kind of test. At least, I had the joy to find a brave person like you! And also some interesting exchange of ideas with other authors.

          I vote in accordance with my admiration for your work and your spirit.

          I hope you find the right person to complement your work in the physical side. And I hope to keep in touch with you.

          All the best,

          Alfredo

            Hi Gary,

            You take a different approach to reality to me. You seem to say that numbers including complex numbers exist, whereas I say that the numbers (including complex ones and pi) and law-of-nature equations symbolically represent an underlying reality: the underlying reality is what exists. So while you might say that the mathematical universe is the full extent of what exists, I would say that there are aspects of reality that can't be represented mathematically.

            One thing I don't understand: is there such a thing as a "true rest frame"? Surely, from your point of view, such a thing could only have existed at the beginning of the universe; or are you saying that the five dimensional coordinates frame is the "true rest frame"? From my point of view, perhaps a "true rest frame" would be the aspects of reality that can't be represented mathematically.

            Regards,

            Lorraine

              Alfredo,

              Many thanks for reading and commenting on my essay. And of course also for the vote of support. I don't know if my essay will reach the final judging but it will be close.

              It is also good to see such enthusiasm. If you look at some of my other work, I recommend reading "Quaternion Dynamics - Part 1" first and then "Part 2". The evolution from P-1 to P-2 is very natural.

              The one-bombs can be very discouraging. It happened several times actually. Entire groups os essays were all scored with 1 values together. I noticed this and I noticed once that someone else went through the same group with scores of 10 ... so the people who were one-bombed got 2 votes with a score of 5.5. That seemed like a pretty clever way to discourage the one-bombing so the next few times it happened, I did the 10 bombing. Then the one-bomber adapted and started to score with 3's. It was not a perfect result but it was an improvement.

              Best Regards and Good Luck,

              Gary Simpson

              Lorraine,

              Thanks for reading and commenting ... and voting:-)

              I am an engineer by education. I think there is an underlying physical reality that is described by mathematics. Mathematics is useful to me to the extent that it provides a method to analyze the physical world. There are also many areas of "Pure Mathematics" that I have never studied. I do not know whether or not there is a "Platonic Realm" of pure ideas or not. I do know that there are many instances where "Pure Mathematics" has found an application to "Applied Mathematics" in the physical word. Geometric Algebra seems to be one of the more recent examples of this. I am content to let the true mathematicians frolic in these realms to their heart's content.

              The difference regarding our thinking is that I need evidence to make me believe that there are "one-off" rules. If two hypotheses make identical predictions then I can not choose one over the other. My default condition therefore is to go with what has already been established unless something else is favored by Occam's Razor. So in short, it is not that I have not heard your ideas or that I have not understood your ideas. You simply have not satisfied your obligations according to the scientific method.

              Ah yes .... the true rest frame. You've caught me. I am one of those aether heretics. The v in Eq 2 is the velocity of the observer's reference frame. Equation 2 let's me return to the concept of a true rest frame and make new predictions. For example, I would predict that if you were in a galaxy that is moving away from us at near light speed, the Mp/Me ratio in your reference frame would be many thousands of times larger than in our reference frame. But, if 2 reference frames are identical, then the equation 2 for each of them simply cancel ... kind of like multiplying by one.

              This also lets me reinterpret our place in the universe. If we are moving much more slowly than other reference frames, then we might not be at the center of the universe, but we have moved away from the center by a snaller distance than other reference frames. Essentially, I do not believe that relative motion A -> B is equivalent to relative motion B -> A. This is in contradiction to part of Relativity. My saving grace is that I want empirical validation.

              The 5-D geometry allows any 3-D space to have its own reference frame by using a different phase angle in the complex plane.

              Best Regards and Good Luck,

              Gary Simpson

              Dear Gary Simpson,

              It is definitely difficult to promote a new idea. I admit having problems with your "absolute velocity of the observer" and your "observed affect".

              Consider me almost an aetherist who denies the aether as something to refer to.

              Perhaps we both already failed getting sufficient attraction for enforcing a serious scrutiny by leading experts.

              I am aware of many sins of mine against the necessity of serving lazy expectations, in particular by my one-way definition of the speed of light in vacuum instead of Einstein's Poincaré synchronization.

              My critical comments on unwarranted interpretation of complex calculus are to be found in earlier essays of mine. I hope for your comment because you dealt with i too.

              Regards,

              Eckard Blumschein