Dear Simpson

I loved the way you closed out the essay, "It is certainly possible - perhaps even likely - that these conclusions are false. However, if that is the case then the reader is left to explain the proton diameter calculation." I would have used a similar closing for my essay as well, had I been able to come up with an exacting calculation similar to what you have done.

Having only recently discovered octonions via Yanofsky's and Dickau's essays, I cannot pretend to have suddenly gained the capacity to validate the calculations you have presented in the essay. But I can recognize simplicity and elegance when I see it, and your work has it. While I can appreciate Dickau's patience with regard to voting (he has more experience with this contest), I would much rather vote right now for an essay that I like and you are certainly one of them. All the best!

Warm Regards, Willy

    Willy,

    Many thanks for reading and commenting upon my essay.

    Physics is very demanding. You must get the right answer and you must do so for the right reason. You are correct to focus upon the proton diameter calculation. As I see it, either a coincidence has led me to a calculation that is also a coincidence, or the Mp/Me ratio and my calculation are not coincidences. I can believe a single coincidence, but two coincidences that are linked seems too much to believe.

    You have begun a new journey. Quaternions, Octonions, and the Division Algebras are very interesting indeed. I have been studying them for a few years now and have barely begun to understand and appreciate them. There is also a related field known as Geometric Algebra. David Hestenes has written several books in this field.

    Essentially, the question that I ask is "What does it mean to move in 5-D space if time is not a dimension?". I'm not certain that Euclid type thinking is applicable. Much of the controversy of Einstein's work was because he imposed Euclid's Geometry onto Relativity ... but what if Euclid is just a subset of the geometry of space? I think this is the path that we now need to follow.

    I will read and comment upon your essay soon.

    Best Regards and Good Luck,

    Gary Simpson

    Best wishes Gary Simpson,

    Hope you will find many more applications using your approach. We can interact later, you can use my mail id as given below.......

    Best

    =snp

    snp.gupta@gmail.com

    Gary,

    Suggest you take a look at the work of David Hestenes on geometric Clifford algebra, if you haven't already. Appears to me much of what you are doing is a subset of that algebra, to pick up on the rest of it might be very helpful to you.

    Several of the contributions to our contest are in that geometric language, including those of Michael Manthey Manthey FQXi essay and Michaele Suisse Suisse FQXi essay.

    Pete

      Pete,

      Thanks for the advice. I have a text by Hestenes but I have not read it yet.

      Best Regards,

      Gary Simpson

      Pete,

      BTW, do you have an essay in the contest? I have looked through the entries and do not see you listed. I always try to read and comment upon everyone's essay who comments upon mine.

      Best Regards,

      Gary Simpson

      Gary,

      Yes, I have an essay in the contest. Michaele Suisse is my co-author, it is submitted in her name.

      "Aims and Intention from Mindful Mathematics: The Encompassing Physicality of Geometric Clifford Algebra"

      Surprised by your comment of earlier today on my thread, that even tho I steered you in the right direction, here it is two days later you still don't get it.

      The only thing i can conclude from that comment is that you didn't understand what you read. The algebra of the physicist's S-matrix of figure 3 of our essay is GA. The wavefunction is comprised of the fundamental geometric objects of the geometric Clifford algebra of 3D space - one scalar, three vectors, three bivectors, and one trivector. This is pure Hestenes from his 1966 book, Spacetime Algebra, very basic stuff.

      Similarly, if one models interactions by taking the geometric products of wavefunctions, that yields a 4D Dirac algebra of flat Minkowski spacetime. Again this is basic spacetime algebra.

      If you take a look at this paper co-authored with Michaele

      "Geometry and Fields: Illuminating the Standard Model from Within"

      you might find it a little easier to see the connection between the math and the physics. It is deep, diverse, and incredibly precise - at the ppb limit of experimental accuracy on many calculations.

      Haven't rated your essay yet, hope to get to that soon.

      Pete

      Gary - went to rate your essay and saw I already did. If I remember correctly that rating pulled you up, from a 4.3 to a 4.8

      Pete

      Gary,

      Just a quick note. I promised comprehensive commentary -- working on it. Meanwhile, you might want to look into the work of this author:

      https://www.researchgate.net/publication/280499966_The_imaginary_unit_i_as_the_temporal_directional_component_of_the_complex_position_vector

      All best,

      Tom

      Hi Gary,

      The mathematician in you has brewed another lovely essay, but I personally still prefer 'Calculus 2.0'. I will not claim expertise on quaternions so I will pick my comments.

      Yes, I agree time is scalar. This is in keeping with the physics of Galileo and Newton.

      But calling the complex i, a dimension may be okay mathematically, but physically it will be a hard sell to me who have become wary of the wares that mathematical physicists peddle these days.

      What is the 'v' in your equation 2 and how is the value to be determined? You say it represents motion, motion with respect to what?

      Then, you give a role to the observer in the determination of mass in your 'prediction' segment. This looks like a Special relativity effect and must share in the flaws of SR theory.

      Finally, when you say that the Earth is moving at 0.006136c with respect to a true rest frame, is this a new prediction? The value is so much higher than the 370km/s speed relative to CMBR.

      Best regards and all the best in the competition,

      Akinbo

        Akinbo,

        Thanks for reading and commenting and hopefully for voting. The one-bombers have been significant in this contest.

        The previous essay actually led to this one. I tried to evaluate some problems in mechanics and found the results unsatisfactory. So I revisited the problem and multiplied by Euler's Equation one more time. That gave me this subset of octonions.

        Your skepticism regarding the complex i as a dimension is wise. I don't know if it is or is not. The only evidence I can provide is that the proton size calculation is accurate and that is only circumstantial evidence. Perhaps it is simply another coincidence or perhaps it actually means something else.

        The v in Equation 2 is absolute motion with respect to a fixed background. It is a variation on the abandoned aether concept. However, relative motion is more complex that what was previously considered and the motion of A with respect to B is not the same as B with respect to A. They are more like inverses ... by that I mean they are more akin to division ... 1 divided by 2 vs 2 divided by 1 as an example. So this puts SR into the hypothesis but in a different form than what we usually have. Maybe it is better, maybe it is worse. But it does contain a fixed reference frame.

        You are correct regarding the value of the velocity. Colin Walker also pointed this out. The value I present is almost exactly 5 times the CMBR value. My best guess here is something that I remember from statistics. There is a certain type of average where you divide a value by its degrees of freedom. In this case, that would be 5. I have not found the statistical reference that I am looking for regarding this yet but I am certain I have read it before. That will provide another clue as to the correct form of the math.

        Best Regards and Good Luck,

        Gary Simpson

        Dear Gary,

        With great interest I read your essay, which of course is worthy of high praise.

        You are absolutely right that «The q0 term must be added to the four-vector to produce an object or structure ... with a scalar term. The author will speculate that the scalar term is related to the vacuum energy/ The author will also speculate that it is possible for the scalar term to be a function of time.»

        I believe that it is provisions of yours that are the key to the answer about the self-organization of matter and to the question set by this contest.

        Your essay allowed to consider us like-minded people.

        You might also like reading my essay .

        I wish you success in the contest.

        Kind regards,

        Vladimir

          Gary,

          Thanks for the score & post which I've responded to. I've read yours again. My maths isn't adequate (I prefer dynamic geometry) but I do think I like scalar values for time, and I'm sure there's really no co-incidence but an important physical truth. May it be hiding in the windings of toroid pairs (3D helices when in relative motion) and the Gottfreid-Jackson angle?

          Refreshing my thoughts on Quaternions I delved back and came across these passages. I wonder if you can make any sense of them?

          "As reality is 3D, complexity may increase by the cubic function. Quaternions are non-commutative continuous field potential functions of two compound parts, real scalar and 'imaginary' 3D vector. We suggest that the 16 symmetry sets may be a handed hierarchy, seven (x2) rotational, one (x2) quasi-translational. Quaternions and Octonians may aid description of the evolution of the dynamic rotations and translation of complex 3D systems.

          and; .."The coherent kinetic power of a (twin vortex, single) toroid translating in air as a 'pressure gradient' form is significant and can knock down buildings, as this video.i But we must also consider from the torus rest frame, where buildings, EM waves and other forms, including complex toroids approach and interact. We suggest such interaction may be valid candidates to consider alongside quantum electron orbitals and 'shells for modelling collisions and particle 'decay' or perhaps rather 'transmutations'. Full 3D vector fields may be theoretically modelled using multiple quaternionic wave functions; s2 +x2+y2+z2 =1 (see 6.8). But we wish to focus here on the conceptual framework of obtaining the classical from the quanta, so need a slightly different approach and thought experiment; Consider the toroid bubble in motion at v through the water. We must always remember that the water may be a stream or flow, a la Fizeau, itself moving in relation to a nearby body of water or a riverbank, but here we only consider the local case. An emitter at rest in the water sends a one second EM signal towards the torus. The DFM predicts that there will be both a temporary trivial propagation velocity D, (at ~ANY orientation), and a permanent propagation angle rotation which is dependent on the lateral vector of the torus. The one second period will then also be changed, which is equivalent to wavelength being Doppler shifted and also to the signal time period being dilated or contracted. This change is purely kinetic and not accounted for in current interpretation."

            ...oops, wrong button!

            I'm sure I once made some sense of the above but now struggle a bit, can you?

            What I also struggle with is the 'absolute motion' you invoke. As an astronomer we've rather found better sense from the most recent data (including the Planck survey) in 'hierarchical' relative motions. Indeed George Smoot first derived that from WMAP for his Nobel.

            To pick just one as a start; Our galaxy is in motion within the local group (itself in motion in the cluster and that revolving around the filament), our local arm is in motion in the galactic rest frame and the sun is moving rapidly through it (witness the strong 'bow shocks' we find at each transition and the 'anomalies' NASA finds & allows for from Pioneer etc) and onwards both up and down. Background frames will then be 'local' not absolute, so the transform depends on how many stages 'up' the emitter was. Is that a problem? or helpful?

            On cosmic redshift, your prediction should be part correct, but with intervening frames to account for. a derivation without needing accelerating expansion and with helical expansion is here; Redshift Video.

            I hope you'll read my essay if you haven't. That also contains an important finding but what it really need is a mathematician with your knowledge to collaborate. Could you enumerate the dynamics identified? (3D extensions of pythagorus theorem).

            Best

            Peter

            Dear Gary,

            It is a pleasure for me to meet you again on fqxi. On my own forum, I posted a reply to your kind comment.

            I read your essay for the first time, needing ca. two days before posting a reply.

            Best regards,

            See you soon

            Peter

            Vladimir,

            Many thanks for reading and commenting upon my essay. I have read through your essay but wish to study it a bit more before commenting. I will do so soon.

            Yes, adding the scalar term to a 4-vector is really the mathematical essence of what I discuss. It produces a structure that fits the Kaluza-Klein Theory which combined electro-magnetism with gravity. Unfortunately, Einstein himself eventually concluded that Kaluza-Klein was not compatible with General Relativity.

            Best Regards and Good Luck,

            Gary Simpson

            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