Boris,

Many thanks for reading and commenting upon my essay. I lack proper academic credentials. Therefore, I have no expectation of recognition. I simply hope to make a few people ask themselves a few questions ... is my calculation also a coincidence? Is there an alternative interpretation to the wave function other than the Copenhagen Convention?

I'm not so sure that I would dismiss quaternions and octonions as a dead end. The Maxwell Equations can be formulated using the quaternions. Therefore, the paradoxes that occur with Relativity might simply be the result of Einstein attempting to preserve Euclidian geometry when it is more appropriate to use a Geometric Algebra.

I will read and score your essay soon.

Best Regards and Good Luck,

Gary Simpson

Hello Gary

Congratulation

Karoly (It took 3 - 4 hours and finally after keeping the site open for an hour your I seen by accident it shown up. Is this site overloaded???

    Thanks Karoly,

    I don't think the site is overloaded ... it probably does not get a lot of traffic compared to most sites. I wonder if there is a problem with your hardware or connection. If I have a problem accessing something, I usually close all my windows and re-open them. Sometimes I also reboot my computer and/or my internet hub.

    Best Regards and Good Luck,

    Gary Simpson

    On this topic..

    There was some research, a few years back, showing that nuclear binding and half-life varied with the solar cycle and could potentially be used to predict sunspots. I think Ephraim Fischbach was part of the research team. I hope this helps.

    Regards,

    Jonathan

    6 days later

    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