Essay Abstract

Much modern theory tries to unify quantum theory with general relativity by making the model of space-time quantized. Perhaps instead the linear function model underlying quantum theory might be replaced with a nonlinear function theory based on geometry and variational calculus.

Author Bio

Name: Alan Hutchinson Birth: 1948 Nationality: British Education: MA, MMath (Cambridge); MSc, MPhil (Warwick) Employment: Programmer (1976-83) Lecturer, Computer Science (1983-85 at UMIST; 1985-2010 at KCL) Married with three children Interests include family, bell ringing, cycle touring, Alpine walking, Go, psychology

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  • [deleted]

Alan,

Congratulations, this is the first essay where the term soliton is used. I had made a statement about the lack of recognition of solitons in a comment to Peter Jackson's essay, topic 1330.

"Einstein developed his theories with 'incomplete information', because he, his generation, and all those preceding, did not recognize that the system we live in provides mechanisms for the efficient transfer of energy, and the soliton is one manifestation of the mechanism."

Even though solitons are being found in all types of processes, the cherished fundamental assumptions have not been updated to account for that "not unusual" wave phenomenon. Solitons easily mesh with an electromagnetic theory of gravity if the EM field has the proper configuration.

    Frank

    Thanks. I have been to meetings where authorities talked about solitons, and have read just a bit about them, but please don't regard me as an expert. They are undoubtedly pretty. Lots of good maths has emerged from the study of differential equations, and I expect there is more to be had from solitons, so it is a bit surprising that they have not excited more enthusiasm. Of course, I am not at all sure that the variational approach suggested in the essay will produce any solitons, but it is a possibility.

    Alan.

    Dear Patrick Alan Hutchinson,

    Absolutely delightful! It's hard to imagine one can pack so much into 9 pages and still be fun to read.

    I was intrigued by your non-linear quantum model, which has similarities to my own, based on a non-linear field, but linearized to allow Schrodinger equation. There are also geometric particle creation aspects of the model that I don't touch on in my current essay, The Nature of the Wave Function. Thus my physical waves cannot be added, but of course the probability amplitudes can. I invite you to read my essay and comment.

    Thank you for a very powerful essay -- Excellent!

    I agree with your conclusion and vote for the "or else" clause. I hope you enjoy my naive approach to this.

    Edwin Eugene Klingman

    • [deleted]

    Dear Edwin

    Thanks for your kind comments. There is a lot in your essay too, and before I shall be up to grasping it all I must read Bell and Christian, which I have never attempted. Christian's algebra looks like a combination of exterior algebra and Clifford algebra, so that much should be straightforward, but Bell's work sounds deep. You have clearly put much thought into it.

    Best wishes

    Alan.

    Dear Patrick Alan Hutchinson,

    Perhaps, the mutual distortion of two interacting particles from their point like description is indicative of the probability of string like existence of particles, in that Functional analysis in calculus of variations is applicable for the transformation and thus the gravity may be expressional.

    With best wishes,

    Jayaker

    Dear Jayaker

    Sorry. I don't understand this.

    Any "point like description" is not an aspect of the model. If ever a particle is perceived as point like, then this would be just what we fallible human beings sometimes perceive, no more. I think psychologists and neurophysiologists sometimes agree that our perceptions are just reflections of flawed representations in our limited brains of incomplete observations of selected aspects of reality. We sometimes perceive "points" when there are no point-like objects. If my proposed model has any similarity to reality then there will be no point-like features in any particles.

    I don't doubt that string theory is wonderful. I have heard a great man whom I admire talk about it more than once. Despite that, nothing has yet convinced me that it has any bearing on reality. If you like, you can look on my essay in part as my excuse for not spending time trying to understand it.

    Best wishes

    Alan.

    Hello again Jayaker

    Please forget most of the long paragraph in my last mail. It was written around midnight and I wasn't thinking straight.

    We do perceive particles as points, and in the essay I went to some lengths to conjecture why, and suggested that perhaps they really are small. If any of those conjectures are right, it will be because the partial differential equations for the connection and metric have such solutions.

    Best wishes

    Alan.

    Having just completed, but not yet submitted, I am in process of reviewing similar approaches.

    I am a simple aged educated swimmer from the "slide rule era", knowing only add, subtract, multiply, and divide with a reasonable understanding of geometry, ala Fuller's Synergetics and Physics.

    The fact that an inscribed sphere, tangent to the faces of a regular tetrahedron have exactly the same surface-to-volume ratio, i.e. boundary to different content content imply equivalent "activity" as free energy. This is a simple model to apply from particle sizes (unbounded) to massive (elephants and the cosmos) to many problems. All things have a frequency of existence for equal activities of matter and energy!

    Comment?

      Ted Erikson

      I too used a slide rule.

      The geometry in my submission is Riemannian geometry, the sort occurring in general relativity. Maybe I should have made that clear.

      Your remark about the sphere inscribed in a regular tetrahedron sounds quite subtle.

      Best wishes

      Alan H.

      9 days later

      Alan

      Frank cited my essay above in context with the soliton. But I find greater consistency with yours as the only other essay so far (I've read) to recognise and explain the importance of the detector as part of the process.

      I go on to explore a real ontological construction, with exciting results, but find only a simple mathematical description (see my end notes) of various relative kinetic cases.

      Long ago I found issues with maths and geometry. Motion is an invalid concept in geometry and I particularly challenged it's validity in algebraic vector space, where the word 'frame' is assumed as a 'wire frame' which can overlap with other in Cartesian systems. Using non point particles interacting, including with just waves, over non zero time resolves this. Space-time is indeed then 'granular'.

      In constructing the ontology with logic I can't express it mathematically, but am sure you can. In particular the nested mutually exclusive structure of truth propositional logic applies, along with an interpretation of the 'interleaved' modes of Propositional Dynamic Logic. (Each representing a discrete and equivalent 'Space time geometry'). Enough of mine but please do read, analyse (beneath the theatrical metaphors) and comment.

      I find the heart of yours in the paragraphs;

      "If the solution were known exactly at some instant before the interaction then a numerical calculation could reveal the free space states which the detectors would converge to afterwards. However, uncertainty is inevitable because we, our memories, and any possible measuring apparatus are part of the solution. No solution is capable of discovering and internally representing what it itself is.

      ...In every free space solution for a detector, either the detector has detected the quantum or it has not. After diffraction, the solution almost certainly converges to just one such set of overlapping free space solution because any other solution would be unstable."

      Please expect a top score from me if only for that. You should find my real local nature equivalent, and I'm quite convinced by the vast evidence I have beyond the essay that we have the key to the toe. (Many others here are also consistent).

      Very best wishes.

      Peter

        Patrick

        Too much excitement. Sorry for the middle name above.

        And just when I'd got head round slide rules calculators and computers arrived. I never did quite get my head round those!

        Peter

        8 days later

        Hello Peter

        Thanks for your kind comment. I have been away, and only just found it. Hope to read yours soon.

        Regards

        Alan (the name I usually use).

        12 days later

        Dear Alan,

        I like your excellent essay and appreciate your viewpoint. I wish you good luck in the contest.

        As you know, our community ratings will be used for selecting top 35 essays as 'Finalists' for further evaluation by a select panel of experts. There is a possibility of existence of a biased group which promotes the essays of that group by rating them all 'High' and jointly demotes some other essays by rating them all 'Low'. Therefore, any biased group should not be permitted to corner all top 'Finalists' positions for their select group.

        In order to ensure fair play in this selection, each participants in this contest should select about 50 essays for entry in the finalists list and RATE them 'High'. Next they should select bottom 50 essays and rate them 'Low'. Remaining essays may be rated as usual, if time permits. If all the participants rate at least 100 essays this way then the negative influence of any bias group will certainly get mitigated.

        You are requested to read and rate my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space".

        Finally I wish to see your excellent essay reach the list of finalists.

        Best Regards

        G S Sandhu

        • [deleted]

        Patrick

        I don't grabbed the essence of your essay .. maybe you'll understand my work.?

        http://fqxi.org/community/forum/topic/1413

        Hello Yuri

        Thanks for your note.

        I have looked at your essay, and you seem to be trying to do something rather different from what I tried to do. Your aim seems to be to fit all the phenomena which experimental physicists observe into patterns such as the ratio "3:1". If you can do this neatly, and in such a way that it lets people make predictions which can be tested, that will be an important approach.

        In broad outline, maybe I am trying to do something similar, but the details are very different. Where you try to fit numerical patterns, I am trying to fit patterns from Riemannian geometry and partial differential equations.

        I once studied in a department led by a lovely man called Jim Eels. When people asked him what he studied, he (I think) sometimes replied "Soap bubbles". The point about a soap bubble is that it is a solution to a problem which can be expressed by a partial differential equation, and in the set of all such solutions it has least energy. This is an example of a "VARIATIONAL PROBLEM". Variational problems and their solutions have been very successful in past attempts to describe physics.

        In this case, I am trying to guess what the right variational problem might be. The lovely aspect which gives me courage to submit this essay is that there are the two features called [math]i[/math] and [math]R[/math] which emerge easily out of algebra which other people have already discovered from the Riemannian geometry. With them, one can easily invent a variational problem which seems to have all the subtlety necessary to construct a unified field theory.

        That is the essence of my essay. Of course, it will all be useless unless someone can show that this variational problem really does lead to a solution which resembles what experimental physicists observe. I am a long way from checking that.

        Regards, Alan H.

        • [deleted]

        Alan,

        I have read and greatly enjoyed your essay. I have spent time attempting to construct computer models of Dirac's version of the electron. Computer models can attempt to show properties of the underlying algebra's. I was struck by your goal:

        "The objective of this essay is to try to shift the emphasis from SM and algebra to GR and geometry." and "How to make geometric models"

        based on

        "The only justification for the algebra in SM is that it fits observed patterns among particles. The algebra in D was invented out of geometry half a century before Dirac's work. GR contains no such algebra. It is essentially pure geometry."

        I would be interested in your comments on my model of a Dirac Spinor at essay 1306 (pg 6), it also includes a link to a video animation to better display its properties.

        I became interested in this model (a blue electrical loop surrounded by a perpendicular torus of red magnetic lines) where one turn of the blue loop only represents 1/2 a turn of the red loop, producing an object with 720 degrees of freedom (it looks upside down after turning 360 degrees).

        Would you consider these types of models legitimate geometric models of your algebras?

        Many Regards.

          Mr. Hutchinson,

          I enjoyed reading your essay. I too advocate geometry as means of better understanding based on visualization of underlying processes in physics. One thing that remained unclear to me in your essay is the number of dimensions in the geometry you propose. And by the way, what do you think of Octonion Algebra? As for me, I offer a geometrical model of space and show that the addition of just one spatial dimension, the 4th, dispels most paradoxes that plague physics today. My vision is purely geometrical and my approach is top down, based on the hypothesis that 4D configuration corresponds to the lowest energy state for the dynamic structure of space. I would very much appreciate your feedback.

            Hello Ed

            Thanks for your note. It is nice to hear you enjoyed it. I looked at yours. I was not able to get the full sense of it because some of your very careful pretty graphics use "flash" which is not open source software, so I have not installed it on my PC.

            Parts of the accompanying text read much like the Bohr model of atomic structure (see Wikipedia for an outline). Since Bohr published it, I think quantum mechanics has gone through two substantial revisions. In the first revision, electrons (and all other particles too) were represented by waves, rather than as small points. In the second, the nature of the kind of measurement which can be made on the force fields between particles was changed. In the Bohr model and its first revision, all measurements of properties of the field just provided a numeric value. After the second revision, any such measurement might cause a change in the field.

            Anyone who can write a program which faithfully models this kind of idea is doing the rest of us a service. I think you are undertaking an ambitions poject.

            Best wishes

            Alan H.

            Hello Ms Vasilyeva

            Thanks for your kind remarks.

            Throughout my essay, I stick to the traditional notion that we are in a space with 3 space dimensions and 1 time dimension. Four space dimensions are very different from three, and three suffice for all I want to write. For instance, it is not possible to tie a knot in a piece of string in 4 dimensions. Other funny things happen, e.g. there are many different versions of the notion of smoothness in 4 dimensions. All this makes good fun for mathematicians. The same goes for quaternions. They are well worth studying for their own sake, but as yet I don't know of any reason to suppose they will help to illuminate physics. I may be completely wrong about this.

            Best wishes

            Alan H.