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]

  • Post #17

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.

      6 days later

      Dear Alan,

      I enjoyed reading your essay, which I think is both well-motivated and well-explained. I have a couple of questions/remarks.

      1. Like you, I tend to find certain aspects of quantum theory and quantum field theory less well-motivated than relativity, which is based on simple physical principles. In particular, even in ordinary quantum theory, I am not very fond of the Hilbert space/operator algebra view, which takes things for granted that are convenient mathematically but physically dubious. I prefer Feynman's sum-over-histories viewpoint, even though the math is harder, because the physical ideas are clear and refer only to entities with obvious physical meaning.

      2. Have you read the essays by Torsten Asselmeyer-Maluga and Jerzy Krol in this contest? They together propose new methods of trying derive quantum gravity from smooth manifolds alone. I find their ideas interesting, but I will warn you that their approach is not something that can be fully understood the first time through, at least not for me. Anyway, since you focus on theories based on geometry, I thought you might find them interesting.

      3. There are some interesting new ways in which Hopf algebras are showing up in quantum information theory these days, which is rather striking for something with essentially a geometric origin. There is a preprint about this by Sasakura, and I have written some about it myself, although unfortunately it isn't in any shape to publish yet.

      Paradoxically, although my mathematical work involves mostly manifolds and algebraic varieties, my ideas about fundamental physics are quite different. I suspect that manifolds are "too good to be true" physically because of their special order-theoretic properties and the fact that they imply things like nonmeasurable sets. My view is that manifolds have dominated physics historically mostly because they are mathematically convenient, much like Hilbert spaces are mathematically convenient for quantum theory. However, a lot of the papers I have been reading lately are causing me to reconsider this, and I like to keep an open mind.

      I prefer to try to build fundamental physics from more primitive notions like causal relations, which lend themselves to information-theoretic and even computational approaches. I note from your bio that you taught computer science; it's a bit ironic that a mathematician such as myself would try to think about physics in terms of information theory, while a computer scientist would think about it in terms of geometry!

      Anyway, I enjoyed reading about your work! Take care,

      Ben Dribus

        • [deleted]

        • Post #23

        Dear Patrick,

        I read your essay with interest. I too have taken a Geometric approach. However, unlike yours, it concerns very simple Geometric relationships leading to trignometric expressions between related phenomena. It makes relativistic phenomena quite understandable visually. I am sure you would like my essay

        The gist of my essay: http://fqxi.org/community/forum/topic/1549

        1. It identifies the PRIMORDIAL Foundational Problems in Newtonian Mechanics (NM) that runs through ALL BRANCHES OF PHYSICS. (Please see the short attachment "Primordial Foundational Problems").

        2. It eliminates the problematic concept of POINT-MASS (common to NM, QM, SRT) to allow internal structure for a particle. This in turn enables to resolve the other interconnected primordial problems.

        3. The result: By taking these two steps, ALL THE EQUATIONS OF SRT are DYNAMICALLY derived by identifying the trignometric relations within the energy-momentum equation, and by restoring Galileo's principle of relativity. (I request you to have a glance at the attachment - "Geometrodynamics of Energy" to verify this claim). - See also comment by L.B Crowell below.

        4. This achievement will establish that I have not just treated these problems at the level a speculative discussion as in other essays, but that the problems discussed are real problems, by virtue of their solution leading to the unification of NM and SRT (by finding an equation of motion which is equally valid for slow and very fast motions).

        Here is the impartial comment made by Ben Dribus (essayist in no 2 position): "One thing I will say is that it appears as if you made an honest effort to answer the question posed by the essay contest rather than just writing down your favorite ideas about physics. You will notice that I made a similar effort..... I am not sure why it was rated so low, but my impression is that many authors automatically rate other essays low to boost their own standing".

        Here's the comment made by LB Crowell (essayist at no. 20 position): "The calculations I just looked at and they seem alright. ...... Your procedure appears to be some euclideanization of relativity. At the end you arrive at equations which are the same as special relativity".

        In order to enable follow up of your comments easier for me, I request you to reply to this under my essay : http://fqxi.org/community/forum/topic/1549

        Best regards,

        VirajAttachment #1: 2_Primordial_Foundational_Problems.docAttachment #2: 2_GEOMETRODYNAMICS_OF_ENERGY.doc

          Dear Peter,

          Thank you for your remarks on my post. I very much enjoyed reading your essay. The idea of an asymmetric component of the metric [possibly implemented through non-commutative geometry] leading from classical to quantum dynamics has always been fascinating for me. I have played around with it in some of my simplistic papers, but without much success yet. More promising, as of now, seems to be the the theory of Trace Dynamics developed by Stephen Adler and collaborators, which seems to have strong elements whereby noncommutative classical dynamics gets connected to quantum dynamics.

          Regards,

          Tejinder

          Hello Ben

          Thanks for your note. Some (maybe) short responses:

          1. Describing states with functions in a Hilbert space does not of itself worry me. The functions are functions on space-time, which seems to be what is wanted if particles are diffuse. The problems arise when one tries to combine this kind of account with GR.

          2. Asselmeyer-Maluga's essay is not easy reading, but it is an eye opener. I have looked at a few of his papers on arXiv, and at a summary of a book cited in one of them. The idea that matter arises through exotic smooth structures appears at first outlandish, but the effect of the sort of surgery he considers on connections seems to fit rather neatly with Einstein's notion of matter in GR. I am as yet far from understanding it all properly.

          3. Hopf algebras seem to pop up in lots of places.

          It will take a lot to disconnect physics from manifolds, after the success of GR. I like manifolds. Have you seen John Milnor's little book: "Topology from the differentiable viewpoint"? I read that long ago, and was hooked. The only caveat is that he says nothing about differential forms. I ought to have understood them too.

          bw

          Alan H.

          Hello Viraj

          Thanks for your comments. As there are so many submissions, it is hard to know where to start reading. I have been trying to understand Asselmeyer-Maluga's ideas. I don't know if his essay will be the winner, but certainly there are enough new ideas in it to keep me occupied for a few months. A lot of the fancy maths which gets talked about seems to be just that. He and the other writers he cites make it seem that the notion of exotic smooth structures could fit neatly into GR. Have you looked at his work?

          As to assessment: it does seem to give each of us reason to not vote as perhaps we should. I don't know what to do about it. Maybe just live with it, and vote with one's heart. It is a bit like the prisoner's dilemma.

          bw

          Alan H.

          Dear Alan,

          I never read that one, which is funny seeing that I've read a fair bit of his other work (K-theory, etc.) But I would consider myself "hooked" as well, at a mathematical level: I like Griffiths and Harris's Algebraic Geometry (complex manifold viewpoint), and Spivak's 5-volume set on differential geometry is good. Claire Voisin has written two excellent books on Hodge theory and complex algebraic geometry. I also like Hatcher's algebraic topology and Adams' old book about spectra. I think Carroll, Wald, and Hawking and Ellis are all good for GR, though at different levels. These days it seems more and more profitable to look for material online, however.

          I agree that "it will take a lot to disconnect physics from manifolds," but "disconnect" is a rather strong word. To believe that manifolds are an immensely useful and astonishingly accurate tool (given their highly idealized properties) to use for physics is not incompatible with a recognition that they also raise some serious issues, which always seem to arise precisely in regard to those properties which seem least physically relevant. In criticizing manifolds as fundamental, I probably come across as much more "anti-manifold" than I actually am.

          By the way, there are some other contributions from the "pro-manifold forces" here which you might enjoy if you haven't already read them: the shape dynamics essays (Barbour, Gryb/Mercati, Alves), the "desingularization" paper by Abhijnan Rej and the "singular" one by Cristinel Stoica, and of course the one by Krol that I mentioned before.

          Anyway, I am sure manifolds have a lot more to offer physics, regardless of my opinions! Take care,

          Ben

          Dear Ben

          Thanks for your note of this morning. In particular, thanks for all the references. Someone once offered to get a copy of the 5-volume Spivak set for me, and I didn't take him up. I should have done.

          In particular, thanks for the suggested reading list of other essays. The range of contributions is enormous, from no maths to the wildest ideas, right up to topos theory. I am just looking at the one by Abhijnan Rej, which seems to touch on the theory of infinite Galois groups and, perhaps, something called the Krull topology which was the subject of the very last lecture of a course which went beyond the syllabus of the final year of my first degree. Out of a large class, only 5 or 6 of us attended it.

          Much of it is wonderful stuff, but what all this might have to do with physics mystifies me. It seems that one can get a very long way with just the ideas underlying the theories of Einstein and Dirac: a 4-dimensional Riemannian manifold, and the algebra derived from its Riemannian structure, and maybe a variational principle. Anything beyond that counts as good clean fun, but not physics until there is evidence otherwise.

          bw, Alan H.

          • [deleted]

          • Post #29

          Dear Alan,

          I agree with you about the role of geometry in physics. Indeed, bundles over manifolds, having as fiber various structures, are responsible for much of the progress attained so far, and even more is expected to come. Quantum mechanics too has much to gain from geometry, which indeed may be the connection between QM and GR. I sketched somethign about this in these slides. Congratulations for the essay and good luck with the contest.

          Best regards,

          Cristi Stoica

            Dear Cristi

            Thanks for reading my essay, and for your kind remarks on it, and for the link to your slides which I have read. Quite apart from your discussion, they taught me some physics I didn't understand before.

            My immediate reaction is that your conclusion "indeterminism exists only in the initial conditions" sounds almost right. Maybe one might add that this indeterminism will never be resolved by us poor mortals 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". One aspect of this is that, in this universe of which we are part, no computer can have more gates and memory cells than there are elementary particles. We cannot construct a computer which will extrapolate numerically from any given possible initial condition with unlimited precision.

            Best wishes, and trusting your slide presentation will be well received. Alan H.

            4 days later

            If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

            Sergey Fedosin

            Write a Reply...