Sorry to barge in at this discussion. I tend to agree with Colin. If the vacuum structure is face-centered-cubic (Kepler packing) of basic building blocks as I think we both agree it might be, then as a sphere gets smaller and smaller the surface will become 'stepped' or pixillated. Eventually you end up with just an icosahedron (?) and then a cube.

Cheers

Thanks Colin - I now remember our discussion of your paper last year. I have a feeling that GR is unnecessarily complex and should not be the 'standard' formulation of gravity, predictive as it might be. Einstein built GR on the basis of SR - tied up as the latter is with an observer-referenced paradigm. Is there an observer needed as a light beam curves around the sun? Without SR the equivalence of gravity with acceleration is enough to describe local linear gravitational density gradients in a flat space. Does that agree with your point (2) ? Again I could not prove that this will serve to replace all of GR but I suspect it might.

Best,

Vladimir

    Dear Vladimir

    My (and probably your) uneasy feeling about general relativity is that it is a top-down formulation. There is no doubt that GR is a complicated set of inter-relations, but at their foundation is one relatively simple equation which has passed every first-order test. This coupling of a simple model with predictive power is compelling in my opinion - so compelling that in the event of failing a second-order test such as LATOR proposed for the end of the decade, I would first try to finagle GR into satisfying the new observations.

    The term "frame of reference" might be more appropriate than the term "observer" which has a subjective connotation. GR has shown that it covers complicated weak-field cases which otherwise would be a hodge-podge. I think SR and the equivalence of gravity with acceleration are sufficient to model strong-field gravity in a flat space given idealized conditions of free-fall, which is in accord with my point (2) from the previous post. Perhaps this could be part of a bottom-up formulation of gravity.

    Colin

    10 days later

    Hello Colin,

    I enjoyed reading your paper. It was especially nice because quaternions and octonions are something I'm enthusiastic about. You'll see them mentioned in my essay, once it posts. But I feel like your essay wandered off topic a bit, and failed to end conclusively. I'm not sure you made your point.

    I think I probably have to read Nikkah Shirazi's paper - which I have downloaded - to understand what you mean at the end. So the relevance was not emphasized enough, and I see there clearly is some. But what you did write about, I enjoyed reading. Good luck in the contest, and enjoy interacting with the other authors.

    Have Fun,

    Jonathan

      Colin,

      If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

      Jim

      Hi Jonathan,

      Your observation about my essay wandering off topic is true. I learned about quaternions and the Higgs mechanism just as I was nearing the end and got completely side-tracked.

      The connection to Nikkah Shirazi's theory is a bit tenuous, but a promising one that seems obvious on looking at spectra of Pauli and Hadamard matrices. His premise is that there is 2+1 areatime existing as a superposition in our 3+1 spacetime. Areatime objects must be described "in terms of a superposition of all possible worldlines of the massive objects into which they can emerge" [from his 2012 essay].

      Now replace "massive object" by "resonance". What I noticed was that the zeroes of quaternion polynomials (those frequencies at which resonance can occur) differed in their dimensionality depending whether the underlying qubit was in a Pauli (real or 'actual') state, or in a Hadamard (superposed or 'actualizable') state. [Taking a quaternion as a qubit (u,v) with a twisted companion (-u*,v*).] While there is a clear and consistent difference in dimensionality, the sense is opposite what I expected - for example, in 3D spectra the zeroes of Pauli states require a plane while Hadamard states produce lines of zeroes (more convincing than 2D but not shown in the essay). Resonance requires inverting the polynomial, so considerations of dimensionality ought to be inverted as well. This notion of dimensionality applying to states of resonance is what I most want to show.

      I hope this gives a better idea of how my essay relates to Armin's dimensional theory. Looking forward to reading yours.

      Now if I can just keep the condensate off these Higgs goggles...

      Colin

      8 days later

      Thanks greatly for the comments Colin,

      Given the content; you might find a lot to like in the essay by Tom Ray, where he talks about fermionic condensates as a model for primordial spacetime. I hope you also get around to reading my essay, now that it has posted. As I said earlier; I mention the quaternions and octonions therein. I expect to be rating your work later today, after a brief review.

      All the Best,

      Jonathan

      Hi Colin,

      I've just sent you an e-mail about available references on quaternion Physics.

      There is a lot out there, and I've been sifting through it for a while.

      I've plenty to recommend or share.

      All the Best,

      Jonathan

      Dear Colin. Hello, and apologies if this does not apply to you. I have read and rated your essay and about 50 others. If you have not read, or did not rate my essay The Cloud of Unknowing please consider doing so. With best wishes.

      Vladimir

      Thanks for the comments on my page, Colin.

      I'm glad you enjoyed the Steinhardt lecture; I thought it was a lot of fun to watch him walk from one side of the room to the other, playing both defending and prosecuting attorney - for the theory he helped develop. I hope your research goes well, and bears interesting fruit.

      All the Best,

      Jonathan

      8 days later

      Dear Colin,

      I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

      Regards and good luck in the contest,

      Sreenath BN.

      http://fqxi.org/community/forum/topic/1827

      4 days later

      Dear Colin,

      I very mucjoyed your essay which also touches on the existence topic from the mathematical angle. This is understandable given your Bio. Mine is more from a logician's point of view.

      I am sceptical about the Higg's mechanism which you mention. But even if correct some of these issues cannot be fully resolved without the nature of space being put to rest. A 6 rating I think is fair on your essay not being a mathematician myself and being limited in this respect.

      Best regards,

      Akinbo

      *If you would be reading my essay, read the JUDGEMENT in the blog in the case of Atomistic Enterprises Inc. vs. Plato & Ors delivered on Jul. 28, 2013 @ 11:39 GMT. In that judgement points and monads turnout to be the possible bits. Thanks

      Hello Colin,

      I like the Quarternion approach. I have a theory based on the tetrahedron that partly unifies the four forces of nature and resolves the three paradoxes of cosmogony. Further it relates the relative masses of the proton, neutron and electron to 99.999988% of prediction.

      I like how you apply your approach to the Higgs field.

      If you get the time please take a look at my essay which deals with dimensionality of observation - perhaps hinting at Black Hole existence, but perhaps suggesting that the singularity can't destroy information and that eventually they release all information.

      I note above you had issues yourself accepting black holes and I think you're right to question them.

      Best wishes,

      Antony

      Hi Colin,

      Thanks for an intriguing perspective.

      > Quaternions arise from the solution of an elementary two-dimensional polynomial, and can be visualized in terms of amplitude and phase spectra by means of a multidimensional Fourier transform.

      I share your enthusiasm for quaternions and I advocate the use of Geometric Algebra. In my essay Software Cosmos you can see how these play into both the explicate world that we measure and also an implicate space. These two spaces (one observable, one not) might be linked via just such a Fourier transform.

      > Two forms correspond to slices through the octonion vector space and are essentially two-dimensional. The third form is a tetrahedron in three dimensions.

      > The Fano plane shows the seven imaginary elements of an octonion having seven sets of quaternion cyclic ordering given by three sides of the triangle (426, 635, 514), the three altitudes (473, 671, 572), and the circle of midpoints (123).

      Sounds like this would be useful in constructing models for quantum contextuality. Michel Planat discusses such models in his essay, including the Fano plane. My comment to Michel suggested he look at k-rational points based on Q(phi), the extension of the rationals by the golden ratio. The coordinates of a tetrahedron (and many other polytopes) would qualify.

      > I can imagine the picture of existence that emerges could be analogous to a quantum computer operating coherently in the Higgs condensate.

      I hope you get a chance to check my essay, as I think my picture nicely complements your views.

      Hugh

      Dear Colin,

      We are at the end of this essay contest.

      In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

      Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

      eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

      And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

      Good luck to the winners,

      And see you soon, with good news on this topic, and the Theory of Everything.

      Amazigh H.

      I rated your essay.

      Please visit My essay.

      Colin - a truly outstanding piece of work. I'm blown away with how few people have noticed the excellence of this essay. You just filled in a critical piece of the puzzle of a mathematical problem I've had for several years. Thank you.

      Kind regards, Paul

      4 years later

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