Thanks, Fred.
The Mathematica code is indeed quite compact. It also shows how powerful Michel's simulation is. In less than million runs it generates an almost perfect cosine curve. It beautifully complements Chantal's simulation, and puts the final nail in the coffin of Bell's theorem.
Best,
Joy
Much has happened since 2012. At least four explicit, event-by-event, computer simulations of my local model for the EPR-Bohm correlation have been independently produced by different authors, with codes written in Java, Python, Excel Visual Basic, and Mathematica. I discuss two of these simulations in the appendix of the attached paper. A compact translation of one of these simulations (from Python to Mathematica) can be found here.
Each simulation has given different statistical and geometrical insights into how my local-realistic framework works, and indeed how Nature herself works. The original simulation written by Chantal Roth, which is most faithful to 3-sphere topology, may appeal to more geometrically inclined, whereas Michel Fodje's simulation, which has its own unique features, may appeal to more statistically inclined. In the end, however, all of these simulations, together with the original analytical model, confirm what I have been arguing for, for the past six years. The full details of my argument, which concerns the topological origins of quantum correlations, can be found on my blog.
Joy et al,
"The original simulation written by Chantal Roth, which is most faithful to 3-sphere topology, may appeal to more geometrically inclined, whereas Michel Fodje's simulation, which has its own unique features, may appeal to more statistically inclined."
This is what I find the most convincing evidence, that a simulation of a continuous function is a continuous function. Regardless of whether one assumes continuous geometry, or discrete points, correlated and anti-correlated values are locally neighboring elements. That is, no matter how apparently entangled two discrete points of a measurement function may appear -- at any distance scale -- random input correlates the entire wave function to an equilibrium state at every distance scale.
In other words, both evolving discrete particle states (Fermi-Dirac) and static geometry (Bose-Einstein) are reconciled to the same unitary and dynamic spacetime.
The implications go far beyond local microscale quantum correlations of the kind described by Bell's theorem. The quantum and classical measure domains are not independent at any time-distance scale.
Ever since the '30s, researchers have tried to find a transition schema to describe where the discrete measures of quantum theory become a classically smooth function. If such an intermediate function is simply the classically random input that we call quantum decoherence (Zeh, Zurek), then all the fundamentally classical wave interactions (reinforcement, destruction, interference) are represented as nonlinear input to the linear order of particle states.
All best,
Tom
Hello All,
I have attached some notes on Bott Periodicity and Cli fford Algebras from Kyler Siegel, which are of general interest or relevance to this forum topic, but also partially answer the question raised by James Putnam above. He asks if I am talking about "'spaces', in addition to but external to our observed universe" and I must answer that instead it only appears that our universe has 3 Euclidean spatial dimensions plus time, because of the way objects are embedded in spacetime, which relativists see as a curved fabric. And what Joy proposes is that this 4-d fabric is topological, with a geometry that is non-commutative.
Instead of being external to the universe; perhaps the higher-dimensional reality is what underlies or gives rise to the appearance of 3-dimensional objects and space. The thing about parallelization is that it gives the fabric a particular weave - a specific warp and weft for any orientation of a suitably situated observer and/or apparatus. This also produces what appear to be non-local quantum correlations. Of course; if the universe has a parallelized topological fabric, this also accomplishes flatness, and so gives the universe the appearance of a Euclidean local geometry. The paper explains why only specific geometries accomplish this.
I think that is what Joy is talking about.
JonathanAttachment #1: BottPeriodicityAndCliffordAlgebras.pdf
I think this will help too..
I attach the slides for Michael Atiyah's lecture at the Simons Center, that covers some of the same material as his talk at the IAS which is referenced by Joy in the introduction for this thread. This speaks to the question of why higher dimensions and higher-order algebras are a part of the natural order. It will also help to explain why some of what Siegel says in his notes above is important stuff to Physics people - or should be.
Regards,
JonathanAttachment #1: 20101103_Atiyah_-_From_Algebraic_Geometry_to_Physics.pdf
Hi Johnathan,
I don't agree with slide 17 in the first attachment above. I believe octonions are necessary for the triality (3-handedness) in the QCD (strong) sector. Gravity is emergent from the Standard Model if interpreted correctly.
Best,
Fred
Let me add a light-cone picture to make this clear:
Oh, well. The picture is too small to see that the initial state (e, t) defined by the set above is in the backward light-cone of both Alice and Bob, and every particle in the state (e, t) ends up being detected by either Alice or Bob, with 100% detector efficiency.
Jonathan,
Thanks for the lovely slides. Makes me wish I had been at the lecture.
I want to pick one nit with your post -- quantum correlations never appear nonlocal. Nonlocality is an assumption of quantum mechanics, to describe results of "the experiment not done" that supposedly imparts action at a distance.
Delighted to see that Sir Michael Atiyah addresses the necessity to incorporate both retarded and advanced solutions to the wave equation.
Best,
Tom
Excellent remarks..
I think the retarded and advanced solutions correspond with the warp and weft in the comment above, Tom, or align with the fabric to give it a specific weave. I agree with Fred's remarks regarding octonions and QCD and I would add that strong force binding and gravitational attraction may be the short-range and long-range manifestation of the same force, which would necessitate such a linkage.
And in reaction to your other comment, Tom; I think the assumption of non-locality by QM folks, as an explanation for correlations at a distance, is perfectly sensible - if one ignores the possibility that the fabric itself could be non-commuting - but appears naive when it is seen that a non-commutative spacetime geometry is actually natural or reasonable.
Again; it's that darn point at infinity which is not correctly reckoned for. In effect; it is the far edge of the universe that sets the local scale of objects. But to think about things this way turns our perceptions inside out, or makes us see the fabric of spacetime that way, when one needs to see that fabric from the outside in - to know its nature.
Regards,
Jonathan
Hello Joy,
Good to hear of the computer simulations confirming your results! Shouldn't it also be possible to confirm this experimentally? From what I understand of your results you mathematically show quantum correlations to be dependent on the geometry of the experimental apparatus. While Bell assumes a "flat" geometry you use "spheres". Any way such design be tested confirming your predictions?
Best wishes,
Constantinos
Hi Constantinos,
Glad to see you are still following this debate. It is indeed good to have several computer simulations confirming my model and its predictions. If nothing else, they prove the critics of my work wrong, as Tom points out.
In the end, however, a computer simulation is only a model of the real thing---a numerical model. Even my original analytical model is just that---a mathematical model. So you are quite right to raise the issue of a real experiment. I have indeed proposed an experiment to provide a final decisive test of my argument against Bell's. Please see section IV of the attached paper for details. Conceptually the proposed experiment is very simple. And it would cost no more than 200,000 dollars---which is peanuts compared to the amount of money required for experiments these days.
Best wishes,
I wanted to add to my comments above..
It is common to assume with higher dimensions, that they are somewhere 'out there,' when the reality is that this notion only works up to a point (~5.25-d) and after that adding more dimensions makes the array smaller, or more compact - at least until we reach 24-d.
So rather than being something 'out there,' higher dimensions could be 'in here' instead. This actually corresponds to the fact that the algebras and spaces are first non-commutative, and later non-associative as well. So our common notions of size and distance, and then of interiority/exteriority, become invalid. This explains how the higher-d reality can be situated 'in here' rather than 'out there' "external to the universe."
All the Best,
Jonathan
Joy,
If I had $200,000 to spare I would have gladly made that investment for science. Perhaps SciAm or other well funded sponsors may seize this opportunity to contribute to the betterment of mankind! Does anybody out there have $200,000 to sponsor the future of physics? Bill Gates? Buffett? Elliason? Anybody? If there are funds for fqxi essay contests, why not for real experiments?
Constantinos
Hi Jonathan,
"..the fact that the algebras and spaces are first non-commutative, and later non-associative as well."
I believe you have it backwards from what Nature actually did. I will say it again this time with some more explanation; In the beginning there was no math (rules), then came sedonions, then octonions, then quaternions, then complex rules, then finally the rules for real numbers. Easy to see that the order here is from no rules to the most math rules. Take a bunch of massless point-like entities and let them go in a complete void that has no math rules to start with. The only property that the void has is it is a stage for the actors. You basically end up going from "infinite" dimensional to 4 dimensions. I will explain more if necessary.
Best,
Fred
Ah So,
Yes you have it exactly right, and I understand - mostly. The point I was making was to clarify that as we move toward discussing higher-dimensions, they need not be seen as something 'out there,' apart from the universe. And accordingly; it is the absence of the rules of commutativity and associativity that mess with our ability to apply the convenient distinction between near and far, or inside and outside, respectively - so that is what makes those dimensions appear compact or within instead.
I like your construction Fred. But I would argue that what you are really talking about is the upper bound on dimensions that shrinks as more rules are applied, and that there is a lower bound at each stage as well. One thing Ray Munroe insisted on that I agree with is that, geometrically speaking, both the minimal case and maximal or extremal cases must be considered as bounding conditions of reality, if we are to completely make sense of things.
All the Best,
Jonathan
Hi Jonathan and Fred,
Let me try to re-express what I think Fred is saying. Having no math rules in this context means having no algebraic rules. Then nature said, let there be sedenions---which is an algebra, so certain algebraic rules---or algebraic restrictions---emerged, but the resulting algebra, being non-alternative, non-associative, and non-commutative, is still pretty structure-less. Or it is structure-full, but not as we know it, because with sedenions we can divide by zero! Then nature decided to drop the zero devisors, and we are left with the division algebra of octonions, which emerged as massive restriction on the sedenions. Next, nature imposed associativity, leading to quaternions, then commutativity, leading to complex numbers, and then unital-ity, leading to reals. Each stage requires a massive restriction on what is possible. Sadly, Bell and his followers are forever stuck on the flatland of the reals, while most of what we know about nature is played out on the 3- and 7-spheres of the quaternions and octonions.
Best,
Joy
I should add..
I agree precisely with your main point above Fred. While people have a hard time imagining a blank slate being a higher-dimensional space, it makes sense that having no rules would allow just that. And one can certainly assert that specific arrays of dimensions would appear as rules were formulated or instated. The sedenions set the stage, or engender the possibility for further evolution, and S15 has only one fibration, yielding O, H, C, and finally R.
So yeah; the Reals are in a way an end product of a process that began with the Octonions, or arguably before that.
Regards,
Jonathan
Thanks Joy,
Glad to see you chime in, and your clarifications of course make sense of things.
Regards,
Jonathan
Yes, thanks Joy,
Since your great discovery of the origins of quantum correlations, we have to take very serious now the aspect of extra spatial dimensions over the 3 that we experience on a daily basis so what I am proposing makes logical sense to me based on the division algebras. Funny that we discovered them in basically reverse order of perhaps how they naturally happened. Of course that "happening" could have been very fast. :-) Maybe there is a clue in this somehow to make all of physics fit together.
Best,
Fred
