Hello Tom

I read your essay twice and am still not very clear about what you are saying. The fault is entirely mine - for example a lack of background in the type of mathematical/logical arguments you used. Another reason is that at my age (73) I was reading not to explore new ideas, but to confirm my own half-cooked ones in a view to develop them further! For example, based on my Beautiful Universe Theory concepts I think there is no inherent probability in Nature, nor is there particle-wave duality, no wave function collapse (which you agree with) and that Bell's Theorem only confuses the issue. At least about the latter I can point to Edwin Klingman's essay here for a more substantive analysis than my one-liners. In my essay here I argue that in a causal local absolute discrete Universe mathematics and physics reduce to the same thing - not themselves, but the micro structure of Nature itself. As always I value your feedback.

With best wishes

Vladimir

    Hi Vladimir,

    I always enjoy your essays. They are delightfully illustrated, meaningful and fun to read.

    Our views of science are diametrically opposed, though. I do not subscribe to the idea that if we just look at the evidence of nature in new ways, all will be clear and obvious. This trendy new philosophy (some call it "embodied cognition") is actually as old as Aristotle and completed by Kant and Wittgenstein. In extreme contrast:

    I am a rationalist.

    To me, the universe only becomes beautiful (or even comprehensible) by demonstrating correspondence -- between the language by which the universe is described, and the mode in which it is experienced. If one wishes to join language to experience as if they were identical, I don't think one is doing science at all. At least, it isn't the science we practiced for over 300 years between Newton and Einstein, as a rationalist enterprise. So when you say:

    " ... although the concept of flexible spacetime 'works' in (SR) and (GR), and that of probability waves 'works' in (QM), they are just mathematical ideas that must be discarded if better models closer to nature can be found ..."

    ... it does not relate an iota to what I think of science, and that is probably why you don't understand the essay.

    Just as you prize your graphic art (and I prize you for it -- your work is extraordinarily graceful and rich with beauty), I prize the art of mathematics as highly as I prize natural language or any other art. It's a knife to my heart when you write:

    "This is more than just a way to seek more elegant theories: understanding nature at its own level is a necessary step to pave the way for further theoretical, experimental and technological discoveries."

    Mathematical theories are independent of experiment and technology. We and our mathematics *do* live at nature's own level, which is why mathematical physicists seek to understand the language of nature, rather than being satisfied with the nature of language. The former speaks to existence on its own terms; the latter fetishizes existence and language. Here's why I think as I do -- you write:

    "The human brain evolved over millions of years in organisms that interacted directly, causally and locally with inanimate nature on a molecular scale15. Is it too much to ask now that our understanding of Mother Nature should also be as simple, direct and realistic as possible?"

    Well of course, I would answer "no." Naive realism driven by direct experience has no independent correspondence to language. The metaphor Mother Nature itself is an anthropomorphic conceit -- when we fetishize the brain as a creation of the mother, we limit our capacity to participate in our own continuing creation. We become alienated from ourselves, and tend to invest the meaning of our existence in such things as technology, artifacts rather than art.

    I admire the honesty in your art, Vladimir, as I admire the honesty in your person. I hope to return the favor. I am younger than you by only 5 years; maybe it's a characteristic of our generation. :-)

    I don't rate essays that I don't understand, nor do I downrate essays that I disagree with. I trust that ethic in you, as well.

    All best in life, and in the competition,

    Tom

    4 days later

    Hi Tom,

    I have printed out your essay and I am going to study it on my next lie down rest my back break. :-)

    Looks like you have been busy here but thought I would inform you if you don't already know that the core part of Joy Christian's model has been proven by Albert Jan Wonnink via the computer program GAViewer. For those interested look here.

    Looks like FQXi's panel of experts were very wrong. But you already knew that.

      Fred,

      I didn't know the latest -- though I knew it was in the works -- and that is really great news! Like you, I have not doubted Joy's framework for a long time now.

      Thanks for the update.

      (I have arthritis, so I relate to back pain. Calm down, take it easy and feel better!)

      All best,

      Tom

      Yeah, it is rather sad that Gill seems to not realize that he has lost the debate since Albert Jan's computer proof of Joy's model. He quite frankly is carrying on like it didn't happen. Maybe some day he will understand geometric algebra and what Joy's true big discovery is. I'm not holding my breath though.

      I would not hold my breath Fred..

      Let each out breath inexorably lead to an in breath, then vice versa, and so on. That each inward path leads to an outward one, and outward to inward, is a suitable imitation of the connectedness of S3. I too enjoyed your summary, Tom, and I have to wonder what it would take - because it appears Gill's criteria are a moving target, just as he claims for Joy.

      It is ironic that RG wants to use Joy's first paper as the bellwether, given that it is only a sketch of the full proof, and that he has ignored that Bell's first paper contained an error that was later glossed over or corrected - as clearly pointed out by M. Goodband. I think perhaps Joy's use of the Kronecker delta is partially at fault; it is a convenient but lossy abbreviation that leaves too much room for interpretation.

      More later,

      Jonathan

      An enjoyable essay Tom..

      It took me a while to work through this paper, but it appears your logical reasoning is solid, even though I found some portions confusing. There is a lot I agree with, though it runs counter to prevailing opinion. I especially like that you wove Euler's equation into the story in such a meaningful way. I'll likely have more to say, but a ratings boost is all for now.

      Regards,

      Jonathan

        Thanks, Jonathan! We agree more than we disagree, actually.

        I think Euler's equation is the real center of the mathematical universe -- the origin of arithmetic and geometry.

        All best,

        Tom

        Hi Jonathan,

        Good to hear your take on this. I do believe that the proof Albert Jan did was all done analytically here on FQXi in the debates of the past. But now there is proof via a geometric algebra computer program that Joy's classical realistic model does in fact produce the prediction of QM, -a.b.

        FQXi is going to have some real embarrassment to deal with in the not too far future concerning their so called panel of experts that claimed the model was wrong. The model works as advertised.

        Hi everyone

        I see there is some discussion here of Albert Jan Wonnink's GAViewer program with which he attempted to verify one line in the first "Bell refutation" paper of J J Christian ... from way back in 2007: quant-ph/0703179

        He immediately ran into Christian's trademark algebraic error. This is the (-1)^2 = -1 error which Christian needs in order to make embarassing bivectorial terms cancel out of his "correlation" (the answer has to be scalar, right?).

        Of course it is easy to "fix" that mistake locally, by an ad hoc subtraction of what you don't want to have. He shows what you have to subtract to Christian's (17) in order to make the left hand side equal to the right hand side.

        What Albert Jan *didn't* do is simulate the whole model. His computer program verifies a patched version of formulas (17) and (19) of quant-ph/0703179. So on the one hand, he shows that Christian's original math was wrong. On the other hand, he still has not checked whether the patch which he introduces to fix the gap between LHS of (17) and RHS of (19) is consistent with the rest of the story. After all, if you change the very definition of geometric product locally in one formula in a complex story, that might have repercussions elsewehere, right?

        In fact, Albert Jan hasn't addressed the challenge yet of actually generating the measurement outcomes A_n(mu) of Christian's equation (16). Most readers, on a superficial reading, would suppose that (16) was a definition of the two measurement functions A(a, mu) and B(b, mu). However if you read carefully it is not a definition at all: in order to make it a definition one still has to specify the mapping from bivectorial measurement outcomes to {-1, +1}. Many are possible. None, of course, can deliver the goods ... because of Bell's theorem.

        It's at this point that one sees the other major error in Christian's attempts to refute Bell: he computes some kind of bivectorial correlation between the outcomes represented as points in S^2, instead of the correlation between the corresponding values +/- 1. Bell is about experiments with binary outcomes. His "correlation" is just the probability that Alice's outcome equals Bob's, minus the probability that it doesn't. Quantum mechanics predicts probabilities; experimentalists observe relative frequencies. The problem is how to explain the relative frequencies?

        In Christian's one page paper, four years later, it is clear that he has seen that there was something missing. He does give a definition of the measurement outcomes and now comes up with his daring bivectorial Pearson correlation instead of the "straight" correlation between the binary outcomes. After all, the labelling of the outcomes +/-1 is just convention.

        His definition of the measurement functions is A(a) = -B(b) = +/- 1 (with equal probabilities for the two possibilities). Thus his model predicts that the correlation is -1. Bob's outcome is always opposite to Alice's.

        "Out of the frying pan into the fire".

        I have written up a postmortem which includes a tutorial section on geometric algebra, so that no one has any excuse any more not to be able to work through the math of these classics, line by line, and check everything for themselves.

        http://www.math.leidenuniv.nl/~gill/GA.pdf

        Amusingly, I was not allowed to post this on arXiv.org: it was seen as a personal attack. I must say that my earlier drafts had a title which was a little bit over the top. Now the paper is simply entitled "Does Geometric Algebra provide a loophole to Bell's Theorem?". The answer is of course, "no".

        Showing that geometric algebra provides an alternative and beautiful way to describe the maths of spin half, including several spin half particles, entanglement and all that, was one of David Hestenes' greatest achievements. Two whole chapters are devoted to this topic in the textbook of Doran and Lasenby. They are worth careful study.

          Hi Richard,

          Thanks for dropping by. I'll be happy to entertain an exchange here, if it remains collegial.

          Your arguments vis a vis Christian always come back to, " ... because of Bell's theorem." Yes, of course, we know that the literature assumes quantum entanglement, such that spin zero decays to spin - 1/2, 1/2. Because you don't acknowledge that quantum entanglement is no more than an assumption, your argument does not even address the issue of an alternative measurement framework.

          Christian, on the other hand, HAS constructed a measurement framework -- published last year in the International Journal of Theoretical Physics -- that purports to demonstrate quantum correlations are NOT " ... because of Bell's theorem." Since one can't demonstrate constructively that the mathematical proof of Bell's theorem is independent of the experimental protocol -- any scientist should welcome an *objective* test that eliminates ad hoc assumptions.

          That is what my essay is about -- the possibility of rational correspondence between mathematical model and physical result. Such correspondence cannot be shown valid, without demonstratiing independence of mathematics and physics. Otherwise, one appeals to mystical, non-realistic explanations for correlated phenomena. Should one prefer realism over mysticism? -- a rationalist is so compelled. If science is a rationalist enterprise, science is also so compelled.

          Your interpretation of Joy's application of geometric algebra is wrong, and the answer to your title question is "yes." You have neglected Hestenes' interchangeability of geometric algebra with Minkowski space, as well as the topological property of simple connectedness in the 3-sphere. Both of which lead to spinor characteristics in our ordinary measure space, which is 4 dimensional.

          Best,

          Tom

          I will give some further explanation about what Albert Jan did with GAViewer so that others are not hoodwinked by Gill's misrepresentations.

          The geometric algebra program GAViewer is fixed in a right handed bivector basis. So in order to see the left handed bivector basis part of Joy's model, all one has to do is reverse the order of the geometric product AB to BA. IOW, from a right handed perspective, one sees the order reversed for the left handed part. Lambda simply toggles between the two orders to correctly represent the model from the right handed only perspective. Pretty easy to understand and the model works as advertised. And what Albert Jan did is simple and elegant.

          Fred,

          Thanks for pointing that out, GAViewer sounds like 'graphic arts drawing' tool to me, and would not be built to select between a right or left mathematical handedness. It also points out the importance of thinking through any proposed experimental protocol, and especially with the growing reliance on computerized simulation. In Theory, a process is an interactive dynamic. In physical practice, a process is a something - like the bump at the end of a bone that the muscles connect to. In Theory all you need for a mathematical process to be complete is to specify an initial state, it will stick together just fine. In Experiment, to get two things to physically stick together initially, you need to add a mechanical process and that can introduce an asymmetry into an otherwise mathematically symmetrical dynamic. Measure twice, cut once. jrc

          Thanks for that explanation, Fred. To my memory, Joy explained it years ago in terms of a video game screen where a character or object disappears at one edge and reappears at the opposite edge. It makes a perfect analogy with the flatness of parallelized spheres.

          Such reversibility is also supported in my explanation of 4 dimensional metric signature reversal using prime pairs.

          That's a truly interesting way to put it, John. The lazy way is just to assume an indescribable phenomenon called "quantum entanglement." :-)

          Tom,

          Thanks, I admit looking first at the entrance to the rabbit hole. A deceased friend of mine had been a machinist, and we were talking once about the decline of the U.S. pre-eminence in hard production capability. He told of a domestic precision spring manufacturer that had sent a Japanese competitor a sample of their tiniest, finest caliber coil spring, and the competitor sent it back with a hole drilled through the wire and one of theirs threaded through it. :-( jrc

          Great story, John. I think it's kind of ironic that W. Edwards Deming -- the father of statistical process control -- found his first customers among the Japanese. After all, a statistical method that puts power in the hands of the individual production worker seems to go against the grain of Japanese business culture, of which one Japanese manager I knew said, "the nail that sticks up gets hammered down."

          And then they proceeded to kick our butts, by exporting American ingenuity. :-)