Dear Lawrence,

i had a similar illness two years ago during the last essay contest. It was the influenza-virus and even after being cured i needed much more sleep. Without that additional sleep i think my that fatigue would have turned into cronical fatique. So please regenerate yourself properly.

I read your essay several times and i like that you try to get the bigger picture on QM. I also liked what you have to say about p-adic numbers, locality and decidability.

Take care and best wishes

Stefan

Lawrence,

Welcome back.

Quite a scholarly piece that penetrates the underlying quantum world and entanglement quite well to prove prediction limits in our classical world. I wonder if you have seen the studies that seem to bridge the two worlds: https://phys.org/news/2018-11-quantum-criticality-superconductivity.html. I cite them in my essay re bridging efforts in overcoming limits. Your topological obstruction theory is quite interesting, at least what I can understand of it.

Jim Hoover

    Lawrence,

    Mine is your 6th rating. I say this because there is someone who gives 1s to a number of us w/o comments.

    Jim Hoover

    DEARS READERS,

    LAWRENCE CROWELL CANNOT CURRENTLY POST IN FQXI WEBSITE. THUS, HE ASKED ME TO POST THE FOLLOWING MESSAGE FOR ALL OF YOU:

    "TO ALL WHO POST ON MY SITE. FOR SOME REASON I CAN'T ACCESS THE BLOG WRITING. AS A RESULT DON'T BE PUT OFF IF I CAN'T RESPOND. SUPPOSEDLY THE FQXI TECH FOLKS ARE GOING TO FIX THIS.

    THANKS LC"

    Lawrence,

    The problem could be your browser. I use google and have only had trouble posting ratings since yesterday.

    Jim Hoover

    Hi Dr Cromwell. I am particularly excited by the 3-tangle turple in Quantum mechanics.maybe it means from the default two observers in the Michelson morley double experiment,what we interpret as qm may be the virtual "third picture/observation" borne from the Human brain supposition of dual state of matter in the quantum world. I have a simple piece on bias out of the paradox in my essay https://fqxi.org/community/forum/topic/3525.you may kindly review/rate on the simple diagrams,any input will be appreciated. thanks .All the best in the essay.

      The 3-tangle is a case with GHZ and W entanglements. These are separated by a topological obstruction. This just means there is no unitary basis by which one can evolve into the other. This is at least as a closed system. These entanglements can lose quantum phase to a reservoir of quantum states, or quantum noise, which mean that ignoring those states, say tracing them out, gives the appearance of the same state. This is then a coarse grained perspective of decoherence.

      I will take a look at your page ASAP. I have been dealing with this Covid19 and it has made me quite fatigued and I have difficulty doing as many things as I used to just 6 weeks ago. I have made a self-promise to really read as many papers here as possible, but by evening time I find myself too tired out.

      Cheers LC

      7 days later

      I enjoyed your earlier version Lawrence...

      I am returning to offer my rating, but I must peruse the revised copy first. It appears that you added some interesting new content, as well as cleaning things up. I commend you for persevering despite being ill. Hopefully you will return to full strength. I know that the recovery can take a while for some, even after the virus is eliminated.

      Best,

      Jonathan

        All I did was to change about 4 words in the abstract. There was a bad misstatement in there. In fact I think you pointed it out.

        I am largely done with the flu-like symptoms, and have been for several weeks. The one problem is the fatigue is still a bit persistent. I am sleeping more, but not up to the 12hour/day a month ago.

        Cheers LC

        Glad to hear you are out of the woods,

        We will all need our strength to get things going and back to normal.

        Best,

        JJD

        This paper is a significant work Lawrence...

        From my view; your work is coming to resemble more and more that of Ed Witten. I mean that both as a compliment and a criticism. On the one hand; you are a truly deep thinker with a good grounding in the Maths that let you express your thoughts. On the other hand; your paper is dense with Math and the reader gets immersed pretty quickly, which can overwhelm some who are less Math-agile, and overload some who are - before they get your point. I get the same effect from reading Connes. I know there is something amazing there, and it's exciting to try to follow it, but it's easy to get lost if you don't know some of the technical terms and techniques well.

        So I give you high marks but not full credit. This work is patently amazing, and it is obvious that it addresses the organizers' questions in a detailed way, but you make me go back to the books a bit too often - in order to fully grasp your point. I am not 100% sure I understand you completely yet, and I feel that this contest is a forum for people like yourself to prove their ability to reach a broader audience. All in all; I think you did quite well. It almost comes across as a advertisement for Szangolies and Palmer in places, though, and they may not need the boost. But I will help you a bit.

        This is a paper I'll probably read multiple times, for what it is worth. There is a lot of meaning to mine from this exploration.

        All the Best,

        Jonathan

        Dear Lawrence Crowell

        The only thing I'm sure of in quantum mechanics is your next sentence:

        "Quantum mechanics requires an extension of real variables of classical mechanics into complex variables."

        After all, I came to that conclusion with my theory, but I can't go further.

        Please answer me if you agree with my general position (assumption):

        Quantum mechanics occurs, in frame exp (i * pi).

        Since I am not educated for the field you are writing about, I do not understand your formulas. So, if you don't understand the formulas in my essay then we are 1: 1.

        The text I wrote is nothing special anyway. In any case, your work deserves high marks. By my criteria, and because it contains formulas.

        Regards,

        Branko

          The equation e^{iПЂ} = -1 is called the Euler equation. It also leads to complex number. Consider the natural logarithm of a negative number ln(-x). In the field of real numbers we are stuck but we can use the rule of logarithms ln(ab) = ln(a) + ln(b). So, ln(-x) = ln(x) + ln(-1) and we can at least peel off the part we don't understand. As a result, with Euler equation write

          ln(-x) = ln(x) + ln(e^{iПЂ}) = ln(x) + iПЂ

          due to the inverse function of the exponent e^{iПЂ}. We can also use e^{iПЂ/2} = I to evaluate the logarithm of an imaginary number ln(ix) = ln(x) + iПЂ/2.

          Quantum mechanics can be thought of as a map of classical mechanics to the quantum according to the Poisson bracket formalism. This bracket {q, p} = (∂q/∂q)(∂p/∂p) - (∂q/∂p)(∂p/∂q) = 1 is replaced with the commutator {q, p} в†' i/Д§[q, p], where these are now operators. The commutator is then equal to i = в€љ(-1). So, in that sense quantum mechanics does have this funny relationship with imaginary numbers.

          The wave function in QM is complex valued. A complex number is z = x + iy. The magnitude of this number is computed with its conjugate z* = x - iy and so zz* = x^2 + y^2. Then with a little trigonometry we have z = zz*(cosОё + isinОё) = zz*e^{iОё}. A polar form of a wave function is of this form.

          Dear Lawrence Crowell

          Thanks for your comprehensive comment, even though you didn't answer my question. Ultimately, it is evident that you are one of the few who speaks about the universe and understands logarithms. My question was related to the boundary case when theta = pi.

          Why is it important. Because in all my works and earlier FQX essays you can see the importance of another borderline case (frame), ie. Exp (2 * pi). You can see the results of such an approach to classical physics through the predictive formulas at the end of my essay this year.

          Regards,

          Branko

          I will try to read your essay in the near future. This issue with the Euler formula hinges around the unit circle in the complex plane with

          e^{iﾎｸ} = cosﾎｸ + isinﾎｸ,

          where this is a way of thinking about trigonometry. the multiplicity of these functions for angles ﾎｸ 竊' ﾎｸ + 2ﾏ\ is a part of the reason ln(-x) = ln(x) + iﾏ\, but also the entire set {..., -3iﾏ\, -iﾏ\, iﾏ\, 3iﾏ\, ...}. This leads to the concept of Riemann sheets, where the complex plane has multiple copies.

          Cheers LC

          Lawrence,

          Hope you have time to check mine out before the deadline: https://fqxi.org/community/forum/topic/3396

          Jim Hoover.

          Dear Peter,

          I believe we are kindred spirits on the topic of spin. I regard it as one of the fundamentals of physics along with charge. As you already know I have derived my theories from scratch, from the basic particles of the Universe to a computational TOE, and a working theory of time. I have given small glimpses of what I have found in some of the many posts I have made but I would certainly value your opinions and insights on a deeper level. It seems that my math and philosophy and even physics are sorely lacking when compared to others, but I have achieved something they haven't.

          Regards

          Lockie

          The quantum numbers such as spin I think are independent. An elementary particle is I think an entanglement of states for each of these quantum numbers. In solid state physics these are called quasi-particles, such as phonons, plasmons, spinons etc. Experiments done recently have shown that an electron can be placed in a state where the spin is in one location and the charge at another. I actually think elementary particles are these entanglements of quantum states corresponding to these quantum numbers.

          LC

          Dear Lawrence,

          Very good and informative essay, with interesting insights and connections, thank you! I liked how you connected different structures and techniques in quantum mechanics to build an argument about the relation with undecidability. Particularly, I am interested in the topological obstructions, but for independent reasons. Thanks again, and I wish you success with the essay!

          Cheers,

          Cristi