RE BELL AND LEGGET INEQUALITIES

JON, a quote from your essay: "So how do physicists know that there isn't some underlying pseudorandom process that could reproduce the results of quantum mechanics in a classical, deterministic way? Even if Bell's Inequality rules out local hidden variables, this doesn't preclude determinism in general."

[Note: "Digital Physics" takes place sometime in the late 1980s before Leggett's inequality was discussed, or I am sure Khatchig would have mentioned that in his Dedekind cut quote."

Jon, since QM breaches both inequalities, you're welcome to have a look at my essay and critique it. There you'll see an interesting mix of "randomness and determinism" (some might say "a pseudorandom" process) emerging from fairly conventional (classical probability) theory.

And though not quite in a "classical deterministic way":* enough to rule in "local hidden variables".

* Recalling Bohr's insight, it cannot be "classical" in QM: In QM, "the result of a 'measurement' does not in general reveal some preexisting property of the 'system', but is a product of both 'system' and 'apparatus'," Bell (2004:xi- xii).

With best regards from your local local-realist;

Gordon Watson: Essay Forum. Essay Only.

    Jon,

    The movie and essay are both stimulating and good contributions to this forum, and I hope the community shows strong support for it. Thanks for putting all the work into it. I liked how this takes place in the 80s in a setting where it was difficult to obtain the computer resources for his quest. It's a good reminder to us today to take advantage of the computing resources we have. Also, one of the ideas in the movie where he looks for patterns to discern physical concepts reminds me of some random walk research I did a number of years ago. To present these inspiring ideas in a dramatic environment where it takes itself seriously and yet to the point where we can have fun with it, strikes a delicate balance - but you achieved it. That is a form of brilliance too. I rate this highly, and hope to see more good things come of it - Thanks again, Steve

      Dear Jon,

      Thanks for this thought provoking piece. I agree with your statement, "... the use of mathematics based on infinite precision "real" numbers by physicists, are both born out of a desire to overcome a logical impediment and reach a desired goal. Both are created for convenience sake... In the case of physicists using continuous mathematics, this technique enables the power of the infinite to be harnessed in order to create elegant closes-formed analytic solutions. Both serve a purpose but NEITHER MAY BE LOGICAL"

      An example of such illogicality is the definition of the infinitesimal in calculus, that dx can be both equal to and unequal to zero, i.e. dx = 0 and dx тЙа 0 are both correct.

      I see motion in the trailer of your movie, Khatchig may have one or two things to contemplate about "digital motion after reading my essay.

      Regards,

      Akinbo

        Dear Mr. Khanlian,

        I thought that your colorful essay was exceptionally entertaining and I do hope that your movie is seen as often as the film THE THEORY OF EVERYTHING, although, alas, perhaps by fewer discerning people.

        Warm Regards,

        Joe Fisher

          Hi Gordon,

          Not that I agree with this point of view, but I believe the traditional analysis view is that 1.99 is 2, so there is no number between them. Maybe what you are pointing out is the reason why they are considered to be the same number from that point of view... The same number can take on different appearances.

          But I still don't like that view point, because there still seems to be that infinitesimal difference. According to Akinbo's post below, I think this is a case where they assume "dx=0".

          Also, I wonder if NJ Wildberger would challenge you to define addition between your infinite reals a little more precisely.

          I'll come check out Akinbo Ojo's forum as soon as I get the chance.

          And as Arnie aslso said, "I'm a cop, you idiot! I'm detective John Kimble!"

          Thanks,

          Jon

          Hey Gordon

          I'll come over to your forum and check out your essay as soon as I get the chance... hopefully tonight. I hope I won't be in over my head. Sometimes it's easier for me to throw out ideas and questions, than to actually critique technical work.

          Jon

          There actually is a "love interest" in the movie, but I don't think people will refer to it as a romantic-comedy... unless they are talking about Khatchig's romantic view of truth in mathematics and physics.

          I started reading your essay last night but I got to the line segment part and then started getting a little confused. I hope to take another look at it soon, as I like how you are trying to start with the most simple model you could imagine.

          Jon

          I appreciate it, Steve. I'm glad you were able to make the Cast & Crew screening and that you enjoyed it so much!

          And to echo your point, can you imagine how much more difficult it would be for people to try to comprehend some of these complexity science ideas before the computer age? Could you imagine somebody analyzing Conway's game of life on a piece of grid paper before the computer age? "Hey guys, look at this crazy pattern that emerges from these simple rules. What, you don't believe me? Well just spend the next 100 hours convincing yourself by checking my work by hand." I bet Leibniz struggled to have anyone appreciate his "digital" vision. Hopefully as computers progress, "Digital Physics" (the movie and the theories) will win over more people.

          Jon

          "Digital Motion", Eh? Is this different than discretely changing positions?

          I'm going to try to get to your, Adel's, and Gordon's essays tonight. Your comment about "dx = 0 and dx тЙа 0" reminds me of the measure theory view that non-computable reals turn a line composed almost entirely of gaps into a continuum, yet the probability of choosing a specific real is 0.

          It feels like there are so many ways in which the assumption of real numbers lead to paradoxes, and yet the refutation of the reals via a reductio ad absurdum proof is never given much credence by almost all modern mathematicians.

          Maybe I'm just not understanding the concepts properly... although I've been thinking about it for way too long!

          Jon

          Thanks, Joe.

          I didn't see "The Theory of Everything" because I heard it didn't have much science in it, but rather focused on love and the triumph of the human spirit, two things I'm not too keen on;) Just kidding... sort of. Anyway, I'm surprised it didn't win the Alfred P. Sloan science in film award, but I guess Mike Cahill's got that locked up.

          I did see "The Imitation Game". I liked it, although I cringed when they butchered the pronunciation of Euler's name. I wish they had worked a little more of Turing's work into the film, but hey, you don't want to scare people away. After all, movies are supposed to be entertaining, not enlightening;)

          Ok, enough sourness from this filmmaker:)

          Jon

          [Jon. Buddy. Psst. Mate. It's Chevy. Undercover again. I got that old job 'cos I was Commonwealth Aircraft Corporation's top apprentice; BA is family. And Good On You Old Son: But it's impossible for me to throw out ideas and questions; I got heaps of 'em.]

          But, Jon, seriously: when you visit over there, it's not like there's actual technical work to critique. If you went to a good high-school, it's all high-school maths! (And remember what got writ in that classic, Jon? 'KISS; keep it simple son'.) Love, Chevy

          Jon,

          I personally find it harder to ask new questions than to repeat well-known answers. Thus I find your questions a very attractive part of your essay. Sometimes a question will invoke a new perspective or realization, and sometimes the question will combine concepts in a way that illuminates these concepts.

          Your question 4: 'If quantum mechanics is a world where things can be both 'yes' and 'no' at the same time ( then Zen... )' is phrased to appear to imply "physical world" but I think your question shows that considering QM a "formal world" makes much more sense.

          Similarly, question 6: How can 1-D info in DNA/mRNA be transferred into a 3-D protein in a 2-D holographic universe? This again emphasizes (to me) that mRNA is real and is 3-D and proteins are real and are 3-D while the 1-D string of info was a formal conception and the 2-D holographic universe is merely a formal construction.

          I believe these are valuable questions that shed light on complex topics. Thank you for them.

          Edwin Eugene Klingman

            Actually I first tried to get a relation between the most general shape, only to end up on the simple line. After discovering the possible relations, now you can generalize to multidimensional with a generalized shape with generally the same outcome as the line.

            I include an attachment to clarify the particle setups(distance) in the programAttachment #1: dist.png

            Jon,

            Thanks for dropping comments on my forum. I have attempted a reply.

            On a movie screen like yours, motion is digital with a pixel changing from the background pixel to the pixel of the moving object. If space is a substance made of 'pixels' (like my extended points), how would motion be accomplished. As you move do the pixels constituting you the moving object change their nature to that of the background pixels, while the background pixels in your direction of motion change their nature to the nature of the pixels constituting the moving body?

            How can a line constituted by pixels be cut if the pixels are infinite in number and cannot be cut since there will then always be a pixel at the point of cutting incidence? If the number of pixel is on the other hand finite, what can lie between them? Certainly, not space since space is made of the pixels?

            These are some of what I address in my essay. You are welcome back to read again when you can spare the time. Thanks.

            Akinbo

            Hi Jon,

            Sorry I took so long to answer. I tried to relate my question to your questions in the sense, that I tried to make a connection between the language of a statement and the meta language that describes the meaning of the statement. But did not succeed.

            So finally it might just be related to the color question. Sorry that I use your forum for that!

            Let the set A contain two sheep. From the point of view of A A cannot distinguish the two sheep. It is symmetric. But we can. Maybe one sheep is black, the other white. Or one is bigger, the other smaller. In a way the two sheep must have other properties, that can distinguish them, that are not defined in A or by A. If the sheep are completely identical, they have at least to different space locations, by which we can differentiate between them.

            What is with space itself? What additional properties can distinguish between 2 space points?

            What with a qbit? The qbit has the full SU(2) symmetry. What distinguishes two different states?

            Logically speaking the set can be seen as the predicate of a proposition. Its elements are the possible subjects: "A sheep is an animal." The predicate could also be called a term. In the greek philosophy eidos. To specify what this term mean, contains, we need other term (eidos), that are not defined by the term itself. The relation between different terms (eidos) is what we call mathematics. Formally it is possible creating terms, that contain themselves, leading to the well known paradox. In the philosophy of Aristoteles the paradox do not arise, because he finally end up with the substance. He defined substance as something, that can only be the subject and not the predicate of statement. The substance is what I would call reality, or factuality.

            On the way down from the eidos to the factual we face the problem how the general becomes a singular. And how we could even speak about the singular (factual), since it is singular.

            In the other direction, we have Humes problem of how eidos could be derived from singular facts.

            Hope this makes some sense.

            Luca

            Hey Luca,

            Thanks for the enlightening and well-written explanation. So do you think it is possible that there isn't the substance at the bottom and we are living in some sort of self-referencing paradox? That we are all just defined in terms of each other? Or that that substance at the bottom that allows us to avoid self-reference is non-physical, like information? Or do you think the substance(s) is physical? Is that particle physics?

            So in your example where the sheep are identical, could we not distinguish the two sheep by saying where they are in relationship to other objects, while avoiding distances associated with space? Imagine a network where you could say sheep A is closer to object B than sheep A'. (I am imagining a network where Sheep/Vertex A shortest route to B is say, 1000 connections away, and Sheep A' is say, 2000 connections away.) Of course with referencing Object B but not defining it, we avoid the self-referencing paradox while leaving the system not well-defined... It's like we have consistency but not completeness. Or we could define B and every other objet and have completeness, but not consistency due to the eventual self-referencing(assuming no substance at the bottom). This seems to jibe with Godel's work, which I guess would make sense since the network is an instantiation of arithmetic and sets. Thoughts?

            Thanks for stopping by and stimulating some thoughts!

            Gordon/Chevy,

            I looked at your paper. That some serious stuff! :) You're defining new things that I would want to have whole conversations about to really understand. Maybe others could take to it a little easier, but that may be the hardest essay in this contest for me to understand. I did not make it past some of your initial definitions :( ... even though they were all math formulas. But if you are on to something and all your work adds up to a different way to look at the experiments that lead to Bell to his conclusions... well that would be... WOW!

            I think you should do a video explanation/lecture of it all, with some pictures or animations if you think that could help people understand it better. Some verbal explanations and maybe some nice animations as you write down the formulas? (Unless you think some of it cannot or should not be visually imagined ...or the math should not or cannot be interpreted.)

            I'm putting your essay on the back burner for a little bit. I hope to come back to it when I have a lot more time to think about it. I hope by that time some other people have helped me to understand it a little more by having conversations with you on your discussion page.

            jon

            Hi Akinbo,

            I think one way to look at "movement" is just to consider it as a changing of relationships between objects.

            Imagine a tetrahedron, with an extra vertex and edge coming off one of the points. To avoid the notion of edges as lines made of points, we could mathematically represent this structure as follows:

            1:{2,3,4)

            2:{1,3,4}

            3:{1.2.4}

            4:{1,2,3,5}

            5:{4}

            And then object 5, which starts one connection away from object 4, discretely "moves" away from object 4 towards object 1 so that it is now 2 connections away from object 4. This is represented as follows:

            1:{2,3,4.5)

            2:{1,3,4}

            3:{1.2.4}

            4:{1,2,3}

            5:{1}

            Is this an acceptable instance of a discrete model with movement?

            I look forward to trying to understand your ideas better.

            Jon

            Thanks for your response, Edwin. I'm glad you felt compelled to offer answers to a couple of the questions. I'm hoping more people will take a stab at some of them. A few of the questions were half-serious, half in jest, and I think you choose two of them.

            With regard to question 4, would you agree that a single emitted particle does not spread out as a wave when it goes through the double slit (so it isn't both here and there, yes and no) but rather, it is only rendered into existence when it hits the plate behind the double slit?

            With regard to question 6, do you think everything in the real world is 3-D? What about the event horizon of a black hole? Does that have thickness? Or is the notion of an event horizon just an idea or formal construct?

            Thanks again for your thoughts! Please feel free to answer other questions!

            Jon

            Hi Armin,

            After Effects is fun once you learn a little. It's just photoshop in motion, if you are familiar with that program. Hopefully you get some time to mess around with it. Maybe you can devote some time to it if you convince yourself that it will help you stay lucid through developing your physics theories.

            Are you saying that you think light cones should really be depicted as warped images instead of perfect cones? (Sorry, submanifolds are not my forte, and the few minutes i spent reading wikipedia didn't offer any immediate insight :) If so, that sort of makes sense in a world where matter warps spacetime... unless the warping of space and time perfectly offset each other so that the light cone looks normal for any object, whether it is near massive bodies or not. (I feel like my understanding is not right, so forgive me if I am off base)

            I will try to respond to some of your explanations that you offered on your page to some of my questions, but I do remember thinking that some of it was a little over my head. Oh well, maybe I'll google some stuff and try to understand it a little better.

            Thanks again for your thoughts.

            Jon