Efthimios,

The ingenuous Lieu and Hillman paper you cited proves that there is no evidence for Planck-scale fluctuations in time and space. So far so good, but then it uses that result to say the ether does not exist. This is a very weak conclusion hinging on the assumptions that probabilistic effects are an inherent property of nature and not merely the result of macroscopic measurements and theoretical interpretation of what may be a very different physical reality at the Planck-scale, presumably the ether granularity level. I have suggested in my my original 2005 Beautiful Universe paper on which I based the fqxi essay, how probability can emerge as diffusion within an exquisitely ordered ether. Such an ether may exist and not contradict Lieu's result.

Atomic interference has been demonstrated, even for molecules, (which incidentally I now conclude in my above paper may be the result of the interference of the gravitational fields surrounding the particles). But how would that give any data for or against a much finer supposed granularity of space? It will be interesting to read the Italian paper if you find it thanks. BTW here is an interesting demonstration of moire patterns it may inspire something!

Good luck. Vladimir

    Vladimir,

    I do not like to post more than one link usually so this is the response to Lieu's paper that attempts to rebut its claims:

    http://iopscience.iop.org/1538-4357/591/2/L87/

    Besides the theory and the measurements, let us think about it in a more fundamental way:

    If spacetime is granular, then what is there between the grains? There must be something because if there is nothing, then space is not granular.

    If space is granular, then it is a virtual space.

    Disproving the granularity of space is equivalent to preserving the autonomy of the world. In my opinion, it is now too late for that.

    Cheers.

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    • Post #19

    Dear Sir,

    We are amused by your joke.

    Millions of people have "seen" mirages. If we describe the truth about it, we are not wrong. The description of the desert, the water and the illusion that appears as water are all correct and real. It is only the misconception of those who believe that it is full of water, that is wrong. If someone wants to belief in the reality of mirage water, we can only advise him to go to that spot and find the truth for himself. We cannot help if someone regards superstition as more scientific than the results of physical experiments.

    We hope you will enjoy this joke.

    Regards,

    basudeba.

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    • Post #20

    Efthimios,

    The point I was trying to make is that the halting probability of a program with choices among a continuous range of variable values is zero. That's the difference between the sign and the - sign in Popper's hypothesis testing criteria.

    So even if your program is a finite state (Turing) machine with infinite processing capacity, there is no possibility that any finite state will return a discrete result from that continuous range of variable values in a bounded length of time even if the bound is infinity. In Popper's example, the reformulation of the twin primes conjecture, there is no possibility that at least one natural number, y, will not be prime given the terms x y and (2 x) y, because twin primes by definition are sums of successive primes, mod 2. Therefore, x y and (2 x) y are the same thing in this context -- there will always be a sum of successive odd primes, mod 2, whether the pairs are twins or not. We're not concerned with sorting twin primes from all other pairs, only with the characteristic that defines them, and we can't use that characteristic to prove that twin primes are infinite, because we already know by Euclid's proof that the prime sequence is infinite.

    The potential proof of the Goldbach conjecture, on the other hand, is not bounded at infinity. We don't know beforehand (as we do with Euclid's proof) that an infinite number of prime pairs (P > 2) sum to an even integer -- that's what we're asked to prove. So why don't we use Goldbach to test our halting hypothesis? Problem is, as I showed in my ICCS 2006 paper, that even though the conjecture, as Popper established, is of the same kind as the twin primes conjecture, we have a pseudo-continuous range of variable values in the field of natural numbers R; i.e., R is of the same cardinality as the infinite prime sequence. The problem input is not bounded at infinity (it is algorithmically compressed), yet the output is. That's what makes the case mathematically interesting because the finite state maps to the infinite sequence, unlike the case of twin primes in which infinite sequence maps to infinite sequence (that is, both input and output are bounded at infinity in the sense that there is no sign change).

    I presented (ICCS) an existence proof of a weakened Goldbach conjecture that removes the problem to a complex Hilbert space. The C* algebra is closed, giving us all the arithmetic functions we would use on R, plus the added dimension we need to establish a kind of congruence (mod 2) between complex numbers with zero imaginary part and the geometric nature of C as Euler described it. The proof could only be made constructive by quantum computing, because the domain would obviate the time dependence of purely classical computation, without sacrificing the continuous range of variable values.

    See if you can get an expert in quantum computing to agree that a polynomial time solution is possible using this strategy and you might get the falsifiable experiment you seek. Obviously, I would be intersted in the outcome.

    Good luck!

    Tom

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    • Post #21

    Dear Efthimios Harokopos,

    I have just downloaded your essay. I will be looking for your support for:

    "I will assume in this paper that reality is fundamentally digital and then based on a modern version of the old doctrine of Cartesian occasionalism I will sketch a model of the world that allows both uncertainty and autonomy within the limits of physical laws."

    You begin with digital and sketch a model that allows for uncertainty. I assume that you mean that uncertainty frees us from a digital universe. I think that uncertainty does not free us from anything. If I have misunderstood your meaning, I will learn that from your essay. Thank you for participating.

    James Putnam

    Hello James,

    As a matter of fact I state the opposite that uncertainty is a feature of the digital word and determinism of the analog. I do not invent these, QM and Relativity say so, respectively.

    In physics, as you know, every model we build is an assumption that must be falsifiable. Thus, regardless my personal beliefs about the nature of reality (I may have none as a matter of fact), I sketch the model of a mechanism continuously recreating a digital universe at single instants of time and I am trying to find a way to falsify it.

    Someone else may come up with a different digital model and find another way to falsify it. You see, analog models cannot be easily falsified. Our best analog model is Relativity and to this date none of its predictions has been falsified although there are a few issues with general relativity that need to be investigated more.

    Thank you for your comments.

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      • Post #23

      Dear Efthymios (and all),

      I wonder if you have a look to my essay. In it there is an idea of "granularity" of space and how virtuality fits in between or "reality" fits in between "granular" virtuality.

      Giving the oportunity, I would like to make clear what I meant in my previous responce to your experiment proposed. Human brain as a huge local computer working with its trementous capacity and following the same rules usually gives various results although the inputs are the same. Because all these different results can not be the "expected" answer this is an indication that there is a limit in the local processing capability. Whether this is THE upper limit I think we will not in a position to ever know as we will never manifacture a machine better than our own brain for the simple reason that its results will be interpreted as faulties.

      Regards, narsep (ioannis hadjidakis)

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      • Post #24

      Very interesting article Mr Harkopos.

      I was under the assumption that Zeno's paradoix was implicitly resolved with the advent of differential calculus and the idea of limits.

      i.e. the sum of an infinite series may converge to a finite value, which in turn represents the limit of the series. The infinitesimal sum of dx(1/dx/dt) approaches a finite value over any abritrary interval on R, prodived dx/dt is continuos, smooth, and exists on the interval.

      The erroneous assumption implicit in Zeno's paradox is that the sum of an infinite sries is always infinite.

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        • Post #25

        Also, all of the variations of Zeno's Paradox also lack any self-consistency and self-referential integrity.

        For example, the argument put forth that in order to travel an interval AD one must first travel half that interval AB, and so on, leads to obvious problems.

        The lack of consistency arises when one states that once one reaches the first half-interval AB, another half-interval awaits and this progression continues indefinitely. One must therefore complete an infinite amount of actions and can never arrive at the end of the interval. The obvious problem here is, you managed to travel the first half-interval AB in a finite amount of actions without encountering infinity.That interval AB itself is arbitrary and contains an infinite number of half-intervals. Since the original intent is to show one can never reach the original interval AD in a finite umber of steps and actions, how is it you came to traverse the sub-interval AB? Based on the assumptions, an infinite number of actions would also have been required for that interval.

        This should immediately tell one that the something is amiss with the idea of actions on intervals as they relate to the infinite.

          Hi Bubba,

          Thanks for an interesting comment. There is no erroneous assumption in Zeno's paradox. If you get the reference I mentioned (Barnes) you will see that the fundamental premise of Zeno is that "nothing can perform infinite many tasks". Calculus does not resolve this issue. Calculus provides asymptotic convergence conditions for mathematics only. The limit of the series as you say, it is only reached asymptotically. In mathematics we call that convergence. But what convergence means in the case of physical motion in infinitely divisible space? I don't know. If you know, I would be interested to find out, namely, when does the body in motion exactly reach its end point.

          Barnes explains the whole issue well and also the argument of Aristotle which was the first and last viable argument against Zeno. Zeno's argument can be transformed to:

          1.Motion is a supertask, because the completion of motion over any set distance involves an infinite number of steps

          2.Supertasks are impossible

          3.Therefore motion is impossible

          There is huge literature on this subject and the concept of infinite supertask machines.

          Actually, Zeno's task can be modeled by a Grandi series, which converges to infinity:

          http://en.wikipedia.org/wiki/Thomson's_lamp

          http://en.wikipedia.org/wiki/Supertask#Zeno

          In order to resolve the paradox many assume that motion is possible and then declare the argument of Zeno unsound using modus tollens.

          However, it is the very possibility of motion that Zeno challenged.

          Note that solution that claim that as soon as motion starts it concluded because each subsequent motion takes less time, so that the time intervals converge to a finite value according to calculus, are naive because according to Zeno, motion cannot even start. Zeno's philosophy was that there is no such thing called motion. Everything is immovable, at rest, and what we see is an illusion. I think what we see may be virtual reality. In a virtual reality, motion is possible because it is pixelized. But again, what I think is not important. It is what experiments will show that is important. Talk is cheap in physics, almost.

          Thanks and regards.

          Hello Bubba,

          I apologize for an error in my post. I wanted to say that the Grandi series converges to 1/2 at infinity. However, at the same time, depending on solution, the series has no sum. Thus, the series diverges.

          So, instead of using the typical calculus approach which sets infinitesimal values to zero, the Grandi series approach should convince you that this is not a trivial problem.

          To illustrate this further, consider S = at^2/2, the known equation. Now, consider that the body moves ds in time dt. The equation becomes:

          s+ds = a(t+dt)^2/2 which with some algebra becomes:

          2s+2ds = at^2 +2atdt+a(dt)^2

          But as^2 = 2s, so we get: 2s+ds = 2s+2atdt+a(dt)^2, which reduces to:

          2ds = 2atdt +a(dt)^2 or ds/dt = at +dt/2

          But calculus tells us that ds/dt = at. How can that be?

          The mathematician response is that in the limit dt goes to zero. But is it exactly zero? If it is exactly zero, then S+ds will be forever equal to s and motion cannot take place. If it is not zero, then s = at+dt/2 and these sums of dt/2 diverge. Of course, mathematicians can always add a few more axioms and get anything they want.

          By this response, triggered by your well put argument, I want to show that calculus wants its cake and eat it too when it comes to justifying motion (although it describes the phenomenon correctly). Things are not that simple. There is a lot of work to be done to transform our naive views of reality to something more advance that can help us to progress.

          All the best.

          Efthimios

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            • Post #29

            As Einstein recognized, the calculus of continuous functions requires specifying boundary conditions. Because "From the standpoint of epistemology it is more satisfying to have the mechanical properties of space completely determined by matter ..." Einstein's finite but unbounded, quasi-Euclidean model of relative matter rest states came mathematically complete, with the origin of inertia assumed at the boundary of a singularity, and otherwise unexplained. (The foregoing is picked up from the technical note in my essay "Can we see reality from here?")

            If motion is primary, as Mach believed, the origin of inertia needs no explanation. We know that this cannot be true, however, because also as Einstein recognized, because of the problem describing continuous function physics without singularities. So cosmology, once subbed as mere philosophy, has taken--if not the leading, at least an important supporting--role in physics.

            Tom

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            • Post #30

            Hi Efthimios,

            .

            btw, I found your article to offer a lot of food for thought and hope you score high on the final ballot. Best of luck.

            Anyway, regarding this issue, I don't think the problem here is one of infinity, it is the way we think about infinity.

            First of all, I think we need to keep in mind that mathematics simply represents a model for reality. You stated, "I want to show that calculus wants its cake and eat it too when it comes to justifying motion."

            I think it was Confucius who said, "Do not confuse the finger pointing to the moon for the moon itself." If we were to rely exclusively on mathematics to form our picture of reality, we would immediately find ourselves in a lot of trouble. This is why we check to make sure a mathematical solution to a problem is physically admissible. If the solution does not conform to what we observe then we do not throw out our observations, we reconsider the validity of the solution or we reevaluate our line of reasoning that led to the solution. Sometimes, a theorist cannot decide whether or not a solution to a problem is a physically admissible one(e.g. String Theory), but that is another story. The danger is relying too heavily on theory to form a complete picture of reality.

            Basically then, in the context of this discussion, motion is possible and exists because we observe it to exist. Any argument or solution that infers motion is impossible must therefore either be reframed or thrown out completely. There is no way around this. Observation and experiment always has the final say in science. So, we are on shaky ground when we expect our mathematics to justify motion.

            I think that the conceptual difficulties inherent in these types of arguments all lie in our ideas about casuality.

            IMO, the fundamental question is not why do things happen the way they do, but why does anything happen at all? This is where Newton, motion, and the concept of inertia comes in. If you think about it critically, the first law is logically necessary in any universe where cause and effect has meaning. This is because the first law essentially reduces to a simple statement about causation--nothing happens without an impetus to action or a reason behind the impetus. If this were not the case, we would simply have random chaos and unpredictability.

            The same applies to any idea of uniform motion--i.e. inertial. In the context of this discussion, there is not an infinite number of actions taking place in inertial motion because there is no action required. Uniform motion is relative and there is no preferred frame of reference. In one frame, an object may appear to undergo inertial motion. In another frame of reference, the object may appear to be at rest. If action was required to maintain inertial motion then motion would not be relative and there must be a preferred frame of reference.

            Zeno's Paradox,in all it's incarnations,therefore leaves out this concept of relative motion. In one frame of reference where an object is undergoing uniform motion and must travel the segment AB, one can find another frame of reference where the object is at rest and the length of the segment is 0. Which one corresponds to reality? Zenos paradox becomes a non-sequitur when relative motion is considered.

            Also, when you inquire-- ."But calculus tells us that ds/dt = at. How can that be?", the answer is because the term 'a' implies an impetus that acts to change unfiform motion or a state of rest relative to an observer. Implicit in the calculation is the concept of non-uniform motion. For each element dt, the object 'caries' with it the velocity it had at t-dt. Through impetus, an additional velocity was added to the object during the time element dt.

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            • Post #31

            sorry, forgot to attach my handle to last post. This is Bubba.

            Thanks for your detailed response. I agree with you about calculus but I disagree - for whatever it worth - with your statement that "Basically then, in the context of this discussion, motion is possible and exists because we observe it to exist." This is not the point of Zeno's paradoxes.

            I will refer to a story that is reported by some ancient Greek philosophers. Zeno, most do not know, was an advisor to Pericles, the man who established Democracy. One day he was giving a speech in the central Agora of Athens, trying to convince people that motion is impossible. When he stated his arguments, the philosopher Antiphon - a real person by the way - got up from his marble sit and started walking up and down in front of Zeno in a silent protest. Everyone laughed. However, by the end of his talk, it was reported that Zeno had convinced everybody in the audience that motion is impossible.

            The point is, we observe something we call motion but is this motion in 3-dimensional infinitely divisible space? This is the issue. Sure, we got motion; it is all over the place. But maybe it is not what people think it is. Maybe it is not motion in 3-D space but something like recreation of 3-D space from a higher dimensionality space, a sort of virtual reality.

            This is the issue. I think it is a misunderstanding that Zeno said motion is impossible. He specifically limited his argument to infinitely divisible 3-D space with absolute time. In Relativity for example, motion is possible because everything is in eternal motion in a 4-D spacetime, as I attempt to describe in the paper.

            Thanks again.

            Efthimios

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              • Post #33

              Dear Efthimios Harokopos,

              Thank you for replying. I see now that I left my point unclear:

              Me: "I assume that you mean that uncertainty frees us from a digital universe."

              Your response: "As a matter of fact I state the opposite that uncertainty is a feature of the digital world and determinism of the analog."

              My point is this: A digital world lacks connection. Since it functions in a cooperative manner, there must be some form of continuity. I presumed that you considered uncertainty to fill in gaps and, in effect, smear a digital nature so that it might connect enough to mimic continuity.

              Your analysis of this would be greatly appreciated. Please be as direct as necessary to make your point. Directness helps me to understand. Thank you.

              James

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              • Post #34

              Efthimios,

              I appreciate enormously your clarification of Zeno's point, because I am reminded of sitting through a conference presentation a few years ago, in which the presenter claimed to have solved Zeno's paradoxes (specifically, tortoise and hare; and arrow paradox) through some assumptions about time and space he had manipulated.

              At the Q & A following, I asked (innocently, in fact), "Well, is motion possible?"

              The reaction was as if I had two heads. Hadn't I just heard the presentation? The presenter and others went through all the main points of discussion about time and space. I asked again, "Then if the paradox is resolved, what's the answer: Is motion possible?" The time-space explanation took off again, with the added suggestion that perhaps I wasn't asking a proper question.

              I replied, "It's the question that Zeno asked."

              And I think that had never even crossed the presenter's mind, as he presented a solution to a problem that had never actually been posed.

              Zeno's question is equivalent to the origin of inertia. We still don't know.

              Tom

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              • Post #35

              There is an interesting story in one of Richard Ferynmans popular lectures on science. A student oncer asked him if, when he was viewing an object, if he was really 'seeing' the object or the light that is reflected from the object.

              He just replied by telling the story of a philophers who slowly starved to death because every time he was presented with a meal, he spent all his time contemplating whether or not the food was really just reflections of light.

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              • Post #36

              Dear Efthimios

              I read the response to Lieu's paper you cited above. Again the assumption is that quantum foam is a reality. This idea is speculative and is based on Born's probability interpretation. In my Beautiful Universe paper on which my present fqxi paper is based I have suggested that on the contrary nature may be precisely local, causal and deterministic at the minutest scale - and still produce quantum effects including probability. I also suggested that the Planck scale itself may be a fiction or much too tiny: G is determined by macroscopic experiments. It may well be that at the granular, ether (or whatever you call it) scale, its value is quite different.

              Concerning your question "If spacetime is granular, then what is there between the grains?"I would say it may be impossible to determine the physical nature of the granularity or any other hidden large dimensions the granules may reside in. We are talking about the stuff that makes stuff so we cannot project (what is the inverse of 'project'?) or macroscopic notions onto the granules of the universe. It will be sufficient to presume they have certain qualities (i.e. in my theory the lattice nodes have angular momentum, density, polarity, etc}.

              You said " disproving the granularity of space is equivalent to preserving the autonomy of the world. In my opinion, it is now too late for that." Can you please explain that interesting statement? thanks.

              Dear Ray et al,

              Concerning Zeno's paradox of divisibility and motion - in an ordered universal lattice where motion occurs by momentum transfer from node to node (as in my theory) , such questions will have obvious answers and will no longer pose any logical difficulties. There may be a message spelled out with the ether granules: "reductionism stops here!".

              Dear Anonymous

              The story of Feynman telling the story of the philosopher (who contemplated the reality of food and the light from it) is typical of his cavalier attitude to foundational questions. Feynman seems - perhaps wisely as far as his great work was concerned - to have adopted a pragmatic stance to unanswered quantum puzzles, using ad-hoc solutions and mathematical formulations even if they were not derived from more basic concepts. By the way a simple phrase like "just reflections of light?" was the foundational question of the 10th century answered for all time by the father of the scientific method, Al-Hassan Ibn Al-Haytham (Hazen) by his meticulous experiments with the camera obscura and their logical analysis in his book Kitab Al-Manazir. Before him it was believed (after Aristotle, I think) that we see because the eye projects visual rays onto an object. Hazen's book, translated from Arabic into Latin influenced the Renaissance and modern science. Moral of the story: foundational questions have to be answered eventually and not swept under the carpet, Feynman-style!!

              Good luck to us all! Vladimir