Klingman writes essays on how quantum mechanics is ultimately a local theory, and he keeps coming up with what Feynman calls towards the end of this recording "ball bearings on springs." I have criticized his essays on other occasions. The problem is that FQXI is attended by many who write these essays and most who write to the blog and who have these ideas. There is a long history of this, and it in part swirls around a physicist named joy Christian. JC is, or was, an FQXI fellow and has hidden variable ideas. While few FQXI fellows are hidden variable mavens who think quantum physics is a local theory, the blog posters and many of the essay writers are. As a result Klingman's essay gets lots of attention and lots of votes on the high side, even if the core idea is hogwash.

You might notice that the blog is populated mostly by complete cranks. It used to not be quite like this, and I think the problem is the lack of minimal moderation has lead to this situation. These essays really should be put to some level of review, even if somewhat cursory, to weed out the crankiest of the cranky ones.

Klingman's claim is rather easy to verify. The spin of a system is measured to have discrete projections along the axis of measurement, and for a spin ½ system there are only two such projections: UP and DOWN (or + and -). This would imply there is some consistent trend away from the discrete spin splitting in the Stern-Gerlach experiment. People have made thousands of such measurements and so far "no cigar" for hidden variables.

Mathematics is entering into a multiplicity of maths. In fact there is a subject called proof theory, which I am not versed in, and my understanding is that there does not appear to be a consistent system for proofs. Instead it appears there exists a multiple draft system of math-proof systems.

Cheers LC

    I forgot the URL for the talk by Feynman.

    https://www.youtube.com/watch?v=_sAfUpGmnm4

    LC

    Lawrence,

    Hopefully "joy Christian" is just one more of your typos, not a deliberate humiliation. I don't intend defending JC and Klingman. I merely dislike your wording "weed out the crankiest of the cranky ones", "hogwash" and ""no cigar"".

    I admit having sometimes problems to understand what you means, for instance "It is likely ... [something] ... ...".

    Nonetheless I intend reading your essay because it seems to address key questions.

    Regards,

    Eckard

      A lot of that stuff is "cranky." I will give both JC and Klingman the benefit that they did some manner of work in their theories. This does not make them right. The matter of quantum nonlocality and that nature is so utterly cockeyed and crazy one almost can't believe it, as Feynman puts it, is very well settled. Since the 1980s experimental demonstrations of nonlocality have become a cornerstone of physics. Even further this is emerging as "quantum technology," where nonlocal properties permit encryption of information and the teleportation of quantum states nonlocally.

      We are really long past the time where we should be fretting over this stuff. I say that maybe those who don't like this must either "get over it," or as Feynman puts it, "go somewhere else." We can't really leave this universe, but a person who really can't stand quantum mechanics should just get out of physics entirely, or at least physics that connects with nature on the atomic-molecular scale and smaller. One can work on orbital dynamics or many forms of engineering without ever seeing a single 徴, and the quantum world is safely outside your domain.

      There are a number of serious cranks that show up on the blog posts. The worst is Valev, who insists that relativity is all washed up. The problem with people like this is that they simply refuse to really learn and hold fast to ideas that they have that are simply wrong. Five years ago and beyond the FQXI blog was not this bad, but it has become an example of "bad money chasing out good." The great majority of blog posts are cranky.

      LC

      LC,

      In order for you to understand what I meant, I will more completely quote the beginning of the last sentence in your bio:"It is likely our inability to work quantum physics and gravity into a coherent whole is likely to be solved ...". Likely is likely?

      Being a German, I did not immediately understand a lot of your slang expressions, for instance "washed up" in the sense of k.o. or "chasing out good".

      I too disagree with Pentcho Valev, however not entirely and not without serious arguments.

      Doctors like us should not use mere humiliation instead of convincing arguments. Don't you blush for deliberately writing joy C.?

      You wrote "standard mathematics has become increasingly shaken on its core". Unfortunately I hoped in vain for a detailed sober foundational criticism of this core.

      I didn't deliberately remove the capital J from Joy's name. It is just a typo error. Anyway, these blog posts are not formal communications.

      The business of axiomatic set theory is something I am familiar with on a semi-formal sense. It is not central to my work or interests. I also made a decision to keep this essay as informal as possible. It seems the more formal these are the less attention they get.

      LC

      Dear Lawrence,

      Just a quick note. There are, of course, many interpretive difficulties with quantum theory. But one that has been settled is that no theory that regards the wave function as purely epistemic can recover the predictions of quantum theory. The proof is by Pusey, Barrett and Rudolph. So your suggestion that one regard the wave function as "not real" cannot be reconciled with the prediction of quantum theory, in the sense outlined by PBR. In addition, the two-slit interference phenomena already testify to the reality of the wave function in the sense that something is physically sensitive to the state of both slits on every run of the experiment, so something is, in this sense "spread out" between the two slits. Every clearly stated interpretation of quantum theory takes the wavefucntion as physically real, not epistemic.

      Regards,

      Tim Maudlin

        I remember the paper by PBR, maybe about 3 years ago, which I believe is this paper http://arxiv.org/abs/1111.3328 . This was found lacking, or it had problems. It has been a while since then, so I don't recall what the issue was. I don't study these matters that closely, preferring string/M-theory stuff. As I see it wave functions are not real; at best we can only say they are complex, or quaternionic. What is meant by reality with quantum waves is either very strange or nonexistent. I think that if quantum waves have some sort of reality, or ontology, then we have to admit there is no objective reality at all.

        LC

        As I am much involved in the foundations of mathematics, I noted some inaccuracies in your essay on this topic:

        "Bertrand Russell asked what would happen if you have a set of sets that does not include itself"

        A consequence of the axiom of regularity of ZF is that no set is ever member of itself. And as in this theory all objects are sets, every set is a set of sets that does not contain itself, and none of the sets it contains contain themselves either. Instead, the reasoning of Russell's paradox starts by considering THE set of ALL sets that do not contain themselves. (I prefer the word "contain" rather than "include" as the latter may be confused with the inclusion relation, which is not involved in the Russell paradox).

        Where you you take this from :"if [a list] does list itself it must list that it lists itself, which means it must list that it lists that it lists,...and so forth" I neither saw any reasoning like this, nor can find any logic according to which any list of lists should also have to "list that one of its lists, lists something". Wondering where you take that from, I see you refer to a writing by Russell in 1903. I'm not going to check if that reference actually contains that fuss or not, but anyway that's a very old reference, and thus not one that I guess any specialist in the foundation of maths would refer to nowadays when trying to explain what the paradoxes of set theory really are, unless of course they would otherwise know that a given idea turns out to be correct and worth quoting, instead of simply trusting what was written at that time. The only thing I see related to the structure of your sentence, is the axiom of regularity which forbids such loops of constructions, however it is only very remotely related and we would need to completely rewrite and reinterpret your sentence in very different ways in order to actually make such a link, and I don't feel like developing this now.

        "Turing demonstrated that no Turing machine can emulate all other possible Turing machines to determine if it halts. To do this it must emulate itself emulating all possible machines, which gets one into the same conundrum that Russell found"

        Sorry, this is definitely not the way the reasoning goes. There is no problem to make an algorithm emulating all other algorithms, including itself emulating all algorithms including itself and so forth. The problem is not with emulation, but with finitely proving a claim of impossibility for some algorithm (or equivalently an emulation of it) to ever stop. In other words, there is no problem to determine that an algorithm halts, in the case it will halt : we just need to run it "long enough". What we cannot do, is to find a general method that will surely happen, sooner or later, to establish that some other algorithm will NOT halt, in case it will not halt. Because no matter how long a simulation we make, the problem is that, in case it will actually never halt, we can continue emulating it indefinitely and not see it halt but we will remain unable to know if the reason we did not see it halting, is because it will actually never halt or because we did not emulate it long enough to see it halting. The claim "This algorithm will never halt" cannot be proven by running the said algorithm any amount of time, but would require a formal proof of that claim, which is something very different from the act of emulating the algorithm. Even if the said algorithm will never halt, the search for proofs that it never halts, is a very different algorithm (which depends on the precise chosen axiomatic system of set theory), which might never halt either.

        "Kurt Goedel's proof that no mathematical system can ever prove all possible statements as theorems about itself"

        This sentence is confusing, grammatically ill-formed and I cannot see any known result that looks like this. One thing he proved instead, for example, is that no algorithm can ever prove all true arithmetical statements, unless it is self-contradictory (also wrongly proving wrong statements). And also, that among the true statements that no algorithm can prove, is the statement that this same algorithm will never prove any contradictory statements (in case it is true).

        I understand that the foundations of mathematics may not be your area of specialization, so that you may be confused about what the results exactly say and how they may be proven. I also understand that, when something is subtle and complicated, it may be uneasy to explain them in a short essay. However I consider that in case you choose to sketch the explanation of something, you should care to do it right ; and if you can't then you should not even try.

        "The diagonal elements in the list when increased or decreased by one can be formed into a string of numbers that does not exist in the list"

        Hmm, which list are you talking about, and to prove what ? Even while I remember there exists a result whose proof involves something like this, you should care to correctly specify which is this result obtained by which kind of argument formed by involving which list of stuff, instead of casting a randomly shuffled list of possible results mixed with possible reasoning involved in the proofs of some results.

        "the existence of unprovable propositions, and further that these statements effectively declare their unprovability"

        It would not be so interesting to find an unprovable proposition, unless this proposition also happened to be true. Also, not any unprovable statement effectively declares its own unprovability, but only a specifically constructed statement does.

        "The second Goedel theorem is that these statements must be true, because their falsehood would contradict the statement declaring its own unprovability."

        If you could prove that a statement is true because its falsehood contradicts something we know, then the statement would be provable, in contraction to what you just mentioned. So there is an argument why it is true anyway, but it cannot be a strict proof of truth. It is something more subtle. The problem is, when an argument is subtle, it needs a clear enough explanation so as to give a proper idea what it is about. Because the very point of paradoxes is that they are about subtle ideas, that require careful distinctions between concepts which feel similar but are in fact different, until we prove that they are indeed sometimes not equivalent in some cases.

        "the cardinality of the continuum, thought to be larger than countable infinity, is not decidable, but where one can construct models independent of the axioms of set theory"

        You meant : that its value (known to be larger than countable infinity, but coming after how many other infinite cardinals) is not decidable but independent of the axioms of set theory, as we can show by constructing diverse models where it takes different values.

        "We have an intuitive sense of numbers and the inductive reasoning for why if there exists the integer N then the integer N + 1 must exist. Goedel tells us that something goes wrong with this; there is something in basic arithmetic that is not computable".

        I never heard about Goedel claiming there would be anything wrong with the idea that if an integer N exists then the integer N+1 exists too. I even never heard of what it might formally mean for the integer N+1 to not exist.

        "We might then ask the question: do all the numbers between these two large numbers exist?"

        It depends what you mean by "exist". Mathematics has its own concept of existence, by which all these number indeed exist, but which is independent of any concept of physical existence.

        "This means if they exist in some meaning according to computation there must be a machine that performs any calculation"

        Here again, it depends what you mean by "exist". We can mathematically consider the mathematical existence of "machines" more powerful than this universe, with the only defect that we can only know the results of some specific cases of its calculations, those that can be deduced by a much shorter method.

        "the Kolmogorov entropy" : it seems you mean the Kolmogorov complexity, which is indeed a concept of entropy, to not be confused with what is called the name of Kolmogorov entropy but that is quite different.

        There is indeed a theorem by Chaitin about Kolmogorov complexity, which is about finding the smallest possible program making a given output, or optimal data compression algorithm, and is inspired from the Berry paradox. However even though I know this theorem and its proof, I could not relate to it the bits of sentences that you sketched and that seemed to me totally incoherent.

        "We know that between 10^10^10^10 and 10^10^10^10^10 there are numbers that have enormous complexity, but we cannot know what is the smallest of these numbers that has no such description"

        Any very big number can always be described as having an enormous complexity ; the question is whether it also admits a simpler description, with complexity smaller than some amount. If n is a reasonable number (such as n=500) and K is a large number that is "quite complex" in the sense that it is not known as having any relatively low complexity (say, < n+100), then we cannot know what is the smallest number larger than K that has a description with complexity < n.

        However your example completely fails : among all numbers between 10^10^10^10 and 10^10^10^10^10, we do know what is the smallest one with a low complexity, and that is 10^10^10^10 itself (since we could define it in a simple manner !)

        In the ordinary double slit experiment, the paths do not wind around the slits, as any contribution of paths that wind around are usually neglected in descriptions of this experiment (they are small corrections from quantum field theory, and do not affect the basic paradoxical aspect of the experiment).

        I can admit a theoretical concept of super-Turing machine which "solves the halting problem" of ordinary Turing machines. However I think you gave a wrong example here : "the problem of whether a light switch that is turned on in the first second, then off in the next half second, then on again in the next quarter second, then . . . , and whether the light switch is on or off at the end." The obvious answer here is neither. Generally for any algorithm that may turn on or off a switch along time depending on some computation, a super-Turing machine may tell whether there is a time after which it will stay on, or a time after which it will stay off, or neither, i.e. that it will keep alternating endlessly (for any time there exists a later time with different result). But if you explicitly assume endless alternation at the start then you no more need any super-Turing machine to discover that you will get endless alternation.

        Unfortunately, this abundance of inaccuracies I found in what I could decipher in your essay as I know the topics, does not leave me quite optimistic about what I cannot decipher, on topics I am not familiar with (especially HOTT)

        A simple web search seems to indicate that there is no such thing as "Polish set theory".

        We have multiple theories for the foundations of mathematics, with possible variants of set theory, but I would not take this as if it meant "we have no particular foundations to mathematics". There is a picture of hierarchy and interdependence between versions of set theory, and there are clear reasons for this. The main reason is that there is not one unique mathematical universe, but an endless hierarchy of bigger and bigger ones, that fit different descriptions.

        Chaitin's work insisted on pessimistic aspects of the foundations of mathematics. This does not mean everything in mathematics is baseless and happens by chance, "by no logical reason". Actually, the incompleteness theorems themselves are examples of remarkable successes of mathematics to handle its own foundations - because they are mathematically proven results !

        You incoherently conclude "It is very difficult to understand how this could be scientifically demonstrated, yet maybe regularities in physics described by mathematics exist for no reason at all. Mathematics and physics have this curious relationship to each other for purely stochastic or accidental reasons; there ultimately is no reason for this"

        You mysteriously remove the "maybe" on the way, replaced by an "ultimately"... seemingly for no reason at all. What can allow you to you positively claim this "ultimate" absence of reason, as if you got a proof for this, while at the same time you say it is very difficult for you to "understand" the possibility to prove it, either that such a proof should exist but you visibly do not know it (otherwise you would understand it) or anyway you strongly believe that this absence of reason is a fact (why ?) ?

        But the worst form of incompleteness, in my opinion, is that of the incomplete understanding of how the foundations of mathematics look like and what do the diverse incompleteness theorems actually say and for what reason, that may be due to a lack of clarity in the way these things are usually presented. I invite you to visit my site settheory.net where I cared to explain as clearly as I could the main concepts and paradoxes at the foundations of mathematics. Maybe you will find there that the real picture of the foundations of maths is more coherent than what you now think.

        Finally, I invite you to read my own essay where I discussed how quantum physics avoids the incompleteness of the infinity which the continuity of physical space naively seems to contain.

          The holographic principle does indicate that the entropy of a system, or the information available about a system is contained on the boundary of the system. So in some sense there is something to be said about the boundary of a volume or a surface. I am not sure about your ideas about the motion of surfaces.

          Cheers LC

          The one problem that I had with this is first off that there is a severe word or symbol limitation and secondly I have to admit I am not a student of ZF set theory. I discussed these set theory parts in a pretty cursory manner, and I may have in doing this in a truncated manner have done some damage. In cutting back the size of this essay I cut mostly from the discussion on Goedel's theorem and set theory

          My point about Russell paradox is that if S = {x|x \notin x} then S \in S implies that S \notin S. So one does the opposite and one gets S = {x|x \in x} then S \notin S implies that S \in S, and one can then think of having to fix this with lists of lists and lists of lists of lists and so forth. Turing's proof is a sort of Cantor diagonal proof, and this does have a "physical" meaning that a universal Turing machine is not able to enumerate all Turing machines.

          I really discussed these matters within little more than a page, and so the discussion is pretty thin. I also presented the ideas in more of a physical sense. The issue of Kolmogoroff entropy or complexity is meant to illustrate how not all numbers are computable. I stand by my statement about the complexity of numbers. Also Godel's theorem does indicate that Peano's number theory is incomplete, and so something funny does happen with N+1

          As a rule with these essays it is best to keep the mathematical pedantry to a minimum. It works best to give readers more of an intuitive sense of these matters than it is to lay down layers of mathematical symbolism.

          http://www.cambridge.org/us/academic/subjects/mathematics/logic-categories-and-sets/descriptive-set-theory-polish-group-actions

          LC

          • [deleted]

          Dear Dr. Crowell,

          Real surfaces are not holograms. When you look upwards at night, you will see a plethora of the real surfaces of myriads of stars. Einstein was completely wrong, it is the real surfaces of real stars that must be traveling at the same constant speed or else it would be physically impossible to see all those star surfaces instantly and simultaneously. Real light cannot travel far from its source as you can prove by noting that the light from the stars remains close to each star that produces it. I am certain that real light cannot have a surface. Real light is the only stationary substance in the real Universe.

          Joe Fisher

          The holographic surfaces that are invariants are event horizons. In some sense these are all travelling the speed of light, at least according to those who cross them. I am not sure what you mean by surfaces all moving the same speed. If I am driving my car I think I would be amiss if I assumed the surfaces of the other cars in the traffic are moving the same speed that I am.

          Cheers LC

          Hi Lawrence,

          Nice essay. I am intrigued by the homotopy type theory. Do you understand its basic points and motivation? On a side note PBR is actually correct (originally I thought I found a loophole there but there is none).

          Cheers,

          Florin

          PS: I think you may appreciate this link: https://www.youtube.com/watch?v=WabHm1QWVCA

            Dear Dr. Crowell,

            When you are driving your car, the surface of your body, the surface of the car, the surface of the road your car is on and the surface of all real objects in the real Universe must be traveling at the same constant speed or they could not travel simultaneously. Although an holographic surface may be an invariant event horizon, the surfaces of the floor and walls and of all of the objects in the room where the holograph is being presented are real and they are all traveling at the constant default speed of surface. Real light does not travel because real light does not have a surface.

            Glad to inform you,

            Joe Fisher

            Hi Florin,

            I am in one sense disposed to Wildberger when it comes to mathematics that is computed or that has a physical meaning. There seems to my mind there are two notions of mathematics with respect to infinity and the continuum. The pure notion, which is the standard approach to mathematics, is in some ways Platonic. I am not particularly anti-Platonic, but the problem I see with Platonism is that it largely has nothing to do with most things you actually want to know. The Platonist type of mathematics, which is embodied by ZF or standard set theory, largely exists on its own, and what is actually calculated in both mathematics and physics is some tiny part of this. I am not really that concerned about the existential aspects of set theory and what might be called Platonism, but I don't think this has what I might call a hard existence. For a thing to have a hard existence it must be computed and there must be a physical way it can be represented. A set, number, function that can't be physiccally represented has a sort of "ghostly" existence at best, and I am not out to exorcize ghosts from mathematics particularly. However, for something to have a hard existence it can't be a ghost, it must have "meat."

            The "ghosts" of pure mathematics are useful in some ways, for they allow us to make various arguements so that there "deltas" and "epsilons" that fortunately cancel out and we don't have to actually produce an infinitesimal number in our hands. In that sense these can of course have a utility, but this works only when the system is such that an actual infinity, or infinitesimal, is removed from the answer.

            This is in a way not that different from nonlocal hidden variables. Do nonlocal hidden variables exists? Maybe, or for that matter sure; I can arrive at a theory (in fact a vast number of them) of nonlocal hidden variable theory. However, there appears to be a serious obstruction to finding any observable consequence to any hidden variable theory. This obstruction is I think a topological property, and has correspondences in sheaf theory. Classical mechanics is map from the reals to the reals. Quantum mechanics is map from the reals, or really complex or quaterion numbers, to a discrete set of numbers corresponding to eigenvalues. Quantum physics says that we can know all sorts of stuff about those eigenvalues, but we have a very limited contact with the continuum stuff that involves waves and fields. Quantum mechanics then might be telling us much this lesson. Any hidden variable theory is then some set of functions, dynamics and so forth, that tell us how the continuum stuff maps to a discrete set of numbers. An obstruction against this appears to be at least similar to a relationship between mathematics that is "ghostly" and that which has "meat."

            I am not an expert on type theory and HOTT, but I have been studying it some. I am not sure about actually using this in physics, but this seems to be a reasonable sort of mathematical foundation for the sort of mathematics that could be relevant to phyhsics in the future. It imposes no notion of infinity, but it treats types as unbounded in their cardinality. There is no fundamental limit to their size, but they must have some sort of index, similar to a homotopy or monodromy, that has to be computed --- it must be inserted into some "register" or "slot." I wrote on this topic because it seemed to be the closest thing that fit the question proposed by FQXI.

            I have visited your blog site some, but have not had much time to contribute entries. Maybe I will try to be more diligent on that before long.

            Cheers LC

            Hi Lawrence,

            If you want to write a guest blog post at my blog about your FQXi entry to advertise it and boost the penetration of your ideas you can do so at any time. In the last few months I got caught in so many "clerical" activities that I had to put on hold learning new things. I'll participate in the FQXi grant contest but I don't know if the ghost of Joy Christian will kill my entry. If I have extra time I might write an essay for the FQXi context but I know I don't have the time necessary to invest to win. If I'll do it it will be only for advertisement purposes.

            Cheers, Florin

            I might take you up on your offer. I probably will not write about the FQXi essay topic, but on a subset of it involved with the Bott periodicity and the large N SU(N) for the structure of an event horizon.

            I think this has some bearing on PR boxes. Quantum gravity requires that the field theory be nonlocal. Standard QFT has local field amplitudes with Wightman causality conditions, such as equal time commutators. Nonlocality occurs with the expectations of the operators over the Fock basis which gives quantum waves. Quantum gravity I think involves further violations of inequalities, which PR boxes or nonsignalling conditions are maybe capable of working with. Maybe there are bounds beyond the Tsirelson bound?

            If you want I can send to you an article I wrote but have yet to submit for publication that addresses some of this.

            Cheers LC

            Dear Sir,

            Ancient Indian texts describe in detail about number theory including what is a number, what is zero, what is infinity, what are negative numbers and irrational numbers, the difference between one and many, why one is the first number, why two follows one, why three follows two, why four follows three, why zero comes after nine, why the number system repeats thereafter, why these numbers are called one, two, etc. Some of it you can see in our essay. They also knew calculus (called chityuttara). These are not primitive, but highly advanced theories related to the physical world. What you call distance between objects is actually space, which is the ordered interval between objects, just like time is the ordered interval between events.

            Our instruments for perception/measurement have limited capacity both in content and time. Thus, what we measure depicts a temporal state of a limited aspect over limited period. The problem comes when we generalize our limited information. We impose our ignorance or inability to know on the Universe and call it fuzzy. Every quantum system (including superposition, entanglement, spin, etc) has a macro equivalent. Unfortunately, instead of looking for it, modern physics chases fantasy like extra-dimensions, dark energy, etc. We have discussed these in our essay including Russell's paradox. Computers are GIGO - garbage in garbage out. It cannot overcome limitations of programming (apart from physical and energy constraints), which is done by a person with limited knowledge. Thus, they cannot answer all questions.

            We have discussed Gödel's incompleteness theorem and Wigner's paper elaborately to show their inherent deficiencies. Regarding two-slit experiments, we have repeatedly wondered why no one has conducted the experiment with protons. That would show the fallacy. Though we know much about electrons, we still do not know "what is an electron". This ignorance leads to fantasy and we call that a theory! The same problem bugs the concept of event horizon that is said to encode the causal structure of Spacetime. Each event in Spacetime has a double-cone attached to it, where the vertex corresponds to the event itself. Time runs vertically - the upward cone opens to future of this event. The downward cone shows past. But if the light pulse radiates in all directions, it should show concentric spheres and not a double-cone. The trick is done by first taking two dimensions and time as the third dimension. But even then it will be concentric circles and not a conic section. Event horizon is the limit of our vision. The recently debated black hole firewall paradox arises out of such misleading manipulations.

            As Carl Popper remarked, modern science is more concerned with the cult of incomprehensibility than finding the truth. There is a need to review and rewrite physics.

            Regards,

            basudeba