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More Smolin Mayhem

  1. Aug 3, 2015 #1
    Any chance of a discussion of this paper? I promise I won't even comment!

    Is it just that it's considered too philosophically speculative to even be lawfully discussed even in BTSM? Or is it just that everyone here but me genuinely thinks he's more or less a crackpot?

    [edit] Yes I forgot the link
    http://arxiv.org/pdf/1507.08576v1.pdf

    Non-local beables
    Lee Smolin
    (Submitted on 30 Jul 2015)
    I discuss the idea that the beables underlying quantum physics are non-local and relational, and give an example of a dynamical theory of such beables based on a matrix model, which is the bosonic sector of the BFSS model. Given that the same model has been proposed as a description of M theory, this shows that quantum mechanics may be emergent from a theory of gravity from which space is also emergent.
    Comments: 7 pages LeTex. Submission to the John Bell Workshop 2014, of the International Journal of Quantum Foundations
    Subjects: Quantum Physics (quant-ph)
    Cite as: arXiv:1507.08576 [quant-ph]
    (or arXiv:1507.08576v1 [quant-ph] for this version)
     
    Last edited: Aug 3, 2015
  2. jcsd
  3. Aug 3, 2015 #2
    Got a link or a full bibliographic reference?
     
  4. Aug 3, 2015 #3
    Hello Jim,

    He certainly is not a crackpot. That's not a fair response to this paper, yes it is a philosophical paper.
    That Quantum mechanics is emergent is not entirely new as you may know, an the non local nature of quantum mechanics is a reasonably correct and good description of measurements scientists around the world perform describe and publish..
    Beables have of course yust a methaphorical meaning.
     
    Last edited: Aug 3, 2015
  5. Aug 3, 2015 #4

    marcus

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  6. Aug 3, 2015 #5

    marcus

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    Yes, that seems right. BTW I want to call attention to a talk Lee Smolin gave at PI recently and an accompanying paper that came out about the same time as this one. The timing suggests there could be some relation to this one. There is video for the talk---and slides PDF:
    http://pirsa.org/15050087/
    Quantum mechanics from first principles
    Speaker(s): http://pirsa.org/speaker/Lee_Smolin [Broken]
    Abstract: Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. This is an expression of Leibniz's principles of sufficient reason and the identity of the indiscernible. The quantum state of a microscopic system is defined to correspond to an ensemble of subsystems of the universe with identical constituents and similar preparations and environments. A new kind of interaction is posited amongst such similar subsystems which acts to increase their distinctiveness, by extremizing the variety. In the limit of large numbers of similar subsystems this interaction is shown to give rise to Bohm's quantum potential. As a result the probability distribution for the ensemble is governed by the Schroedinger equation. The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically. This proposal could be tested by constructing quantum devices from entangled states of a modest number of qubits which, by [their] combinatorial complexity, can be expected to have no natural copies.
    Date: 12/05/2015 - 2:00 pm

    This strikes me as a very simple idea: macroscopic systems are unique, so they behave classically. microscopic systems are part of herds so must behave quantumly in order to establish their individuality. When you have an idea which is very simple AND you can DERIVE stuff like Schroedinger equation from it this is always interesting. No matter how strange the simple idea is, if you can logically derive QM from it this could lead somewhere--to a deeper insight. So here is is the paper that has essentially the same abstract as this talk:
    http://arxiv.org/abs/1506.02938
    Quantum mechanics and the principle of maximal variety
    Lee Smolin
    (Submitted on 9 Jun 2015)
    ...
    ...
    The measurement problem is naturally and simply solved. Microscopic systems appear statistical because they are members of large ensembles of similar systems which interact non-locally. Macroscopic systems are unique, and are not members of any ensembles of similar systems. Consequently their collective coordinates may evolve deterministically.
    This proposal could be tested by constructing quantum devices from entangled states of a modest number of qubits which, by [their] combinatorial complexity, can be expected to have no natural copies.
    24 pages.
     
    Last edited by a moderator: May 7, 2017
  7. Aug 3, 2015 #6
    Yeah I took that measure of similarity In "Maximal Variety" to be orthogonal to the classical measure of locality. It also seemed to me (somehow) to be pointing at Verlinde and the idea of entropic gravity. As mentioned in post #5 he also described testable predictions.
     
    Last edited: Aug 3, 2015
  8. Aug 3, 2015 #7
    I'll have to work out what is the difference between a non-local beable and a string I guess.
     
  9. Aug 3, 2015 #8

    marcus

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    http://www.scholarpedia.org/article/Bell's_theorem#Bell.27s_definition_of_locality
    Here's a discussion of Bell's definition of "beable"
    ==sample excerpt==
    "Beable" is Bell's term for those elements of a theory which are "to be taken seriously, as corresponding to something real"22. As an example, Bell cites the electric and magnetic fields of classical electromagnetism:

    In Maxwell's electromagnetic theory, for example, the fields E and H are 'physical' (beables, we will say) but the potentials Aand ϕ are 'non-physical'. Because of gauge invariance the same physical situation can be described by very different potentials.23
    As Bell points out, it is therefore no violation of locality "that in Coulomb gauge the scalar potential propagates with infinite velocity. It is not really supposed to be there."24

    The beables of a theory have values that (according to the theory) are supposed to exist independently of any observation or experiment. In this regard Bell contrasts the notion of beable with the notion of "observable" which features prominently in orthodox quantum theory:

    The concept of 'observable' lends itself to very precise mathematics when identified with 'self-adjoint operator'. But physically, it is a rather woolly concept. It is not easy to identify precisely which physical processes are to be given the status of 'observations' and which are to be relegated to the limbo between one observation and another. So it could be hoped that some increase in precision might be possible by concentration on the beables, which can be described in 'classical terms', because they are there.25
    This woolliness suggests that the notion of "observation" should not appear in the formulation of (candidate) fundamental physical theories. Indeed, every aspect of a physical process (including those processes we humans classify as "observations") should be completely reducible to the actions and interactions of some physically real objects — some beables. In an "observation", both the "observed system" and the relevant experimental apparatus, for example, must be made of beables, and anything like a measurement outcome which (say) emerges anew from the system-apparatus interaction must be contained in the final disposition of those beables.

    Locality is the idea that physical influences cannot propagate faster than light. It thus presupposes a clear identification, for a given candidate theory, of which elements are supposed to correspond to something that is physically real. Here is how Bell makes this point: "No one is obliged to consider the question 'What cannot go faster than light?'. But if you decide to do so, then the above remarks suggest the following: you must identify in your theory 'local beables'"26. (We will discuss this again later.)

    Local beables are those elements of a theory which should correspond to elements of physical reality living within spacetime. Those should include the representation of the ordinary objects of our experience, such as tables, chairs and experimental equipment. As Bell puts this:...
    ...
    ...
    ==endquote==
     
  10. Aug 3, 2015 #9

    marcus

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  11. Aug 3, 2015 #10
    I need a better foothold on what is meant by a "matrix model". I can picture a diagonal - orthonormal basis matrix. I can picture (the idea of) complicated asymmetric matrices describing coupled differential equations (But those seem a zoo). I can picture a matrix representing a coordinate system or even a tensor field (kinda sorta). And I can picture model matrices that map independent and dependent variables (like a control matrix)... Is there any intuitive way to picture the kind of "matrix model" he is referring to, something to chew on while I try to read?

    http://arxiv.org/abs/hep-th/0201031
    High Energy Physics - Theory
    Matrix models as non-local hidden variables theories

    Lee Smolin
    (Submitted on 5 Jan 2002)
    It is shown that the matrix models which give non-perturbative definitions of string and M theory may be interpreted as non-local hidden variables theories in which the quantum observables are the eigenvalues of the matrices while their entries are the non-local hidden variables. This is shown by studying the bosonic matrix model at finite temperature, with T taken to scale as 1/N. For large N the eigenvalues of the matrices undergo Brownian motion due to the interaction of the diagonal elements with the off diagonal elements, giving rise to a diffusion constant that remains finite as N goes to infinity. The resulting probability density and current for the eigenvalues are then found to evolve in agreement with the Schroedinger equation, to leading order in 1/N. The quantum fluctuations and uncertainties in the eigenvalues are then consequences of ordinary statistical fluctuations in the values of the off-diagonal matrix elements. This formulation of the quantum theory is background independent, as the definition of the thermal ensemble makes no use of a particular classical solution. The derivation relies on Nelson's stochastic formulation of quantum theory, which is expressed in terms of a variational principle.
    Comments: 25 pages, latex, no figures
    Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
    DOI: http://arxiv.org/ct?url=http%3A%2F%2Fdx.doi.org%2F10%252E1063%2F1%252E1454379&v=44ba819c [Broken]
    Cite as: arXiv:hep-th/0201031
    (or arXiv:hep-th/0201031v1 for this version)
    Submission history
    From: Lee Smolin [view email]
    [v1] Sat, 5 Jan 2002 19:39:18 GMT (19kb)
    Which authors of this paper are endorsers? | What is MathJax?)
     
    Last edited by a moderator: May 7, 2017
  12. Aug 4, 2015 #11

    julian

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    In bojowald's book "once before time":

    "Lee Smolin is a physicist's physicist: a daring explorer, not afraid or unashamed of undertaking bold raids deep into unknown territory even at the risk of coming home beat up. He is most creative in suggesting possible physical phenomena that may also be wrong."

    He is extremely good at maths that makes him a unique talent.

    edit: Thinking of it Smolin calls Chris Isham a "theorist's theorist" - making Isham a physicist's physicist's theorist's theorist?
     
    Last edited: Aug 4, 2015
  13. Aug 4, 2015 #12
    I really dig Smolin for a lot of reasons. And In some other papers of his I've been able to hang on a good way, but after a few tries I have to say I'm stuck on the initial setup of this one, and the sources related to it just go deeper into M and string theory. I've read some things about that (strings), but lay stuff, and none of it is connecting.

    "The beables of the theory are d, N × N real symmetric matrices... The classical, local observables are taken to be the eigenvalues of these matrices, λai . These can be imagined to give the positions of N particles in d dimensional space. Relative to these, the matrix elements are non-local, as a shift in the value of any one matrix element perturbs all the eigenvalues.

    I don't suppose anyone could paraphrase what these NxN matrices represent? Just an idiot's walkway. I'm able to read the notation and I I've had linear algebra. But I am not getting what physical scheme these represent? What is an example row, column? How can something as abstract as a mathematical matrix be a "beable"?
     
  14. Aug 5, 2015 #13
    Not so hard for mathematical realists.
     
  15. Aug 7, 2015 #14
    Believe it or not that actually helped.

    a matrix everywhere for each degree of freedom or dimension, sized to relate all "things" to all other things, in that dimension or degree of freedom. So really it is more of a set of d coordinate systems.

    The eigenvalues are results of the rules of coordination for each dimension. The rules are the eigenvectors.
     
    Last edited: Aug 7, 2015
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