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Spin network euristic for pre-quantum picture

  1. Oct 3, 2006 #1

    marcus

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    spin network heuristic for pre-quantum picture

    this is about Smolin's two most recent
    http://arxiv.org/abs/hep-th/0605052
    Generic predictions of quantum theories of gravity
    Lee Smolin
    For inclusion in "Approaches to Quantum Gravity - toward a new understanding of space, time, and matter", edited by D. Oriti, to be published by Cambridge University Press
    "...generic consequences...of a class of background independent quantum theories of spacetime called causal spin network theories.... Within the last few years three possible generic consequences have come to light. These are 1) Deformed special relativity as the symmetry of the ground state, 2) Elementary particles as coherent excitations of quantum geometry, 3) Locality is disordered. I discuss some possible experimental consequences of each."

    in this paper (among others) is presented an idea of residual non-locality in emergent 3D space---as the spatial network evolves out of Planck conditions by a process of local moves: expansion moves and exchange moves performed on the network.

    this picture of spatial evolution, by which expansion moves gradually almost but not quite eliminate all non-local relations and lead to a nearly perfect emergent 3D space, has apparently served as an HEURISTIC to give a promising idea of a deterministic process from which quantum mechanics emerges

    http://arxiv.org/abs/quant-ph/0609109
    Could quantum mechanics be an approximation to another theory?
    Lee Smolin
    10 pages
    "We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by averaging over variables which are not internal to the subsystem, which may be considered non-local hidden variables. We find conditions for arriving at quantum mechanics through such a procedure. The key lesson is that the effect of the coupling to the external degrees of freedom introduces noise into the evolution of the system degrees of freedom, while preserving a notion of averaged conserved energy and time reversal invariance.
    These conditions imply that the effective description of the subsystem is Nelson's stochastic formulation of quantum theory. We show that Nelson's formulation is not, by itself, a classical stochastic theory as the conserved averaged energy is not a linear function of the probability density. We also investigate an argument of Wallstrom posed against the equivalence of Nelson's stochastic mechanics and quantum mechanics and show that, at least for a simple case, it is in error."

    ===my irresponsible comment :smile: ====

    the heuristic idea is actually very simple.
    if you start with a network of random connected nodes (undefined primitve idea) symbolizing very hot dense Planck regime where any node has a chance to be "adjacent" to any other, and then if you
    EVOLVE that by expansion moves where a node can be replaced by several nodes in simplicial network, and by other local link-swapping moves
    then eventually the expansion will WIPE OUT THE NONLOCALITY and some recognizable space will emerge where you can SAY who is close to whom and who is between which and it all makes sense

    but there will still be ROGUE LINKS left over from plancktime which didnt get ironed out in the regularization that happened thanks to expansion.

    and these rogue link suckers could span across vast reaches. one in the chair you occupy could reach to the other side of the Big Whatever.
    But you wouldnt know about it, because expansion has washed almost all the nonlocality out. We DON'T SEE THE SPORTS.

    now comes the good part, where you want to DO COPENHAGEN ON IT and you place a plastic baggie around some part of the universe and you scrutinize inside the baggie (the System) and you deem that certain non-deterministic things are going on inside the baggie.

    I better make a separate post about that.
     
    Last edited: Oct 4, 2006
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  3. Oct 3, 2006 #2

    marcus

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    this is very serious, I think, which is why it sound like I am joking.

    it is one of the crazy ideas that is sent to us by the grace of the Crazy One. it could be.

    here is what it says in conclusions on page 9 of the more recent paper

    However in the approaches studied in [2, 3], we are in a very different situation from ordinary thermodynamics, because the interactions between the reservoir and system are mediated, not by heat flow across a wall, but by a network of non-local interactions. These are given by off diagonal matrix elements in Adler’s formulation and by explicit non-local interactions in the formulation in [3]. It is then not impossible that the conditions found here to be necessary could be satisfied[15].
     
  4. Oct 3, 2006 #3

    marcus

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    the illusion of quantum mechanics arises from a THEORY OF THE WHOLE UNIVERSE when one places a baggie around a certain part of it and proceeds to do measurements on what is inside

    then it appears that quantum things are happening in the System under observation BECAUSE....

    you tell me.

    because the stuff inside the baggie is connected to the whole frigging outside universe by a tiny residue of nonlocal links that we can't see

    =====================================
    in this sense a theory of the foundations of Quantum Mechanics has to be the same thing as a theory of the whole Universe


    quantum theory and spacetime are, at root, the same thing---Baez was saying this from a categoric POV.

    also this idea of Smolin's gets rid of certain troubles. or perhaps one can say that it transcends certain enigmas.

    I urge present company to read this "...Another Theory?" paper and comment.

    Another Theory is what I'm privately calling smolin's latest (quant-phys/0609109---"quant-phys September one-oh-nine") because the full title is a lot to say:
    "Could Quantum Mechanics Be an Approximation to Another Theory?"

    Chronos has sagely observed that the title has an innocent air about it.
    Chronos suggests the question is slightly tongue-in-cheek---the proper answer being It Sure Could :biggrin:
     
    Last edited: Oct 4, 2006
  5. Oct 3, 2006 #4

    selfAdjoint

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    Just one question. Why did you spell it euristic? There's a rough breathing in the Greek source word, usually represented in English by the letter h. I've even seen it argued that Archimedes, in the famous bath incident, was yelling HEUREKA, not the word usually cited. The argument was that an Eastern Greek, say an Ionian, might elide the rough breathing, but a western Greek like Archimedes (from Sicily) never would.
     
  6. Oct 3, 2006 #5

    marcus

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    well you are a welcome sight! long time no see!
    yes, I thought "how do you spell EUREKA"
    which is the past tense of the verb
    and then I said to myself that euristic must be spelled the same way

    which of course was wrong, I should have done a check


    the real Greeks wuz Cockney, guv'ner, and dropped their haitches!

    Hipparchus, Pythagoras, Aristarchus, they were all Ionians from the anatolian west coast (the California of its day).
    I expect many of those Cockney Ionians migrated to Sicily and Magna Graecia when the Persians got too obnoxious---anyway that's my excuse :smile:
     
    Last edited: Oct 4, 2006
  7. Oct 4, 2006 #6
    This proposal must be a joke (btw. let me point out to you that in one of my conversations with john baez on this forum about his spacetime view on entanglement I was joking ``wheter he believes in invisible threads carrying the nonlocality involved'' on which he replied ``for sure not'' :zzz: ). There are so many obvious arguments against such proposal : (a) how can these non local connections survive over distances of 10^{27} planck lengths (molecular scale) ? (b) in a lab, we prepare an entangled state, so how to dynamically create the threads ? (c) give me a dynamical model which shows a phase transition from ``surviving'' to ``cut'' non local links at some length scale x(T) and some time T after the big bang (d) why are all the links not cut yet ? And so on and so on ... but I liked your thread about Burton Richter, wise man.

    Careful
     
  8. Oct 4, 2006 #7

    marcus

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    I corrected the spelling, as per suggestion.

    ======================

    well to continue, we have a situation where everybody from David Gross on down is saying that to take the next step they expect they may have to give up their idea of space and their idea of time and have these amenities EMERGE from some deeper entity.
    and roughly speaking it is a case of mostly talk and no action

    but what Smolin is presenting here (not for the first time) is an heuristic model of PRE-SPACE from which usual familiar space can emerge and incidentally this pre-space suggests some ideas of PRE-QM.

    an heuristic model is a good heuristic model if it SUGGESTS worthwhile ideas to investigate. you probably don't need to take the model LITERALLY in order to get the good out of it
    ======================

    another thing is that this heuristic picture of PRE-SPACE that I'm going to give you is partly my own re-construction. In the paper, Smolin is talking about familiar format phase-space with positions and momenta and Hamiltonians and limits and integrals. He is NOT TALKING ABOUT NETWORKS. That is obvious, just look at the paper----it is couched in CONVENTIONAL STATISTICAL MECHANICS.

    so I am kind of reverse-engineering the discrete combinatorial pre-space that I think partly inspired this venture into statistical mechanics foundations of QM. and drawing on things Smolin has written elsewhere.
    ======================

    when you think about the pre-space the important thing is just to think of a batch of NODES. they are abstract nodes.
    the only purpose is to give you something to draw arrows between---to connect by the adjacency relation

    in pre-space, there is no space as we usually picture it---just this formless batch of nodes.
    an appearance of "space" will eventually arise from the nodes

    a node is nothing in particular, it has no characteristics or structure. it exists only so that you can have ADJACENCY RELATIONS between the nodes. we have a matrix which keeps track of WHICH NODES CAN "FEEL" WHICH OTHER NODES

    that is all, it is purely abstract, so far there is no space and adjacency does not imply any spatial adjacency. yet.
    ======================

    heuristically, to suggest ideas, we symbolize the "planck regime" at around the time of the big bounce by a batch of nodes each of which is equally likely to be adjacent to any other node
    it is a completely disordered linkage of the nodes that symbolizes very high density and temperature, they are all moving around and any one is likely to be adjacent or feeling any other, like some kind of drunken Romans-whooping-it up orgy.

    ======================
    heuristically, again, we symbolize the expansion of space by a process of applying local moves to the set of adjacency-relations, where in an "expansion move" one node is replaced by a CLUSTER of interconnected nodes.

    ================
    at the conference in October 2005, Smolin discussed some work by Hal Finkel where he simulated this sort of thing in a computer. you started with a "big bounce" situations where all the nodes were adjacent to each other or within a few steps, and you had a selected repertory of local moves which you applied. and the EXPANSION ones were allowed to dominate over the simple RECONNECTION ones (which dont increase the number of nodes)

    the upshot of this kind of computer simulation of the expansion of pre-space is that eventually ORDERLY DIMENSIONALITY EVOLVES AND YOU GET SOMETHING LIKE A LATTICE with even some idea of DISTANCE which is just the number of links or nodes you have to go thru to get from here to there.

    so the thing gets untangled and flattens out "of its own accord."

    so you start with just a bunch of abstract nodes, which are related by some "adjacency matrix" which just keeps track of who feels whom. and that is a pre-space. and some selected local moves allow it to evolve
    and pretty soon you have the ILLUSION of usual space, and an idea of usual distance,
    and then you can begin to say things like "between", "next to", "near", "far", "inside of", "outside of", "area", and all those nice things.

    that's what "emergent" means.

    I guess the idea of time should emerge from the pre-time concept of the occurrence of the local moves---but this is just an heuristic. it is supposed to suggest ideas to try.

    NOW WE HAVE TO SEE HOW QUANTUM MECHANICS ARISES AS A RESIDUE of the wild connections left over from the big bounce (before there was any space, there was only this "planck regime" of nodes all interconnected everywhichway and disorderly-fashion)
     
    Last edited: Oct 4, 2006
  9. Oct 4, 2006 #8
    I have learned in high school that you do not suggest something exotic unless you have serious evidence for it. Moreover, exotic ideas which are seldomly written about are usually thought of by those people who remain silent and realize the idea has severe shortcomings.

    Careful
     
  10. Oct 4, 2006 #9

    selfAdjoint

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    Well, I think that's a property of the model. This new physics, remember? Saying that old physics doesn't handle the case is kind of irrelevant. By the same token though, this new physics better come up with some detailed predictions pretty quick, lest it fall into the state of string theory.

    (b) in a lab, we prepare an entangled state, so how to dynamically create the threads ? [/quote]

    In the lab we prepare states as dense and notionally of the same potential as the big bang states, so how do we dynamically create a big bang?

    (c) give me a dynamical model which shows a phase transition from ``surviving'' to ``cut'' non local links at some length scale x(T) and some time T after the big bang [/quote]


    Yep, that's a requirement. If this model has any legs somebody will be doing just that.[/quote]

    (d) why are all the links not cut yet ?[/quote]

    I believe Marcus gave a heuristic explanation of that? No?
     
  11. Oct 4, 2006 #10
    You seem to miss my point that no matter what physics one thinks about, such result is extremely unlikely in any case.


    I hope you were joking since the wavelengths needed to prepare entangled states are in the optical range, that is wavelengths of the order 10^{-7} - 10^{-6} meters, quite far removed from 10^{-35} I must say.

    Well, if someone proposes a realistic model of this kind, I promise to go on foot from Brussels to Paris.

    No, he did not. The reason why I am sceptical is because I have given such scenario's some thought myself, in the end they just convince you more and more that strict locality need to hold. People seem to forget that spacetime is known to be smooth on distance scales of 10^{-18} meters (or even beyond) and that entanglement carries (as is spectacularly claimed) over distances of 10^{5} meters ! It doesn't require much to realize that this whole invisible thread idea is kind of nonsensical if you know how big 10^{23} really is. In other words : quantum foam is a high energy phenomenon, it would be very strange indeed (and actually against the spirit of renormalizability) that the latter is leaving such an imprint on the low energy sector.

    Careful
     
    Last edited: Oct 4, 2006
  12. Oct 4, 2006 #11

    marcus

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    the heuristic idea is to see Quantum Mechanics uncertainty as arising from the RESIDUAL DISORDER left over from the bounce.

    it really is so simple it sounds like a Kipling Just-So
    or sunday-school theology (which is the same root style excecpt that Kipling laughed)

    ================

    IIRC the "sports" would typically be between points separated by billions of lightyears (in our ordinary emerged metric).
    They did some rough statistical estimates about the prevalence of rogue links, and their length in conventional terms.

    My impression is that if you are thinking in terms of links of a few meters or a few hundred kilometers, then you simply don't understand what the research is about, or what is serving as heuristic inspiration for this paper.

    Of course i could be mistaken. The paper itself is NOT ABOUT spin networks, or any kind of discrete combinatorial model. It does not stipulate or make precise about the networks business.

    I am hoping someone will read the actual paper, which is just 10 pages.
     
    Last edited: Oct 4, 2006
  13. Oct 4, 2006 #12

    selfAdjoint

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    And you seem to miss MY point. Just because there are low energy methods for creating entangled states doesn't mean that entangled states can't be a feature of high energy physics. It seems like a completely irelevant argument to me.
     
  14. Oct 4, 2006 #13
    I did not miss that : as I said before, extremely unlikely and against the spirit of renormalization (where you assume high energy physics is not leaving a trace in the low energy sector) :smile: The transition from the planck scale to the hundreds of kilometers in EPR photon experiments is simply too high for any reasonable high energy mechanism to be responsible for entanglement if you believe it exists in the first place of course. It is even worse than saying (if I remember my numbers correctly) that the earth is directly connected with any celestial body in the entire universe.
     
    Last edited: Oct 4, 2006
  15. Oct 4, 2006 #14

    selfAdjoint

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    Yes , but RG is just itself a heuristic based on low energy observations. Nobody went up on Sinai and took his sandals off to receive it.
     
  16. Oct 5, 2006 #15
    Right, and tomorrow it could rain angels; the read sea might open again and devils raise from the earth. :tongue2: I have never been a proponent of renormalization, but still I think it is madness to assume you can cook up a non-local model which has all the right predictions and manages to bridge more than half of the logarithmic scale of the universe. Another miracle which would have to occur is that this phase transition would have to happen at exactly the right spot so that you don't get planets connected by Newtonian rods.

    Careful
     
    Last edited: Oct 5, 2006
  17. Oct 5, 2006 #16

    Chronos

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    Careful, I'm pleased you brought up on renormalizability and feel it is very relevant. While Wilson's renormalization groups have proven remarkably successful, I have this haunting suspicion a few ghosts may still lurk in the shadows.
     
  18. Oct 5, 2006 #17
    I cannot agree more with you, no theory which claims to be fundamental should use renormalization (at least in my mind) since the latter teaches us we are missing something; but this is entirely different from saying that Planck scale physics can bridge half the logarithmic scale of the universe !!

    Careful
     
  19. Oct 5, 2006 #18
    To remind you, it was you who said that entanglement should emerge from these non local links. I said, that it was unlikely, not that these links were a few meters or hunderd kilometers long, YOU actually said that, I said that entanglement is claimed to carry that long ! :rofl: :rofl: Actually, from your first post, I quote

    ``but there will still be ROGUE LINKS left over from plancktime which didnt get ironed out in the regularization that happened thanks to expansion. and these rogue link suckers could span across vast reaches. one in the chair you occupy could reach to the other side of the Big Whatever. But you wouldnt know about it, because expansion has washed almost all the nonlocality out. We DON'T SEE THE SPORTS.''

    What is unlikely is that the correlation length carried by these non local links is that large (given as you said, that the dynamics is local). But, let me ask you, how would you explain entanglement between two photons 10 kilometers apart if it were not that these two entities were connected by one link. Since suppose this link would be chopped into many pieces connected to different nodes, then braking this entanglement would spread out through these nodes I assume. But then you might be dealing with multiparticle entanglement (which has much lower two point correlation functions). Anyway, just some silly intuition, so instead of telling around whom you think understands this or not based upon misunderstanding the other person ; someone who does``get'' this proposal should cook up an explanation of why this correlation length can be that high and still big objects satisfy local equations of motion. And no, I am not doing in ``heuristic inspirations''. Calm down, don't be so negative and find some arguments, if there are none, then be it so !

    Does that matter in a ``heuristic idea'' ???

    Careful
     
    Last edited: Oct 5, 2006
  20. Oct 5, 2006 #19

    marcus

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    I did not recall anywhere in Smolin's article where he used the word "entanglement" or any related word like "to entangle". And I didn't recall using those words in this thread! So I was mildly amused by what seemed like funhouse (or madhouse:smile: ) distortion.

    Just to be sure, I went back to check Smolin's paper to see if I had missed something, but no, on doublechecking I didn't find any talk about entanglement.

    It is an open forum so everybody please just read the paper, and put whatever spin you want on it. But READ THE PAPER!

    ==========
    I will try to make time to do some more interpretation. This is one heck of an interesting paper!
     
  21. Oct 5, 2006 #20
    What do you think these nonlocal connections are for ? For the satisfaction of Santa Claus or so or do you think we put them in for jolly good fun ? :bugeye: I just reacted on your comments above (just glanced upon the paper till page 2, until he spoke out the word nonlocality :biggrin:) and until so far you did not answer any of my worries on what you said. Are you going to tell us now that you did not realize these nonlocal connections are there for the sake of entanglement ? :uhh: That would be the ultimate madhouse ...

    By the way, you spoke about rogues before as being the links which survive : I remember ``rogues'' from the Rideout - Sorkin dynamics, they were causal sets wich were indistinguishable on the basis of their stems (special sub causal sets), however they have measure zero (in the measure induced by the Markov growth process) in the set of all future infinite (and past finite) causets. Has this anything to do with the rogues you were talking about ?

    Careful
     
    Last edited: Oct 5, 2006
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