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Planck wall

  1. Oct 15, 2009 #1
    I am interested if you know somebody who did research, a theory beyond the Planck length, equal to 1.616252(81)×10−35 meters; between 0 meters and Planck length.
    Are some Big Bang theories...
     
  2. jcsd
  3. Oct 15, 2009 #2

    marcus

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    Sure, we pretty much all know the research of Jan Ambjorn and Renate Loll---it studies conjectured spacetime behavior at scales smaller than Planckian but without experimental or observational support.

    That's not necessarily a bad thing to be doing. I think it is a good thing to be doing. But it can't, at present, be conclusive. It can only be suggestive. And one of their results, by surprise, tied in with some findings by some other theorists working in other nonstring frameworks (Loop, Safe Renormalization, Horava's new approach).

    I have a link to a SciAm article by Loll and coworkers in my signature at the end of the post. It is a good introduction to the whole field of 4D nonstring quantum geometry/gravity, because Loll's approach is easier to understand and describe in layman terms and it illustrates what all the 4D quantum gravity programs are trying to do. Understand Loll's and you automatically understand the other approaches better too.

    Loll's approach has no smallest length. It is a 4D mathematical model of dynamically evolving geometry that they can program into a computer. So they can have little universe simulations come into existence, in the computer, and go inside and study them.

    Some of the universes are only 20-some planck lengths in maximum size----to be less vague I should say 120-some planck length maximum circumference.
    At scales of a few planck lengths they behave surprisingly like our familiar geometry, as specified by Einstein rules!
    There are quantum fluctuations but they average out, over many sims, to look like a familiar deSitter style universe governed by classic General Relativity.
    But Loll and friends found some curiously different geometric behavior at smaller-than-Planck scale.
    It is suggestive, not conclusive. You could read the SciAm article about it.

    If you try, and have trouble with the link, ask.
     
    Last edited: Oct 15, 2009
  4. Oct 15, 2009 #3
    You can find some related information here:
    https://www.physicsforums.com/showthread.php?t=323417

    and

    https://www.physicsforums.com/showthread.php?t=294666

    and
    https://www.physicsforums.com/showthread.php?t=323557&highlight=discrete+spacetime

    I'm beginning to wonder if spacetime and life have some sort of related emergence, like a self organizing character maybe, that over time makes each virtually inevitable. Causal Dynamic Triangulation (CDT) is sure fascinating but it seems like an awful lot of requirements to emerge from nothing...in other words on one hand it seems overly complicated but even so, over sufficient time and perhaps an infinity of quantum excitations, everything (all combinations) will emerge sooner or later...

    right now we don't have a good theory at Planck scales as general relativity and quantum mechanics which serve so well in general don't there...hence Marcus' reference the quantum gravity research which it is hoped will apply.
     
    Last edited: Oct 15, 2009
  5. Oct 15, 2009 #4
    Is anyone working to overcome this impass noted in the Ambjorn Loll paper:

    That's one of the apparent findings that seems to me to be real BUMMER! .

    I just can't help thinking we have overlooked or not yet discovered something fundamental or right next door. Maybe the only answer now is that during an infinite number of quantum fluctuations, one WILL inevitably emerge with causality.... or maybe at those sub Planck scales there is an ever so minor difference between space and time...or maybe.....oh well.
     
  6. Oct 15, 2009 #5

    marcus

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    I appreciate your attitude but people have different perceptions of what constitutes a bummer.

    I don't think Ambjorn Loll pointed to an impasse. I think they pointed out something kind of nice. In a certain sense spacetime is made of the causality relation. There is nothing more fundamental. As we delve deeper and deeper, we give up familiar things. We give up familiar impressions based on our experience in the human-scale world. Like galilean relativity and like synchronicity.

    I think the way is open to delve deeper and I would expect causality to NOT be one of the things we have to give up. The idea of locality might weaken, and the idea of scale, might weaken, before causality is compromised. I think. It's just a hunch.

    Mathematically, causality is represented by an interlocking web of lightcones. Every event has its backwards lightcone holding things that might have caused it, and it has its forward lightcone holding things it could influence. And this web of lightcones is the most basic thing there is about spacetime, trumping in importance all its other features. It is the causal skeleton of existence. Spacetime geometry is just a nice sexy fleshing out of that armature of causality.

    It's a hunch, but it's also the theme of Gerard 't Hooft's latest arxiv paper. For me he is kind of an archetypal physicist. He never does math for its own sake. He is always wrestling with and guided by his physics intuition. Even when it sounds odd, I try to listen. http://arxiv.org/abs/0909.3426
     
  7. Oct 15, 2009 #6

    apeiron

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    It may be important here to distinguish between causality and locality.

    What Newtonian and relativistic mechanics explicitly presume is locality - causes are localised in that it takes time to cross space and have an effect. But there is also already known a global aspect to causality - QM nonlocality. So we have to be more specific in distinguishing hypotheses about "causality".

    And taking the particular issue of the "emergence" of global properties such as nonlocality, or a thermodynamic arrow of time, there are two ways this could happen.

    It could indeed be emergence. Or it could instead happen the other way round - so all causality starts as global and gets restricted to become localised. The global set of freedoms becomes constrained to create crisp locality (which is why QM mysteries become classically reduced to the quite trivial-in-effect nonlocalities observed).

    So instead of the emergence of global arrows of time, it could be the decoherence of local temporal flow. Or what I actually believe to be the case (following a Cramer transactional approach to QM), each scale is actually forming the other as its limit case.

    I guess this ought to be called super-emergence or meta-emergence as both aspects of causality emerge mutually and synergistically.

    But whatever, a lot of the philosophic problems of physics seem to stem from a too simple equation of causality with locality. Locality is a subset of causality.
     
  8. Oct 15, 2009 #7

    Haelfix

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    You are asking about the TransPlanckian regime. Energy levels much higher than typical quantum gravity effects.

    Its expected on pretty physical grounds that if you were to take an accelerator and smash particles together with that type of energy, you cease to probe substructure and instead lose resolution b/c you end up creating bigger and bigger blackholes (the energy density exceeds the Schwarschild radius and you end up worrying about horizons and things like that).

    This is called asymptotic darkness, and its expected the theory that precisely probes this regime is not quantum gravity (whatever that is), but rather simply general relativity. The world ceases to be quantum and becomes classical again.

    No one really knows for sure, but it makes a lot of sense.
     
  9. Oct 15, 2009 #8

    Fra

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    From my POV causality and locality as somehow strongly related. Causality for me, in the sense of the relation between cause and effect are simply the relation between expectation and action, in the sense that the predictable part of rational decision makers action, depends on it's expectation only. This imposes a differential form of causality IMO.

    Locality can be seen in that the expectations are inferred only from available("local") information. This says nothing of the correctness or universality of the expectation, it just makes IMO a plausible conjecture about rationality that I find acceptable.

    This rationality, then coupled with the "differential causality" in the form of the expectation-> action connection, should allow for emergent structures.

    My defense for this starting point is that, a non-rational system, ie. not obeying the differential causality constraint of expectation->action, would be self-desctructive, and thus such behaviour would erease itself from the population. I think this condition is a premise for "self-preservation".

    /Fredrik
     
  10. Oct 16, 2009 #9
    In my view beyond the Planck wall we have imaginary time; time is a complex number.
    This means the world ceases to be quantum but not becomes classical again.

    We can not talk here about causality and locality.
     
  11. Oct 16, 2009 #10

    apeiron

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    Yes, the "planck wall" deflects the observer in an orthogonal or asymmetric direction. The observer trying to go smaller finds himself instead getting warmer.

    Which suggest we dwell within a broken symmetry, a phase transition, in which energy density and distance are orthogonal aspects of existence.

    Which in turn suggests that the trans-planckian realm is a state of (unobservable by us) higher symmetry.

    We can also say that this trans-planckian realm exists to either side of the planck scale. So "outside" the asympotic limit, it must be both smaller and hotter, yet also larger and colder. Just as people forget that planckian locality is a small/hot deal, so they also forget that there is a limit on absolute rest or zero degrees K (what would it be to colder than absolute zero?), and equivalently, what would it be to be larger and flatter than an asymptotically large and flat universe?

    Which is where the suggestion that the trans-planckian realm is a higher symmetry is borne out. You have both small/hot and large/cold as the local and global limits. Which added together cancel out to produce planckian symmetry.

    This is just the first law story of the big bang to heat death story of the universe of course.
     
  12. Oct 19, 2009 #11
    Hi Marcus:
    Hey, in your post #5 you quote a supposed post of mine...but I did not make that post...or I can't find it if I did!!.....my "bummer" comment, reflecting some disappointment, was regarding a different situation...

    I suspect it does, somehow, but we don't yet understand how.

    I like your comments and find this quote satisfying:

    Where did that come from?....I like it and agree with your comments....but it was my interpretation that this is NOT what was found by Loll and Ambjorn and hence I was disappointed....
    because they said:
    so they had to "add" "glue into their work and that is what I believe means we have missed something...just pure speculation on my part....
     
  13. Oct 19, 2009 #12
    How about that: in Hydrogen the negative charge is smeared quantum mechanically over an atomic size, say, a0. The positive charge is smeared quantum mechanically around the atomic center of mass over a smaller but finite size:

    (me/mp)a0.

    In an excited state a0 is replaced with an. These "clouds" can be observed experimentally. There is nothing non-physical here, no complex times. I do not understand how transition to shorter distances (due to heavier masses) can spoil physics.
     
    Last edited: Oct 19, 2009
  14. Oct 19, 2009 #13

    apeiron

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    The usual issue here is that people are expecting the large scale to emerge out of the small when actually the small can emerge from the large. As in solitons and other local features that arise as the result of global contextual forces.

    QM says that when you observe things on a very small scale, you are in effect removing the usual decohering context and so you are removing constraints. If the global arrow of time, of causality, is a global feature, then that is what you are removing. The ambient flow, the current which sweeps all events along in a direction. And so on the local scale, with context gone, the mechanics become symmetric. Time loses its directionality. You start to think we must live in a block universe.

    Physics is stuck in the belief that all causality must be localised. In the systems science view, causality is hierarchical. It is split between local and global levels - material and formal causes in the Aristotelian jargon.

    So local causality is the constructive kind, global causality is then the constraints. We can argue global constraints or organisation emerge (and they do). But then so do locally constructive actions - in the fashion of solitons or wave function collapses.

    It seems such a simple shift in viewpoint about causality that would do away with so much interpretational angst.
     
  15. Oct 19, 2009 #14

    marcus

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    My fault. I misinterpreted what you were saying. If I use the regular quote function here, then all what YOU quoted will drop out, so I will copy your post complete like this:
    ==quote Naty==
    Hi Marcus:
    Hey, in your post #5 you quote a supposed post of mine...but I did not make that post...or I can't find it if I did!!.....my "bummer" comment, reflecting some disappointment, was regarding a different situation...

    Computer simulations dashed the (Stephen Hawking) hope that casuality would emerge as a large scale property from microscopic quantum fluctuations​
    I suspect it does, somehow, but we don't yet understand how.

    I like your comments and find this quote satisfying:

    [so far, the causal ordering of events seems fundamental, more solidly fundamental for instance than spacetime scale or spacetime dimensionality]​
    Where did that come from?....I like it and agree with your comments....but it was my interpretation that this is NOT what was found by Loll and Ambjorn and hence I was disappointed....
    because they said:
    Euclidean geometry indicates that space and time are treated equally....and does not build in a notion of causality...we must enforce causal gluing rules...an arrow of of time..

    so they had to "add" "glue into their work and that is what I believe means we have missed something...just pure speculation on my part....
    ==end quote==

    What we have to do is explain the blue thing, which is what Ambjorn and Loll say. You and I understand it differently. You've already said how you take it. I will explain how I do. I think it points out that Euclid 4D geometry has a weakness. It is an unsatisfactory math model. Because it does not capture something fundamental about real spacetime geometry.

    Euclid 4D does not express causality.

    But in my opinion the cause and effect ordering of events is fundamental. It does not "emerge" as a byproduct of some more elaborate fancy math. You don't get it for free. It is a basic part of reality so you have to build it into your model from the git-go.

    Of course they put it in by hand! That is what you do with whatever is most basic and fundamental, when you are making an idealized math model of the world.
    The other stuff is what you derive from the axioms or structure that you put into the model.

    So as I interpret it, what they are saying is in fact this:

    [so far, the causal ordering of events seems fundamental, more solidly fundamental for instance than spacetime scale or spacetime dimensionality]

    Which I think is true! Causal ordering of events IS fundamental, so when they built their model they poured it into the foundation. But dimensionality is NOT fundamental in the world this model describes. In fact they measure dimensionality "experimentally" in computer simulations and find that it varies with scale.

    Euclid geometry now seems flakey and inadequate for two reasons, to me, one is that it is missing the vital cogwheel of causality and the other is that it has the same dimensionality everywhere and at all scales. But in a quantum-uncertain geometry, the dimensionality of the space around you should be a quantum observable, down at Planck scale where geometry is expected to be chaotic and indeterminate. Dimensionality should only "appear" to be 4D to us macroscopic classical-scale animals. Macroscopic 4D dimensionality should be an "emergent" quality of the world. That's how I think anyway. So I like the Ambjorn Loll model of spacetime better than the Euclidean model.

    It strikes me as very Occam. You put in the minimum and you get the rest to "emerge"---you derive it as features of the macro classical limit.

    So I interpret the red is the point of the blue, when you spell it out. The blue is saying what is wrong with Euclid 4D. But you disagree, I think. You interpret what they are saying in a different way. Which is fine.
     
    Last edited: Oct 19, 2009
  16. Oct 19, 2009 #15

    apeiron

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    While generally agreeing that a sum over histories approach would be the way to produce spacetime, I don't see that it is a good idea to pour causality into a model's foundations.

    The causality model you have in mind is an equilibrium approach - the satisfaction of global constraints. Like we find in tensegrity, self-organising criticality, spin glasses, etc. Order emerges as local variety pulls itself into line.

    With spin glasses, of course, the essential local property - the EM dipole - is indeed wired in locally, part of the foundations. This is the equivalent of wiring a causal time direction into CDT triangles. But then, with spin glasses, we would have to go down yet another level to account for the existence of atomic dipoles.

    A better approach - a ToE - would have to be bootstrapping. It would have to account for the emergence/development of the local dipoles as well as the global magnetic field, so to speak.

    Again, there are two approaches to modelling emergence - one superficial (or supervenient), the other deep (or systematic).

    It seems definitely true that reality has causal structure, its temporal symmetry is broken at the level of observers. And so theories that represent this would be an advance on ones that seem to say time is symmetric. But we would surely want a fundamental reason for the symmetry breaking rather than a trivial one?
     
  17. Oct 20, 2009 #16
    Marcus,
    I'm probably starting to get confused now with all the points above, and especially my age, but I think I was saying

    "... something seems to be missing, I think, because causality doesn't emerge on it's own.." and I'd really like an approach where that happens.....

    My only thought was:
    "Maybe the only answer now is that during an infinite number of quantum fluctuations, one WILL inevitably emerge with causality.... " (and that will be the one to emerge because Loll says without it things just crumple up..)

    and to solve that missing casuality you guys had some different specific suggestions:

    I like Aperion's comment
    I like Marcus comment:
    Ok!! So I'm largely, I think, on the same page as you guys....and if I'm not, likely I'm the one who has lost my place!!!....in any event, we have three crazy ideas...the issue is whether they will be crazy enough!!!
     
  18. Oct 20, 2009 #17

    marcus

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    Don't bet on it. As a rule, I lose my place three times before breakfast. It's part of my secret plan :biggrin:

    In a slightly solemner vein, but BTW, did you know that QFT on curved spacetime does not as a rule have particles.
    The idea of particles emerges in the special case of doing QFT on flat Minkowski space. The idea of a particle is not fundamental. Yet QFT is the basic mathematical model for particle physics.

    In mathematics, you have to decide what is the most important (the absolutely indispensable essential) and you put that in by hand. Then you derive the other stuff, making whatever conditional assumptions might be needed, like turning gravity off so that the background geometry is flat, so that you get unambiguous particles.

    The really important basic stuff is like the axioms. That give meaning to the definitions, as in set theory the idea of belonging, being a member of, and in geometry the ideas of point and line. As mathematician you don't expect to get the really important things by magic, you're not ashamed to put things in by hand, but rather proud to have finally boiled it down and realized what was absolutely key.

    And then you see how much in results you can derive from how few axioms. Its a very Occam game---economy, austerity, minimality, elegance etc. and conversely power. I can just see Miss McP*** now, my highschool geometry teacher. A severe maiden lady of a certain age. I believe she understood, and got a little thrill from proving a theorem.

    So we come at this from different directions. You (I think) want causality to pop out of the hat like a theorem. I want it recognized as a basic stuff of existence that you put in at the very beginning like an axiom. It's just two attitudes. I think we can both appreciate each other's point of view. Perhaps mostly a matter of taste.
     
    Last edited: Oct 20, 2009
  19. Oct 21, 2009 #18

    apeiron

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    But surely if the aim is a background independent description of reality, then causality - in the guise of locality - must be a result rather than an axiom? There seems more here at stake than taste.
     
  20. Oct 21, 2009 #19

    Fra

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    Maybe there are different levels of picture locality and causality, as much as there are different levels of BI.

    In it's most general form BI can be interpreted as a kind of "context-independence". If we by context means the choice of "observer-frames" defined by a certain class of localized transformations in SR or GR, then that's the BI I think Marcus usually means?

    About locality, that refers to a distance measure. Without a distance measure, there is no meaning in "local". So what could locality possibly mean in a more abstract scenario when spacetime as we know it is not well defined?

    My starting point is that there is a natural "distance" just defined by the visible hypothesis space of a given context, a bit like like information divergence is a measure of disagreement. If we then picture spacetime to just be a specieal subset of the general "information space" then locality would IMO be expected by construction whenever the space is at equilibrium. I think non-local interactions mean that locality is quickly restored by deforming space.

    So in the evolving picture, maybe locality and causality is not hardcoded, but a general feature of equilibrium, or close-to-equilibrium conditions so that a world with non-local or a-causal interactions would quickly reorganise into respecting localit and causality, at least in the statistical sense. Then locality and causality might even be considered statistical in nature, and when the continuum of the statistics breaks down, locality or causality just doesn't make sense.

    The "assumption" that I put in by hand, is that the decidable part of the action of a system depends only upon the distinguishable information. This is to me both a rudimentary ofrm of both locality and causality. But this leaves open that there are undecidable parts, and when the undecidable parts becoming to dominate, then nothing is distinguishable, but then that's not constructive. This is why I think a constructive logical system, necessarily has some form of locality and causality in it but it doesn't have to be precisely deterministic or decidable. In particular do I think it's unavoidably circular, this I think induces a sort of "flow" where the logic system evolves, and this is what I think of as time (local time with respect to the inference system). So time is as real as anthing gets, but not observer independent.

    So this "assumption" is to me somehow the basically the rational assuption of a rational player, but projected onto physical actions of a physical system. This doesn't mean that ally players are rational, it just postulates that it's the most rational assumption any player can have about the other players placing the bets. This is why there is undecidability here. But I think that is unavoidable - or at least it remains my hypothesis until someone can prove me wrong.

    /Fredrik
     
  21. Oct 21, 2009 #20

    apeiron

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    You seem to be agreeing with me then. Locality/causality is not hardcoded but would emerge through development/interaction/decoherence/whatever.

    Locality demands a context to be "seen". You need a spacetime reference frame to tell that causes preceded their effects. So it is suspect to wire in locality into little spacetime triangles, no matter how small we then shrink them.

    I agree that causality would be statistical, that it is an equilibrium story.

    And that should then lead us to the question of what exactly is being equilibrated (decohered)? I would say in some sense local and global information.

    And also what do we call the state where the statistical continuum breaks down (I offer the technical idea known as vagueness).

    A crucial point is that causality in fact seems to have two faces.

    At the most local level - an interaction like a photon exchange between two particles - I would take seriously the Cramer transactional approach to QM and say this is a symmetric and timeless event. It is ambiguous in itself (seen without a context) and reads equally well in both directions. Cause and effect are indistinguishable (though something has happened).

    Then at the global level, a world in which many events are woven together, a thernodynamic arrow of time emerges. A history of events, a history of expansion and cooling, develops.

    So locality is a combination of the two. Or an equilibration of the two. A locally symmetric looking emergence of an event being played out against a globally asymmetrically developing context.

    And it is a bootstrapping approach as events add up to create the context just as the context bears down to constrain, shape, decohere, the events.

    In CDT modelling terms, this would make me think that a triangle would need to exhibit a strongly asymmetric time arrow when the scale is large, and the arrow become symmetric as scale shrinks to planck distances and energies.

    On the other hand, as Marcus keeps telling us, lattice type approaches do seem to lose their spatial dimensions at extremes of shrinking. As global context disappears from sight, it is no longer possible to tell if an action is in this direction (as opposed to two other directions) and so all that can be said is there is an action in some direction.

    So this kind of modelling may be a partial physical model of a background independent or bootstrapping realm.

    But actually, it still seems inside out, wrong way round, as an explanation. It is not how a system loses its constraints that is interesting but how it gains them. So it is the reason why we would go from "actions in an undefined direction" to "actions oriented within three spatial directions" which would be the desired output of a background independent theory.

    An event in spacetime is always about both an exchange that takes place between two locales (two particles and the photon they swapped), but also all the other places in which something could have happened, but didn't. The light cone within which a sum over histories just took place.

    So spatially-speaking, it involves one positive direction and two null directions. And all three directions are informational you would agree. So what a background independent approach must explain is not the loss of dimensionalities with shrinking, but the reason why just three dimensions with expansion of scale.

    Yes. it is helpful perhaps to demonstrate as with CDT that dimensionality is lost as context is eroded. But the real issue is how that quite narrow choice of dimensionality is gained in the first place - why QM foam would arrange itself into decohered global contexts of this kind.
     
    Last edited: Oct 21, 2009
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