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Phase transitions of space-time?

  1. May 25, 2007 #1
    Don't you know what are these Calabi-Yau crystals? Horse-radish,:grumpy: you will understand that.:cry:

    What I imagine.
    At the beginning there was space-time and it was a solid, a crystal. Then there was the Big Bang, there came a Brane and knocked space-time, as a result space-time heated and started to melt. Now the space-time is a liquid or a gas, right?
    Oh, idea! Just have thought up, that space-time when it is solid or liquid must evaporate too, and there must be space-time steam. This steam may come even from other brane. :biggrin:
     
    Last edited: May 25, 2007
  2. jcsd
  3. May 27, 2007 #2
    "Space goes quantum at Stony Brook"
    Does a melting crystal provide the key to developing a quantum description of gravity? Advances at the first Simons Workshop point to a connection.

    Is it like I imagine or what I just can't get that. :confused: :redface: :biggrin:

    Why haven't they found "dual" liquid or gaseous theory, interesting?


    What? Ooh? Ah? hoo? Who linked this topic back to motl's blog? :bugeye:
     
  4. Jun 5, 2007 #3
    Listen. I was watching Lenny Susskind's "Cosmic Landscape: String Theory and the Illusion of Intelligent Design".

    What he said:
    This process of eternal inflation it looks obscure incomprehensible to me. How does it work exactly? So when I saw these Calabi-Yau crystals... This is it, right? Quantum foam melts and gives a needed Calabi-Yau manifold?

    And suddenly after that another thought have come :biggrin:
    Remember I was asking about "string" computers?
    "Quantum information science and M-theory"
    What is the answer to a question Why there are no computers which are more powerful than quantum ones? I asked experts:biggrin:, they said "But I did once query the best available wetware oracle: Ed Witten. Witten said that he didn’t see any new computational power in quantum gravity, then cited the holographic bound."
    It seems like some mechanism exists which forbids their existence, what is this mechanism? Quantum foam is computationally infinitely powerfull, but when it goes phase transition to spacetime it becomes less powerfull.:biggrin:

    Want to hear any comments on all this, what do you think?
     
  5. Jun 5, 2007 #4
    to my thinking the Beckenstein bound limits quantum computation really in terms of 'bandwidth' of the interface- you can extract the answer as fast as polynomial time [with an ultimate limit of the B bound]- but the nature of a quantum computer says that it actually computed all the possible answers at once- which includes all possible states- and some of those must correspond to the n-qubit quantum computer in a state of an n-qubit quantum interface to an unlimitedly larger quantum computer or network lying in one of the infinte states of the multiverse- [and that to a larger- and so on ad infinitum]essentially there are paths of computation which ultimately harness the entire quantum multiverse if needed- so the upper limit of accessing the answer is the Beckenstein Bound- but the computation itself is virtually limitless in a sense- because fundamentally the quantum computer is like a logic structure which connects to an already existing infinite hilbert space of 'all possible answers to all possible problems'

    as for classical computation- the power and speed of classical computation is determined by the physics of the spacetime in which the computation occurs- here are some nice papers which explore the possibility of infinite classical computation in different types of spacetimes- such as the Malament-Hogarth space near certain types of black holes:
    http://arxiv.org/abs/gr-qc/0104023
    http://arxiv.org/abs/gr-qc/0609035

    ultimately what is being called 'omega point' computation in computer science circles these days [borrowed form Tipler's big cruch omega point http://www.idsia.ch/~juergen/computerhistory.html ] - that is virtually infinite limitless computation- is considerd quite solvable and inevitable- infinte computers have been anticipated since the 60s [ Marvin Minsky, “Computation: finite and infinite machines”- Englewood Cliffs, N.J., Prentice-Hall, 1967]
     
    Last edited: Jun 5, 2007
  6. Jun 5, 2007 #5

    Kea

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    This is really very intriguing! Thanks for the links. And yes, melting crystals are important for understanding quantum gravity. Think of a 3D Young diagram (like the 2D diagrams inside squares in the plane) - this is like the corner of a cube of crystal, melted away. Now cubic paths are essential to the combinatorics of the categorical non-commutative Fourier transform, which underlies the higher categorical structures needed to axiomatise QG. Hope that helps.

    :smile:
     
    Last edited: Jun 5, 2007
  7. Jun 6, 2007 #6
    Thanks for the links :biggrin:
    In other words you said that it is me who is limited in computational power but not a quantum computer. :confused:
    This statement confuses me, have you looked at Scott Aaronson's blog, he says that probably quantum computers will not be able to solve NP complete problems.
    Oh, that all is so intricate, I can't understand. :redface:

    Thanks, Kea, but no, it doesn't help :biggrin::redface:
    There is some obscure thing in this melting crystalls article
    They say:
    Why this "projection"? Why they just don't say that crystall melts into 6 dimensional Calabi-Yau? And what is the dimension of a crystall itself? Oh.:confused:
     
  8. Jun 6, 2007 #7
    in a nutshell- quantum computers ARE limited by the Beckenstein bound and can only produce answers in polynomial time- but the bottleneck is "bandwidth" and not "processing power"- which is fundamentally limitless because a quantum computer is a quantum system in perfect superposition of all possible states where the desired state is extracted- however this limit is also the limit of observable information of our universe anyway

    also- here are several methods for using quantum computation to solve NP complete problems:

    http://www.arxiv.org/abs/quant-ph/9912100
    http://www.arxiv.org/abs/quant-ph/9801041
    http://www.arxiv.org/abs/quant-ph/0508177
     
    Last edited: Jun 6, 2007
  9. Jun 6, 2007 #8

    Kea

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    Calabi-Yau spaces are complicated things. One also needs to know, for instance, about maps of surfaces sitting inside Calabi-Yau spaces. These 'projections' are an important part of the picture. Now physically, one doesn't want to take string compactification seriously, but the Calabi-Yau spaces will still arise as 3 dimensional analogues of elliptic curves (and quantum gravity needs some fancy number theory, by the way) in a heirarchy of quantizations.

    :smile:
     
  10. Jun 7, 2007 #9

    Fra

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    Oddly enough, I am not a string fan, but ignoring this fact and just reading it, the "eternal-inflation" idea is plausible to me, and to me this can have meaning beyond string theory. I think if you can infere options, but no principle to choose one over the other something is wrong. I doesn't make sense that these options appeared in the first place? I suspect the introduction of options is made in a mathematical way, therefore noone understands what the options mean outside the mathematical formalism.

    I've always had the feeling that the string theory, has alot of mathematical fiddling that's done without knowing what it means in terms of reality. I guess the reliance is on some mathematical consistency and they hope to find out later what it all means. I personally have really hard to understand the driving motivation of the individual in such approach. At least it's not the way my head works.

    Anyway, I strongly belive that we need generic evolutionary models, regardless of wether it's string theory or not.

    A bold guess is that if they find the right evolutionary selection mechanism I'd expect that the "string" or brane starting point is not needed in the first place. Then, perhaps I could like it too.

    /Fredrik
     
  11. Jun 7, 2007 #10
    I just wanted to say, that all these bubbling nucleating universes, what is it that thing which is "boiling", is it quantum foam or what? And there is no explanation why it is "boiling", right?

    Mmm.:redface: Thanks, setAI. I am trying to understand Scott Aaronson's
    "Limits on Efficient Computation in the Physical World"
    "Computational Complexity and the Anthropic Principle"

    But the idea that computational complexity classes are somehow connected to phase transitions, is it good what do you think?

    Mmm. :biggrin: :redface:

    I think I finally understood what all those things about n-categorical description of quantum gravity are about: There are two landscapes one is mathematical (I read Eugenia Cheng's "Higher-dimensional category theory: the architecture of mathematics") and the other is a landscape of string theory (physical landscape), but really they are the same thing! :biggrin:


    Also wanted to ask somebody about Susskind's lecture.
    He says:
    This statement about neighbours is strange, little fluctuation they can stop but not a bigger one. :confused: I wonder if there are any papers which explain this mathematically or is it just a speculation? Just curious:biggrin:
     
  12. Jun 7, 2007 #11

    Kea

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    A bit of an oversimplification, but on the right track! :biggrin: The classical reality of many worlds is made of the very motives of mathematics. I don't think it helps, however, to think of the landscape as a collection of stringy vacua. QFT looks quite different when formulated in a categorical language. Strings are there more like the way they were in the early days of hadron physics, when dual resonance had contact with experiment. This categorical landscape does not imply an effectively arbitrary set of SM parameters. On the contrary, particle masses (for instance) are computable precisely because they are localisable in the numerical landscape.

    It is often said that the physics of Geometric Langlands is just the geometric correspondence and not about the whole number theory thing, but this is no longer true in categorical QG. We are finding that generalised number theory underpins everything. This brings us to a close connection with the voluminous work of Matti Pitkanen, who has worked entirely on his own for many years trying to understand this generalised number physics from the TGD viewpoint. In particular, he identified the heirarchy of quantizations early on. Second quantization is only the first step of an infinite process which is required in order to represent physical numbers constructively. Mass cannot be investigated without going to the third level, where the 3D melting crystals come in, and non-associative as well as non-commutative algebras arise.
     
  13. Jun 7, 2007 #12

    Fra

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    Without going into specific models, what makes sense to me is there is always a certain "noise", that originates from constraints in information representation and processing in a changing environment. It seems hard enough to even come up with a single foolproof statement
    without having an small opening to it.

    I think there's always possibilities "cooking" around the corner, but for reasons I suspect again has to do with observer constrains, memory sizes etc possibilities below some confidence treshold are sort of auto repressed. Only significant possibilities grow. An intuitive picture is that due to memory and processing constrains, it is unfavourable to consider(process/explore) low quality options.

    I think in the biology analogy, in physics we are considering organisms, systems, or observers that feed, and grow on information. And as any organisms, there is no need to fill your memory with noise, when there are more interesting data to process. So data, and any dimensions hiding there, is effectively marginalized.

    Similarly I picture that in times of starvation, we are desperate enough to process noise.

    I think physical systems are organisms feeding on order in evironment for their own growth. And since, order is relative, there seems to be no such thing as "ultimate disorder".

    I'm currently working on some similar ideas, having nothing to do with string theory, but I can't help seeing strong analogies on the interpretational sides in many of the standard approaches. I am looking for a stronger, and clearner information theoretic approach.

    I'm inspired by approaches simiar to that of Ariel Catichas ideas of bayesian inference, ME methods and information geometry and how that links to the physical world and dynamics. Ultimately there need only need to be a generic information representation, and a learning/evolution rule.

    /Fredrik
     
  14. Jun 8, 2007 #13
    :surprised Generalized number theory?! Mmm. (I am scratching my head) :confused:


    :uhh:
    Sorry, Fra. I am completely confused by what you are saying.:biggrin:
     
  15. Jun 8, 2007 #14
    basically: Pythagoras was right after all
     
  16. Jun 8, 2007 #15

    Kea

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    Fra, I think you have an insightful way of expressing things. I look forward to hearing more about your work.

    Yes, that's a simple way of putting it! Pythagoras did not know about octonion Jordan algebras or higher categories, but he sure understood the importance of symbolic reasoning and relationalism.

    :smile:
     
  17. Jun 9, 2007 #16
    Oh! Indeed. I am recalling that something whistled near my snout while I was rushing along don't know myself where. :smile: And also those p-adic strings.


    To setAI: Here's another thing about computers from Michael R. Douglas "Understanding the landscape"
    He points to [1] http://arxiv.org/abs/quant-ph/0412187
     
  18. Jun 12, 2007 #17

    Fra

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    Kea, I am not too familiar with the original motivation of the formal category approaches, but your typing is strikingly similar to seemingly unrelated and more philosophical lines of reasoning. Indeed the quantization procedure is an induction step in an expansion model. This is completely in line with what I'm hoping to accomplish, however my motivation is intuitive and I am trying to find the formalism that matches intuition. I smell that this abstract things will nicely merge with a very natural philosophy. But I suspect that the hardcore guys working on the math have another motivation, but I suspect we will meet somewhere in the middle. It's too similar to be a coincidence.

    I take you you more or less get what I mean, so I'll throw out this fuzzy question: It's clear that the model evolution at first seems to go on forever, increasing complexity indefinitely. That is a problem because at some point the model complexity alone with dominate the system in a certain sense.

    I'm currently trying to understand howto find the balance here, I picture the model is somehow formualated by someone, an observer or a system in general. And the model needs some representation - memory. And limited memory will limit the evolution, because the _model itself_ i think must required representation and thus ultimately take on physical properties... but this can't go on forever or the system would get infinitely heavy.

    If the question doesn't make sense, ignore it. But if it does, can you roughly note if and how this problem is solved in your approach?

    /Fredrik
     
  19. Jun 12, 2007 #18

    Kea

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    Hi Fredrik

    This is good to hear. What I have been thinking is not really like 'traditional' formal higher category theoretic physics (if such a thing exists) but it does bear some relation with certain CompSci ideas. I agree that the more mathematical string philosophy seems to be heading towards the heirarchy too, albeit with an entirely different, and seemingly unclear, motivation.

    Oh, I think I see. I am convinced that a second major QG principle, which I simply call Mach's principle, acts on the heirarchy to link the observer's internal view to the actual cosmic model. In Pitkanen's TGD this is an atman-brahman principle, wherein the whole constructed reality must reside in the model of self. String theory vaguely picks this up with its web of dualities, but misses the n-alities (triality, ternality etc.) entirely because it fails to consider the higher levels. This Machian balance is absolutely crucial to constraining physical amplitudes, which I see as 'pairings' in the universal cohomology between the atman and brahman manifestations of the observable. Sorry if this isn't clear.

    You mention memory. Pitkanen has thought a lot more about this than I have. Basically, the fundamental duality can create the memory half of reality. A memory operation is just like how we see it inside our own heads: a reaching out to distant events along a path in a secondary (immaterial) space, which is intertwined with the material model in such a way that we cannot hope to describe it without the balance principle. Note the influence of Penrose's thinking here. I think that this secondary principle is inherently gravitational (hence the term Machian).

    Cheers
    Kea

    :smile:
     
    Last edited: Jun 12, 2007
  20. Jun 13, 2007 #19

    Fra

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    Hello Kea, thanks for your response. This sounds like it's potentially interesting, and I'm impressed that you seem to be able to decode the fuzzy question of mine considering that this is our first communication :smile:

    If this atman/brahman/balance principle is some kind of standard element in this view, do you know of any good links to papers that explains the fundamental motivation for this principle? (And not just the implementation of the principle in the specific model) I have no prior familiarity with Pitkanens work.

    It sounds from my interpretation of your writing, that this principle might have common denominators with my thinking. My idea of the balance principle involves what I like to describe as the "observer" (in my thinking, any subset of the universe can formally be treated as an observer - this should be required by some symmetry principle), constraining it's own understanding. A physically limited observer has at first a limit to what it can encode, then either it reaches a stable steady state, or it has to physically grow larger to encode more info. And "growing" involves dynamics. My idea is that all this need not be put in ad hoc, it can rather emerge as natural mechanisms from a generalized probability/learning theory, whose foundations I think will be natural enough for most to accept.

    I'm curious to see if there's a connection between my thinking and the ideas you mention? I do not have any papers yet, and the papers I've found by others on this illustrates some of the ideas, but is far from complete.

    But perhaps the different fields are sometimes doing the same things, but in different disguises :rolleyes: I want to see if I can see through the view-specific representation, which is not the important thing anyway. I think the same story might be told from several views.

    /Fredrik
     
  21. Jun 13, 2007 #20

    Fra

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    Note: I also agree with your association with "gravity". Which I put in quotation marks, because I think it's not necessarily the standard gravity as we know it, but rather a generalistion of it. And it will involve news views on what is mass and what is energy in terms of information.

    /Fredrik
     
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