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Featured A Ed Witten on Symmetry and Emergence

  1. Nov 11, 2017 #41

    Fra

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    Fearing the discussing is diverging too much, i will try to keep the follow up short. As speculations arent allowed here.
    IMO the physical essence of gauge theory is the concept of "observer equivalence". Ie the law of physics "must"(or must they? see below) be the same to all observers. This constraint as a constructing implies the transformations EXPLAINING the "apparent" disagreements.

    In SR and GR, when you apply this to two sub-classes of valid equivalent gedanken observers. However in classical physics the observers is imagined to be able to make gedanken experiments without interacting with the system. The "physics" is contained here in the entire equivalence classes and their internal relations.

    QM improves this by describing the "PHYSICS of measurementprocess", not just imaging gedanken experiments, like you can go in classical physics. Also in QM, the gageu equivalences are not as always as CLEARLY interpreted as observer equivalence as they relate to "internal symmetries". But in the below these are unified. There is no principal difference. to understand how spacetime splits off from internal structurs is a different discussion.

    However, the measurement process is only PART of the complete what i call inference process.

    So howto combined these?

    Now, if we try to understand the old contstraint of observer equivalence in terms of inference, what does this mean? That means to say that any observer "must" infer the same laws of physics. IF you think about this, you realize soon that this is not a logical constraint, and its not generally true. It rather corresponds to an kind of equilibrium, steady state or attractor point, where interacting observers are in supporting agreement. The scenario which they do not agree, means that they exert a kind of evolutionary selctive pressure to each other so as to - "revise or die". Ie. evolution. the concept of intertia in spacetime and internal spaces, also gets it unification here. In inference the correspondence of intertia is simply the confidence in the prior, that shows resistance to conflicting new information. In this view, there is now placeholder for timeless law - it is considered "speculative" in the strict inference view.

    This is just brief description, as an answer to the question. A longer attemp at explanation would be wrong. Formally all i do here is to hint, and stimulate reflections in the direction. If the above doesnt give you a hint, then cross your fingers that i will be able to work this out an publish something.

    /Fredrik
     
  2. Nov 12, 2017 #42
    I was puzzled by this passage in Witten paper referenced in the first thread myself...

    "To put it differently, global symmetry is a property of a system, but gauge symmetry in general
    is a property of a description of a system. What we really learn from the centrality of gauge
    symmetry in modern physics is that physics is described by subtle laws that are “geometrical.”
    This concept is hard to define, but what it means in practice is that the laws of Nature are subtle
    in a way that defies efforts to make them explicit without making choices. The difficulty of making
    these laws explicit in a natural and non-redundant way is the reason for “gauge symmetry."


    To others besides Fra, how do you understand the passage? What did Witten mean the centrality of gauge symmetry in modern physics is that physics is described by subtle laws that are “geometrical.”. He said the concept was hard to define and he only spent 2 sentences for it. At least a paragraph would be more descriptive.. kindly rewords what it means (or the way you understand it). Thanks.
     
    Last edited by a moderator: Nov 12, 2017
  3. Nov 15, 2017 #43
    If no one really understands that passage of Witten either.. here's a simpler question.. what can serve as possible boundary/bulk in reality (in our actual universe).. can the boundary be located inside the planck scale?
     
  4. Nov 16, 2017 #44

    Fra

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    I assume you mean an explicit example where both the bulk side and boundary side has a standard interpretation without exotic stuff?
    I am not aware of any, because no standard things seems to have a natural interpretation as AdS, and this is the only bulk form where i think there is an explicit duality known? Someone correct me if i am wrong.

    On one hand the principle is just a mathematical duality, where one version is easier to solve or work with.

    But as such a mathematical tool, one need not worry about the physical reality of the dual side, no more than one need to worry about the physical basis of changing dependet varibles. Its just a computational trick, where the boundary version is more strongly coupled and harded to compute things with.

    Here is a paper with a very pragmatic name.

    AdS/CFT Duality User Guide
    "...The AdS/CFT duality originated from string theory, so it had been discussed in
    string theory. But the situation is changing in recent years, and AdS/CFT has been
    discussed beyond theoretical particle physics. This is because AdS/CFT is be-
    coming a powerful tool to analyze the “real-world.” Examples are QCD, nuclear
    physics, nonequilibrium physics, and condensed-matter physics..."
    -- https://arxiv.org/abs/1409.3575

    And one the other hand one cant help but to ponder about if there is any conceptual generalized meaning of the principle. Geometrical interpretations is one thing, cool as it is, beeing the basis for alot, it does not add anything to my intuition, because i do not think of reality in terms of geometry, that maybe einstein did. I seek an an inferential interpretation, as that is the task i see at hand.

    IMO, i see the holographic (boundary) side of things as a compressed code, that is the result of trying to encode more information in the same physical memory capacity. Obviously a compressed code is more tricky to work with, having stronger and stranger couplings between parts, than the uncompressed version. So while the bulk version may be easier to work with - it takes up more storage. So there seems to be an interplay between computation complexity and a kind of compression. These two fight each other. This is also intutive for computer users. Sometimes you have to choose between space or speed. And in an inference perspective, both this things are important. There is also lots of research on these things which fringes to computer science, but few approaches make what i think are the right combination of things.

    I think we need more cross-sub-discipline thinking to solve this, and some ideas unfortunately get stuck inbetween chairs.

    /Fredrik
     
  5. Dec 7, 2017 #45
    Fra.. when only you described the above.. and because they are not peer reviewed.. naturally serious people would tend to not take serious interest in them. So honestly I didn’t take any serious look at it. But after rereading Lee Smolin Three Roads to Quantum Gravity.. I encountered the concept of Relational Quantum Theory.. and became very interested in all you had to say. At the end of Smolin book was written

    · “The present formulation of quantum theory will turn out to be not fundamental
    · “The present quantum theory will first give way to relational quantum theory, according to which “the quantum state of a particle, or any subsystem of the universe, is defined, not absolutely, but only in a context created by the presence of the observer”, and there is a “division of the universe into a part containing the observer and a part containing that part of the universe from which the observer can receive information
    · Eventually, the new unifying theory of physics “will be reformulated as a theory about the flow of information among events.

    Wiki described RQM as “The essential idea behind RQM is that different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, "collapsed" eigenstate, while to another observer at the same time, it may appear to be in a superposition of two or more states. Consequently, if quantum mechanics is to be a complete theory, RQM argues that the notion of "state" describes not the observed system itself, but the relationship, or correlation, between the system and its observer(s). The state vector of conventional quantum mechanics becomes a description of the correlation of some degrees of freedom in the observer, with respect to the observed system.”

    This makes a lot of sense. About your statement “Another conclusion is that we here have a hiearchy of observers, which corresponds to energy scale. And the symmetries are emergent ONLY when parts interact. The symmetry emerges in the observing systems internal structyre. At least its how i see it.”

    Do you have any reference about this? I’d like to establish connections between Rovelli Relational Quantum Mechanics and Witten Symmetry and Emergence.

    Lastly. There is something I can’t understand in Smolin book. He said “The final theory will be non-local, or, better extra-local, as space itself will come to be seen only as an appropriate description for certain kinds of universe, in the same way that thermodynamical quantitis such as heat and temperature are meaningful only as averaged descriptions of systems containing many atoms. The idea of ‘states’ will have no place in the final theory, which will be framed around the idea of processes and the information conveyed between modified within them.

    I can’t understand the analogy. Does he equal space as like heat? What is he describing.. why would the final theory will be non-local? What is the context.. you know that when there non-local information transfer in SR, there would be frames that would go backward in time.. so how would his model handle this?
     
  6. Dec 9, 2017 #46

    Fra

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    Hello star apple!

    Like i think i said beore the detailed proper explanations on this, are still open questions (to me as well, even thought i have a farily detailed vision to implement this) and due to forum rules i try my best to contribute and participate in some discussions and not merely quoting what others said(=publiched) already, but without crossing the lines.
    I think serious people TRY to make their own conclusion based on content. However in the ages of massive information flow, it is merely a survival strategy to filter out information. One efficient way to do that is to reject anything based on its source. I do this too, not because its "ideal" but out of necessity of limiting processing power.
    The ramp up to Rovellis reasoning on RQM is excellent, until a certain point, where is strongly disagree with hime. There is a nd old thread.https://www.physicsforums.com/threa...able-in-classical-and-quantum-gravity.220841/

    There are alot of other attemps to axiomatize QM that are partially in line with my thinking, but which has problems. Lucien Hardys spirit and some others from cox axioms by ariel caticha are sniffing the right way but looking for generalised inference or probability, but in my view the mistake in hardys axioms is that he is too lighlty in introduction the uncountable numbers and dimenstionality. Ariel does the same. I think there is an alternative way, where you go one step and just talke about complexions.

    Let me think if i can add anything more without crossing any lines.
    /Fredrik
     
  7. Dec 9, 2017 #47

    Fra

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    IMO, Smolins writing style is lenghty. In principle he could probably summarise the main points briefly in short paper, but i think smolins writing style is to first start with history to get the reader on the same page, in order to motivate the new ideas. This is motivated because apparently alot of professional scientists does not seem to understand or want to understand why certain things are problematic. But for a reader that are already on the same page, and share the basic descriptions of the problems, smolins books are lenghty.

    But i think what he says is that spacetime, is neither fundamental nor a universal background - it is emergent, and so is "state spaces". And at the point where spacetime itself starts to dissolve into something else, then so does "locality" in the traditional sense. I think this is essentially what it means. For this reason extralocal is a better word, to avoid peoeple thining we are violating relativity in its appropriate domain.

    IMHO, what likely replaces the locality principle in a theory of inference - when 4D spacetime - as we know it, is undefined, is a principle of locality in an abstraction where an "inference" or computation is only affected by available data", you can even put this so that it becomes self-evident, and plausible as axioms, but the challenege is to connect to known physics.... and to attach the abstractions to physical parameters such as time, mass, energy etc. So there are some gaps to fill in. This locality principle makes locality as referring to spacetime, a special case. But I am not aware of anyone that "cleanly" published anything the way i want it. This way locality is built-in. But its "locality" in a generalized sense.

    /Fredrik
     
  8. Dec 9, 2017 #48
    In Witten Superstrings, spacetime is emergent from the dynamics of the strings even when the background is unknown (or even flat). It is the strings that create spacetime from spin 2 gravitons. Smolin is anti superstrings so I wonder why he would state it. Is it not Loop Quantum Gravity is all about background independence. Here spacetime is not emergent. Is there any further works where Smolin detailed about this emergent spacetime?

    Superstrings would make a lot of sense if the strings themselves have hidden access to other dimensions. This is why superstrings is still very attractive.. but if Supersymmetry won't be detected by the LHC even up to 100 TeV. Can Superstings still be true? What you think and others about this. Can Superstrings still work if the Supersymmetry is near the planck scale (I think Urs or Lubos talks about this I forgot where).

     
    Last edited by a moderator: Dec 9, 2017
  9. Dec 10, 2017 #49

    Fra

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    Hmmm...

    This kind of "simple" emergence of spacetime geometry, in the perturbative approach from a classical geometry and a given topology is a very weak form of emergence that I dont think is not what Smolin means, and for sure not what i have in mind, without going into details.

    Smolin generically talks about emergent statespaces in an evolutionary sense, but this is in his later books, i dont remember how far these ideas was expressed in the early books like three roads.
    https://www.amazon.com/Singular-Universe-Reality-Time-Philosophy/dp/1107074061
    or
    https://www.amazon.com/Time-Reborn-Crisis-Physics-Universe/dp/0544245598
    or
    http://pirsa.org/08100049/

    The connection between "evolution of law", and the emergence of symmetry, and the concept of observer depdenent observer invariance as an hierarchy of observers, is probably not too easy to explain briefly simply because noone to my knowledge does it this way, but you can understand the vision maybe by as a synthesis of the below spirits exemplified by some quotes, like take the good parts of each, try to deform it to make it selfconsistent, dump the rest, and what do you get? ;-)

    "However, the rules of classical probability theory can be determined by pure thought alone without any particular appeal to experiment (though, of course, to develop classical probability theory, we do employ some basic intuitions about the nature of the world). Is the sametrue of quantum theory?"
    -- Lucien Hardy, https://arxiv.org/pdf/quant-ph/0101012.pdf

    "Entropic dynamics, a program that aims at deriving the laws of physics from standard probabilistic and entropic rules for processing information, is developed further."
    -- Ariel Caticha, https://arxiv.org/abs/0808.1260

    The problematic common denominator of all the various statistical emergence problems is that they fail to give the appropriate observational physical footing to the probability spaces. One part of this is also how lightly the concept of uncountably many alternatives are introduces in the theory, becuase it destroys computability of the inference system. It also seems intuitive that finite physical systems does not encode infinite amounts of information. So why the need for continuum models? That is often easier to work with from the point of view of analytical appraoches, but computers prefer finite sets. And nature might well too, who knows?

    Then add these ideas..

    " We need determinism only in alimited set of circumstances, which is where an experiment has been repeated many times. In these cases we have learned that it is reliable to predict that when we repeat an experiment in the future, which we have done many times in the past, the probability distribution of future outcomes will be the same as observed in the past. Usually we take this to be explained by the existence of funda mental timeless laws which control all change. But this could be an over-interpretation of the evidence. What we need is only that there be a principle that measurements which repeat processes which have taken place many times in the past yield the same outcomes as were seen in the past."
    Lee Smolin, https://arxiv.org/pdf/1205.3707.pdf

    To be honest i dont think that Smolin managed to explain this as good as it maybe could. As i see it, you can easily misread this suggestion and find it completely ridiculous, but then think again. The idea is, could the reason for the APPARENT timeless law, that most of use think of as constraints, simply be explained as a principle where nature tends to (in a sense of induction) respond as it always did? Seen the right way, this is a rational action principle in disguise. It also is a kind of solution to the problem of induction, as we know the problem is that the induction can be flat our wrong (ie no black swans). But this might not be how nature works! Its not a matter ot true or false, its a matter of best guess. If you only have seen white swans, betting on another white swan may still be a goot bet. Sometimes the best guess is wrong, and sometimes its exactly this explains certain interactions.

    You can apply this reasoing also to "symmetries" if you consider the actual observer symmetries of an observer. If a certain observer has evidence for a certain symmetry, it will itself proabably behave "as if" this was law. But it is not. And sometimes a black swan actaully appears and breaks the illusion. But nature might be a stable illusion, and how else to explain it?

    This is a way to also then understand evolution of law.

    Then add the ideas of evolving laws of smolin, and you arrive at my position.

    /Fredrik
     
    Last edited: Dec 10, 2017
  10. Dec 11, 2017 #50

    Fra

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    It was some time since i read these things, but here is one connection in smolins paper to is getting close to what I am doing.

    This connects all this to the inference and computational perspective, and evovling law perspective. If you think about this, you see a way to "attach" a the foundations of a generalized probability theory in physical structures bu identifying the "computing devices" with matter.

    /Fredrik
     
  11. Dec 11, 2017 #51


    Thanks for mentioning this book. I didn't know he wrote this. I just bought one and it completes my collection of all Smolin books. I like the part where he mentioned:

    "* the fundamental theory will not be quantum mechanical.. but quantum mechanics will emerge in the case of small subsystem.
    * the fundamental theory will not exist in space, but space will be emergent in some eras of the universe."

    Do you know of authors or papers where they explored the "dna of physical law" as you put it? Where there is perhaps some idea of elementals that embody certain forces of nature... this is the truly radical theory.. smolin stuff is just not radical or powerful enough to explain all of nature.

     
  12. Dec 11, 2017 #52

    Fra

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    No I don't. Given how the field looks like, i think its equally probably to find that book in shops written anyone, as it is to work this out all on your own and write it yourself.
    Its exactly when you think about this that not even QM as generalized probability theory in the sense of hardy and entropic dynamics solves the problem. The problem is that these ideas solve the problem that was created when we went from classical physics to QM. And where we still have a classical observer, to "attach" probability to. The limit of small subsystems is imo related to the limit of a large classical observer. Its the same thing relationally. As long as we are in this domain, the generalized probability theory works fine.

    But in cosmological theories of measurement, and when you consider the logic of unification, i think the problem is much worse. And the revolution needed here is larger than the transition from classical realism to QM, now some 100 years ago. After all, the "probability" in QM is still realistic. The "generalization" needed is much more radical i think.

    Some people are still thinking the classical->quantum is a problem (which it partly is) but to the point where they dont see the next generation of the bigger problem. If one thinks quantum mechanics is "weird", the new thing we seek is going to be far harder to "grasp".

    /Fredrik
     
  13. Dec 11, 2017 #53
    Fra. I'm looking for a theory or paper where this whole spacetime/matter being emergent from something else and relational quantum mechanics and information flow thing by Rovelli and Smolin, etc. can be related to Dark Matter.. that is.. matter and dark matter being part of the fundamental theory that uses relational (or inference) measurement thing that doesn't use quantum mechanics (as mentioned by Smolin). Remember the fact of the matter is that there is no theory of dark matter consistent with all the data. So use dark matter as extension of matter in the fundamental theory that won't use quantum mechanics nor occur in space as Smolin mentioned but where space is emergent. Is this possible? Please give the fundamental ideas (or any paper) if any author has explored this before. Thanks.
     
  14. Dec 12, 2017 #54

    Fra

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    There are so many of papers out there, and while its important to somehow be aware of that others have done it is a huge task on its own. All I can say is that there are no papers i have stumbled upon that is doing things that fully complies to my thinking. But as we just discussed there are many that i think partially in the right direction.

    Maybe someone else can advise. Marcus that isnt with us anymore used to do a good jump by monitoring and highlightning new papers. I dont really spend any time at all screening papers, its more that i stumble upon them due to references etc.

    But if we turn this around, and ask pragmatically if I had to pick one of the major programs that i think is the "least bad" with biggest potential then i would probably be string theory after all. While i think the program by design is not addressing the foundational quesitons rationally, it has at least the potential to maybe work out their problems and actually turn into a theory of inference (although i am in doubt as it needs to change so much that the "strings" would be something else), where the branes and various dual -theories correspond to different inference systems, which in turns correspond to different "observers" and the landscape is then real, and should be understood evolutionary. The missing part is to understand the evolution mechanisms withing the landscape; why are certain theories not manifest in nature while others are? I think there are no deductive answer to this, but the answer maybe lies in evolutionary learning algorithms. But if you se it this way, the original starting point of constructing string theory from quantiing a classical string is not the right way to understand it. This is just the historical path, which i consider to be accidental, providing no insight - probably just confusion! This is the reason why i still enjoy some of wittens writings, just to try to guess what new ideas that may come from there.

    Just a remote hope there was this thread, but still far from the vision
    https://www.physicsforums.com/threa...old-the-thought-of-jonathan-j-heckman.923630/

    /Fredrik
     
  15. Dec 12, 2017 #55
    I thought you read every paper at arxiv. Ok. Good to know you like Superstrings.. and not a hater of it like some LQG folks. i'll google everything I could read about Superstrings without SUSY and relational QM and how they combine the two. I need a good background of superstrings and will read about it (and contemplate it) for the remaining days of the year. Thanks a lot for sharing.
     
  16. Dec 12, 2017 #56

    Fra

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    /Fredrik
     
  17. Dec 12, 2017 #57
    There is a nice name for this problem that there are too many papers and everyone is struggling to keep up with what's happening: Research Debt. However, so far there is no good solution.
     
  18. Dec 20, 2017 #58
    The part that I got caught on is what models are there that can describe a system that starts with no symmetries (isn't this like as a non-repeating fractal?) but develops/supports symmetries?
    This seems to be the implication that "symmetries are emergent": To some observer there ain't any in the raw ingredient but they show up in the pie when you mix and bake those ingredients.

    I was struck by how there are fractals that are non-repeating and there are fractals that repeat periodically (have symmetric states?).
    What I wondered is whether there are multi-fractals that start with more than one of the first kind (non-repeating/a-symmetric) and produce the second (repeating/supporting symmetries). It's one mathematical model that I can think of that at least maybe could support the idea of the symmetry pie with purely asymmetric ingredients- though maybe there are others.

    I have this naive cartoon that strings start with symmetries - because the simplest strings themselves are symmetric (identical). So strings already require the support for symmetry.

    I know this is all naive, please consider it a question.

    [I am certainly confused about the difference between irrational numbers and non-repeating fractals, maybe that's obvious]
     
    Last edited: Dec 20, 2017
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