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I Theories without Fundamental Space and Time

  1. Sep 8, 2018 #21

    Fra

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    I dont blame you for this impression! I supposed i thought you would connect without having to write more, but i was clearly wrong.

    I have a physics education and would say i have been thinking about the logic of science more than many working physicists. However I made the decision to leave the academic route, because i have too strong ideas on my own that i need to work on, and i could not bring myself to align with mainstream.

    So my main "problem" is I have far too little time to wokr on this, so progress is slow.
    Hmm Maxwells equations is not the best starting point. My questions does not concern specifically differential equations per see, its related to the logica systems.

    Maybe can rewind to this thread https://www.physicsforums.com/threads/why-higher-category-theory-in-physics-comments.899167/ But let me go back and read up on your (excellet) ncat pages on homotopy type theory and i will try to see if i can rephrase my points in something that is more your technical language. As I am not fluent in that mathematics, it takes some time to read up. Let me get back on this. I see that you may have insights that i have not seen yet - so this interests me, but i am a man that has the ambition to make serious progress having at hand not many hours per week. Otoh, those hours i can focues exactly where i want without compromising and not have to worry about publications or funding, or risk having my own idea beeing biased by those. Its pros and cons.

    So sorry for the incoherence, let me get back when i had time to read your ncat pages and phrase it at least a little closer to your terms.

    /Fredrik
     
  2. Sep 8, 2018 #22

    Fra

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    As there is wast body of simply terminology of the field here, that easily obscures the core points, i will start by linking to where i feel we are on the same page.

    First very conceptually.

    "Hence if we ask “What is an observer?” at a truly fundamental level, in a realm of genuinely fundamental Planck scale physics where everyday intuition will have broken down and the pure mathematics is all that remains, then a promising way to find an answer to this is to make sense of formalizations of physical theory within type theory.

    Interestingly enough, type theory, being an incarnation of constructive mathematics, is an intrinsically observational formalization of mathematics in itself. In type theory, the proof of any truth is provided by finding “terms” of a certain “type”, and these terms, once found, are called “witnesses exhibiting (conclusive) evidence” (e.g. section 1.11 of (1)). Hence for a fundamental physical theory formalized in homotopy type theory, every truth about the physics is to be exhibited by a mathematical observation in this sense, as if the logic of the universe were observing its own derivation. In terms of the identification of mathematical proof with experimental observation, at the most fundamental level of reality, in the presence of genuinely mathematical laws of nature, to observe anything in nature is to find mathematical truth in the mathematical system describing it, and vice versa."

    -- Froms David Corfield and Urs Schreiber, https://ncatlab.org/schreiber/show/Physics+of+the+Observer

    The bold things where are indeed what i refer to. The infereces is talk about, are loosely speaking "constructive proofs". And these "constructive proofs" are the abstractions of observation and interactions. For example, i argue that even physical law, are subject to the constraints of subjective proof, (i use the term looseley here) i call it general inference, and i am not sure if its 100% one-to-one to homotopty theory, but its ceratinly close enough and related.

    more later...(jsut to set the perspective here, the above is also fuzzy, but as its from Urs own page i presume it is suffient to get us to the same page)

    /Fredrik
     
  3. Sep 8, 2018 #23
    May I know what versions of string theory where the "initially fixed spacetime can be seen as emerging from the movement of strings" and the thing about the movement of strings causes spacetime to emerge. Atyy stated it to be so, then it may be so since he is very well read and familiar with it all.
     
  4. Sep 8, 2018 #24

    atyy

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    Perhaps I was too loose with my language there. I was thinking that gravitons are vibrations of strings, and curved spacetime can be thought of as a coherent state of gravitons. This is discussed in https://books.google.com.sg/books?id=jbM3t_usmX0C&source=gbs_navlinks_s, section 3.7.
     
  5. Sep 8, 2018 #25
    There are two separate statements.. does the above address the first or the second...

    the first is: "initially fixed spacetime can be seen as emerging from the movement of strings"
    the second is: "the thing about the movement of strings causes spacetime to emerge"

    Did you mean your "I was thinking that gravitons are vibrations of strings" being an answer to "initially fixed spacetime can be seen as emerging from the movement of strings"

    and your "curved spacetime can be thought of as a coherent state of gravitons" being an answer to "the thing about the movement of strings causes spacetime to emerge"?

    Please confirm if the above is correct or your answer is only to either one of them only?
     
  6. Sep 8, 2018 #26

    atyy

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    You should forget about what I said (since that was in the context of another thread, and I don't want to keep looking that up).
     
  7. Sep 8, 2018 #27
    The context of what it means the movement of strings causes spacetime to emerge is this: "graviton=spacetime emerges from strings, and gravitons contribute to spacetime curvature"... this is the punchline.

    String theory is about particles.. so it has graviton which General Relativity doesn't have.. Therefore you can look at it dually.. either as classical spacetime or graviton. Now if strings are gravitons.. perhaps this is what atyy meant strings causes spacetime to emerge.. or strings being graviton being spacetime emerged from strings.

    Therefore the statement "the movement of strings causes spacetime to emerge" is only true if you take into account gravitons and not classical spacetime. Because when you use the context of classical spacetime, then the statement is wrong.

    My analysis is correct above?


     
  8. Sep 9, 2018 #28

    Fra

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    Don´t take this precise as I have not case my work into your langauge mainly because i am not fluent in it. But here is a quick attempt to put the ideas i talk about, as well as my take on evolving law a little close to your context. Lets see if this makes any sense to you?

    The background is that this the abstractions i personally use in my own research; but the point here is not my personal views, but the general abstractions i referred to. I have some conjectures and visions about what an Observer is and how it interacts with its environment, refining this in a way that explains physical law from general rules of inference is my resaarch problem.

    For any given observer O, there is a category of all possible set of microstructures as i label it.
    Ignore the details, but we should roughly associate this to the quantum state relative to a given observer (but observer in a generalized meaning).

    Ob(O) / "objects"
    ~ All possible ways to ENCODE the observers information about its environent, given
    the resources of the observers (here is a builtin, cutoff complexity M that limits the amount of data that
    can be coded) meaning this structure contains an "inferred" picture of its own environment. Lets ignore the explicit details of these structurs.

    hom(O) / "transformations" ~ All possible ways to transform one state of the information in Ob(O) to another state. This corresponds to internal alternative ways fo datacompression.

    Informally the deterministic time evolution of QM, in this abstractions follows from that the category has a natural internal flow. Ie a given class has spontaneous transformations that transformst the objects. This by design is unitary, and can be understood conceptually simply as the momentum of hte "inference" that keeps in motion in between information updates. And i propose that the physical law, is implicitly encoded in this class.

    Next, we consider many such classes interacting with each other. Wich can be understood so that different observers has different "views" on physical law; and this in itself is the explanatory power of some interaction. They can be _explained_ but the difference views. This is analogous to conflict psychology, some conflices are fully explained by the two parties having inconsistent views on each other.

    The category of all Observers, K
    Here we allow the complexity of the observer to change, and change in this picture includs the measurement, so we do NOT have unitary evolution here. Instead its more like a learning model.

    Ob(K) / "objects" ~ All possible categories O
    hom(K) / "transformations" ~ all possible deforming transformation that brings one observer into another one, in a way that is non-unitary, and it also allows for loosing or gaiing complexity.


    But the point now, is that the explanatory power is tehre only for the class which has made this inference from observing such fellow classes interact, and abduced this from data. This is then analogous to the gauge symmetry, one needs a class of much higher complexity to make this transformation POSSIBLE. This is possible for HEP when the observer is the lab fram, but breaks down for hyopothetical planck scale observer.

    Is here that the "evolution of law" enters the picture. As per the logic of reality of law as per smoling, the state of final fixed law is never reach for cosmological models. Ignoring this leads to what he calls cosmological fallacy. Ie. applying things we know work from HEP - to cosomology. This is a fallacy.

    Anyway, the open problem as it see it, is howto from this picture of evolving categories (which given that one observer, can observer other groups of observers in the environment) leades to evolving categories of categories - make some generic insights that help us get real predictability out of this, rather than just descriptions.

    It was in this sense i wonder if you have any insights? For example, this is analogous to a hypothetical landscape of theories, where you may ponder in HOW the different theories evolve into each other, and wether this is to be understood as a physical process or not? My perspective is that is is a physical process, but one that requires new framework for foundational physics, and our understanding of symmetries etc.

    But I have a feeling that while one can probably phrase this question in terms of higher categories, the physical problem lies in the relation and evolution of these categories, and i suspect that the key to make progress here might not like in these category theories? Unless you are aware of some extremely clever theorems or something that physicists simply hasnt understood the possible use of?

    In view the categories of categories or just a refinement of the microstructure of the Objects, and the set of possible transformation of the morphisms, so instead of an hierarchy, i expet that we have an evolving classes - that interact - and we are looking for some preferred popupation of classes that are "consistent" with each other, and this corresponds to the laws of physics. but paradoxalyl to understand this consistent state i think we need to relax it and see that there is not physical law that we should use as constraints.

    That task is then to, out of these pure abstractions (singled out preferred mathematical structures) identify all the "baggage" such as 4D spacetime, mass. and of course all interactions.

    This is very abstract, so it is hard to explain shorly, and which is why i have lots fo work todo before i will seriously publish any of this. I usually dont bother, but from reading some of Urs work I think there is a chance that you might understand my main points, even though indeed all i write here is just words. I have not phrased or cleaned this up in a proper formal way. Thats also quite some work as i am not used to this mathematics, nor am i familiary wit all the symbolic notation. I also suspect the quality and denseness of your technica work is hard to digest for many physicists, but you have done a really good job on the ncat pages to start to explain why this is relevant to physics.

    Does this many any sense? or still too fuzzy? IF so, rephrasing this deeper will take more time i have at ahdn for the moment. To be hoenst, in the stuff i work on secretly now, i use a basic probabilistic notation, in terms of combinatorics and microstructures. So i do not so far cast anything in any "advanced framework", as i do not yet KNOW which the right framework is, except i know its general inference. And computational theory and the types and terms are indeed related to this. The observers microstructure are then also ~ types. And terms are transformatiosn.

    But in the category of categories, we have a type that is evolving also constrained by the original terms. And ther terms i view as spontaneouis processes. So no ad hoc laws are needed as input.

    /Fredrik
     
  9. Sep 9, 2018 #29

    Fra

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    Forgot to mention this:

    When thinking about this one should associate the difference in computational complexity of dual theories (generalizations of Ads/CFT) as a clue to the physical selecetion mechanism for WHICH observer classes that are "preferred" and thus populate our universe. In this, the inequivalence lies no in the results, but in the smaller computatioanl resources requires, and that tehy can litterarly be fitted into less complex observers.

    /Fredrik
     
  10. Sep 10, 2018 #30
    I don't know what reference I read it before.. about combining loop quantum gravity with string theory. I can't find it now. Any papers about this?

    String theory is about particles.. about gravitons... but what if you want string theory version of something that precedes space-time (where space-time is really emergent... remember loop quantum gravity doesn't really have emergent spacetime as Urs argued earlier that "The definition of LQG is to start from a Hamiltonian formulation of 3+1 dimensional gravity, then encode the field variables as SU(2)-connections, then encode these as parallel transport, then pass to "generalized connections" (which is where they go astray) and then quantize."

    I want something where spacetime and the dimensions are truly emergent (something that creates spacetime.. which string theory can't do because once you have strings.. or particles.. you already assume there is spacetime).

    We need more complex theories with more degrees of freedom.
     
  11. Sep 11, 2018 #31

    Fra

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    In order to not loose predictability we need to relax what is to be explained in a very constrained way otherwise we will create new landscape situations.

    So we do not need theories that a priori are more complex. I think we need to understand transitions between theories of complexity within the context of evolving laws.

    Dimensional transitions can conceptually be explained as embedding dimensions vs computational complexity so that these are spontaneous processes.

    My hunch is that in string theory no answers to this can be found within the context of perturbative treatment with a handoicked background. This is for reasons that are independent of technical details. The key must lie in understanding transitions between theories in the context of some evolving landscspe. I figure this ia also where there is research. Alll the dualitires are indeed interesting, but what is the right way to understand them? Here the main problem of ST seema to be its rather not predictive enough. Wether that is due to missing principles or a too complex problem that are not reasonably computable makes no practical difference.

    Flexibility is needed but not so much that we loose the ability to compute the odds. Then somerhing is missing.

    / Fredrik
     
  12. Sep 11, 2018 #32

    Can you give example(s) of what it means to create new landscape situations by creating more complex theory?

    And for separate questions. Is it right to say that Perturbative string theory may not be able to model the dynamics before strings even occur?... And does it mean nonperturbative string theory is what can model what happens before strings exist (when spacetime was still being assembled such as from spin networks (LQG, etc)?

     
  13. Sep 12, 2018 #33

    Fra

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    The most famous example is of course string theory.

    The general idea is that
    - in order to unify or explain what are currently fixed or theoretically "unexplained" or to explain something in a coherent way as opposed to patchwork of effective theories -
    one needs to put these things in a larger context which relaxes them. This is the idea behind explaining law as evolution or negotiation.

    The idea of strings is in tradition of kaluza klein to consider compactified small extra dimension. Ie in each 4d point there is a 6d manifold that can varying topplogy etc. Then try to "explain" and unify all forces from the interaction propertirs of this manifold in 4d space. This increase the complexity and sometimes this has more than one solution.

    The story is that in string theory is that people conjectures that there are so many ways to compactify the 6d manifold while constraining the cosomlogical scale of 4d part to deSitter space that one speaks of the string landscape. Now a RECENT debatw in string community is that larger part of this landscape is rather wrong (they call it swampland)

    Originally there was some hope that there would not be a landacape. Once realized even string theorists startew to talk abouy evolution of law. Smolins evolving law was originally proposed as a conceptusl solution to string landacape problem. But right now i think it transcends itm

    There are real string theorists on here that can give you better answers.

    I just relate to other researc programs and have opniona on their logic but my own view does not contain strings or no continuum in the starting points.

    I am not sure how you want to combine lqg and st. I have no meaningful comments.

    /Fredrik
     
  14. Sep 12, 2018 #34
    I'm still checking what books or articles I read it but the following seems to describe it too:

    https://www.quantamagazine.org/string-theory-meets-loop-quantum-gravity-20160112
     
  15. Sep 13, 2018 #35
    I think I read it in Sabine Hossenfelder book "Lost in Math" but the above is more detailed. Is she one of the very few emphasizing they could be two faces of the same coin? The key points above are:

    "Loop quantum gravity, by contrast, is concerned less with the matter that inhabits space-time than with the quantum properties of space-time itself. In loop quantum gravity, or LQG, space-time is a network. The smooth background of Einstein’s theory of gravity is replaced by nodes and links to which quantum properties are assigned. In this way, space is built up of discrete chunks. LQG is in large part a study of these chunks.

    This approach has long been thought incompatible with string theory. Indeed, the conceptual differences are obvious and profound. For starters, LQG studies bits of space-time, whereas string theory investigates the behavior of objects within space-time. Specific technical problems separate the fields. String theory requires that space-time have 10 dimensions; LQG doesn’t work in higher dimensions. String theory also implies the existence of supersymmetry, in which all known particles have yet-undiscovered partners. Supersymmetry isn’t a feature of LQG.
    "

    Why is loop quantum gravity and string theory seem only to be the game in town? Is not Barbour Shape Dynamics also a valid theory or model?

    And about this thread called Theories Without Fundamental Space and Time. Barbour is the theory without fundamental time in its active form.. remembering loop quantum gravity is just about assembling pieces of spacetime.. while Shape Dynamics is about Weyl Invariance. According to wiki: https://en.wikipedia.org/wiki/Shape_dynamics

    "In theoretical physics, shape dynamics (Shape Dynamics) is a theory of gravity that implements Mach's principle, developed with the specific goal to obviate the problem of time and thereby open a new path toward the resolution of incompatibilities between general relativity and quantum mechanics.

    Shape dynamics is dynamically equivalent to the canonical formulation of general relativity, known as the ADM formalism. Shape dynamics is not formulated as an implementation of spacetime diffeomorphism invariance, but as an implementation of spatial relationalism based on spatial diffeomorphisms and spatial Weyl symmetry.[1] An important consequence of shape dynamics is the absence of a problem of time in canonical quantum gravity.[2] The replacement of the spacetime picture with a picture of evolving spatial conformal geometry opens the door for a number of new approaches to quantum gravity.[3]
    "

    Is not Shape Dynamics more elegant? How do you tell when a theory is more elegant? According to the following excellent Barbour Shape dynamics intro site.. http://discovermagazine.com/2012/mar/09-is-einsteins-greatest-work-wrong-didnt-go-far General Relativity is not really relative.. What do you make of it? Wiki summarized it thus:

    "Mach's principle has been an important inspiration for the construction of general relativity, but the physical interpretation of Einstein's formulation of general relativity still requires external clocks and rods and thus fails to be manifestly relational.[4] Mach's principle would be fully implemented if the predictions of general relativity were independent of the choice of clocks and rods"

    Isn't Barbour model more elegant that it obeys more the spirit of relativity? Generally.. What makes a theory more elegant?
     
  16. Sep 15, 2018 at 5:53 PM #36
    Fundamental space and time is indeed the classical spacetime. And I guess all quantum gravity theories are going beyond fundamental space and time. The following list is taken from the quantum gravity entry of Wikipedia (they are in addition to the leading candidates of string theory and loop quantum gravity). There are just so many possibilities and models. I'm specifically looking (or filtering) for ones where the quantum degrees of freedom (of whatever) that makes up or create emergent space and time can be directly influenced or manipulated. Anyone care to share what models can do this? With so many models and possibilities. We need guidance from any data (no matter how unconventional) to have any chance to arrive at the right quantum gravity theory.

     
  17. Sep 16, 2018 at 4:18 AM #37

    MathematicalPhysicist

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    Aren't superstring theories already incorporate supergravity and supersymmetry?
     
  18. Sep 16, 2018 at 5:22 AM #38

    Fra

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    IMO the way stringtheory treats spacetime is too conservative. Sure, it does include strange extra dimensions and things which to some is weird, but it is still fairly faithful with respect to the geometric programs that presume a spacetime continuum.

    And from my perspective of inference, order and countability is extremely important to warrant stability and computability to be able to actually get some expectations out from it. And I prefer to start from elementart starting points such as distinguishable states, and to construct expectations on the future states.

    But when complexity gets very HIGH, it is often easier to consider things embedded in a continuum. This is fine but To maintain control when you step into that one must distinguish between the physical and the mathematical degress of freedom, and extremely careful integration measures must be defined to prevent mathematical divergences which obviously are not physically motivated. Here we have imo a gigantic mess in current models.

    I think a program must step back, analyze and rectify these problems to bring back order and computability in order to not get lost on fake landscapes that is created by physicists messing with complex mathematics of continuum models, where we since long lost track of what we are really doing.

    I see many reasons to suggest that we need a discrete starting point, and in these programs the generic idea is that regular spacetime will be recovered in the large complexity limit as embedding dimensions or similar. Thus the spacetime continuum in the sense of background for all the happens is IMO likely an approximation only - rather than the other way around! However, one would probably expect that the complexity limit where the continuum should be effectivel be recovered is still beyond experimental reach except for the "indirect support" that a discrete model may come with explanatory power that extrapolates into states of unification etc.

    /Fredrik
     
  19. Sep 16, 2018 at 8:11 PM #39
    Einstein tried to unify general relativity with electromagnetism but failed because he missed the weak and strong forces. Could we say that our present attempt to unify the forces can only fully succeed if we take into account other possible forces or dynamics besides that in the Standard Model? How many acknowledge this scenario to be the possible case.. or is our attempt to unify spacetime with the quantum is irregardless of whether they are other unknown forces, etc.?
     
  20. Sep 17, 2018 at 9:07 PM #40
    For perspective... LQG is the attempt to unify spacetime with the quantum irregardless of whether they are other unknown forces, etc. While string theory is said to be still trying to find the basic guiding equations. For other forces than the standard model, there is the proton radius problem where some force could be at work but not greatly debated (for example reference: https://phys.org/news/2016-08-deuterium-nucleus-proton-radius-puzzle.html)... but could it affect unification significantly or only have small contribution? I was wondering about none-gauge forces. They say the Higgs boson can be thought of as mediating a "fifth force" that is not a gauge force. It is an example of a type of interaction (force) called a "Yukawa interaction" rather than a gauge interaction. What other interaction forces other than them?

    So if there are new forces.. could it be normal gauge forces.. or none gauge ones.. or if gauge theory was just emergent.. could the new forces be the more elementary constituents.. or are they in the form of other objects like branes and extra dynamics or degrees of freedom, etc.

    Ok. I need reference (articles, books..) that give more clarity on the above lines of thoughts concerning possible new forces of nature and what forms they may take.
     
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