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I Theories without Fundamental Space and Time

  1. Aug 31, 2018 #1
    Can string theory be made without time equations?

    According to Carlo Rovelli in his latest book "The Order of Time"


    "The equations of loop quantum gravity on which I work are a modern version of the theory of Wheeler and DeWitt. There is no time variable in these equations."

    then later...

    "For this intermediate phase, where time is wholly indeterminate, we still have equations that tell us what happens. Equations without time.

    This is the world described by loop theory.

    Am I certain that this is the correct description of the world? I am not, but it is today the only coherent and complete way that I know of to think about the structure of spacetime without neglecting its quantum properties.

    Loop quantum gravity shows that it is possible to write a coherent theory without fundamental space and time—and that it can be used to make qualitative predictions.

    In a theory of this kind, time and space are no longer containers or general forms of the world. They are approximations of a quantum dynamic that in itself knows neither space nor time. There are only events and relations. It is the world without time of elementary physics."

    A theory that knows neither space nor time appears to be more elegant.. too bad LQG folks still haven't approximated General Relativity in the classical limit. Can string theory be made to work without fundamental space and time too? How?
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  3. Sep 1, 2018 #2
    What is the difference between spacetime and fundamental space and time?
  4. Sep 1, 2018 #3
    Im not sure but I got the word from the passage "Loop quantum gravity shows that it is possible to write a coherent theory without fundamental space and time—and that it can be used to make qualitative predictions."

    There are many "fundamental" words in the book.. for example.. a part reads:

    "At first no one could understand the significance of an equation without a time variable, perhaps not even Wheeler and DeWitt themselves. (Wheeler: “Explain time? Not without explaining existence! Explain existence? Not without explaining time! To uncover the deep and hidden connection between time and existence . . . is a task for the future.”) The issue was discussed at great length; there were conferences, debates; rivers of ink flowed. I think that the dust has now settled and things have become much clearer. There is nothing mysterious about the absence of time in the fundamental equation of quantum gravity. It is only the consequence of the fact that, at the fundamental level, no special variable exists."

    It's a great book.. who has read it too? I got the book about reading Sabine Hossenfelder article about the interview with Rovelli at: http://backreaction.blogspot.com/2018/08/guest-post-tam-hunt-roasts-carlo.html
  5. Sep 1, 2018 #4
    To make the question more tractable.

    The movement of strings causes spacetime and spacetime curvature to emerge and in many cases, even some of the initially fixed spacetime can be seen as emerging from the movement of strings. Are the strings only belonging to the graviton particle? Or does other strings like electron string also causes spacetime or spacetime curvature to emerge or causes initially fixed spacetime emerging from the movement of the electron string?
  6. Sep 2, 2018 #5


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  7. Sep 2, 2018 #6


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    Some years ago i got and started to read up on Rovellis ideas, and in particular to analyse his line of reasoning. At first it seems excellent, brilliant etc, but very soon, early in his logic he imo looses clarify and enters a haze he never seem to escapes from.

    How one thinks about this is related to a more general topic the nature of symmetry, or rather than nature of observer equivalence. If you have thought about this one will see its a chicken and egg situation. Rovelli seems to want to describe the equivalence class itself, without the set that defines it to get rid on the redundancies and get the observer invariance manifest. But this is what i think is wrong, he is throwing the baby out with the bathwater.

    A good constrast to Rovellis view is Smolins reality of time. If you check both let me know which you think is the most sound of them both.
    and the as far as i know most recent and most promising way out the metalaw dilemma

  8. Sep 2, 2018 #7
    I'm rereading Time Reborn. I still can't decide whether it's Smolin or Rovelli's..

    The main two points of Smolin book that I'm questioning now are the ideas.. firstly:

    "THE MAIN MESSAGE OF Part II so far has been that for cosmology to progress, physics must
    abandon the idea that laws are timeless and eternal and embrace instead the idea that they
    evolve in a real time. This transition is necessary so that we can arrive at a cosmological theory—
    one that explains the choices of laws and initial conditions—that is testable and even
    vulnerable to falsification by doable experiments."

    But is there no way to evolve laws without any real time? Can't the originator of the evolving laws transcend time?

    The second point.

    "In a word, in general relativity size is universal and time is relative, whereas in shape
    dynamics time is universal and size is relative. Remarkably, though, these two theories are
    equivalent to each other, because you can—by a clever mathematical trick that isn’t necessary
    to go into here—trade the relativity of time for the relativity of size. So you can
    describe the history of the universe in two ways, in the language of general relativity or the
    language of shape dynamics. The physical content of the two descriptions will be the same,
    and any question about an observable quantity will have the same answer."

    Let's say Bob is 30 years old. Alice is 10 years old. If Bob is near a black hole. He ages less so when he and Alice met.. Alice is more than 100 years old while Bob is just 31 years old or less (remember the scene in Interstellar). How do you apply Shape Dynamics here where time is universal and yet Alice is 3 times the age of Bob. If they would take Shape Dynamics into perspective. Can or how do they retain their ages?
  9. Sep 3, 2018 #8

    Urs Schreiber

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    As the reference to Wheeler and DeWitt indicates, the general idea of the Hamiltonian constraints in relativistic field theory replacing the Hamiltonian time evolution in non-relativistic field theory is old and, in fact, standard. For instance, quantizing the Hamiltonian constraint for the relativistic Klein-Gordon particle is well-known to yield the Klein-Gordon equation. (See the references at relativistic particle.)

    This makes it seem a good idea to quantize gravity, non-perturbatively, by "simply" quantizing the Hamiltonian constraint of general relativity. If it were known how to do this, there would be little to no debate that this is successful non-perturbative quantum gravity.

    Unfortunately, what sounds easy turns out to be intractable.

    The reason that "LQG" apparently solves this problem is only because it doesn't solve the problem, but changes the problem to something else before solving it (by passage from real connections to "generalized connections"). I have explained this here.
  10. Sep 4, 2018 #9


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    Time will not be "real" as in a global time. As I see it, reality of time just refers to the reality of a succession of states. Where the generalized sense of state is used where you unify state and law. In newtonian paradigm we separate things into initial conditions, law and states. In the evolving view, all these things should be treated more unified.

    If you take an inference perspective to measurement/observation, and consider an observer to infer/interact with its environment, then ALL the qualifiers must go through the inferential pipeline. This in itself puts interesting "constraints" on what is allowed and whats not. One implication is for example that timeless symmetries has not place. All symmetries must be a result of an inference. And the confidence of the inference is influence by the inference structure and the amount of data.

    In this view ther is no fundamental notion of space or time, the fundamental notions are what is somewhat certain and what is uncertai about distinguishable states. Typically the past is certain, the future is uncertain. But the past typically has an arrow of time, based on what is uncertain. Space are them emergent embedding dimensions only in the large complexity limit. And that large scales are 4D is something that should be predicted from this. The spacetime CONTINUUM has no fundamental place in my thinking. The reason is that computationally infinite and in particular uncountable sets are really troublesome. I rather seem the continuum models as a large complexity "approximation" of the real thing, rather than the otherw way around.

    So the abstractions i look at are mathematical models for inference, whose "execution" corresponds to time evolution. They can grow or release "control" of complexions in their environment to gain or loose mass. And when a collection of such things interact, where will be an evolution of the population of "preferred" mathematical structures. Thats briefly my version of whats along the lines of smolins suggested direction. But this is really abstract and even more "from scratch" than string theory.

    So i think evolution without time as we know it is possible. But the evolution itself is a progress indicator that is at least partially objective, at least in certain approximations. But its certainly not the kind of time that can be lined out as complete histories because tracing the history is not a reversible process informationwise.

  11. Sep 6, 2018 #10

    Urs Schreiber

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    It's hard for me to see what you guys are really trying to understand here. Let's take a step back:

    Are you all familiar with what is called generally covariant differential equations of motion? Such as Maxwell's equations or, notably, Einstein's equations? Do these fit your bill of "laws not evolving with time"? I suppose the latter is meant to refer to Hamiltonian formulations of field theory?
  12. Sep 6, 2018 #11


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    A system of differential equations constitute "fixed laws" and the only evolution is that of the state in time, within a given state space. Ie. But the solution is the entire system. This kind of "time" is not real. Its just an independent parameter.

    My perspective is really that of inference, and the "fixed laws" corresponds to "100% confident deductive rules", so what is important to me is if we think there are elements that are not subject to evolution/change/revision. The "time" itself is not the big thing for me. Time just happens to be what we call the "parameters" we use to describe a history of states.

  13. Sep 6, 2018 #12

    Urs Schreiber

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    Okay, in that case one can say something concrete as to the relation of such general covariant laws to Hamiltonian laws depending on time, and on the quantization in the two perspectives. Namely, this is the perspective of the "covariant phase space" in contrast to the phase space associated with any given Cauchy surface. This is the topic of Chapter 8: Phase space of the PhysicsForums QFT lecture notes.
  14. Sep 6, 2018 #13


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    I dont think we are talking about the same things after all. It seems you refer how to change from the observer invariant (diff invariant in this case) view to inside view (where an observer is chosen). I understand this, but in my view the observer invariant perspective per see is not observable in the physical sense. Note that i dont have any problem with the mathematical relation here between gauge symmetries and gauge choices, the problem is to me where to attach reality/physics in these abstractions. To talk about quantizing an observer invariant object needs to be phased in form of a real inference, and my conclusion is that no observer CAN infer a perfect invariant (not observable).

    With laws evolving in time, i don't mean laws explicity evolving in time as per a deterministic rule. That is indeed equivalent to a fixed law as long as the dependence on time is given. This would then correspond to a "meta law". The core problem of smolins view is to understand what evolution of law means, without adding from behind a "meta law", which in fact is just another law again.

    The key is rater to find an intrinsic evolutionary model where only the evolutionary steps are given, and where the future possible states can not be predicted without the actual backreaction from the environment. And for reasons of computability and information limits, this can not be capture in a confident certain rule.

    Have you read anything about Smolins views of evoling law? I really enjoy your insights, and mathematical perspective, and I agree more stringency is needed. But there are also the part where one need to somehow attach the abstractios to physics and conceptal understanding. I might guess you find smolins talk fuzzy, but would really like to hear your sincere opinon if you really read any of it. The reason is that it puts the finger on the observer problem, and that laws need to be, not "observer", but in the generalization "inferred/abduced" from interactions, and that therefore all laws must be the result of evolution (or i would say inference). I think smoling could be clearer.

    And how do you interpret all this in terms of categories of observers? Where you need another category to even define the category of categories?

  15. Sep 7, 2018 #14

    Urs Schreiber

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    No. But, to be frank, if you are trying to advertise any insights that might be found there, you are not doing them a favor here, because they come across as really confused.

    I wish I knew what you are asking here, because then I would really try to help. But I fail to make sense of what you are saying or asking or trying to understand. What is "all this"? Which "categories of observers"? And how on earth should something purely formal like the (large) category of all (small) categories suddenly make any appearance here?

    To be frank, it does sound quite crackpottish! Maybe it's not, sometimes people sound this way when they are beginning to acquaint themselves with scientific thinking.

    Could you try to boil down your question to something more or less well defined? Maybe stick to something concrete, like Maxwell's equations. What is it you would like to know or say about them?
  16. Sep 7, 2018 #15


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    The issue which I think is confusing you is that in loop quantum gravity, dimensions of space-time are emergent rather than fundamental properties of the theory.

    Thus, rather than simply saying that "space-time has three space dimensions and one time dimension" as we do in general relativity, or "space-time has 11 dimensions" as we do in M-theory (which is the master theory of all string theories), loop quantum gravity says "points can be connected to other points according to these rules". From that source principle emerges an approximately four dimensional space-time in the world we see in every day life, and an approximate but not absolute ordering of points in the emergent space-time that creates the illusion of locality and smoothness of what is fundamentally a non-local, discrete theory. In loop quantum gravity, dimensions are approximate descriptions of a space-time in which any two points can, in theory, be connected to each other.

    (Incidentally, not all theories of the loop quantum gravity type that try to quantize space-time rather than particles in space-time lack causality. Many kindred theories, e.g. causal dynamic triangles, instead assume a flow of time as an organizing principle that makes time an inherently different kind of dimension than space.)

    It is also important that you be clear that string theory (which quantizes a carrier boson of gravity rather than space-time itself) and loop quantum gravity, are competing theories that differ greatly in their fundamental assumptions. You can't carry over something said in one of these theories to the other.
  17. Sep 7, 2018 #16


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    This sounds like a confounding of two different theories. In string theory, the movement of strings causes spacetime curvature to emerge, but does not cause spacetime to emerge. In string theory, the dimensionality of spacetime is set, a priori, as an assumed fundamental part of the theory. Sometimes string theory articulates spacetime itself as a "brane" which is not a string.

    String theory is based on the assumption that all of the Standard Model particles, the graviton, and probably additional fundamental particles that have not been discovered yet, all arise from vibrations of a single kind of more fundamental particle called a string. Heuristically, the fact that, in string theory, all particles are basically the same thing deep down, and that all mass and all forces are associated with particles, makes the universal application of gravity to everything that has mass or energy make more sense.
    Last edited: Sep 7, 2018
  18. Sep 8, 2018 #17

    But according to Science Advisor atyy.. the movement of strings causes spacetime to emerge. This is his exact words:

    "It is true that spacetime isn't fully emergent in perturbative string theory (or at least not obviously so). However, it is true that the movement of strings causes spacetime (and spacetime curvature) to emerge. Furthermore, in many cases, even some of the initially fixed spacetime can be seen as emerging from the movement of strings."

    Reference https://www.physicsforums.com/threads/true-background-independent-particle-physics.484720/page-2

    Here, atyy stated that the movement of strings causes spacetime to emerge. You don't agree.

    So does the movement of strings causes spacetime to emerge or not? Maybe it's the context.. so I hope atyy and ohwilleke can resolve this.

  19. Sep 8, 2018 #18
    But again, according to Science Advisor atyy in the thread referenced above: "In string theory, spacetime is emergent ie. the fundamental dynamical entities are not related to spacetime in any simple way. In loop quantum gravity, the fundamental entities are essentially pieces of spacetime, so spacetime is not as drastically emergent."

    You and atyy are two of a kind. Non-physicists but well versed in physics technicalities so I hope you can settle on the context and perhaps let a full time physicist declares what is the correct concepts and terms to use.

    Last edited: Sep 8, 2018
  20. Sep 8, 2018 #19

    Urs Schreiber

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    This is not really correct, at least not in the original "canonical" LQG (maybe in some variant of CDT). 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.

    The reason that Ashtekar variables involve SU(2) (whence the whole business of "spin" networks) is directly related to 3+1 dimensions.
    Last edited: Sep 8, 2018
  21. Sep 8, 2018 #20

    Urs Schreiber

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    That's about right. In a sigma-model ("geometric") string background, a target spacetime is fixed, and the string perturbation series provides an S-matrix for perturbative quantum gravity on this background spacetime, encoding, if you wish, perturbative quantum fluctuations of the metric tensor, hence of the curvature of spacetime. As you said.

    One subtlety here is that a string background need not be defined by a geometric sigma-model. A priori it is defined simply by specifying a suitable 2d conformal field theory on the worldsheet. In this perspective, no target spacetime geometry is manifest. But then one may still compute the string perturbation series, and then ask which QFT on which actual spacetime has the same scattering amplitudes (S-matrix) like that, at low energy. If one finds such a QFT, one may regard the spacetime that it is defined on as having "effectively emerged" from the excitation spectrum of the worldsheet theory.

    This is just as in Connes-style NCG, just with worldlines promoted to worldsheets. There is a PF-Insights article with more on this kind of "emergence" at Spectral Standard Model and String Compactifications
    Last edited: Sep 8, 2018
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