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Is the universe continuous?

  1. Nov 4, 2014 #1
    GR models of the universe describe it as a continuum, a smooth manifold, on the other hand the universe contains matter and matter is considered discrete.
     
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  3. Nov 4, 2014 #2

    phinds

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    This is a somewhat contentious issue with no known resolution. There are numerous threads on this forum discussing and you might do a search to check them out, but what it boils down to is we don't know.
     
  4. Nov 4, 2014 #3

    marcus

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    There are indications, are there not?, that geometry is also discrete when probed at small enough scale. What are these indications? You certainly know some. We can't be sure yet, but there are reasons to suspect geometric discreteness---what are some of them?

    Jacobson's 1995 derivation of GR as a thermodynamic equation of state?
    So what might be the geometric molecules of which GR is the EoS?
    Finite entropy beyond bh horizon?
    Continuum GR cannot be entirely right since it fails at extreme density?
     
  5. Nov 4, 2014 #4

    marcus

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    I wonder if this old (1983) paper of Rafael Sorkin is relevant.
    http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/31.padova.entropy.pdf
    He argues for geometric discreteness simply based on the finiteness of bh entropy
    ==quote Sorkin intro==
    The evidence is very strong that a black hole presents itself to the outside world as a thermodynamic system with entropy proportional to its surface (horizon) area. Yet the physical origin of this entropy is far from clear. In fact the formula S = k lg N , on which our general understanding of the Second Law is based, entails the absurdity S = ∞; for— unlike in flat space—a bound on the total energy does not suffice to bound the number of possible internal states. In particular the Oppenheimer-Snyder solutions [1] already provide an infinite number of possible internal configurations for a Schwarzschild exterior of fixed mass.

    A related observation is that the internal dynamics of a black hole ought to be irrelevant to its exhibited entropy because—almost by definition—the exterior is an autonomous system for whose behavior one should be able to account without ever referring to internal black hole degrees of freedom. In particular one should be able to explain why it happens that a sum of two terms, one referring to exterior matter and the other only to the black hole geometry, tends always to increase.
    ==endquote==
    ==quote Sorkin conclusions==
    On dimensional grounds it is easy to see that S will be ultra-violet infinite in the continuum limit l→0. ...
    To obtain an entropy of the correct order of magnitude for a black hole, the cutoff l must be chosen approximately equal to the Planck length. Conversely, if Sext really can be identified as the black hole entropy we obtain evidence of the physical necessity for such a cutoff to exist.
    ...
    ...
    ==endquote==
     
    Last edited: Nov 4, 2014
  6. Nov 4, 2014 #5

    Chronos

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    Spacetime quantization is an active area of research, but, the results are inconclusive. In theory, extremely energetic gamma rays from distant sources should suffer measurable dispersion if spacetime is quantized. It is expected this would result in a time delay vs the arrival time of lower energy photons. This, of course, assumes that GRB gamma emissions at different frequencies occur at a single point instantaneously, which is obviously debatable. The Fermi LAT gamma ray telescope has been utilized to conduct such measurements. Data to date is inconclusive. One possibility is quantization occurs at sub-Planck scales. This is somewhat unpalatable to some scientists, but, I'm unconvinced the Planck scale is a brick wall as opposed to a human convenience - e.g., obviously matter exists at sub Planck mass scales. For further discussion see: http://arxiv.org/abs/1109.5191, Bounds on Spectral Dispersion from Fermi-detected Gamma Ray Bursts; and, http://arxiv.org/abs/1406.4568, Lorentz violation from gamma-ray bursts.
     
  7. Nov 4, 2014 #6

    Chronos

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  8. Nov 4, 2014 #7

    marcus

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    Note that Sorkin's approach to geometric discretness preserves Lorentz Invariance.
    This is one of the first things proved in the Perimeter lectures on Causal Sets, that Dowker and Sorkin presented a year or two back.
    Same with LQG, there is that paper by Rovelli and Speziale proving Lorentz invariance.

    So we don't want to get geometric discreteness MIXED UP with the old idea of "graininess" which somehow leads to higher energy gamma arriving EARLIER or as other people imagined LATER than other light. That old idea never seems to go away, does it? : ^)
    There is it cropping up in that "Astronomy Cafe" piece by Sten Odenwald! The old L.I.V. idea ("lorentz invariance violation")
    We have to learn to make a sharp distinction.
     
  9. Nov 4, 2014 #8

    marcus

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    T.D.
    You might be interested in this January 2014 paper by Chirco et al. They take Jacobson's 1995 idea one step farther and identify what the microscopic DoF of which GR is the equation of state could actually be!
    ==quote page 1 of http://arxiv.org/pdf/1401.5262v1.pdf ==
    ...The microscopic degrees of freedom are those of the quantum gravitational field and the Einstein equations express only the classical limit of the dynamics. The entropy across the horizon measures the entanglement between adjacent spacetime regions. Its finiteness is evidence for the quantization of the gravitational field: this is analogous to the fact that the finiteness of the black-body electromagnetic entropy is evidence for the quantization of the electromagnetic field.

    We show that the Jacobson result is consistent with this simpler and tighter scenario. The finiteness and the universality of the entanglement entropy across spacetime regions indicates ultraviolet quantum discreteness, as it did for Planck and Einstein at the beginning of the XX century.
    ==endquote==

    Forgive me if I say something in probably the dumbest crudest way, by comparing geometry (as we come to understand it now) with LIGHT as people came to understand it early in XX century.

    there is no need to imagine that light is "grainy" when it is just traveling along minding its own business. The quantization is observed when it INTERACTS with something material---when it is emitted, or absorbed, or scattered, etc.

    So I am not imagining that spacetime is a grainy material or "fabric". It can be as continuous as it wants ON ITS OWN TIME when I am not making some geometric measurement. Or not! I think it is meaningless to talk about how geometry is when there is no interaction. In any case, the discreteness comes in only when I interact with it, e.g. have some materially physically defined angle, or area, or volume. I have something I want to measure, and therefore there is an interaction of some kind.

    Just quietly sitting there being the geometry, defining the geodesics and what the triangles would add up to IF you bothered to measure, that is neutral, it is the "default" It is not an interaction for light to be following the geodesics, because where else is it going to go?

    The geometric quantumness only shows up when there are events. Am I being inconsistent, or too vague?
     
    Last edited: Nov 4, 2014
  10. Nov 4, 2014 #9
    Is it meaningful to ask if these two questions are the same?

    1] Is the universe continuous?
    2] Is spacetime continuous?

    And... continuity of what, exactly?

    Is it meaningful to distinguish asking about the continuity of what comprizes the universe or spacetime, or asking about the continuity of the "physical laws" (in the universe or spacetime)?

    Also, doesn't the universality of local c assume or require some strict assumptions about continuity? Continuity is always a locally applied concept so even under GR continuity would hold "everywhere"... right?
     
  11. Nov 4, 2014 #10

    marcus

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    Let's talk about the geometry , not about "space-time" as if it were some naive thing like a "fabric", or some weird sort of material substance.

    Geometry means measurements (...metry) and it means geometric relationships, and geodesics, and between/not between, bigger area than, or not, intersecting, or not. Bigger or lesser angle.

    if someone has to think of it as some kind of material thing, let it be a WEB of measurements/relationships.

    "Continuous" would mean you can keep dividing a distance by two forever. No smallest MEASUREMENT.
    "Discrete" means you can't. You can't measure below a given positive size.

    I think there probably is a a smallest distance that you can measure, and if you try to measure a smaller distance then you might more or less randomly get a zero result, or the minimal eigenvalue. Have to go.
    Back now. Yeah, the idea is that if you TRY to measure a width that is less than the minimal positive measurable distance "l" then Nature won't allow it and you will get a "fluctuation" between zero and the minimal "l".

    We are not concerned with what somehow "really exists" down at that scale---it doesn't mean anything. Only measurements matter. We are concerned with how Nature responds to measurements. That's what geometry is. And why I'd say it is not continuous.
     
    Last edited: Nov 4, 2014
  12. Nov 4, 2014 #11

    td21

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    Planck constant may be the smallest piece we can measure. But I still cannot comprehend what discreteness means in terms of space.
    In my opinion, space is defined to be continuous (isn't it)? One may assign values to certain space-coordinates (to create the discreteness), but the coordinates itself is always continuous.
     
  13. Nov 4, 2014 #12
    wouldn't extreme gravity be a factor in this. if the universe can be warped by "super" black holes wouldn't that allow for other forces to affect the shape and continuity of the whole?
     
  14. Nov 4, 2014 #13

    marcus

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    For the sake of general awareness of what we're talking about maybe we should clearly acknowledge that neither "space" nor "space-time" are necessarily continuous by definition and they certainly do not necessarily involve coordinates.
    http://www.signalscience.net/files/Regge.pdf
    That goes back to 1960 when Regge was at Princeton. His 1960 paper was called
    General Relativity Without Coordinates
    It is a famous paper that introduced a famous approach (Regge calculus) that succeeded in doing Einstein General Rel without using coordinates.
    That link gives a fax of the original paper.

    Since then there have been many ways developed to treat spacetime using discrete entities, like simplices, cell-complexes, or graphs, rather than using the usual continuum model (the differential manifold).

    Just to take one example, there is so called "CDT" (causal dynamical triangulations) as developed by Renate Loll and Jan Ambjorn, with others.

    I wouldn't say that a clear winner has emerged in the competition for "best discrete model of spacetime geometry" but it cannot be said that it is
    "continuous by definition." : ^)
    Causal Sets, as developed by Rafael Sorkin and Fay Dowker, with others. If anyone wants they can do a search by author names at arxiv.org and find a large collection of paper that appeared over the past 10 years, and some earlier.
     
  15. Nov 5, 2014 #14

    td21

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    Thank you for introducing me to this wonderful paper. I said space is continuous by definition because I don't know what the stuff in between would be called if space is discrete.:H
     
    Last edited: Nov 5, 2014
  16. Nov 5, 2014 #15
    Ideal measurements are obviously discrete, then one could argue that in practice no ideal measurements can be made.
    I think we could all start by agreeing that nature is not scale-invariant, and what that implies.
    For many experts this simple fact discards both a fractal and a continuous universe, solving the issue in favor of discreteness.
     
  17. Nov 5, 2014 #16

    phinds

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    But it seems to me that ideal measurements measure what IS. If what IS is not continuous then it would not measure as continuous. a simple example would be making measurements of the distance between a series of fence posts that are 10 feet apart. It just doesn't make sense to talk about a measurement of 23.78... feet in that realm.
     
  18. Nov 7, 2014 #17
    I don't think that is correct.

    GR describes spacetime as smooth, but you can insert singularities like particles from quantum field theories in semiclassical physics or perhaps idealized black holes (I'm not well versed in GR).

    - If you ask if there is a problem, evidently not. GR is known to be an effective, quantizable theory, so it both allows and has particles (at low energies, at least). Same goes with string theory, discrete strings on smooth branes.

    - If you ask if space (or time) is discrete, it is an open question.

    As Chronos notes observations arguably seem to imply relativity (so smoothness) is valid below scales where presumed discreteness ought to have kicked in.

    I would like to see a reference. All previous examples failed to do that, as would be expected. All discrete approaches to gravity also fails to have a dynamics (no harmonic oscillators) mainly due to that they fail to have an energy (no lower energy bound), so the attempt to use thermodynamics should be erroneous.

    Sorkin's other paper is simply claiming to put harmonic oscillators of quantum field theory (say) on a lattice, but it could as well be a particle gas of some well defined density. It is a bait-and-switch, "it is a tale. Told by an idiot, full of sound and fury, Signifying nothing."*

    That looks like another bait-and-switch. The Regge paper makes its skeleton spaces into differentiable manifolds by smoothing them.

    Sure, geometry (of GR, say) can be expressed without coordinates. So what? String theory use that, doesn't it, when it puts up a GR scaffold solution and then remove it (with or without coordinates) as I take the procedure is?

    *I'm not saying that Sorkin is an idiot, maybe I am. And he is technically proficient in his field, which isn't mine. But the intent of the paper looks superficially like idiocy.
     
  19. Nov 7, 2014 #18

    martinbn

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    http://sigrav.na.infn.it/tullio-regge/
     
  20. Nov 7, 2014 #19

    Wow, so to you GR is quantizable and discrete. I think this indicates your admitting not being well versed in GR is somewhat an ironic understatement.
     
  21. Nov 7, 2014 #20
    These are important points, to the first I would reply that universe is not necessarily the same as spacetime, for instance if we make the distinction between spacetime as something different from its content.
    The second is also key, continuity of what? Depending on whether one is essentialist, substantialist, ... Etc will respond differently.
    The thirs leads us to discuss about how to define physical laws, and relate it to whatever it is that we consider discrete or continuous.

    Since in reality there are no ideal measurents by definition we find that physical measurents must introduce some sort of scaling and coarse graining that deviates from what otherwise would be a scale independent process, this is usually dealt with when studying the renormalization group.
     
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