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Could GR's background independence be a theoretical artifact?

  1. Sep 26, 2009 #1
    Could GR's "background independence" be a theoretical artifact?

    ==quote from Rovelli "Unfinished Revolution" (2006) page 2==

    ...Others, on the other hand, and in particular some hard–core particle physicists, do not accept the lesson of GR. They read GR as a field theory that can be consistently formulated in full on a fixed metric background, and treated within conventional QFT methods. They motivate this refusal by insisting than GR’s insight should not be taken too seriously, because GR is just a low–energy limit of a more fundamental theory. In doing so, they confuse the details of the Einstein’s equations (which might well be modified at high energy), with the new understanding of space and time brought by GR. This is coded in the background independence of the fundamental theory and expresses Einstein’s discovery that spacetime is not a fixed background, as it was assumed in special relativistic physics, but rather a dynamical field.

    Nowadays this fact is finally being recognized even by those who have long refused to admit that GR forces a revolution in the way to think about space and time, such as some of the leading voices in string theory. In a recent interview [1], for instance, Nobel laureate David Gross says: “ [...] this revolution will likely change the way we think about space and time, maybe even eliminate them completely as a basis for our description of reality”. This is of course something that has been known since the 1930’s [2] by anybody who has taken seriously the problem of the implications of GR and QM. The problem of the conceptual novelty of GR, which the string approach has tried to throw out of the door, comes back by the window.
    ==endquote==
    Would it be possible to develop a theory of gravity that is background dependent, a fluctuating field over a fixed metric, that reproduces all known GR results where GR has been tested? What about the spin-2 field on flat QFT?

    I wonder if BI is a theoretical artifact that, while a valid conclusion based on GR"s field equations, are invalid when applied to nature. In otherwords, while GR succeeds as modeling gravity as encoding the geometry of spacetime, what gravity fundamentally is is some sort of emergent van der waals type interaction of something more fundamental.
     
    Last edited: Sep 26, 2009
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  3. Sep 27, 2009 #2

    atyy

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    Re: Could GR's "background independence" be a theoretical artifact?

    Could one have both? In AdS/CFT, the CFT has a fixed background, but it describes an almost fully "dynamic" metric in AdS space, being fixed only at the boundary.

    There is also a comment I don't understand in Hamber's http://arxiv.org/abs/0704.2895 "It is possible though to formulate quantum gravity on a flat hypercubic lattice, in analogy to Wilson’s discrete formulation for gauge theories, by putting the connection center stage. In this new set of theories the natural variables are then lattice versions of the spin connection and the vierbein." I do understand it enough to know that gravity is not emergent in the approaches he is discussing.
     
    Last edited: Sep 27, 2009
  4. Sep 27, 2009 #3

    Fra

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    Re: Could GR's "background independence" be a theoretical artifact?

    I think that's more than possible, and I see arguments that it is in fact more plausible than the realist type of background indepdence in the sense of perfect observer independent diff-invarance symmetry.

    However, there are different ways to think of this.

    1) To replace one fundamental realist type of symmetry with another one (more fundamental), is generally suspect becuase it just replaces one fixed symmetry with another fixed symmetry (relative to which the prior one is emergent as a subsymmetry per a particular mechanism).

    2) The other option, which I find most attractive, is to really find a new understanding of the physical basis and the status of symmetry that does NOT incorporate realist fictions. Usually symmetry is a constraint that allows us to make inferences. But if we are looking for a MEASUREMENT THEORY, and not a realist type of old style model, then we should wonder what is the origin of these symmetries? shouldn't we? Because all the effective symmetries we do now, are actually inferred from nature. We find the apparent symmetries of nature from experiment and measurement, to guide further measurements. They are not god given constraints as far as I see it. This detail are rarely acknowledged in many types of models. And it sure disturbs me, and I can't come to terms with this inconsistency.

    /Fredrik
     
  5. Sep 27, 2009 #4

    tom.stoer

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    Re: Could GR's "background independence" be a theoretical artifact?

    Background independence, diffeomorphism invariance and gauge symmetry are in some sense always a theoretical artefacts. Assume you have a path integral Z which incorporates all relevant physical information (eigenstates, spectrum, scattering amplitudes, ...). Assume for a moment that it's possible to write it as

    Z = ∫Daphys exp iS[aphys]

    Here everything is written in terms of physical fields a(x).

    Instead we usually start the development of a theory with an expression like

    Z = ∫DA exp iS[A]

    where A(x) and S refer to fields and action with some (local) symmetry. Therefore A(x) are no physical degrees of freedom (no observable quantities), but one must implement a local symmetry in order to get a well-defined path integral.

    Usually this is done via

    Daphys = DA / symm

    which means that we "factor out" the symmetry group of the action S.

    If we were able to write down these expression directly in terms of physical quantities, then nobody would care about these local symmetries.
     
  6. Sep 27, 2009 #5

    ConradDJ

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    Re: Could GR's "background independence" be a theoretical artifact?


    Hi Fredrik –

    What you’re calling a realist model is one that takes the world as consisting of given facts... so then the purpose of theory is to express as concisely as possible the order of those facts. Uncovering symmetries is a basic way to do that.

    But since physics gives us many different kinds of symmetry – some exact and some “broken” or only approximate – I agree that we need to look for a deeper explanation of each symmetry. And in a realist model, where do we even look for that? The equations of GR express a remarkable kind of symmetry – but we don’t really have any basis for judging whether diffeomorphism invariance is fundamental, as Rovelli thinks, or emergent, as I think the OP is suggesting. And we don’t know how to relate this to the many other kinds of symmetry of the Standard Model.

    In what you call a measurement theory, on the other hand, physics not only describes actual (measured) facts, but also structured systems of possible fact – I'm thinking of the quantum wave-function, describing the physical situation in which a certain type of measurement can be made, but where the outcome is not yet given.

    If the quantum-type theory is fundamental, then symmetries have a natural explanation in terms of sequential levels of physical possibility-structure... i.e. where some aspects of physical structure become determinable before others.

    Maybe at a very “primitive” level – e.g. in the quantum vacuum, or in the very early universe – the possibilities of interaction are essentially unconstrained by any law, and nothing is determinable.

    At a very “high” level – that of our “macroscopic observation” – the physical measurement-context is so structured by physical law and so densely redundant, giving so many ways of measuring things, that the world looks like a body of precisely determinate fact, with no dependence on the measurement-context at all.

    Symmetries would arise in between, in the intermediate levels where some aspects of physical structure are already given, other aspects are determinable through interactions (measurements), and some are not yet determinable at all.

    Take a very simple, non-physical example of spatial symmetry –

    > Suppose the topology of possible points on a 2-dimensional surface is already determined.
    > Suppose the distance from any given point to another point is determinable, at this level –
    > Suppose the direction between any two points is not yet determinable.
    Say we randomly select (measure) points at a determined distance from a given point. If we then look at the result from a higher level – where directions as well as distances are determinate, and we can see the surface as a plane – the we see our selection has resulted in a symmetrical circle.

    So – where in a “realist model” a symmetry is just a fact-pattern – in a “measurement model”, symmetry indicates the order in which different aspects of structure become measurable. From that standpoint, symmetries in the laws of physics indicate levels of interaction-structure in which some parameters are physically definable (measurable) and others are not.

    GR would then be telling us that the aspects of physical interaction that make the smooth connectedness of the spacetime manifold determinable are “more primitive”, more basic than the aspects that let us measure spacetime intervals and coordinates – which supports Rovelli’s viewpoint.

    As another example, the CPT symmetry of all known physical laws would indicate a very deep level of interaction-topology that “predates” the structures that let us determine the +/– charge, left/right parity or the forward/back direction of the time-arrow.
     
  7. Sep 27, 2009 #6
    Re: Could GR's "background independence" be a theoretical artifact?



    In QED in the Coulomb gauge (or in Dirac's gauge-invariant variables) the formulation is in fact a gauge-independent, i.e., only physical degrees of freedom (that carry and exchange the energy-momentum) are involved.

    Why not to do the same thing for the gravitational field?
     
  8. Sep 27, 2009 #7

    atyy

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    Re: Could GR's "background independence" be a theoretical artifact?



    Would it be better defined if the question were rephrased as "Does the classical limit of the quantum theory contain the full solution space of classical general relativity"?

    In the case of Asymptotic Safety (if it exists) and string theory, I think the answer is almost all, and hopefully the missing topologies are not required. The caveat in string theory is that non-perturbative definitions are only known for some sectors, while other physically relevant sectors are still only perturbatively defined.

    In cases where the quantum theory has a fixed non-relativistic background such as Horava-Lifgarbagez, the classical solutions are different, eg. no exact Schwarzschild, and a scalar graviton in addition to the usual spin-2 one:
    http://arxiv.org/abs/0905.2798
    http://arxiv.org/abs/0905.2579
     
    Last edited: Sep 27, 2009
  9. Sep 27, 2009 #8

    tom.stoer

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    Re: Could GR's "background independence" be a theoretical artifact?

    Yes, of course, it works for QED, and for QCD as well.

    1) The main problem with QG is that the path integral seems to escape standard renormalization and therefore seems to be ill-defined.
    2) The standard treatment of non-abelian gauge fields requires gauge-fixing via Fadeev-Popov ghost, which is not really a formulation in terms of physical degrees of freedom only. Something similar applies to QG as well.
    3) In addition there's the problem that one must never use any reference to a background metric, as this metric must not be used as input (e.g. in order to define polarizations, positive and negative ferquency conditions etc.)

    I agree that in principle this approach should be possible, but as far as I know it never worked due to technical inconsistencies.
     
  10. Sep 27, 2009 #9

    tom.stoer

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    Re: Could GR's "background independence" be a theoretical artifact?

    I am not sure what you mean. The question was if these symmetries are theoretical artefacts. I tried to explain why this is - in a certain sense - always true. Gauge symmetries and diffeomorphism invariance are coordinate symmetries only.

    It may not be true if a more fundamental theory from which spacetime emerges is correct. Then it may be possible that these symmetries are only valid in a low-energy / long distance limit.

    But my argument remains valid if you exclude certain sectors of GR. If e.g. spacetime is restricted (for some reason yet to be discovered) to one topological sector, then factoring away these symmetries simply means that the group you factor away is smaller.
     
    Last edited: Sep 27, 2009
  11. Sep 27, 2009 #10

    atyy

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    Re: Could GR's "background independence" be a theoretical artifact?

    I agree with your argument. Gauge invariance is an "artifact" even of classical general relativity. I was rephrasing the original question in such a way that "background independence" is not an artifact in classical general relativity, ie. let's only consider the physically allowable metric geometries, and take background independence to mean that classical general relativity has no geometry that is common to all allowable physical configurations, and the geometrical configurations and matter configurations specify each other, ie. let's define "background independence" not as "general covariance", but as "no prior metric geometry".
     
  12. Sep 27, 2009 #11

    marcus

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    Re: Could GR's "background independence" be a theoretical artifact?

    Tom, I'd be interested to learn what you think of the following line of reasoning.

    A fixed metric on a manifold imposes a causal structure----it decides for us which events could cause or influence which other events.

    Suppose one takes a manifold and fixes a metric g, and then one introduces a disturbance "on top of that" so that the real metric is g+h.

    In a kind of naive or braindead way, g is the fixed background and h is the "gravitational field" defined on top of the fixed geometry specified by g.

    This will typically change the logical (or lightcone) structure. So the logical structure originally specified by the background is no longer being followed by nature. Nature goes by the full g+h geometry.

    So not only the gravitational field but all of the field theory that one defines on top of the fixed background is generically invalid. This includes all the matter fields, as well as the phony (because only partial) "gravitational field" called h, which one has added to the picture. They do not take into account the real causal structure.

    Because the logic of causality and locality is one, the gravitational field is one. It cannot be divided into a main or fixed background part and an additional field of "forces" or "gravitons" which are supposed to be empty of logical effect. That kind of picture is a useful mathematical fiction with a limited applicability, but can't be taken as in any sense fundamental.

    That's one way to look at it. Do you see anything obviously wrong with that point of view?
     
    Last edited: Sep 27, 2009
  13. Sep 27, 2009 #12

    tom.stoer

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    Re: Could GR's "background independence" be a theoretical artifact?

    I fully agree. Splitting g = g°+h is plainly wrong.
     
  14. Sep 27, 2009 #13
    Re: Could GR's "background independence" be a theoretical artifact?

    Well, there is the A.A. Logunov's relativistic theory of gravity (RTG) where splitting g=η+h is meaningful because the equations for matter contain the entire g (equivalence principle) but the gravitational field equations contain η - the Minkowsky metric. The main space-time is flat, its curvature R is equal to zero, and the gravitational field η is as physical as the electromagnetic one. In such a formulation the inertia forces are different from the gravitational ones since transition into an accelerating reference frame does not change R=0.
    This theory describes well all observable effects but works in the frame of a flat space-time.

    I think such a formulation is very promising since after removing the self-action from interaction this theory will not need renormalizations at all. The calculations will turn into calculations of compound systems, like in atom-atomic scattering, i.e., with no conceptual and divergence problems.
     
    Last edited: Sep 27, 2009
  15. Sep 27, 2009 #14

    marcus

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    Re: Could GR's "background independence" be a theoretical artifact?

    Logunov's 1984 RTG (relativ. theor. grav.) is a good illustration of the difficulty.
    It was formulated by a highly respected older physicist (he was born in 1927) and yet it never caught on.

    It has some problems like predicting that black holes cannot exist, because there is a fundamental fixed Minkowski flat. It is hard to see how a universe with that basis could expand a thousand-fold, and do all the other neat stuff that our universe evidently does.

    Logunov formulation seems kind of arbitrary and unnatural, but it certainly is good for doing a certain limited class of calculations.

    Here is the main 1984 paper:
    http://www.slac.stanford.edu/spires/find/hep/www?irn=1280147 [Broken]

    It is listed as having been cited only 7 times.

    People like James Hartle and Gary Gibbons have cited Logunov's RTG---there is awareness of it, it has not been overlooked.
    But the citation I checked out was to illustrate why something doesn't work. It is used as an example of a flawed or inadequate approach.
    Like "half a dozen different authors have tried it but if you want to take way seriously you have to deal with the....[lightcones]..." or words to that effect.

    The idea is say call the Minkowski metric g and the additional field h. So the total is g+h. Then the artificial assumption is that the other fields all know about g+h, and live on the full g+h geometry. But the gravitational field h only knows about Minkowski geometry g and lives on the partial geometry g.
    Why should the gravitational field be treated differently? And if you do this then you are permanently stuck with this clumsy stiff Minkowski space and cannot do things like black holes and big bangs and expansion and all the other really curved stuff. Like wearing a wooden shirt.

    However I gather that Logunov is well respected for his excellent work in other areas of physics such as nuclear and particle physics. He has received many honors. Only this slightly odd idea of his about gravity so far at least until now did not fly.
     
    Last edited by a moderator: May 4, 2017
  16. Sep 27, 2009 #15

    atyy

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    Re: Could GR's "background independence" be a theoretical artifact?

    Well, maybe Logunov had a good idea nonetheless - do you think these are in the same spirit?

    http://arxiv.org/abs/hep-th/0009230
    External Fields as Intrinsic Geometry
    John Madore, Stefan Schraml, Peter Schupp, Julius Wess
    "There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external fields which can be absorbed into an appropriate redefinition of the geometry, this time a noncommutative one."

    http://arxiv.org/abs/hep-th/0212262
    Noncommutative Field Theories and Gravity
    Victor O. Rivelles
    "We show that after the Seiberg-Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background. ........... This shows that noncommutative field theories can be seen as ordinary theories in a gravitational background produced by the gauge field with a charge dependent gravitational coupling. "
     
    Last edited by a moderator: May 4, 2017
  17. Sep 27, 2009 #16
    Re: Could GR's "background independence" be a theoretical artifact?

    It is not so, the RTG predicts heavy blackhole-like objects but it is free from non-physical singularities.

    It preserves the energy-momentum conservation and treats the gravitational field as physical rather than as the curvature of the true space-time. In this respect it is advantageous and quite natural.

    It is implementation of Einstein's equivalence principle for matter.
    Academician A. Logunov has given his motivations in many articles. As to me, I prefer working in the Minkowsky space-time where I have the energy-momentum conservation laws and the gravitational fields (static and waves) are as physical as the electromagnetic and other fields. There is nothing especially artificial in RTG. On the contrary, it is a return to good physics.

    The problem of his approach is in revealing some crucial drawbacks of GR, it is an "anti-Einstein's" approach. Many are scared to follow it - they do not want to be excluded from researching. It is a serious matter.

    There is a fresher reference: http://arxiv.org/abs/gr-qc/0210005
     
    Last edited: Sep 27, 2009
  18. Sep 27, 2009 #17
    Re: Could GR's "background independence" be a theoretical artifact?

    Do not tell me that the Riemann space-time is a custom-made suit. GR is even more non-linear and difficult than RTG.

    Big Bang is an extrapolation backwards in time, not an experimental fact.

    Black holes and singularities are a serious problem in GR, not good (physically acceptable) solutions.

    It seems physicists started to believe too much in their weird results (black holes) and patches like bare particles, vacuum polarizations, appeared in late practice to somehow make senseless actions meaningful.
     
  19. Sep 27, 2009 #18
    Re: Could GR's "background independence" be a theoretical artifact?

    It is not exactly so - the gravitational filed "knows" about both: g and h, but they do not enter as a sum (g+h) in the equations. Thus the Minkwsky space-time is in fact separated in the theory (RTG) from the effective Riemann geometry felt by matter.
     
    Last edited: Sep 28, 2009
  20. Sep 27, 2009 #19

    atyy

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    Re: Could GR's "background independence" be a theoretical artifact?

    Following papers which cited Rivelles I came across:
    http://arxiv.org/abs/0903.1015
    Matrix Models, Emergent Gravity, and Gauge Theory
    Harold Steinacker

    The Steinacker paper is commented on by - in the same breath as quantum graphity:
    http://arxiv.org/abs/0909.3834
    Analogue Models for Emergent Gravity
    Stefano Liberati, Florian Girelli, Lorenzo Sindoni
    "The second option is probably the most viable, conceptually appealing, but most demanding in terms of new concepts to be introduced. If no reference is made to a background Minkowski spacetime, but rather the graviton emerges in the same limit in which the manifold emerges, then there is no obvious conflict with the Weinberg-Witten theorem. Simply, what is called the gauge symmetry in terms of fields living of spacetime is the manifestation of an underlying symmetry acting on the fundamental degrees of freedom in the limit when they are reorganized in terms of a spacetime manifold and fields (gauge fields and gravitons in particular). There are already two examples of this possibility, namely matrix models and quantum graphity models. In both cases, the very notion of spacetime manifold is immaterial for the foundations of the theory. The manifold and the metric are derived concepts, obtained in precise dynamical regimes of the theory. The interested reader can find additional comments and references in [10, 40]."

    Maybe Marcus will like this one - it's got a bounce! :smile:
    http://arxiv.org/abs/0903.0986
    Cosmological solutions of emergent noncommutative gravity
    Daniela Klammer, Harold Steinacker
    Ooops, it's in 10D :redface:
     
    Last edited: Sep 27, 2009
  21. Sep 27, 2009 #20

    Haelfix

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    Re: Could GR's "background independence" be a theoretical artifact?

    Oye, there is no problems with causality or locality by splitting the metric up in terms of a weak field, provided that (wait for it), the field is weak! Just such a procedure is discussed in most textbooks, for instance MTW or some other GR book.

    Pure relativists use this technique all the time, for instance when they might be interested in gravitational waves like at LIGO or when they are analyzing binary pulsars or other thorny time dependant solutions.

    The problem is not that the approximation is invalid or breaks the 'spirit' of GR (whatever that means), instead the problem is that you can't always use it. This is completely analogous to situations in certain field theories where you can't always use a background field method and you have to get creative in order to make progress (here reffering to gauge fields, as opposed to a metric tensor).

    Fortunately its nearly always the case that you can pick some frame or some physical context (perhaps sufficiently far from where there is violent geometry), that still captures the essential physics for most questions one might be concerned with. So for instance, if we are interested in blackhole information loss, we know that our calculational tools clearly break down near singularities. So what do you do, you simply ask a question about horizons instead, for instance at a point right after the formation of the bh, and then compare it to one right after its evaporated. The complicated mess that takes place at the singularity is kind of bypassed that way (even if it contributes in some nontrivial way tothe final answer), but we still have a well defined problem that we can now calculate (and lo and behold, we end up with Hawkings theorem and an information loss paradox).
     
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