Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Diff invariant (measurement theory and observables)

  1. Nov 28, 2008 #1

    Fra

    User Avatar

    The recent threads makse we want to as a simple question.

    How many considers the notion of a _fundamental_ "diff invariant observables" as a clear and unquestionable requirement of the future theory of QG?

    To me this far from clear from the conceptual point of view. It's not even clear what the physical basis of such a definition is. To start with, global manifolds are clearly abstractions. If this is to have any deeper plausability, shouldn't the structures be induced from some generic interaction picture?

    I see two explanations to such a viewpoint.

    - You have a realist idea of the existence of this symmetry. But isn't such things fundamentally disturbing the very intellectual foundation of a "measurement theory"?

    - I can see the sense in it beeing a possible limiting (emergent) symmetry, in the sense that a large observer is simply unlikely to observe and breaking of this symmetry, in the sense that a broken symmetry with imply interactions between observers to restore their observed symmetry by internal transformations. But what about the physics between small systems, where the symmetry breaking is more probable? And what about non-equilibrium interctions? One might argue that these things are unlikely to be observerd except transiently which renders it indistinguishable from noise, but at least from a conceptual model-building point of view it seems severly disturbing to me.

    Do you think that these questions even beyond the point (of physics)?

    /Fredrik
     
  2. jcsd
  3. Nov 30, 2008 #2

    marcus

    User Avatar
    Science Advisor
    Gold Member
    2015 Award
    Dearly Missed

    One must first think what diff-invariant means. I remember that perhaps 10 years ago Rovelli wrote a paper called "The Meaning of Diffeomorphism Invariance". It was co-authored with Marcus Gaul, at Munich.

    I think the message in that paper, IIRC (if I remember correctly), is that spacetime is gauge. Individual points of the continuum have no physical reality, there is only relationship.

    It is a common thing that happens in math. You put in too much, because it is mathematically convenient to do that, and then you factor it out.

    So with GR, in the end you consider the true gravitational field to be the equivalence class of all the metrics which are diffeo-equivalent to each other.
    If two metrics are solutions to the main GR equation, and if one metric (with its layout of matter) can be mooshed and morphed into the other (with its layout of matter) then they represent the same physical reality---the same gravitational field.

    If you were defining the gravitational field, and you could discover a purely relational way to do it. If you could define it without using a manifold, without coordinate patches, with out all that physically unreal gauge stuffing. Then you wouldn't NEED diffeo-invariance, because there would be nothing to factor out!

    Each equivalence class would already consist of just one unique representative.

    But that is a fantasy. How could one ever define the gravitational field without first having a continuum to define the metric on?

    I remember Loll saying in a recent paper something like this: "Look at all the work we are saving. We define our different geometries without coordinates. So we don't have to factor out coordinate transformations. Because we describe geometries by triangulation, with different numbers of triangles meeting around a point, there is less gauge. It is more intrinsic. We don't make extra copies that we then have to get rid of." That was not how she said it. She used different words.

    Two geometries which differ only by a re-parametrisation, a change of coordinates, are the same physical situation. So you have redundancy. The clever Loll avoids this source of redundancy by not using coordinates, so she has less to gauge trash to dispose of. does it really work that way? I don't know for sure, but she gets fascinating results---like the emergence of deSitter spacetime, that was not put in. Like the emergence of regular non-uniform dimensionality.
    =====================

    So far I am just talking to share my thoughts on the topic. But you asked a question. Am I a realist about diffeo-invariance? Do I believe in the physical existence of diffeomorphisms? Fra, I am not a realist about the points of the manifold, :biggrin: so how could I believe in the physical reality of the smooth mappings! Didn't Einstein say that the principle of general covariance (i.e. diffeo invariance) removes from points of spacetime the last remnant of physical reality?

    What I believe instead of that is the principle of general covariance---or rather what diffeo-invariance tells us---namely that only the web of relationships is real. Causal relations, events, collisions, coincidences---these are the essentials. If you could build a mathematical model with only that, and no stuffing, then you would not have to factor anything out and you would not have any diffeomorphisms because you would not need them. If you could buld a model consisting only of Feynman diagrams :biggrin: that was perhaps a joke.
     
  4. Dec 1, 2008 #3

    Fra

    User Avatar

    Marcus, thanks for your response!

    This sounds like what I would call a realist view of the relations. Rovelli in his RQM, said that there are no absolute (insert word of choice), there are only relations! However he also said that neither are there any absolute relations, only relational relations. And the relations he has in mind as far as I understand him is a quantum mechanical one. IE each observer only quantum mechanically konws the relations. But it is at this point he avoids the "problem of QM". Although *technically* this is a possibility, I can't not accept the speculative step made here. I am totally with Rovellit that there are not xxx, only relations, and moreover only relational relations. But the point is that QM is a very specific and unexplained case, if we by QM adapt the ordinary rules of QM.

    That's one thing, the other thing is that, just because there are no absolute states and spacetimes, doesn't mean there doesn't exist. I think this is the paradox of symmetry. It's first when the symmetries are sort of broken, in two different views, that the original symmetry shows it's utility.

    I think it is good to acknowledge the relations, but this is overdoing it in the other way I think. Because a physical observer, does experience spacetime. Indeed though, this spacetime is not fundamental since there are many other observers that see it differently, but that doesn't mean the observer can think of themselve as non-physical. I think non-physical and non-absolute are different things. I think physical reality isn't necessarily absolutely establishable, this is why I am also lead into reasonings of evolution of physical law.

    I think these recent discussions are great. Because this very thing puts the focus on a key point.

    To illustrate whay disturbs me, the realism here is really analogous to a remnant reliasm also in QM. The existence of a unique and unambigous limit defining probability, that usually comes from pictures of infinite experiment series etc. QM is still a deterministic theory, and the realism still lives at the "relations between probabilities" level.

    This is the common denominator I see between the two problems. And Rovelli avoids the probability issue.

    That was a quick response, I might add more later.

    /Fredrik
     
  5. Dec 1, 2008 #4

    atyy

    User Avatar
    Science Advisor

    Here's my rampant speculation. I think already in Newton's theory the metric is a coordinate independent object. It's the number of atoms in a rigid ruler. You can move your experiment around without moving the ruler, or in the case of Newtonian gravity, even if the planets move you can still use light rays which travel in straight lines as the ruler. The difference in GR is gravity affects everything, so the metric and matter must be determined self consistently. Thinking of metric as "geometry", then I do think that the need to define metric and matter together, not separately, will remain in quantum gravity. I actually like the emergent geometry scenario, but I think there may be several layers of quantum gravity - just like at present we have QFT in the standard model, which becomes QM for single atoms, but QFT re-emerges when we consider many-body systems.
     
  6. Dec 1, 2008 #5

    Fra

    User Avatar

    Yes, I think this is the essence of GR. I have no problems with this, in the classical sense. The question is, when you try to merge this with a theory of measurement, you are suggesting the the observer is a gauge? Ie. does the observer has a physical basis?

    Isn't this somehow the problem in a nutshell? or how do you view this? Sure, one can picture that there is a theory of the RELATIONS between observers, but then again, eithre you put this in a context of a measurement theory, or you don't, in which case we can conjecture a realist level, that restores the gauge choices?

    I'm not sure if my point gets through. My issue isn't the the mathematical meaning of diff invariance, it's the physical or observable basis of it. The quest for this is the lesson I bring from QM foundations, although I think fixed hilbert spaces similarly lack physical basis.

    /Fredrik
     
  7. Dec 1, 2008 #6

    Fra

    User Avatar

    More reflections, let me know what you think of this.

    To abstract this a little bit.

    The idea of an equivalence class of all observers, and that there exists a relation that transforms one observer into another one would be nice. But I think that the existence of such a thing is not certain, although possible! I think our model building should reflect this uncertainty - ie the difference between what is merely possible and even plausible, and what is unavoidable.

    It seems at first a modest constraint to suggest the ALL observers must see an apparent reality that is consistent with each other. However, I think again that is rushing too fast. Instead, perhaps it is the case that our views are constantly evolving, and that the perfect consistency is not unique?

    Instead my view of this consistency, impled by that all observers must see the same laws, is that that's an ambition, that can possibly be formualted as a principle of constructivity. In this sense, given infinite time for the universe and it's parts to equlibrate, consistency is expected, because the opposite would contradict itself, and thus be self destructive.

    So while I think that diff invariance is an _expectation_ I think it will can be kown to be exact only in an emergent sense. And to only consider the limiting case of the emergence, is possibly missing interesting physics. This is why I would expect that the emerging process itself, is itself interesting physics.

    /Fredrik
     
  8. Dec 2, 2008 #7

    atyy

    User Avatar
    Science Advisor

    A real Lorentz-FitzGerald contraction
    Carlos Barcelo, Gil Jannes
    http://arxiv.org/abs/0705.4652

    They discuss a toy problem relating to: "When looking at the analogue metrics one problem immediately comes to mind. The laboratory in which the condensed matter system is set up provides a privileged coordinate system. Thus, one is not really reproducing a geometrical configuration but only a specific metrical representation of it. This naturally raises the question whether diffeomorphism invariance is not lost in the analogue construction. ......The standard answer to this question is that diffeomorphism invariance is maintained but only for internal observers, i.e. those observers who can only perform experiments involving the propagation of the relativistic collective fields."
     
    Last edited: Dec 2, 2008
  9. Dec 3, 2008 #8

    Fra

    User Avatar

    That paper makes many good key reflections. The symmetry here is emerging as a tension between two views. The large fishbowl as they call it, and the set of internal observer in the ball. But not how assymmetric this is, because the observer talking fishbowl is not on the same footing. One can imagine that this observer, with his effective fishbowl is still part of a bigger, intergalactic fishbowl. So the symmetry is acquired withing a global view, I think without the global view, the microstructure in which the internal observers "live" is unknown. I think this is agood piont.

    About intrinsic "inside measurements" they note.

    In lack of a better namn, this is what I have called the requirement of "instrinsic measures" in several posts. I think this is a fundamental point, and to me this general reflection raised the question, how, in the general case the construction of inside measures, are constrained - could this even give us information of the possible action forms? I personally expect it can.

    /Fredrik
     
  10. Dec 3, 2008 #9

    atyy

    User Avatar
    Science Advisor

    Moshe's blog (http://diracseashore.wordpress.com/2008/12/03/where-is-the-gauge-theory/) pointed to Elvang and Polchinsky's paper (http://arxiv.org/abs/hep-th/0209104), which seemed to reflect your sentiments?

    "....Note however the complete change of interpretation: time is no longer associated with Hamiltonian evolution, rather it must emerge ‘holographically’ from correlations in the states. .......... The essential point is that gauge symmetry and diffeomorphism invariance are just redundancies of description. In the examples where they emerge, one begins with nonredundant variables and discovers that redundant variables are needed to give a local description of the long-distance physics. In general relativity, the spacetime coordinates are themselves part of the redundant description."

    BTW, I was linked to Moshe's blog from Lubos's which says "Gauge theory is the only exact description of the physics" and "Gauge theory requires no string theory". http://motls.blogspot.com/2008/12/background-independence-in-ads-spaces.html
     
    Last edited: Dec 3, 2008
  11. Dec 3, 2008 #10

    atyy

    User Avatar
    Science Advisor

    Why things fall
    Olaf Dreyer
    http://arxiv.org/abs/0710.4350

    He has a very similar point of view to yours? I quite like it, because to me Einstein's vacuum equations don't make much sense. They require massless, energyless test particles to probe the geodesics, but such particles don't exist. If we use particles with energy, then we have to use the full Einstein equations in which matter and metric are defined together, and there's no need for a separate geodesic equation of motion.

    "Instead we are taking seriously the fact that we only know geometry through matter. Only by using matter, the proverbial clocks and rods, can we infer geometry; geometry alone is not accessible to us. .......... The logic of Internal Relativity is thus as follows. We start with a quantum mechanical system. It has no gravitational degrees of freedom and it is not obtained from the quantization of a classical theory. We then find the ground state of the system together with its low lying excitations. We use these excitations to construct rods and clocks. We then argue that these clocks and rods will feel the force of gravity by showing that Newton’s law of gravity applies to them. The resulting geometry is thus a Lorentzian curved geometry. It is currently a conjecture of Internal Relativity that if one continues in this direction, adhering to a strictly internal point of view, one will find the Einstein equations.
     
  12. Dec 3, 2008 #11

    Fra

    User Avatar

    Atyy, you're good at digging up papers. I have never heard of him before as far as I can remember. I will to read that paper later!

    /Fredrik
     
  13. Dec 4, 2008 #12

    Fra

    User Avatar

    I don't have time to read this in full right now but just skimmed the abstract

    This sounds fully in line with my thinking.

    This is actually something I fully agree with as well. I have an idea how this can be done, but it's entangled up with other problems, so I have not formalized it yet. The emergence of an maximum signal propagation is emergent, it should follow directly from the fact that the only possible parameterizations are internally distinguishable ones.

    Even this sounds in line with my thinking, although I haven't read the details yet. In my thinking gravity is emergent as a result of true instrinsic observers interacting, and the key point is that the gravitational drift is a result of their instrinsic actions depend on their incomplete information about each other - the result is attraction, but only predictable from the POV of a third observer.

    I need ot read his paper in detail!

    /Fredrik
     
  14. Dec 4, 2008 #13

    Fra

    User Avatar

    I am not near as well informed about the diversity of researchers as others here, so I tried to search.

    Here's what wikipedia says about Olaf Dreyer.

    "Olaf Dreyer is a German theoretical physicist, currently a Marie Curie Fellow at Imperial College, London. His previous post-doctoral work was at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada"
    ...
    Dreyer proposed a connection between the Barbero-Immirzi parameter in loop quantum gravity and the asymptotic behaviour of black hole quasinormal modes (in numerical general relativity), building on the previous insights due to Shahar Hod.
    ...
    Dreyer's dissertation advisor was Abhay Ashtekar."
    --http://en.wikipedia.org/wiki/Olaf_Dreyer

    Also (as usual) Marucs has reported papers from him ages ago.

    "Olaf Dreyer: the Cosmological Constant paradox"
    -- https://www.physicsforums.com/showthread.php?t=41893

    /Fredrik
     
  15. Dec 4, 2008 #14

    Fra

    User Avatar

    I found this too and I have to say at first glance this reasoning sounds unusually good, but I'm curious about more.

    "Dr. Olaf Dreyer
    Massachusetts Institute of Technology

    Project Title:
    Quantum Space II

    Summary:
    In the beginning of the last century theoretical physics was revolutionized with the emergence of quantum mechanics and Einstein's theory of general relativity. These theories have been extremely successful in explaining nature at very small scales and at very large scales. However, two problems have remained open since the inception of these theories. One problem concerns the foundations of quantum mechanics. Although quantum mechanics is so successful it is still fundamentally unclear how to relate the theory to the classical world around us. Quantum mechanics, in principle, allows for states of nature in which the same large object is in two places at once. This means we need a reason why we have not seen such states. In our proposal, we give such a reason by proposing a new relation between the classical world and the quantum world. The other problem concerns the union of quantum mechanics and general relativity. These two theories have been around for nearly a century but we still have no way of combining them. We are lacking a quantum theory of gravity. We propose such a theory by providing a new mechanism for the emergence of gravity. No propagation without gravitation is the basic principle behind our approach.

    Technical Abstract:
    The research in this proposal is concerned with the foundations of quantum mechanics and with quantum gravity. On the first subject, we argue that three misguided steps in the standard understanding of quantum mechanics prevent us from solving the measurement problem. The first step is the notion of classical objects. We argue that the classical world can be understood as consisting of special quantum mechanical states. The second step is the tension between the deterministic nature of the Schroedinger equation and the observed probabilistic nature of quantum mechanics. We show that with our definition of classicality probability is a necessary consequence. The last step is that we assign properties to microscopic objects that they cannot have. We show that these three steps are the problems that make quantum mechanics so puzzling. Taken together our solutions to the three problems constitute a solution to the measurement problem. In quantum gravity we continue the program of internal relativity. We propose to derive geometry from the low-lying excitations of a solidstate system. We show how Newtonian gravity naturally arises in such a system. We furthermore propose to apply the theory to the early universe and show that we can reproduce the observed spectrum of the cosmic microwave background radiation. "
    -- http://www.fqxi.org/large-grants/awardee/details/2008/dreyer

    I am not sure if there is a paper on this somewhere? If so, does anyone know where to find it?

    The highlighted in blue, is what directly connects to the concept of intrisic measures, and thus by consequence, intrinsic actions (and thus properties).

    /Fredrik
     
  16. Dec 5, 2008 #15

    Fra

    User Avatar

    I skimmed Olag Dreyer's paper last night that atyy digged up.

    Why things fall
    Olaf Dreyer
    http://arxiv.org/abs/0710.4350

    The paper seems to mainly provide general arguments for an idea, and to convey a way of reasoning, but since it was so close to my reasoning I directly connect to it.

    I have to admit that while as far as I understand his papers, there are some big differences, there are also on the level of spirit of intent, some striking similarities to my own preferred reasoning. I think this guy has good ideas, the type of logic that i see in that paper is among the better ones I have seen in quite a while!

    "We claim that the internal point of view has not been taken far enough. If one strictly adheres to it, one finds not only special relativity but also general relativity. This is the central novelty of Internal Relativity."

    This essence, is very similiar to what I advocate. It is also in fact, not too alien from Ariel Catichas idea that the laws of physics (he considres GR in particular) follows from a general principle of reasoning from incomplete information. This is the same core idea as Olaf conveys, although one can put it differently. However I am not sure Ariel fully acknowledges that the choice of reasoning (induction), is fundamentally intrisic to the observer.

    The spirit of his view on the duality of geometry and matter is also dead on, that puts a proper perspective on both the measurement problem, problem of time and idea of symmetry.

    "In our view, matter and geometry have a more dual role. One can not have one without the other. Both emerge from the fundamental theory simultaneously."

    "Our objection to this setup is that one does not have direct access to the geometry; we use matter to infer lengths and times. We believe it is desirable to have a theory where there is no geometry without matter, instead geometry and matter arise simultaneously."

    "This problem is called the problem of time. The approach presented here shows this to be an unnecessary complication that arises because of an unphysical idealization that does not take into account that geometry and matter arise together. By neglecting one part, matter, and just focusing on the other part, geometry, one introduces the problem of time. The problem of time is the price one pays for not realizing that pure gravity is an unphysical
    idealization."


    "In our approach the relationship between particles and symmetry group is exactly reversed. It is the particles that determine structures like the light cone and the symmetry group. We are thus proposing not to use the Poincaré group and its representation theory in the basic setup of the theory."

    If you add to this the association that matter sort of represents the physical basis of and inside observer - you have an angle to the measurement problem.

    I agree to spirit in these points, it makes very good sense to me. Now to the point where I might disagree. I can not clearly see his view of QM, and probability. In my vision, not only will SR and GR follow from the "principle", even quantum logic might emerge. I am not sure if he has something like that ine mind. He wa focused mainly on the SR/GR stuff in this paper. Also it's not clear how his abstraction of the constraints of intrisic measures will work out. In my thinking of this, I am led to a discrete picture, in which the continuum itself is emergent. How he views this is not clear from this paper.

    Interesting guy for sure. I think it will be worth watching what he comes up woth.

    /Fredrik
     
    Last edited: Dec 5, 2008
  17. Dec 5, 2008 #16

    Fra

    User Avatar

    Just stumbled on this Dreyer talk from loops 07.

    internal relativity: a progress report
    http://www.matmor.unam.mx/eventos/loops07/talks/7A/Dreyer.pdf

    It seems like this is very much in progress, but I will keep his name in mind. His general vision is unusually plausible at minimum. This can not be said of many other ideas IMO.

    /Fredrik
     
  18. Dec 5, 2008 #17

    atyy

    User Avatar
    Science Advisor

    Yes, I don't think any of the emergent approaches (Visser, Volovik, Wen, AdS/CFT) have QM as emergent. Volovik explcitly says he expects QM not to broken until way above the Planck scale. Wen has a model of emergent electrons and light, and the Hamma paper apparently takes the "internal" view to show the model has an effective light cone. Gu and Wen also seem to have linear emergent gravity, which Marcus posted long ago.

    Photons and electrons as emergent phenomena
    Michael Levin, Xiao-Gang Wen
    http://arxiv.org/abs/cond-mat/0407140

    Lieb-Robinson bounds and the speed of light from topological order
    Alioscia Hamma, Fotini Markopoulou, Isabeau Premont-Schwarz, Simone Severini
    http://arxiv.org/abs/0808.2495

    A lattice bosonic model as a quantum theory of gravity
    Zheng-Cheng Gu, Xiao-Gang Wen
    http://arxiv.org/abs/gr-qc/0606100
     
    Last edited: Dec 5, 2008
  19. Dec 7, 2008 #18

    atyy

    User Avatar
    Science Advisor

    Quantumness without quantumness: entanglement as classical correlations in higher dimensions
    Vlatko Vedral
    http://arxiv.org/abs/quant-ph/0701101

    He has wild speculations at the end that seem similar to yours.
     
  20. Dec 7, 2008 #19

    Fra

    User Avatar

    Thanks for digging up these paper Atyy. I will skim them later. I skimmed the last one, it seems true that they are asking similar questions that I do. For example, wether quantum logic can be seen to be emergent from classical logic if you add the intrinsic view. However it doesn't seem like their specific answer is totally in line with my vision. But it's great to see a variety of people that at least step forward and insist on asking the questions.

    I don't like the distinction of quantum vs classical, and quantum model always starting with a classical model, and then perform a procedure. In this sense I think there is a more natural explanation. As I see it the problem is the realism in the classical models. And once you realise that was an illusion from start, one can go back from the foundations of statistical mechanics and probability theory and think again, and perhaps there one will see that classical logic (as in realism) was not the only possibility to start with.

    /Fredrik
     
  21. Dec 7, 2008 #20

    Fra

    User Avatar

    IMHO, the starting point, closes to beeing called "classical" that might evolve into QM, is that of classical probability theory and stat mech.

    One can imagine a "classical" memory structure: a classical microstructure, whose microstate is used as a memory storage. In this picture certain questions naturally appears. For example, could the classical hardware, be rebuilt into another microstructure, or system of related microstructures, so as to serve as more efficient mmeory storage? In particular, what about a system of microstructures, related to the original structre, in the way a real function relates to the fouriertransformed state? Could this proved to be more efficient for certain period datastreams? Can this serve as a selection mechanics for evolution of mictrostructures if one considers classically noisy microstructure? Another issues is also that in the classical picture, any realistic scenario will have finite memory. Thus, there are no functions defined on a continuum, and no continous values.

    This is more related to my starting point. That begs a new probability concept, which can not rely on a continuum. It also puts the ergodic hypothesis in a evolutionary context.

    I prefer the conceptually abstracted level. One you can simple examples, like the classical ising model, it always come with speicla choices and that may obscure the conclusions.

    I like to go back, to the foundations of statistical mechanics, and the foundations of probability theory and information theory, and start there.

    /Fredrk
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Diff invariant (measurement theory and observables)
Loading...