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General Relativity + Quantum Mechanics?

  1. May 9, 2009 #1
    the Theory of Everything is supposedly just a combination of the theory of general relativity, and quantum mechanics. I have two questions:

    1) Why cant we combine these theories into a single unified theory of everything?

    2) Will the combination of these theories be able to solve ANYTHING? and how would it be possible to solve anything with these theories?
     
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  3. May 9, 2009 #2
    So I'm not advanced enough to answer 1) as well as others can (although the answer would probably be pretty involved mathwise!) but here's a basic outline: GR poses gravity as an effect of spacetime's curvature. So it's qualitatively different from forces such as electromagnetism, which can be described by quantum mechanics. In order to unify the two, quantum mechanics needs to be put in curved spacetimes (I think at the moment it's only well-defined in flat spacetime) to be able to include gravity. There's other issues, renormalization and such, but I'm a wee undergrad and can't understand such things :)

    As for 2), we hope that a combined theory will help us to describe situations where the effects of both quantum mechanics and general relativity become significant. As it turns out, there are some really important scenarios where this is true. GR effects become significant for really massive things (or long distances), whereas QM effects are important on very small distance scales. So we have trouble right now describing things that are both very small and very massive. Black holes come to mind (we have no clue what happens at the singularity!), as does the early universe around the big bang.
     
  4. May 9, 2009 #3

    marcus

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    Another way to think of it is that geometry itself has to be formulated as a quantum state---with uncertainty and superposition and all that. The geometric observables---like area, volume, angle, dimensionality around a given point...etc. These measurements must correspond to operators on the hilbertspace of states of geometry.

    The geometry of space and of spacetime is conjectured to be highly chaotic and dynamic at small scale.

    What you say, putting quantum field theory on a fixed curved spacetime, is not so hard--and does not accomplish very much. Just doing quantum mechanics on another fixed classical spacetime doesn't cut the mustard.

    A good example of quantum geometry is Ambjorn and Loll's article in the Scientific American. I have the link in my sig, in small print at the end of the post. It is the "signal lake" link.

    The big challenge now is to construct a new mathematical model of the continuum----quantum space and time geometry. Unification of quantum geometry with the quantum theory of matter will logically come after that step is taken.

    To get an impression of where the field is at present, here is a literature search of work published after 2006 with keyword "quantum cosmology", at the Stanford Spires database, ranked by citation count (a rough measure of a research paper's importance).
    http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE+%3E+2006&FORMAT=www&SEQUENCE=citecount%28d%29 [Broken]
    Don't read the stuff in detail, too technical, just scan some of the abstracts, the summaries, or glance at the list. You will see that (rightly or wrongly) quantum geometry gets rid of black hole and big bang singularities and pushes physical description on beyond them.

    Probably the best overview description of this state of affairs is Carlo Rovelli's essay "Unfinished Revolution", the first chapter of a new multi-author book that just came out last month.
    http://arxiv.org/abs/gr-qc/0604045
    The Rovelli chapter is available free, it's short, and non-technical written. The book as a whole (600 pages) is not! :biggrin:
     
    Last edited by a moderator: May 4, 2017
  5. May 9, 2009 #4
    There is no problem to define operators of distance, angle, area, etc. within ordinary quantum mechanics.

    For example, if you have a system of two particles with position operators [tex] \mathbf{r}_1 [/tex] and [tex] \mathbf{r}_2 [/tex], then the distance between them is defined as [tex] |\mathbf{r}_1 -\mathbf{r}_2| [/tex]. Similarly, if you have three particles, you can define quantum-mechanical operators of the angle and area (of the triangle).

    However, apparently, this is not what you have in mind. I think you want definitions of observables relevant to the "empty space" without any particles. I don't understand why you would need them? No physical observations can be made in the empty space. So, the idea to define a Hilbert space and operators of observables for the position space or space-time just doesn't make sense to me.
     
  6. May 9, 2009 #5
    um... im only in high school, i cant really understand what you guys are saying, no matter how much i google every other word you use.
     
    Last edited: May 9, 2009
  7. May 9, 2009 #6
    Hi um0123,

    your problem is that you've asked deep and interesting questions. Nobody knows good answers to them. So, be prepared to listen to a lot of BS and don't complain.
     
  8. May 9, 2009 #7
    im not expecting a short and definite answer, just one that i can understand. But it looks like thats impossible, so i guess ill do more research.

    ive already read alot of general relativity. But being only in high school, anything on quantum mechanics is a little out of my league. Seeing as how general relativity is semi-easy to explain using diagrams and basic math.
     
  9. May 9, 2009 #8
    force is acceleration in verse fluent pressure differential

    A simple yet definitive answer might simply be Authority is just now beginning to allow consideration even space might be in verse fluent – as in flow.space.time.
    It seems not all still Believe in dark and warp.

    'The river model of black holes'
    Andrew J. S. Hamilton, Jason P. Lisle
    http://arxiv.org/abs/gr-qc/0411060

    To the best of my current understanding: flow predicts better than dark.

    There is further discussion >Physics Forums > Astronomy & Cosmology > Astrophysics > Blackhole article on cnn
    https://www.physicsforums.com/showthread.php?t=310159

    Please feel free to ask anything else you might simply wish better understand.

    Peace
    ron
     
  10. May 9, 2009 #9
    Unification of general relativity and quantum mechanics is difficult for one simple reason. The main assumption of general relativity is that space and time are unified in one 4-dimensional continuum, and that gravity is nothing but curvature of this continuum induced by the presence of masses. On the other hand, in quantum mechanics space and time are treated very differently. Positions (of particles) are represented in this theory by (Hermitian) operators, and time is just a numerical parameter, so they don't fit into one 4-vector. This conflict in the treatment of space and time is in the heart of the unification problem.

    For decades best minds in physics are trying to solve this problem. There are lots of proposals. Some suggest to abandon general relativity. Others want to modify quantum mechanics, or to scrap both theories and build something new instead. So far, nothing has worked out.

    Most likely, future theory of quantum gravity will not solve any practical problems. The gravitational force is very weak, and quantum gravitational effects are almost impossible to observe. So, the real motivation behind this work is purely theoretical. People are frustrated that they don't have good understanding of such simple and basic concepts as space and time.

    My personal opinion is that solution is very simple. We should abandon the description of gravity as the curvature of the 4-dimensional space-time continuum. It is possible to describe all relativistic gravitational effects (precession of the Mercury's perihelion, light bending, Shapiro time delay, gravitational red shift, etc.) simply by adding small velocity-dependent terms to the usual Newtonian potential. Then classical relativistic gravitational dynamics of massive particles and photons can be described in terms of usual Hamiltonian equations of motion. It is very easy to switch from a classical Hamiltonian theory to fully quantum formalism. So, a consistent quantum theory of gravity can be formulated without problems.
     
  11. May 9, 2009 #10

    marcus

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    most efficient thing would probably be for you to read Rovelli's essay. I gave the link:
    http://arxiv.org/abs/gr-qc/0604045

    It's short and written non-technical style. Let me know if you still don't understand.

    You are on the wrong track if you are thinking "empty space". There should be some matter to help define areas, volumes, locations. I guess the main point is that Euclidean and Minkowski geometry are unrealistic---not how nature really is. When you were defining operators naively you were using Euclidean metric. That metric fails in certain key situations (although in others it can be a good approximation). It also cannot be assumed to apply down at very small scale---there geometric measurements are apt to be uncertain.

    Best however if you read Rovelli's brief simple overview essay, then talk some more.
     
  12. May 9, 2009 #11
    Thanks for the reference. Rovelli's assumption is that both GR and QM must be preserved. I agree about QM. It has overwhelming experimental support. However, I'm not sure about GR and curved space-times. It might be possible to describe all GR effects within ordinary relativistic Hamiltonian mechanics simply by adding certain velocity-dependent corrections to the usual Newtonian gravitational potential. For example, it is known that in the [tex] 1/c^2 [/tex] approximation the gravitational dynamics is well described by the Einstein-Infeld-Hoffmann Hamiltonian. So, if we take this Hamiltonian (plus higher order corrections) as a primary object and forget about the (supposedly more fundamental) curved space-time picture, then our gravity theory becomes fully consistent with both QM and experimental observations.


    Do you have any evidence (besides speculations about the Planck length) that Euclidean geometry is inadequate?
     
    Last edited: May 9, 2009
  13. May 9, 2009 #12
    you guys seem very intelligent! may i ask what degrees you have? as an aspiring particle physicist i am interested to know what you have studied, and how much experience you have in each field.
     
  14. May 9, 2009 #13

    marcus

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    No. What I say is that it cannot be assumed that geometry is Euclidean down to arbitrary short lengths.

    I would say that if anyone wants to claim it is, the burden is on them to show it.

    As it happens, three quite different quantum geometry approaches predict that spacetime dimensionality declines from macro 4D to around 2D at small scale. It doesn't prove anything but it was a strange coincidence. Reuter's Asymptotic Safe QG, and Loll's CDT approach both came to that unexpected conclusion, then something similar has been found in the Loop QG context.
    From these theoretical investigations it appears that micro-geometry could be fractal or foamy. Fractional dimensionality as often occurs with fractals, continuously declining as scale shrinks. Dimensionality around a given point is then a quantum observable---something to measure, not postulate.

    So if since the theories seem to think small scale geometry is more chaotic and that the smooth Euclidean only appears at macro scale, I would say that if you want to say no, that's wrong, it is Euclidean all the way down to Planck and beyond, then you need to give evidence.

    I don't have any experimental evidence, but then I am not claiming anything. As far as I am concerned, the jury is still out.
    On the other hand I would not describe my understanding of the subject as based on "speculations about the Planck length".

    There is a literature about this that has little or nothing to do with the Planck length as such. For a popular article check the "Loll QG SciAm" link in my sig. For technical articles check arxiv for recent stuff by Benedetti, by Modesto, by Ambjorn and Loll, they will have references to Reuter's papers.
    I'll be glad to get links if you want to check it out, just ask. Loll's for example has nothing to do with Planck length. The theory has no minimal length. They do computer simulations of small universes coming into existence and evolving. That's fairly typical. I don't think any of those I mentioned base their models on the Planck length or speculations about it. Maybe that was more the case 15 or 20 years ago. You may be thinking of how people would do rough estimates about the smallest measurable length etc etc, back then, as a kind of motivation for what they were working on. More to say, but I have to go. I'll be back later.
     
    Last edited: May 9, 2009
  15. May 9, 2009 #14
    If you want to see the profile of each participant you can click on his/her nickname in the upper left corner of each post. Some of them have websites with personal data.
     
  16. May 10, 2009 #15
    I don't know any experimental data that would suggest the violation of Euclidean geometry at short lengths. Theoretically, this simple assumption does not introduce any contradictions either. So, why abandon it?


    As far as I know, these advanced theories have not made any testable experimental predictions yet. So, why should I trade neat and time-tested relativistic quantum mechanics or QFT for this messy and complicated stuff?
     
  17. May 10, 2009 #16
    Marcus,

    Thank you for your offer. I think I saw enough of this kind of works. It seems that their common theme is that the space-time is some kind of dynamical object that should be described by its own observables in a Hilbert space. This strikes me as something contradicting the letter and spirit of quantum mechanics. There is nothing to be observed in empty space, so there can be no observables associated with it. So all this fractal/foamy/dynamical micro-geometry does not make sense to me.

    Possibly I am just too old-fashioned. I think that physics (theoretical physics included) is supposed to describe (or even better, predict) results of observations. Experimental observations are normally made on physical systems made of particles, atoms, etc. So, all physical observables (position, momentum, spin, etc) refer to these material systems. In QM these observables are represented by operators in a Hilbert space. Empty space or space-time is not a physical system; no meaningful experiment can be performed there... Oh well, I am repeating myself...
     
  18. May 10, 2009 #17

    Fra

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    I agree that the observability is important and to me, and I also have conceptual objections to pure gravity theories for the same reason that I would object to a measurement theory without observers. I think matter is usually the physical basis of observers.

    But this is IMHO also why QM as it stands, does not make sense, because it does not put it's massive baggage (hilbert spaces, lagrangians) into a measurement perspective. IMO, all these background structures make up the identity of the observer. If you acknowledge that explicitly, then those structures should also be constrained by the size of the observer.

    I think if you take the measurement perspective serious, nothing should escape from this. Take for example the hilbert space. I want to know the physical process in which the hilbert space is emergent. In theory this could be constructed from a large statistical data sets from measurements. But how do you identify the operators themselves, before the space is defined?

    So while I share your measurement perspective, I think that is exactly why normal QM is inadeqate. The observers, provide the dynamical context/background, that justifies the measurements. Here we have some seeds to evolving relativistiv models like GR - the measurements provide feedback that implies forces on the observers (think matter), and matter in turn (think observers) are the container for their relations (spacetime).

    I'm personally more tuned in on that that starting point is a reconstruction of QM, and if this is done properly, hopefully gravity will be emergent. Because the completixy(masses) of hte observers determined both their impact on it's environment, and it's inertia against the forces the environment excerts.

    Rovelli started well in his relational QM, but at the point in reasoning where he ignored the physical implementation of "probability" I think things went took the wrong turn.

    The physical basis of probability, is closely related to informaiton capcacity and the physical basis of the contiuum IMO.

    Similarly, to justify the contiuum, we need an observer that can distiniguish the continuum from the rationals. That somehow doesn't commute with the expectation that an observer only holds a finite amount of information.

    /Fredrik
     
    Last edited: May 10, 2009
  19. May 10, 2009 #18
    Here I would like to stand in defense of QM. QM makes a sharp distinction between a measuring apparatus and a (measured) physical system. This is not bad (as some people think), because such an distinction exists in any real experiment. Each experimentalist knows where his physical system ends and where his measuring apparatus begins. So, I am against the (often expressed) idea to treat measurement process as a kind of dynamical interaction between the measuring apparatus and the physical system. If you do that, then you already expanded your physical system to include the measuring device as well. So, in order to stay within quantum mechanics you now need to define what is your new "super" measuring apparatus. You always need to draw a line somewhere.

    Some people hate this feature of quantum mechanics. Intuitively, they want to have a grand theory, which encompasses the physical system, the measuring apparatus, the observer, and the entire universe. I don't think such a theory can be formulated even in principle. Physics is an experimental science, and the role of theory is to describe results of experiments. In each experiment there is a clear separation between "what/who is observing" and "what is observed". Our theories better reflect this fundamental fact.

    So, if we clearly separated the measuring apparatus from the physical system, we cannot (and should not) treat this apparatus dynamically. The apparatus should be present in theory in an abstract form. In fact, it should be described (as usual) in terms of the corresponding Hermitian operator. So, if an experimentalist measures particle momentum, then the entire setup for doing that should be represented in theory simply by the Hermitian operator of momentum. You are right that in real life measuring devices often measure not exactly desired things. Measurements are not exact, the mass of the measuring device may introduce gravitational distortions, etc. Shall we still use ideal Hermitian operators to describe such less-than-ideal measurements? My answer is yes. These errors and distortions are not theoretical problems. They are experimental problems. Let experimentalists improve their techniques, or set appropriate error bars to their observed results. It is unfair to ask theory to correct all these defects.
     
    Last edited: May 10, 2009
  20. May 10, 2009 #19

    Fra

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    I appreciate your defense of QM, but I can not stretch myself to agree.

    The idealisation of the boundary between observer and observed, essentially is the same as suggesting a sharp boundary between what you know and what you don't know.

    Even though you defend it you seem to admit is an idealisation.

    I agree that our ambitions must be truncated somewhere, but this uncertainty of boundary is IMO not just a subtle practical issue. I think it's of fundamental importance, and I think the analysis of this will be constructive.

    In my view, QM structure, hilbert spaces etc are subject to evolution, and QM would hold more in a differential sense than globally. I think to understand this evolution would also come with an understanding of how fundamental forces relate. But the physical material makeup of the observer is what encodes this QM baggage.

    The idea to consider larger and larger systems doesn't work because it would also require a larger and larger observer (more and more mass to encode all this information). For any given observer, there are set limits, although the limits are themselves dynamical rather than fixed.

    Standard QM makes perfect sense for most particle experiments, because relative to the collision domain the entire apparatous and the apparatous environment is in principle part of our (the observers) control.

    In cosmology, this symmetry is rather flipper around. And there are also many in-between scenarious.

    I disagree strongly. There is no sensible distinction between theory and experiment. In my view, they are two interfaces of the same thing. Theory is needed to construct and setup experiment, and experiment is what gives feedback to evolve the theory.

    Experimental feedback has an abstraction in my view, it's the backreaciton from the environment to the observer. This is of fundamental importance IMO.

    /Fredrik
     
  21. May 10, 2009 #20
    I don't suggest to "consider larger and larger systems", because I have no ambition to build the "wave function of the universe" or something like that. My goal is to describe specific experiments, and each specific experiment has a clearly drawn border between the experimental apparatus and the physical system. So, if my theory (quantum mechanics) also has such a border, I consider it an advantage rather than a drawback.
     
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