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Quantum Mechanics & Singularities of Black Holes

  1. May 15, 2005 #1
    Hi. Can Quantum Mechanics explain what happens at the singularity of a black hole? If so, how?
  2. jcsd
  3. May 15, 2005 #2
    To combine QM and GR is a job that not completed until now. But we have got many insteresting results, as far as i know. i don't know the singularity you mentioned is the coordinate singularity, i.e. the singularity at r=2GM, which can be removed by redefination of coordinate, or the singularity lies at r=0. so i both say something about them.

    the r=2GM one: Entropy and Hawking radiation is explaining what happens, it can be easily found in posts before.

    the r=0 one: in GR, it is considered as a point having very large mass, i.e. with infinity density. but if we consider string thory, we find energy given to a string has two effects, one is to explore nearer in space to the string, another is to enlarge the string's size, when the energy is large enough, the
    latter is more important and the singularity is no longer a point, and becomes bigger and bigger.
  4. May 16, 2005 #3
    No, he means the point where "all of the universe" was confined to one single point. We call this the singularity because when going back in time, the equations will blow up at this point. A possible way out is the 10 dimensional string theory or more generally, the brane-vision of M theory in 11 dimensions. For example, our universe is a brane. Nothing says that we are living on the only brane, so there are others. It is when two branes collide, matter is generated and the singularity can be bypassed. The big bang is just a collision of two branes.

  5. May 18, 2005 #4
    QM cant explain it as far as I know, if it could I would have heard of it, also string theory hasnt had any experimental confirmation so I think its a bit early to close the question. String theory is still waiting for that one graviton to leave our brane.

    One might also question whats so wrong with the singularity, as far as I remember GR nothing will ever reach it in the rest of the worlds time anyway and since its covered by the eventhorizon, we can never se it. I actually dont think GR is wrong at or near r=0.
  6. May 18, 2005 #5
    The point is that such a singularity isn't defined. It is a "point with infinity small lengt". And if a length is smaller than the planck-length we can't work anymore with physical theories.
  7. May 18, 2005 #6
    I have a problem to understand how one can mix GR with QM results in order to make reasonable predictions (and not simply guesses that no one is able to falsify with an experiment).

    In GR, an infinitesimal distance is to be compared with normal GR objects (i.e. size of objects, a planet, a star, a galaxy > 1km => 1m is a very small distance) while in quantum it is to be compared, for example, with the size of electrons and protons (~10^-15m => 10^-18m is already an infinitesimal distance).

    An infinitesimal object in GR could be a very huge object in QM (up to 10^18 times!).

    Therefore, how can we compare a black hole real size of GR (a size that could be in the meter range, an approximated infinitesimal small size in a GR toy model) with the sizes involved in QM (10^18 m) in order to make reasonable deductions on the QM vs GR effects?

  8. May 18, 2005 #7
    @Terra Incognita: Sorry, but I don't know what you want to say.
  9. May 18, 2005 #8


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    I think you are making difficulties that don't really exist here, because you have failed to sufficiently internalize the concept of scaling. GR is a classical theory and scales fully. You can change the measurement scale from light years to meters and from meters to Planck lengths without any trouble at all. Perhaps the theory will become unphysical at the Planck length scale, but the theory itself doesn't care. In fact it is common for physicsists to use Planck measurements because they make c, G, and h all =1.

    The wave function too is scaleable ("unitary"). The reduction ("measurement") operation is nonlinear and may not scale, but the GR results can be applied to the wavefunction first and then reduced.

    There are certainly problems using QM or QFT and GR in tandem, but they are more technical than differences of scale.
  10. May 18, 2005 #9
    I think my point of view is not clearly expressed enough. We usually apply QM to objects in the micron range while GR is applied to planet, stars etc (in the range of thousands of km).
    When we use toy models in a given theory, we always assume that they are approximations of "reality" (for example a planet may be considered as a point in order to study its path around the sun).
    In GR, assuming that a black hole has a real size of 1 cm or 0 cm does not make any difference as long as all the test objects are at distances bigger than this size (no impact of size uncertainty on the results). In other words, in order to test the real size of a real black hole or most of GR objects, I suppose we need to construct experiments that are sensible up to the required size.
    Now, assuming that the closest black hole is located at proxima centauri, I assume that the most accurate experiment we can build, can only test if its size is lower than let's say 1 km (an upper bound to the size of the object).
    Once you accept you only know the GR object size with a 1 km uncertainty, how can you apply QM results to this object? Quantum effects are rather, let’s say, in the micron range, except for hypothetic macroscopic phenomena.
    If the uncertainty on the geometric size of the GR object is so huge to be used in QM theory, how can we apply QM results to this object?
    We may apply and compare QM and classical mechanics results to the electrons (e.g. path, energy etc...), because the uncertainty in the size of the electron is compatible with both QM and classical mechanics theory requirements. However, the uncertainty in the size of a black hole is incompatible with the QM theory requirements to make valid predictions.

    If this is not the case, I would like to understand better the subject.


    P.S. I hope this time my point of view is clearer. (may be not?)
    P.P.S. I am not testing the planck scale, I just do not know any experiment that can test the size of a real black hole object for sizes let’s say less than 1km (far more than the Planck scale). Therefore, when I hear that the theory may become undefined at planck scales, I smile, and I question before if the object models at scales on the km range are still valid.
    Last edited: May 18, 2005
  11. May 19, 2005 #10
    Actually black holes have size, they all have the size r=2GM (geometric units) as previously mentioned. Thats the event horizon radius.
  12. May 19, 2005 #11
    That's only correct for an object which used to be uncharged with constant mass distribution, possessing no angular momentum (and some other constraints which i can't remember right now) that has collapsed.
  13. May 19, 2005 #12
    And during most of the 19th century, I could say that the size of atoms is null. Please, I am not saying the mathematical model is not correct. It is jsut a toy model. The event horizon is one property of the mathematical model that allows one to look only at distances greater than this horizon. Like for point planets models, it is better to look at distances greater than the (in the order of) radius of a planet. For smaller distances, we have to change the model.
    The OP question was about the effects at the singularity (r=0), where the “gravity forces” are supposed to be greater than em, electroweak, etc forces. I am just questioning the utility of such a model, underlying the fact that what we call “small” in GR (the observed effects of GR) is large in QM.

    Or If you prefer, how can we check that a small object in GR is also small in QM?

  14. May 19, 2005 #13
    haha I wouldnt say GR is a toy model, if it is then QM is a toy model aswell. We only have toy models!

    Actually GR is well defined inside the event horizon and with a coordinate change you can calculate everything that would happen to you on your way from infinity to the singularity. Ofcourse you would never reach the singularity.

    Even thought most event horizon arent spherical cause of charge, rotation and other things, the event horizon always exists. And if the black hole is big enough you can fly your space ship through it but never back again. And if the hole is rotating you might run into yourself when circuling arround the singularity!?

    Sure enough people believe that GR must be wrong at and near the singularity and somewhere close to it QM will have to take over. Thats one of the aims of string theory to combine the two theories but that theory hasnt had any experimental support yet nor has it been disproved ofcourse.
  15. May 19, 2005 #14
    I say a black hole is a toy model as the point electron in QM is a toy model sufficient to describe some properties but that needs to be enhanced for other ones (e.g. the QFT model of electrons). Do no mix the objects of the theories ("the toys") and the theories.

    Last edited: May 19, 2005
  16. May 19, 2005 #15
    Oh world, it seems to be difficult to be understood in this planet :cry: (I have a difficult post in the thread decoherence: surely the dark side of the force).

    Tell me, what are the results (of concrete experiments) we have concerning the toy model verification of a black hole? (the size of the singularity: a point or sphere of 1km? => this has a direct inpact on QM results and not on the main GR results)
    Have you fired particles on a black hole to verify that the interaction is closed to what this simple model says (the uncertainty on the size).

    In physics particles, it is used to fire particle onto other particles to measure the spatial distribution of the interaction and the effective size of particles. These are concrete results. They allow to say that a toy model is sufficient and another one not.

    Where have you the same things for black hole? (do not forget that we need results on the range of the micron to be able to make reasonable QM predictions).

    So, How can you reasonably connect the results of QM theory (size of objects in experiments ~ < microns) to GR theory (size of objects in experiments > 1km) on a single theory without test objects that may be used (experiments) in both theories?

    In my opinion, the "real" black hole is such a candidate if we can "measure" its size and if it is compatible with the size of QM objects (where we may apply QM results to see if there is some differences). Without that, the results of a common theory of GR and QM have no raisonable fundations (branes, etc ..).
    If we are not able to evaluate, with sufficient precision, the size of a real black hole, we have to wait for QM validation on super macroscopic objects, or for other GR objects.


    Science is made of facts not believes.
  17. May 19, 2005 #16


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    Luke, come to me ! We will do grand things together...

    You are of course right that there is no experimental guidance in the area where QM and GR are supposed to get into conflict. That's a serious problem recognized by everybody. So from there on, you can do several things:

    1) "sit on your ass". You can say, because science without experimental verification is bogus, let's do something else ; solid state physics for instance.

    2) "try to do something". You can say: let us see where our current theories take us theoretically, even if it is in areas that have never been explored experimentally, and try to do things with that. The results of these trials are of course, as such, highly speculative. As much as I dislike people talking about things like Hawking radiation as if it were a fact of life without putting up a caveat that these are results that come from a mixture of known theories, used beyond their tested realm, mixed with some educated guesswork and speculation, as much I think that this is a courageous thing to do. Now, as long as out of that speculative work only comes predictions of experiments we can never do, I think it doesn't serve a big purpose. But you can never know that some verifiable experimental predictions CAN come out of it.

  18. May 19, 2005 #17
    Oh, dark side of the force, I just want to breathe freely. :tongue2:
    By the way, I am claustrophobic. I do not know if I can handle a helmet day and night. :biggrin:

    A simple question of the humble padawan :shy: :
    Why not investing time in the creation of an object that has testable properties in both theories *before* making speculations on a theory of QM and gravity?

    Last edited: May 19, 2005
  19. May 19, 2005 #18
    Have you taken any course in GR ? not just read popular litterature concerning it that is.
  20. May 19, 2005 #19
    Do you call Robert M Wald General Relativity a popular litterature?
    I have read other books of this type and some courses.
    I am just a humble padawan after all :biggrin:. I ask for some evidences, some experiments and some values, not hypothetic possibilities.

  21. May 19, 2005 #20

    I think there are experiments that can be done that uses both QM and GR without crashing a blackhole with a neutron. For example the experiment with "gravity induced quantum interferrence" shows that gravity have an affect on experiments.
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