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Thread: Quantum Gravity and Geometrogenesis

  1. #1 Quantum Gravity and Geometrogenesis 
    Moderator Moderator Markus Hanke's Avatar
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    Lately I have been thinking much about the problem of singularities ( both gravitational and cosmological ), and what the resolution to those could be; I'd just like to share some of my thoughts, perhaps in the hope that others members can contribute their own perspectives.

    Let us start with a simple fact which, in my mind anyway, has tremendous implications - that one can associate entropy with the event horizon of a black hole, as described by Hawking and Bekenstein in some length and detail. All an event horizon is, is in effect the boundary of a region of space-time; entropy on the other hand is a measure of how many different ways one can arrange a thermodynamic system without affecting the overall dynamics, in other words, a measure of the number of microstates a system has. The surprising fact here is that the entropy of a black hole horizon is a finite, well defined number; this tells us that the region of space-time enclosed by the horizon has a finite, well defined number of degrees of freedom, i.e. a microstructure. If space-time were smooth and continuous ( or if it contained a physical singularity ), the entropy would be infinite - but it isn't.

    Another important issue we have is the one of localisation, or rather the inherent impossibility of it - trying to localise a given event at higher and higher precisions implies probing space-time with higher and higher energies in smaller and smaller regions, eventually resulting in the event itself becoming hidden behind an event horizon, again enclosing a region with a finite number of degrees of freedom. This strongly hints at the existence of a minimum length scale, beyond which the very notion of space-time itself becomes meaningless.

    Given these two issues, there is a strong argument to be made for the existence of a microstructure of certain degrees of freedom to space-time. The question then is of course - what are those degrees of freedom, and how do they relate to the smooth space-time manifold we observe on macroscopic scales ? Surely, the fact that regions of space-time can have entropy and temperature are unlikely to be mere coincidences - I would thus like to continue my train of thought in the context of statistical mechanics, since this is the area in classical physics that gives rise to the notions of both entropy and temperature.

    Suppose now we had a "quantum liquid" of fundamental simplexes ( units ), which in themselves are not spatio-temporal in nature, but merely fundamental units of "pre-geometry" of sorts. These could correspond to the spin-foam networks of LQG, or the simplexes of CDT, or something else entirely - there is no way to tell for the moment. The idea now is that these fundamental units can interact dynamically, but only in certain, well defined ways; in other words, these units have certain degrees of freedom, which, it must be said again, are not of a nature that has anything to do with space or time. They are just generic degrees of freedom which allow these units to dynamically form certain states. This is all very similar to the idea of ordinary atoms - they are basic entities which can be described by given degrees of freedom, such as number of electrons, nucleons, orbitals etc etc. Now, the crucial bit is to realise that, given those degrees of freedom, atoms can dynamically interact and form larger, more complex structures, thus giving rise to emergent properties.

    Consider for example hydrogen and oxygen atoms. One of the obvious ways for them to dynamically interact is to form H2O molecules, which, given suitable boundary conditions, will in turn interact to form ordinary water in one of its various phases. They could arrange themselves into ice crystals, or liquid water, or vapour. Each of these has completely different macroscopic properties; yet they are all just different phases of the same underlying substance. Through this simple example we can see the idea of emergence - ice emerges from isolated H2O molecules through a phase transition, and all its macroscopic properties emerge in the process. Water emerges from ice through a phase transition. Vapour emerges from water through a phase transition. All of these have very different properties, yet they all emerge from one common substance, being units of H2O.

    So what about if space-time itself is just an emergent phenomena of some more fundamental state ? What if the underlying state if the universe is not spatio-temporal in nature, but some other dynamical system, from which space-time is merely an emergent property, like water is an emergent property of interacting H2O molecules ? We could, for example, take the fundamental ground state of the universe to be some form of "quantum liquid" of pre-geometric units of some form or another, which possess well defined degrees of freedom, and can dynamically interact in certain ways; space-time would then be an emergent property of this liquid through a phase transition, like ice emerges from water through a phase transition. The basic geometric law of space-time, the field equations of General Relativity, can then be understood as thermodynamic equations of state for the fundamental units, whatever those are. I am not talking about a mere discretization of space-time here, but about space-time being an emergent property of an underlying system of fundamental units, which are in and of themselves not spatio-temporal in nature. With the field equations becoming equations of state, the fact that black holes have temperature and entropy is then no longer a surprise, but both expected and necessary.

    Immediately, there are two important consequences - the BB event now becomes a simple phase transition, where the underlying "quantum liquid" gives rise to space-time as an emergent property of the dynamic interactions of its fundamental units. This does not involve any time-like or space-like processes in the traditional sense, but more the realisation of one among many superimposed quantum states of the liquid.
    Secondly, there will be no more singularities - the gravitational collapse during the formation of a black hole, as the density of energy-momentum increases, then once again becomes a phase transition - just as water "dissolves" into essentially unbound H2O molecules during excessive heating, space-time will quite literally "dissolve" back into its underlying constituents, being non-spatio-temporal units. What is hidden behind the event horizon is then not a singularity, but a phase transition where space-time as we know it quite simply ceases to exist and make sense.

    Evidence ? I don't have any. These are just thoughts I have upon putting together several concepts and ideas I have been reading about recently, specifically Erik Verlinde's "Entropic Gravity", Wheeler's "Geometrogenesis", and of course CDT, though you will find that the above isn't quite like any of these.

    Anyways, what do you guys think - am I totally off the bat, or would you consider this workable in any way, shape or form ? I have no maths to present yet, wouldn't even know where to begin with that, tbh. However, any criticisms or comments will be appreciated.


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    KJW
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    I can't really say much because my ideas are in a state of flux. However, I feel that the best approach is to look at what quantum mechanics is really saying. The notion of quantum superposition has to be central to any unification of GR and QM.

    It is often said that GR is incompatible with QM, but I think GR is also somewhat incompatible with thermodynamics. Firstly, the notion of entropy is incompatible with continuous functions due to the wrong limit behaviour. Secondly, the notion of probability, in particular, transition probability is not covariant. This is actually quite an interesting problem which I'll detail at some later time.


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    I can't say much (because I don't have the depth of understanding) but... the two areas that are most intriguing to me are non-locality and the symmetries that underlie these theories. (which is why it was so disappointing when Garret Lisi's "Exceptionally Simple Theory of Everything" turned out to be a dud.)

    am I totally off the bat
    I don't think so, conceptually, at least. Simply because so many other theories are trying to head in the same direction. The idea that much of the complexity is emergent from something simpler wouldn't be too surprising because it happens so often in nature.

    On the other hand, I was thinking the other day about the fact that there are no analytical solutions to the equations of QM or the Einstein Field Equations for realistic situations. And then we are supposed to combine them in some way ... Maybe the universe really is just too complicated for us to ever understand, or even model beyond some point.
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    Quote Originally Posted by KJW View Post
    I can't really say much because my ideas are in a state of flux.
    Quote Originally Posted by Strange View Post
    I can't say much (because I don't have the depth of understanding)
    Well, there's that too!
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    KJW
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    One thing that might help reduce the barrier between GR and QM is the removal of the "" sign from expressions such as:

    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    One thing that might help reduce the barrier between GR and QM is the removal of the "" sign from expressions such as:

    Can you elaborate on this ? I don't quite understand the connection to QM...
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by KJW View Post
    One thing that might help reduce the barrier between GR and QM is the removal of the "–" sign from expressions such as:

    Can you elaborate on this ? I don't quite understand the connection to QM...
    If one were dealing purely with Riemannian geometry (as distinct from pseudo-Riemannian geometry or general relativity), one would use the expression:



    But because in general relativity is negative, one finds that is used instead to ensure that it is real-valued. However, maybe is negative in general relativity so that is indeed an imaginary number. As well as the ubiquitous presence of complex numbers in quantum mechanics, the above expression is equivalent to action in general relativity, and is therefore quantised ( is an action)
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    Quote Originally Posted by KJW View Post
    Secondly, the notion of probability, in particular, transition probability is not covariant
    ...which once again raises the question of whether the QM wave function really can be considered an inherent property of a system or particle. I would argue that the information contained in the wave function is better understood as a relation between the system and the observer; viewed in this way it comes as no surprise that QFT excitations in curved space-time loose their interpretation as asymptotic particles, in fact, it is a necessary and logic consequence. That's just my own two cents' worth though

    I think GR is also somewhat incompatible with thermodynamics
    I disagree. I think there is a deep connection between the two, and at least to some degree that can be made mathematically rigorous, as first demonstrated by Jacobson ( and others after him ) in his landmark paper Thermodynamics of Spacetime: The Einstein Equation of State. I do acknowledge though that this is just my personal opinion, and that much work remains to be done in this area; it may well turn out to be a dud in the end. I am an advocate of this being worthy for further research, though.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by KJW View Post
    Secondly, the notion of probability, in particular, transition probability is not covariant
    ...which once again raises the question of whether the QM wave function really can be considered an inherent property of a system or particle.
    Actually, the quantum wavefunction is covariant. What I said was specifically about probability. If one performs the transformation , then a transition probability becomes negative and therefore no longer represents a probability. Suppose one has a row of coins on a table and we create a rule that says that after a specified period of time, the coins are turned over with some probability. Then given an initial number of coins in each state, we can statistically deduce the expected number of coins in each state at the next step in the future. But if we reverse the time ordering, the original past states are not determined statistically from the original future states with the same probability. In other words, to say that there is a probability of X becoming Y, even if there is the reversibility of the same probability of Y becoming X, carries with it a definite time direction in the sense that the probability is applied only to the past versions of X and Y becoming future versions of Y and X, not to future versions of X and Y becoming past versions of Y and X. This conflicts with general relativity.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    Actually, the quantum wavefunction is covariant. What I said was specifically about probability.
    Hm, interesting; I wasn't really aware of this. It's definitely something to think about.
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  12. #11  
    KJW
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by KJW View Post
    I think GR is also somewhat incompatible with thermodynamics
    I disagree. I think there is a deep connection between the two, and at least to some degree that can be made mathematically rigorous, as first demonstrated by Jacobson ( and others after him ) in his landmark paper Thermodynamics of Spacetime: The Einstein Equation of State. I do acknowledge though that this is just my personal opinion, and that much work remains to be done in this area; it may well turn out to be a dud in the end. I am an advocate of this being worthy for further research, though.
    With regards to general relativity, the problem with such notions as blackhole entropy is that there is nothing within general relativity itself that says that a blackhole has entropy. If one considers the Schwarzschild metric, then this metric can be scale-transformed to any other Schwarzschild metric. That is, all Schwarzschild metrics are equivalent, which conflicts with the notion that the entropy differs between them. This is particularly significant for entropy because entropy is about information content and general relativity is not providing that. I should stress that I'm not saying that blackholes don't have entropy, only that the entropy doesn't come from general relativity.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    If you guys are having issues dealing with all this, just imagine what a numbnuts like me is having trying to piece this together Now be gentle with me, I may be stepping off a cliff here........*crank alert, defences up*.

    What appears to stand out to me in this regard is a current incompatibility between theories such as GR (a classical theory applied to explain how we measure our world exploiting principles of covariance and principles of symmetry to help 'remove the noise by dependencies' and focus on things that matter namely that which is independent of reference frame) against probabilistic theories such as QM (a theory exploiting the statistical interpretation of isolated fundamental states from abstract spaces (a theoretical world) and how these emerge in the classical realm) and thermodynamics (a theory exploiting principles of describing system states, large number statistics (once again using probabilities) and how they evolve in our classical world.

    Each of these theories do exceedingly well on their own working to their particular strengths but the issues that we appear to be discussing on this thread is looking at the perceived gaps in each of these theories and how we can use one theoretical framework to help answer questions in another. As Markus has pointed out it appears that the Beckenstein bound provides a potential bridge to examine concepts such as entropy, the arrow of time (I added this into the mix), fine scale structure of spacetime and whether spacetime is an emergent feature of a deeper underlying reality......I am hoping I am on the same page still with you guys at this point as I am now going to go for a leap of faith, just for the fun of it....

    What appears evident to me is that the conundrum facing me is that I am seeing an asymmetry in thermodynamics, which is evident with the notion of a directional physical bias which is not being answered by either QM or GR. The time reversible nature of the mathematics being applied to both GM and QM is suggestive that everything is based on symmetrical principles. The bias is reflected in QM however not with the underlying maths associated with abstract spaces but in the classical expression it takes through features such as wave-function collapse, probability ampliutude etc.

    In my mind this is saying.....perhaps we should be looking seriously to resolve how questions such as an arrow of time, principles of causality etc. in our efforts to connect these theories before progressing to the next level of enquiry......or perhaps it is more useful of applying reverse engineering to establish a connection between these different theoretical models before we proceed again.

    KJW's comment such as questioning the application of a sign in ther maths of GR picked my interest as it is suggestive of the notion that we are biasing the mathematics of GR for a classical outcome. I can therefore see why KJW is in the multiverse camp' with his thinking processes. This is also leading me (in my confused brain mindset) to a notion that a deeper reality exists which is mathematically solvable but inevitably observationally unobtainable. It is also supporting Markus's thoughts in a round-about way that perhaps spacetime is an emergent phenomenon based on how variable states (information) is plucked from the quantum realm and mapped to our perceived classical reality. I am stuck in no mans land at the moment with Strange's suggestion that it all lies in symmetry principles to an urge to say....well perhaps a fundamental asymmetry exists in the construction of our classical world and this maybe be a perceived asymmetry or real asymmetry that gets the whole ball rolling.

    I can also see where Susskind has emerged with the concept of a holographic universe when pondering some of these puzzles. Maybe it is just all about how we piece together information that gives a notion of a classical reality as in Wheelers "It's from Bits' notion. Information theory is a useful notion that may bear fruit in respect to answering some of the questions that deal with bridging the gap between competing theoretical models. Building a classical universe using information theory builds in asymmetric notions such as a temporal direction, entropy etc. to its evolution by virtue of the mapping of cause and effect informational relationships.

    ...now before anyone says it, *dribble, dribble, dribble..*

    Carry on gentlemen :-))
    Last edited by Implicate Order; November 1st, 2013 at 08:17 PM. Reason: Removing fluff and typos
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  14. #13  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by KJW View Post
    With regards to general relativity, the problem with such notions as blackhole entropy is that there is nothing within general relativity itself that says that a blackhole has entropy.
    Yes, and that is precisely because GR assumes the underlying space-time manifold to be smooth and continuous ( singularities aside for now ), so the notion of entropy on the boundary surface of an enclosed region cannot be consistently defined in pure GR terms.

    If one considers the Schwarzschild metric, then this metric can be scale-transformed to any other Schwarzschild metric. That is, all Schwarzschild metrics are equivalent, which conflicts with the notion that the entropy differs between them.
    I am not sure what you mean here; whereas the volume of a black hole ( being the integral of a volume form ) will be coordinate dependent, the event horizon area is most definitely not, and is invariant for all observers ( light-like surface and all...). In the case of a Schwarzschild BH, it is just a combination of some fundamental constants as well as the BH's rest mass, all of which are the same for all observers, and in all coordinate systems. I am thus unclear what you mean by "entropy differs between them".

    I should stress that I'm not saying that blackholes don't have entropy, only that the entropy doesn't come from general relativity.
    Oh, I completely agree with that, and it does not in any way surprise me. I would not expect GR to be able to yield an expression or definition for entropy, for reasons pointed out above and in my OP.
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    It is also supporting Markus's thoughts in a round-about way that perhaps spacetime is an emergent phenomenon
    I would like to stress again that this idea is merely a hypothesis - in no way am I implying that this is indeed what is happening ( though I must admit that my gut feeling tells me that there may be something to this - too many coincidences here ). I am really just wanting to examine possibilities, and I am open to any and all ideas with regards to QG, so long as they have scientific merit.
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    Forum Masters Degree Implicate Order's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    I would like to stress again that this idea is merely a hypothesis - in no way am I implying that this is indeed what is happening ( though I must admit that my gut feeling tells me that there may be something to this - too many coincidences here ). I am really just wanting to examine possibilities, and I am open to any and all ideas with regards to QG, so long as they have scientific merit.
    Totally understood Markus. I am only trying to encourage you guys to stretch things a bit and step into a more uncomfortable land of supposition. It may actually add a bit of credibility to the *unspoken* realm of pseudoscience. I have known KJW for a long time and he revels in pushing me to the limits with his KAPOW!! statements before he deftly in a few succinct lines crushes me into non-existence. It's all fun and games until someone loses an eye. :-))
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    Quote Originally Posted by Implicate Order View Post
    Totally understood Markus. I am only trying to encourage you guys to stretch things a bit and step into a more uncomfortable land of supposition. It may actually add a bit of credibility to the *unspoken* realm of pseudoscience. I have known KJW for a long time and he revels in pushing me to the limits with his KAPOW!! statements before he deftly in a few succinct lines crushes me into non-existence. It's all fun and games until someone loses an eye. :-))
    Well, in the end we can all agree on a very simple fact - gravity sucks
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    KJW
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by KJW View Post
    If one considers the Schwarzschild metric, then this metric can be scale-transformed to any other Schwarzschild metric. That is, all Schwarzschild metrics are equivalent, which conflicts with the notion that the entropy differs between them.
    I am not sure what you mean here; whereas the volume of a black hole ( being the integral of a volume form ) will be coordinate dependent, the event horizon area is most definitely not, and is invariant for all observers ( light-like surface and all...). In the case of a Schwarzschild BH, it is just a combination of some fundamental constants as well as the BH's rest mass, all of which are the same for all observers, and in all coordinate systems. I am thus unclear what you mean by "entropy differs between them".
    A scale transformation is not a coordinate transformation. It is a transformation of the metric of the form:



    where is a constant. When combined with a compensating coordinate transformation, it changes the mass of the Schwarzschild blackhole, but the form of the metric remains identical, hence Schwarzschild blackholes of different masses are equivalent. Given that entropy represents the number of distinct ways that the blackhole can exist, and that the scale-mapping is one-to-one, the equivalence implies that all Schwarzschild blackholes have the same entropy, or even that the entropy is zero (one distinct way that the blackhole can exist).
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by Implicate Order View Post
    In my mind this is saying.....perhaps we should be looking seriously to resolve how questions such as an arrow of time, principles of causality etc. in our efforts to connect these theories before progressing to the next level of enquiry
    This is an excellent point.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    it changes the mass of the Schwarzschild blackhole
    Yes exactly - so how do you arrive at the conclusion that all BHs have the same entropy, since the entropy is a function of mass ? Let's work through it - the horizon "surface" is at r=2m in SM radial coordinates, so at a fixed time we get a surface metric of



    The determinant of this is just an area element of a 2-sphere :



    Integrate over all angles to get the total surface area, and obtain



    in natural units. The entropy S(A(m)) is a function of this surface area, which is in turn a function of mass; so, if you rescale the original metric by some constant factor in the way you suggested, the mass increases ( as you rightly noted ), and so does the entropy. I therefore really don't follow your argument that the entropy is the same for all BHs, or that it is zero. However - see my next comment below.

    Given that entropy represents the number of distinct ways that the blackhole can exist
    I think this is the crucial bit - if we stay purely within GR and ignore all quantum effects, then space-time is smooth and continuous, and all mass is concentrated into a singularity. In that case you are left with only one degree of freedom, being total mass. There are no other ways to distinguish black holes from one another. In that sense, all BHs should have the same entropy, since there is exactly one "state" to each BH - is that what you meant to point out ?
    At the same time it is clear that this is a violation of the laws of thermodynamics ( since adding more matter would not change entropy or temperature ), so I am taking this as an indication that extrapolating GR all the way to the end result of a gravitational collapse is not physically meaningful. In other words - this is an indication that there is no singularity hidden behind the horizon, but some other structure with distinct and dynamic degrees of freedom. That was the starting point of my OP - that Hawking's and Bekenstein's arguments amount to there not being a singularity present.
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    Quote Originally Posted by Markus Hanke View Post
    since the entropy is a function of mass
    That is not made manifest by the metric itself. For general relativity to be an adequate description of anything, then everything has to emerge directly from the quantities of general relativity. For example, if I were to hand you an exact metric of a system, then you would have to be able to determine from the metric alone every property of the system. (I used the word "exact", to highlight that I'm not referring to the inadequacies of an approximation, but intrinsic to the description itself).


    Quote Originally Posted by Markus Hanke View Post
    if we stay purely within GR and ignore all quantum effects, then space-time is smooth and continuous, and all mass is concentrated into a singularity. In that case you are left with only one degree of freedom, being total mass. There are no other ways to distinguish black holes from one another. In that sense, all BHs should have the same entropy, since there is exactly one "state" to each BH - is that what you meant to point out ?
    Yes, but I chose to avoid consideration of the central singularity and instead focus on the notion that the metric, as a description of the full spacetime associated with the Schwarzschild blackhole, is not describing a spacetime with the degrees of freedom to account for the entropy. But anyway, I think this has gotten too far from my original point which was that general relativity itself is somewhat inadequate to describe a system possessing entropy. Actually, I wasn't so much considering blackholes but ordinary lumps of matter.


    Quote Originally Posted by Markus Hanke View Post
    At the same time it is clear that this is a violation of the laws of thermodynamics ( since adding more matter would not change entropy or temperature ), so I am taking this as an indication that extrapolating GR all the way to the end result of a gravitational collapse is not physically meaningful. In other words - this is an indication that there is no singularity hidden behind the horizon, but some other structure with distinct and dynamic degrees of freedom. That was the starting point of my OP - that Hawking's and Bekenstein's arguments amount to there not being a singularity present.
    In the Hawking-Susskind debate over the blackhole information paradox, it is now generally accepted that the event horizon contains fluctuations which contain all the information about the infallen matter. In that case, we are no longer dealing with a purely Schwarzschild blackhole, but an object which can possess entropy proportional to the surface area.
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    Quote Originally Posted by KJW View Post
    That is not made manifest by the metric itself. For general relativity to be an adequate description of anything, then everything has to emerge directly from the quantities of general relativity.
    Yes, that's true. I agree with you that the notion of entropy does not follow from GR itself.

    the notion that the metric, as a description of the full spacetime associated with the Schwarzschild blackhole, is not describing a spacetime with the degrees of freedom to account for the entropy
    That was my thought in the end, and I agree with you. A metric alone does not contain the physical information necessary to compute entropy.

    But anyway, I think this has gotten too far from my original point which was that general relativity itself is somewhat inadequate to describe a system possessing entropy.
    I agree with that.

    In the Hawking-Susskind debate over the blackhole information paradox, it is now generally accepted that the event horizon contains fluctuations which contain all the information about the infallen matter. In that case, we are no longer dealing with a purely Schwarzschild blackhole, but an object which can possess entropy proportional to the surface area.
    This raises another peculiar issue - to put it simply, how does the information about in-falling matter get onto the event horizon in the first place ? If there was a curvature singularity behind the horizon, all matter would just simply continue freely falling into that singularity, at which point all degrees of freedom carried along would simply vanish. I see no mechanism how any entropy could become encoded on the horizon. So once again, I take this as an indication ( not evidence ) that there is no curvature singularity inside a BH.
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    About that could someone explain me why there cannot be loss of information about infalling matter? I did not understand that assumption at all. Why would it be a problem?
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    Quote Originally Posted by Gere View Post
    About that could someone explain me why there cannot be loss of information about infalling matter? I did not understand that assumption at all. Why would it be a problem?
    It's a problem because it would reduce many physical states into just one state, thus destroying information. If you have a wave function, you can apply an evolution operator to it to obtain its future evolution ( unitarity ); at the same time any physically meaningful evolution operator always has an inverse ( apparently this can be formally proven, but I don't know how ). If you combine the two, you can deduce that information always must be preserved in some form; a black hole without entropy and temperature would violate this conservation principle. See here :

    Black hole information paradox - Wikipedia, the free encyclopedia
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  25. #24  
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    Quote Originally Posted by Markus Hanke View Post
    a black hole without entropy and temperature would violate this conservation principle.
    I would like to adjust this to say that it's the perfectly thermal nature of Hawking radiation that violates this conservation principle, and therefore the resolution is that the radiation is not perfectly thermal, containing within it the information about the infallen quantum states.
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  26. #25  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by KJW View Post
    In the Hawking-Susskind debate over the blackhole information paradox, it is now generally accepted that the event horizon contains fluctuations which contain all the information about the infallen matter. In that case, we are no longer dealing with a purely Schwarzschild blackhole, but an object which can possess entropy proportional to the surface area.
    This raises another peculiar issue - to put it simply, how does the information about in-falling matter get onto the event horizon in the first place ? If there was a curvature singularity behind the horizon, all matter would just simply continue freely falling into that singularity, at which point all degrees of freedom carried along would simply vanish. I see no mechanism how any entropy could become encoded on the horizon. So once again, I take this as an indication ( not evidence ) that there is no curvature singularity inside a BH.
    The way I see it, from the perspective of an external observer, the blackhole never forms and all the matter remains outside the event horizon, so the whole issue of blackhole evaporation doesn't make sense to me.
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    Quote Originally Posted by KJW View Post
    The way I see it, from the perspective of an external observer, the blackhole never forms and all the matter remains outside the event horizon, so the whole issue of blackhole evaporation doesn't make sense to me.
    I am going to have to probe you a bit on this.

    The suggestion is that GR in its current application should cease at the event horizon itself with no need to consider its extension to the interior of the black hole.... with the requirement that GR is further extended to fully describe thermodynamics through its metric description. That would be a nice discussion point and assist in digging deeper into Markus's original query.

    I can see why thermodynamics and information theory ends at this boundary with no need for a further description or the 'need' for an extension beyond this boundary. The issues we seem to be having is our use of GR in describing what occurs beyond the event horizon. The mere fact is that from the point of view of an external observer, we do not need to extend the theory into this domain as this would be purely a mathematical exercise that can never be plumbed observationally.

    In adopting this posture, this would therefore put an end to the no hairs debate and questions over Hawking radiation being purely thermal.......plus some other associated temptational baggage associated with the reasoning of what exists at the interior of black holes such as 'bridges to alternate universes, time travel paradoxes etc. Is this what you are suggesting KJW? :-))
    Last edited by Implicate Order; November 2nd, 2013 at 08:25 PM. Reason: GR does not 'fail' at the event horizon, but rather is no longer 'useful' in its application beyond that point.
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    Quote Originally Posted by KJW View Post
    The way I see it, from the perspective of an external observer, the blackhole never forms and all the matter remains outside the event horizon, so the whole issue of blackhole evaporation doesn't make sense to me.
    That's an interesting perspective...I haven't even thought about this simple point or its implications. On the other hand though that very same observer would be able to detect and measure the Hawking radiation emitted, and, if he sticks around long enough, see and measure the black hole slowly shrinking and getting hotter. In effect, for him a black hole is a machine that merely converts in-falling matter into outgoing radiation, so that overall everything remains conserved, with the internal mechanisms and workings of the machine being entirely irrelevant. I need to ponder this for a while.

    P.S. If one was to replace the interior region of the BH with an Einstein-Rosen bridge, as we had discussed before over on TPF, then no change would occur to the entropy on the horizon surface. In other words - removing the interior region entirely makes no difference to the number of micro states of the BH. I am going to have to ponder the implications of this, too.
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    Quote Originally Posted by Markus Hanke View Post
    That's an interesting perspective...I haven't even thought about this simple point or its implications. On the other hand though that very same observer would be able to detect and measure the Hawking radiation emitted, and, if he sticks around long enough, see and measure the black hole slowly shrinking and getting hotter. In effect, for him a black hole is a machine that merely converts in-falling matter into outgoing radiation, so that overall everything remains conserved, with the internal mechanisms and workings of the machine being entirely irrelevant. I need to ponder this for a while.
    Perhaps this would be a time to discuss whether their is an information paradox or whether this paradox exists through the assumption that information is lost in transmission across an event horizon. If no such paradox exists then there would be no need to consider Hawking Radiation. If we disregard GR altogether in our discussion and can satisfy information conservation in our consideration through quantum mechanical encoding at the event horizon as Susskind, Hooft, Verlinde etc. are debating then we could possibly conclude that spacetime and gravity is an emergent condition which can fully be satisfied by GR in its current form.

    There are some interesting areas of research underway looking at whether or not the event horizon is purely quantum mechanical in nature. See Information paradox simplified - physicsworld.com :-))
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    Quote Originally Posted by Implicate Order View Post
    There are some interesting areas of research underway looking at whether or not the event horizon is purely quantum mechanical in nature. See Information paradox simplified - physicsworld.com :-))
    Well, it couldn't be purely QM in nature, since the event horizon is one of the central predictions by GR ( which doesn't contain quantum effects ). However, the concept of tunnelling through the event horizon is most interesting; this never occurred to me before, but is really quite logic if you think about it.
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    Quote Originally Posted by Implicate Order View Post
    In my mind this is saying.....perhaps we should be looking seriously to resolve how questions such as an arrow of time, principles of causality etc. in our efforts to connect these theories before progressing to the next level of enquiry......
    Interesting point but, if those things are indeed emergent properties, then I'm not sure much more can be gained by thinking about them (an awful lot of time and paper has been spent on scientific and philosophical speculation about these without leading any where much). I suspect these questions are going to be resolved as a consequence (almost incidental) of some new theory.
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    I have always imagined GR as emergent from quantum mechanics, but could a hypothesis like in the OP suggest that this might not entirely be the case? That they might emerge independently or just partially one from the other?


    This, though much more rigorous, reminds me of my own attempts at dabbling with some fundamentals all the rest are emergent from.
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    Quote Originally Posted by KALSTER View Post
    I have always imagined GR as emergent from quantum mechanics, but could a hypothesis like in the OP suggest that this might not entirely be the case? That they might emerge independently or just partially one from the other?
    I think whatever the underlying degrees of freedom actually are, they will need to be inherently quantum in nature. Ultimately then both QM and GR emerge from a more fundamental system which is in itself neither one of the two.
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  34. #33  
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    Quote Originally Posted by Implicate Order View Post
    Quote Originally Posted by KJW View Post
    The way I see it, from the perspective of an external observer, the blackhole never forms and all the matter remains outside the event horizon, so the whole issue of blackhole evaporation doesn't make sense to me.
    I am going to have to probe you a bit on this.

    The suggestion is that GR in its current application should cease at the event horizon itself with no need to consider its extension to the interior of the black hole.... with the requirement that GR is further extended to fully describe thermodynamics through its metric description. That would be a nice discussion point and assist in digging deeper into Markus's original query.

    I can see why thermodynamics and information theory ends at this boundary with no need for a further description or the 'need' for an extension beyond this boundary. The issues we seem to be having is our use of GR in describing what occurs beyond the event horizon. The mere fact is that from the point of view of an external observer, we do not need to extend the theory into this domain as this would be purely a mathematical exercise that can never be plumbed observationally.

    In adopting this posture, this would therefore put an end to the no hairs debate and questions over Hawking radiation being purely thermal.......plus some other associated temptational baggage associated with the reasoning of what exists at the interior of black holes such as 'bridges to alternate universes, time travel paradoxes etc. Is this what you are suggesting KJW? :-))
    Actually, my statement was based on a simple question: When does the external observer actually see the blackhole evaporate?

    A blackhole is not as straightforward as one might think. I don't know if you ever saw it, but I derived a wormhole metric by applying a coordinate transformation to the Schwarzschild metric, thus removing the entire interior region of the blackhole. The Kruskal-Szekeres coordinates of a Schwarzschild blackhole were derived as a maximal extension the geometry. Thus, what I did was the opposite in that I reduced the geometry. The point is that by the appropriate choice of the coordinate system, one can alter the embedding of the real manifold within the complex manifold. Thus, in spite of the fact that these are just different coordinate systems, the physical geometry has been altered. The question then becomes: Which geometry is the correct geometry?

    A problem with GR is that it tends to present a "god's eye view" of reality, whereas the perspective of the observer is perhaps the most important. Unfortunately, the question then becomes: Which observer? In the case of the blackhole, there is still the infalling observer to consider.
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    Quote Originally Posted by Strange View Post
    (an awful lot of time and paper has been spent on scientific and philosophical speculation about these without leading any where much).
    *Sniggers*. You said it

    Quote Originally Posted by KJW
    I don't know if you ever saw it, but I derived a wormhole metric by applying a coordinate transformation to the Schwarzschild metric, thus removing the entire interior region of the blackhole
    No missed it unfortunately. It must have been when I was remodelling my hair piece.

    Quote Originally Posted by KJW
    Which geometry is the correct geometry?
    Well come out with it man, and don't give me this mumbo jumbo multiverse explanation../TIC

    ....anyway my brain hurts and it is time for my medication. Night all :-))
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    Noa, I believe we also asked that you post your ideas in the appropriate section, not in other people's threads. I'll move this to New Hypothesis.
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    I have an unusual theory about gravity that tops any that I've heard so far. Mine involves gravitation as a quantum object that is only weak as a result of a directional scattering from its source. My unusual hypotheses.
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