tag:blogger.com,1999:blog-3832136017893749497.post7976439470324067353..comments2023-09-29T08:49:30.765-04:00Comments on Elliptic Composability: Florin Moldoveanuhttp://www.blogger.com/profile/01087655914212705768noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3832136017893749497.post-50190570383346211772015-02-10T21:18:15.808-05:002015-02-10T21:18:15.808-05:00Thanks for the firewall explanation.
See this htt...Thanks for the firewall explanation.<br /><br />See this http://fmoldove.blogspot.com/2015/01/quantum-groups-and-curved-space-time.html and the archive link within to a paper which discusses horizons in curved spacetime. Florin Moldoveanuhttps://www.blogger.com/profile/01087655914212705768noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-15126482621609848002015-02-10T18:35:55.580-05:002015-02-10T18:35:55.580-05:00The firewall is due to the following. A particle ...The firewall is due to the following. A particle that is emitted by a black hole is associated with a particle that enters the black hole. The particle that enters the black hole has negative energy and removes the mass from the black hole. For fermions this connects deeply with Dirac’s insight about negative mass particles in the negative part of the momentum light cone. This means the black hole is entangled with the Hawking radiation emitted. As a result the amount of entanglement information of the black hole increases. This happens with a hot cavity that emits photons. However, as the hot chamber cools some of the atoms entangled with previously emitted photons emits photons that are entangled with those prior photons and the entanglement information or entropy declines. This does not happen with black holes.<br /><br />The problem is that the entanglement entropy increases and eventually at some point this grows to exceed the Bekenstein/Bousso entropy bound. That is a disaster. One has two choices; the first choice is to say the black hole ends up as a remnant with a huge amount of information, which violates unitarity, or one demands that the black hole reaches a maximum which means the horizon can no longer become entangled with anything. This converts the horizon into a type of singularity (the firewall) and information entering the BH is simply annihilated. This violates the equivalence principle. We are in a way back to the problem of reconciling general relativity with quantum mechanics. We are closer, but not yet there.<br /><br />The problem could be reconciled if the black hole-Hawking radiation entanglement can be exchanged into a larger entanglement. However, entanglement does not do that in a unitary manner. In keeping with my idea about a new form of nonlocality, I think entanglements with quantum gravity are themselves uncertain. A bipartite entanglement is only one amplitude with a tripartite or GHZ entanglement. This is in part what my papers are paths into. The phase change as the acceleration g --- > g_{planck} ~ 10^{53}cm/s^2 is a form of what Mathur calls a form of “hair.”<br /><br />I have a lot more I could related with respect to this.<br /><br />Cheers LCLawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-15129045529936286022015-02-10T18:34:51.663-05:002015-02-10T18:34:51.663-05:00The quantum gravity case is difficult. The proble...The quantum gravity case is difficult. The problem is that the field is spacetime. It is then not possible to assign equal time commutators = 0 conditions, such as Wightman conditions, on the field. This means we probably no longer have locality on the field level. There is a deeper level of nonlocality, which means there is a generalization of Tsirelson bounds for quantum gravity. This is what in part motivates my thinking about associators. A field that is very close to the horizon, or on what is called the stretched horizon has some uncertainty about its causality condition with fields interior and exterior to the black hole. The paper I sent deal with some of this, though I don’t mention nonassociative physics.<br /><br />There is an old idea from back in the 1970s about shadow states. This involves old ideas about bootstrap theory and the rest. These are vacuum states that have no physical states. They have no expectations of observables in the sense of Born’s theorem. These can in the language of virtual fluctuations couple to particles and have consequences. It may be possible that nonassociative physics involves shadow states. After all with black holes, one can’t observe X and Y outside the BH with Z inside and X outside and Y and Z inside --- by definition. However, if this is a condition for a quantum fluctuation, a term I sometimes do not like, then this condition might exist as something that is not directly observable.<br /><br />I agree that standard QM has the * = σ + Jħα/2 is such that J^2 = 0 is classical , with Bell inequalities and QM diverges from this, but the associator is zero. If we could show there is field nonlocality with nonassociativity, and that nonassociativity is a quantum gravity result that might be worth something. Of course it could still be wrong.<br /><br />continued due to text limitationLawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-47450971942998875702015-02-10T16:56:55.673-05:002015-02-10T16:56:55.673-05:00When J^2=0 there are actually 2 associative produc...When J^2=0 there are actually 2 associative products which can be defined. First from the associator relationship there is sigma, the usual function multiplication in the setting of Poisson manifolds. With this associative product one obtains the usual formulation of classical mechanics in phase space. Then there is a second associative product: sigma + J alpha (with J^2 = 0) which leads to the classical mechanics in Hilbert space formulation.<br /><br />The BH case is a tricky business and I don't fully understand what is going on at this time. Is the firewall real? Florin Moldoveanuhttps://www.blogger.com/profile/01087655914212705768noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-87490841059285946412015-02-10T16:27:30.999-05:002015-02-10T16:27:30.999-05:00I am interested in the question of the associator ...I am interested in the question of the associator and J^2 = 0. The classical case is for J^2 = 0, while the general product rule is<br /><br />X(YZ) – (XY)Z = Xσ(YσZ) – (XσY)σZ – J^2ħ/4{Xα(YαZ) – (XαY)αZ} = 0.<br /><br />The is an obstruction to a nonzero associator. I agree with this result for quantum fields in classical spacetime. However, for a quantum mechanical description of spacetime this may not be generally true.<br /><br />Consider a black hole with three field amplitudes. One amplitude X is exterior to the black hole, one is interior Z and one is very close to the horizon Y. We may then associate these operators according to which can communicate to the other. We would have X◦(Y◦Z) if Y is interior and (X◦Y)◦Z if Y is exterior, for ◦ either of the two products. The bracket means the two fields are in the same spacetime region. If the horizon is fluctuating considerably there may be significant deviations in the two operations so this is not zero.<br /><br />Cheers LCLawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-36316906667444914392015-02-08T21:25:49.440-05:002015-02-08T21:25:49.440-05:00Hi Lawrence, please send me your paper. My email i...Hi Lawrence, please send me your paper. My email is: fmoldove@gmail.com <br /><br />Cheers, FlorinFlorin Moldoveanuhttps://www.blogger.com/profile/01087655914212705768noreply@blogger.comtag:blogger.com,1999:blog-3832136017893749497.post-84181542953044703512015-02-08T19:24:59.327-05:002015-02-08T19:24:59.327-05:00Florin,
I think my attempt failed. I read up to ...Florin,<br /><br />I think my attempt failed. I read up to the point you discuss Jordan algebras. I have been either godsmacked or kicked in the face by the mule of stupidity. Your composition approach appears to be a way to look at my large N, or large SU(N) approach to entanglement with black holes. I can send to you if you want a paper I submitted to the GRF essays. The paper I mentioned I would send to you is related to this. <br /><br />I have been wondering how to get this to work with Jordan algebras, and then looking at your page reminded me of you idea here. It seems perfect. I need an address to send that to.<br /><br />Cheers LCLawrence Crowellhttps://www.blogger.com/profile/12090839464038445335noreply@blogger.com