Re: [Vo]:Entanglement and rotating balck holes
Nature's version of quantum encryption. See if you can unscramble it http://extremeplanet.me/2013/05/21/analysis-of-the-2013-moore-tornado-the-deadliest-oklahoma-tornado-in-modern-history/ We reside in a false vacuum. Like ants, we build our mounds, they get wiped out occasionally and we start again. Spacetime curls up routinely, bending electromagnetic radiation and releasing nuclear yields of dark energy. https://en.wikipedia.org/wiki/2013_Moore_tornado#/media/File:NWS_2013_Moore_radar_loop.gif We were born entangled in uncertainty Just my take on it. On Sun, Jul 19, 2015 at 5:54 PM, Axil Axil janap...@gmail.com wrote: Black Holes and Quantum Entanglement In Natural Philosophy on October 5, 2011 at 3:24 am Note to regular readers–apologies for not writing all month. I have been really busy with my research in the mathematical domain. My ongoing work is on the question of the persistence of quantum entanglement around rotating black holes. This is interesting because, first of all, no one understands by what underlying mechanism entanglement works. I outlined it my post on the nature of reality, but let me give a shorter explanation here. Entanglement for soccer moms Suppose you have two fair coins. Imagine that every time one comes up heads the other comes up tails, i.e., they are perfectly correlated–even though they still have probability 1/2 of coming up heads individually! This is basically the case of maximal entanglement. Of course, we don’t observe this with coins but that is because of decoherence so that the probability of this happening with coins is vanishingly small. What is crazy is that this actually happens with quantum phenomena like spin, as has been verified experimentally innumerable times. No one knows by what mechanism such coordination takes place so this is a very mysterious phenomena. One would like to understand it better. Rotating black holes Theoretically, it’s clear that entanglement persists at arbitrarily large distances in flat spacetime. Might this be true for curved spacetime? This is quite relevant since we quite obviously live in the domain of general relativity (GR). In fact, our GPS devices would be a few hundred yards off if they did not make GR corrections to Newtonian mechanics. Essentially, one wants to know if this works the same way in spacetimes that are exact solutions to Einstein’s equations of general relativity. Mathematically, rotating black holes are just an interesting example of such spacetimes with just enough symmetry to allow for analytical solutions (Crucially, the Dirac equation for spin-1/2 particles separates into purely radial and axial equations which can then be solved explicitly.) [Nerd alert: This has to do with the existence of Killing-Yano tensors, which not only guarantee the separation of variables, they also ensure complete integrability–which means that the number of constants of motion that exist equal the dimension of spacetime. For a freely falling particle these are the rest mass, energy, angular momentum and the surprising fourth first integral called Carter’s constant which comes from the Killing-Yano tensor as well.] Now, one would like to investigate whether entanglement persists in the extremely curved vicinity of a rotating black hole, maybe with one particle inside the event horizon? The point being that the resolution of each particle’s spin is then independent of the curvature of spacetime (gravity). Or, more interestingly, that it gets entangled with the black hole itself. Since the spin of a particle couples to the curvature of spacetime, spin-spin entanglement spills over into entanglement of spin and momenta which are both described by the spinor representing the particles. (Entanglement is expressed by both particles having the same wave function which is just a spinor in differential geometry.) A rotating black hole has a very interesting feature. The event horizon is the boundary of the black hole–from which even light, and therefore nothing else (current results about superluminal neutrinos aside) can escape. There is another horizon outside it called a Killing horizon. Between these horizons, in what is called the ergoregion, you have to rotate with the black hole; it takes infinite energy not to. I suspect that this spilling of spin entanglement into spin/momenta entanglement reaches a limit as one hits the Killing horizon and enters the ergoregion. However, this is an open question. The vicious interior The interior of a rotating black hole is considered unphysical. Mathematical physicists literally call it vicious, which is a technical term for a region where time travel is possible. In fact, the situation is much worse. One can go from any event–a point in spacetime (t,x,y,z)–to any other event in the interior by going enough number of times around the ring singularity (it is quite literally a time machine). However,
[Vo]:Entanglement and rotating balck holes
Black Holes and Quantum Entanglement In Natural Philosophy on October 5, 2011 at 3:24 am Note to regular readers–apologies for not writing all month. I have been really busy with my research in the mathematical domain. My ongoing work is on the question of the persistence of quantum entanglement around rotating black holes. This is interesting because, first of all, no one understands by what underlying mechanism entanglement works. I outlined it my post on the nature of reality, but let me give a shorter explanation here. Entanglement for soccer moms Suppose you have two fair coins. Imagine that every time one comes up heads the other comes up tails, i.e., they are perfectly correlated–even though they still have probability 1/2 of coming up heads individually! This is basically the case of maximal entanglement. Of course, we don’t observe this with coins but that is because of decoherence so that the probability of this happening with coins is vanishingly small. What is crazy is that this actually happens with quantum phenomena like spin, as has been verified experimentally innumerable times. No one knows by what mechanism such coordination takes place so this is a very mysterious phenomena. One would like to understand it better. Rotating black holes Theoretically, it’s clear that entanglement persists at arbitrarily large distances in flat spacetime. Might this be true for curved spacetime? This is quite relevant since we quite obviously live in the domain of general relativity (GR). In fact, our GPS devices would be a few hundred yards off if they did not make GR corrections to Newtonian mechanics. Essentially, one wants to know if this works the same way in spacetimes that are exact solutions to Einstein’s equations of general relativity. Mathematically, rotating black holes are just an interesting example of such spacetimes with just enough symmetry to allow for analytical solutions (Crucially, the Dirac equation for spin-1/2 particles separates into purely radial and axial equations which can then be solved explicitly.) [Nerd alert: This has to do with the existence of Killing-Yano tensors, which not only guarantee the separation of variables, they also ensure complete integrability–which means that the number of constants of motion that exist equal the dimension of spacetime. For a freely falling particle these are the rest mass, energy, angular momentum and the surprising fourth first integral called Carter’s constant which comes from the Killing-Yano tensor as well.] Now, one would like to investigate whether entanglement persists in the extremely curved vicinity of a rotating black hole, maybe with one particle inside the event horizon? The point being that the resolution of each particle’s spin is then independent of the curvature of spacetime (gravity). Or, more interestingly, that it gets entangled with the black hole itself. Since the spin of a particle couples to the curvature of spacetime, spin-spin entanglement spills over into entanglement of spin and momenta which are both described by the spinor representing the particles. (Entanglement is expressed by both particles having the same wave function which is just a spinor in differential geometry.) A rotating black hole has a very interesting feature. The event horizon is the boundary of the black hole–from which even light, and therefore nothing else (current results about superluminal neutrinos aside) can escape. There is another horizon outside it called a Killing horizon. Between these horizons, in what is called the ergoregion, you have to rotate with the black hole; it takes infinite energy not to. I suspect that this spilling of spin entanglement into spin/momenta entanglement reaches a limit as one hits the Killing horizon and enters the ergoregion. However, this is an open question. The vicious interior The interior of a rotating black hole is considered unphysical. Mathematical physicists literally call it vicious, which is a technical term for a region where time travel is possible. In fact, the situation is much worse. One can go from any event–a point in spacetime (t,x,y,z)–to any other event in the interior by going enough number of times around the ring singularity (it is quite literally a time machine). However, the case with one observer inside and one outside is still of purely mathematical interest. As fascinating is the (mathematical) existence of wormholes. In a maximal extension, one wants to account for the entire history of all photons (light rays or null geodesics). Now Kerr spacetime (an isolated rotating black hole) has a maximal extension with an infinite tower of spacetimes smoothly connected by wormholes. Information loss The topic under discussion is of course related to the question of whether information is lost inside black holes. Do we lose the information contained in the internal degrees of freedom of particles that disappear inside a black hole? We have good reason to believe that
