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The “one of the virtual particles of the pair created in the vicinity of the black hole’s horizon falling in leaving the other one to escape to infinity as radi

by qubex 8y ago

The “one of the virtual particles of the pair created in the vicinity of the black hole’s horizon falling in leaving the other one to escape to infinity as radiation whose mass-energy must be subtracted from that of the black hole” view of Hawking radiation is a pedagogical construct thought up by Hawking himself after calculating the effect by other means for the sake of public promulgation. In reality it has to do with the restriction of the resonant modes of quantum fields imposed by having a border (horizon). Case in point: if the full truth were that of infalling versus escaping virtual particles there’d be a definite trajectory associated with the escaping particle that would convey information about where, approximately, the virtual particle/antiparticle pair popped into existence, violating Heisenberg uncertainty. In reality, Hawking radiation has wavelengths comparable to the diameter of the black hole that make it impossible even in theory to resolve where the supposed particle/antiparticle pair “popped” into existence, preserving the uncertainty principle. This is also why radiation becomes more energetic as the hole shrinks in size: that’s because the associated diameter shrinks and allows wavelengths of emitted radiation to contract, packing more energy into those waves. If it really were particle/antiparticle being shorn apart by the hole’s gravitational attraction you’d expect more radiation to be emitted by a big hole (vacuum activity per volume area being constant, and thus a bigger hole would border more unit volumes and allow for greater interaction with the quantum vacuum that would slow down as it shrank).

XorNot 8y ago
Hang on, Heisenberg's uncertainty principle doesn't need to be preserved with virtual particle/anti-particle pairs - that's the point of Hawking radiation - the particles are no longer virtual, and so much must acquire a real value of energy from somewhere (and do so from the mass energy of the black-hole). You're very much trying to draw a line here that QM doesn't support - everything is a particle and a wave at the same time, and the interpretation that one pair of a particle in-falls is at least as valid as the interpretation that it's to do with the exclusion of wavelengths. EDIT: For example, the proposed argument with bigger black holes falls down by a similar interpretation to the wavelengths - for virtual particle pairs with sufficient initial velocity to escape the gravity of the black hole, the initial location of them by necessity becomes very indeterminate, or their mass very light - in both cases making it progressively less likely with black hole size that one part of the pair appears initially inside the black hole event horizon, or makes the resulting energy of the radiation less and less.
raattgift 8y ago
> pedagogical construct No, it was in his 1975 work [1], which considers a non-interacting quantum field in a Schwarzschild black hole spacetime [2]. The negative energy infallers keep the spacetime static, which is handy for preserving a timelike Killing vector field that is orthogonal to the spacelike hypersurfaces at each Schwarzschild time coordinate. That picture made it straightforward to show the mechanism for evaporation; perturbing the picture does not make Hawking radiation vanish, but does make it much harder to calculate. > sake of public promulgation It [1] was a hard academic paper aimed at experts. That should be abundantly clear not far down its first page and certainly by its second. > restriction of the resonant modes of quantum fields imposed by having a border It has to do with vacuum states. > the [bh] shrinks and allows wavelengths of emitted radiation to contract I think you run into controversy (and indeed a bit of inconsistency in your "true picture" argument) with "emitted". There is a secondary issue surrounding gravitational time dilation, depending on where you think Hawking quanta are found. > Heisenberg uncertainty How does that enter into the (non-string) picture except at the latest times when the radius of curvature is on the order of Planck length? I'm genuinely curious to see how you'd use Heisenberg uncertainty except in an argument involving remnants (in which a generalization of HUP could dynamically prevent complete evaporation, with the dynamics becoming important at some small minimum BH mass). Anyway, I strongly recommend Wald [in [2]] to you. - -- [1] https://dx.doi.org/10.1007/BF02345020 https://dx.doi.org/10.1007/BF02345020 [2] It's hard to summarize this better than Wald in the Hawking Radiation section of https://dx.doi.org/10.12942%2Flrr-2001-6 https://dx.doi.org/10.12942%2Flrr-2001-6 notably starting with 'The original derivations [54, 98] made use of notions of "particles propagating into the black hole", ...' and I don't want to plagiarize him.

by qubex 8y ago

XorNot 8y ago

Hang on, Heisenberg's uncertainty principle doesn't need to be preserved with virtual particle/anti-particle pairs - that's the point of Hawking radiation - the particles are no longer virtual, and so much must acquire a real value of energy from somewhere (and do so from the mass energy of the black-hole). You're very much trying to draw a line here that QM doesn't support - everything is a particle and a wave at the same time, and the interpretation that one pair of a particle in-falls is at least as valid as the interpretation that it's to do with the exclusion of wavelengths. EDIT: For example, the proposed argument with bigger black holes falls down by a similar interpretation to the wavelengths - for virtual particle pairs with sufficient initial velocity to escape the gravity of the black hole, the initial location of them by necessity becomes very indeterminate, or their mass very light - in both cases making it progressively less likely with black hole size that one part of the pair appears initially inside the black hole event horizon, or makes the resulting energy of the radiation less and less.

raattgift 8y ago

> pedagogical construct No, it was in his 1975 work [1], which considers a non-interacting quantum field in a Schwarzschild black hole spacetime [2]. The negative energy infallers keep the spacetime static, which is handy for preserving a timelike Killing vector field that is orthogonal to the spacelike hypersurfaces at each Schwarzschild time coordinate. That picture made it straightforward to show the mechanism for evaporation; perturbing the picture does not make Hawking radiation vanish, but does make it much harder to calculate. > sake of public promulgation It [1] was a hard academic paper aimed at experts. That should be abundantly clear not far down its first page and certainly by its second. > restriction of the resonant modes of quantum fields imposed by having a border It has to do with vacuum states. > the [bh] shrinks and allows wavelengths of emitted radiation to contract I think you run into controversy (and indeed a bit of inconsistency in your "true picture" argument) with "emitted". There is a secondary issue surrounding gravitational time dilation, depending on where you think Hawking quanta are found. > Heisenberg uncertainty How does that enter into the (non-string) picture except at the latest times when the radius of curvature is on the order of Planck length? I'm genuinely curious to see how you'd use Heisenberg uncertainty except in an argument involving remnants (in which a generalization of HUP could dynamically prevent complete evaporation, with the dynamics becoming important at some small minimum BH mass). Anyway, I strongly recommend Wald [in [2]] to you. - -- [1] https://dx.doi.org/10.1007/BF02345020 https://dx.doi.org/10.1007/BF02345020 [2] It's hard to summarize this better than Wald in the Hawking Radiation section of https://dx.doi.org/10.12942%2Flrr-2001-6 https://dx.doi.org/10.12942%2Flrr-2001-6 notably starting with 'The original derivations [54, 98] made use of notions of "particles propagating into the black hole", ...' and I don't want to plagiarize him.