On Jan 19, 2016, at 9:26 AM, art wagner <This email address is being protected from spambots. You need JavaScript enabled to view it. > wrote:
HEAT AS AN INERTIAL FORCE: A QUANTUM EQUIVALENCE PRINCIPLE
Karun Thanjavur1 and Werner Israel1
Ver 1, 14 Jan 2016
ABSTRACT
The firewall was introduced into black hole evaporation scenarios as a hypothetical device designed to break entanglements and preserve unitarity (Almheiri et al., 2013). Here we show that the firewall actually exists and does break entanglements, but only in the context of a virtual reality for observers stationed near the horizon, who are following the long-term evolution of the hole. These observers are heated by acceleration radiation at the Unruh temperature and see pair creation at the horizon as a high-energy phenomenon. The objective reality is very different. We argue that Hawking pair creation is entirely a low-energy process in which entanglements never arise. The Hawking particles materialize as low-energy excitations with typical wavelength considerably larger than the black hole radius. They thus emerge into a very non-uniform environment inimical to entanglement-formation.
Subject headings: Black holes: evaporation — firewall — Unruh temperature
When quantum effects come into play, matters become more interesting. Forty years ago, Unruh showed that a particle detector accelerating in vacuum reacts just as if it were at rest but in contact with a thermal bath at a temperature proportional to its acceleration (Unruh, 1976). The bath is fictitious, but it provides an internally consistent description of physics in the detector’s rest- frame if we choose to ignore its acceleration.
All this becomes relevant to Hawking evaporation when we recall that our conception of pair creation by black holes and the resulting entanglements leans quite heavily on a simple mental picture. Two entangled excitations of very high energy emerge at or near the horizon. One falls into the hole; the other escapes and gets red- shifted to become a Hawking particle with typical energy on the order of the Hawking temperature.
But the formal theory lends no direct support to this simple picture. Hawking’s original derivation (Hawking, 1975) was based on an asymptotic S-matrix approach. Evaluations of the stress-energy tensor in the Unruh state show that expectation values are everywhere finite, with no sign of high energy at the horizon (Fabbri & Navarro-Salas, 2005).
Seemingly at odds with this is the fact that a particle detector stationed near the horizon becomes highly excited (Fabbri & Navarro-Salas, 2005). But this detector is statically supported against gravity and therefore strongly accelerated. Its response is due entirely to the Unruh effect (Unruh, 1976). We have no reason to think that any of it stems from the black hole, and have no evidence for a high-energy origin of the Hawking particles.
1 Department of Physics & Astronomy, University of Victoria, Victoria, BC, V8P 1A1, Canada;
These intrusive heating effects of acceleration are the price one pays if one is studying physics near the horizon from a stationary platform. But they are unavoidable if we want to follow black hole evaporation over a long stretch of time. They are inertial effects in the same sense as the inertial forces of classical mechanics, and must be taken into account for an internally consistent description of the static observer’s experience. They are an inseparable part of his virtual reality.
Hawking excitations emerging from the horizon in this virtual narrative are at once enveloped in a bath of acceleration radiation (the firewall, located on a sphere at the radius of the observer) and heated to relativistic energies. They become in fact the excitations of our simple mental picture. And the firewall, acting over timescales comparable to the evaporation time, will sever any entanglement that might exist between outgoing partners of early and late pair-creation events. (We recall that this was the crux of the AMPS bigamous entanglement paradox (Almheiri et al., (2013), henceforth AMPS13).
This narrative, although quite divorced from reality, is internally self-consistent, and correctly predicts observable effects – in particular, that bigamous entanglements never occur.
But clearly this is not the way it actually happens. The firewall is only a fiction, an artefact of the static observer’s virtual reality.
In the real, low-energy scenario we are advocating here, the partners of a pair-creation event materialize with wavelengths substantially larger than the size of the hole, i.e., into very nonuniform surroundings. Entanglements will easily form only if the environment allows easy exchange of the partners’ positions, which is not the case here. It seems plausible that no entanglements will arise in the first place.
Thus the AMPS13 bigamous entanglement paradox is resolved in both the real and virtual scenarios, though in completely different ways. However, it must be emphasized that the virtual scenario may be fictitious, but it is very far from being superfluous and useless. Because it is an elegantly clean and consistent scenario, its predictive power is very much greater. For instance, it
arXiv:1601.04319v1 [gr-qc] 17 Jan 2016
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& Israel
makes the correct observable prediction that the Hawking spectrum is thermal. This is completely lost in the fuzzy picture of the real scenario seen by a free-falling observer. Therefore we go as far as to claim that the quantum equivalence principle (QEP) is not just a magnificent cultural ornament, but is directly applicable and useful to science.
Our argument can be strengthened to provide a proof that information cannot be lost in black hole evaporation. In the static observer’s virtual reality, information falling toward the hole is intercepted by the Unruh firewall and reradiated to the outside. None of it enters the hole in this scenario, and none is lost. QEP then guarantees that information is ultimately preserved also in the real scenario, though in a much more complicated way.
QEP bears a superficial resemblance to BH Complementarity (Susskind, 2008), long championed by Leonard Susskind. Both contrast the experiences of static and free-falling observers near the BH. However, QEP asserts that the static experience is not complementary in the sense of Bohr, but completely different and fictitious (“virtual reality”). And it exposes and emphasizes the key role of Unruh heating in the contrast. But in their operational philosophy, the two approaches have much in common.
To conclude on a speculative note: Einstein’s equivalence principle served as a bridge between Newtonian gravity and classical general relativity. Could a thermally extended quantum version, of the sort adumbrated here, play a similar role as passport to a successful quantum theory of gravity? Perhaps. Optimism is tempered by Einstein’s admonition: “A good joke should not be repeated too often”. But that was addressed to Heisenberg, and concerned his quantum uncertainty principle.
ACKNOWLEDGEMENT
One of us (W.I.) has enjoyed the support of the Cana- dian Institute for Advanced Research for thirty years. He is indebted to colleagues in the CIFAR Cosmology and Gravity Program, in particular Bill Unruh and Frans Pretorius, for many stimulating interactions.
A. Almheiri, D. Marolf, J. Polchinski, & J. Sully, High Energy Phys., 02,062.
A. Fabbri & J. Navarro-Salas Modeling Black Hole Evaporation, Imperial College Press, London (2005)
S. W. Hawking Commun. Math. Phys.,43, 199.
L. Susskind The Black Hole War, pp254-6. Back Bay Books,
(2008)
W. G. Unruh Phys. Rev. D,14, 870.