Interactions and the Consistency of Black Hole Complementarity

Abstract

Presentations of black hole complementarity by van Dongen and de Haro, as well as by 't Hooft, suffer from a mistaken claim that interactions between matter falling into a black hole and the emitted Hawking-like radiation should lead to a failure of commutativity between space-like-related observables localized inside and outside the black hole. I show that this conclusion is not supported by our standard understanding of quantum interactions. We have no reason to believe that near-horizon interactions will threaten microcausality. If these interactions reliably transfer information to the outgoing radiation, then this response to Hawking's information loss argument should amount to a version of the bleaching scenario. I argue that the challenge facing black hole complementarity is that of reconciling this commitment to bleaching with the expectation that the event horizon will be locally unremarkable. This challenge is most promisingly met by proposals that postulate a consistent account of the limitations of our local semi-classical theories, but no support is added to these postulates by appeals to verificationism or to the interactions considered by 't Hooft.

Acknowledgements

I would like to thank two anonymous referees of International Studies in the Philosophy of Science for helpful comments and suggestions.

Notes

Hawking has since abandoned this position (Hawking 2005); however, discussion of this shift lies beyond the scope of this paper.

I believe that van Dongen and de Haro misrepresent BHC in this respect when they claim, ‘Black hole complementarity purports that [the outside observer] finds that in-falling matter gets scrambled and remains hovering outside the horizon until the black hole system has radiated away all its energy. . . . [A] membrane forms outside the horizon which retains the microscopic information that fell into the black hole’ (van Dongen and de Haro 2004, 513). This seems to imply a remnant scenario; advocates of BHC instead claim that the ‘infalling matter’ (i.e. the matter's mass-energy, charges, and ‘information’) will be returned in the Hawking-like radiation emitted by the heated membrane at the stretched horizon.

Of course, these considerations are defeasible, and it may well be that quantum gravitational processes (such as Hawking radiation) involve violations of microcausality over astronomical distances. Investigations into the behaviour of superstrings in black hole space-times (Lowe et al. 1995) suggest such large-scale failures of microcausality.

At some points it seems that van Dongen and de Haro might be cautious about endorsing 't Hooft's position, e.g. ‘horizon interactions that have—purportedly—been overlooked in Hawking's analysis’ (van Dongen and de Haro 2004, 516). However, in the overall thesis of their paper, this line of argument is asked to do a substantial amount of work (as we shall see below).

Of course, one's interpretive preferences might influence how one wishes to respond to the information loss paradox. For example, if one were attracted to a spontaneous collapse solution to the measurement problem, one might be unconcerned about the non-unitary evolution of black holes (Penrose presumably falls in this category). Alternatively, if one gives up on locality to save unitary evolution, one might then be attracted to a hidden variable interpretation such as Bohm's with its hitherto distasteful non-locality. On this point, it is worth mentioning in passing that 't Hooft has more recently (1999) suggested that considerations of black hole evolution give us reason to expect that a deterministic hidden variable theory underlies quantum theorem. 't Hooft believes that this theory would be local, despite the obvious conflict with Bell's theorem; however, if one accepts that locality must be sacrificed in a hidden variable theory then 't Hooft's reasons for advocating a hidden-variable theory might push us towards a Bohmian interpretation. A careful discussion of this aspect of 't Hooft's account is, however, beyond the scope of the present paper.

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Notes on contributors

Peter Bokulich

Peter Bokulich is at the Department of Philosophy, Boston University.