Abstract
A procedure to derive a unitary evolution law for a quantised black hole has been proposed by the author. The proposal requires that one starts off with the entire Penrose diagram for the eternal black hole as the background metric, after which one has to invoke the antipodal identification in order to see how the two asymptotic domains of this metric both refer to the same outside world. In this paper, we focus on the need to include time reversal in applying this identification. This forces us to postulate the existence of an ‘anti-vacuum’ state in our world, which is the state where energy density reaches a maximal value. We find that this squares well with the deterministic interpretation of quantum mechanics, according to which quantum Hilbert space is to be regarded as the ‘vector representation’ of a real world. One has to understand how to deal with gravity in such considerations. The non-perturbative component of the gravitational force seems to involve cut-and-paste procedures as dynamical features of space and time, of which the re-arrangement of space-time into two connected domains in the Penrose diagram is a primary example. Thus, we attempt to obtain new insights in the nature of particle interactions at the Planck scale, as well as quantum mechanics itself.
Highlights
There is general agreement that a theoretical study of black holes in a regime where quantum mechanical effects play a role is important for a more complete understanding of General Relativity and/or some modifications of this theme, in its relation to quantum mechanics
How do we introduce quantum mechanics in a black hole? According to one doctrine, when subject to quantum mechanics, even large black holes exhibit problems with information loss [1,2,3,4,5] and firewalls, Ref. [6] that can only be understood if one invokes superstring theory and/or AdS/CFT
Quantum mechanical effects would be limited to the effects of Hawking particles, which have low energies, and as such have very limited effects on the global space-time structure, at least when regarded over limited stretches of time
Summary
There is general agreement that a theoretical study of black holes in a regime where quantum mechanical effects play a role is important for a more complete understanding of General Relativity and/or some modifications of this theme, in its relation to quantum mechanics. The emergence of superimposed states, where the early implosions and the late explosions occur at superimposed moments in time, causes superpositions in what we intended to use as our background metric, and this explains why we avoid the use of a background metric that includes the effects of such events, replacing it by the metric of an eternal black hole. This formalism will get its a posteriori justification later. Technical aspects of our calculations are to be found in the references, but these overlap a lot; much of what we need will be summarised in this paper
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