Abstract
We show that a generalized version of the holographic principle can be derived from the Hamiltonian description of information flow within a quantum system that maintains a separable state. We then show that this generalized holographic principle entails a general principle of gauge invariance. When this is realized in an ambient Lorentzian space-time, gauge invariance under the Poincaré group is immediately achieved. We apply this pathway to retrieve the action of gravity. The latter is cast à la Wilczek through a similar formulation derived by MacDowell and Mansouri, which involves the representation theory of the Lie groups SO(3,2) and SO(4,1).
Highlights
Almost one hundred years of attempts to quantize gravity suggest that physical perspective may be responsible for this failure (Garay, 1995)
We focus on a specific alternative approach: we show that when the holographic principle is reformulated from a semi-classical to a fully general, quantum-theoretic principle, gravity emerges as a gauge theory along the lines of the gauge formulation of gravity, as proposed by Wilczek (1998)
This relation can be made explicit by stating: Generalized Holographic Principle (GHP): Given any finite-dimensional quantum system S AB meeting the conditions of Theorem 1, the thermodynamic entropies of A and B over a coarse-grained time, over which A and B only interact through Eq 2.4, are S(B) S(A) N bits, where N is the number of operators in the representation (2.4) of HAB
Summary
Almost one hundred years of attempts to quantize gravity suggest that physical perspective may be responsible for this failure (Garay, 1995). The gauge principle has purely quantum-theoretic roots and characterizes all finite systems in separable states This is a formulation similar to a previous one envisaged by MacDowell and Mansouri, which involves the representation theory of the Lie group SO(4, 1), but without explicit symmetry breaking.
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