A discrete, unitary, causal theory of quantum gravity

Abstract

A discrete model of Lorentzian quantum gravity is proposed. The theory is completely background free, containing no reference to absolute space, time, or simultaneity. The states at one slice of time are networks in which each vertex is labelled with two arrows, which point along an adjacent edge, or to the vertex itself. The dynamics is specified by a set of unitary replacement rules, which causally propagate the local degrees of freedom. The inner product between any two states is given by a sum over histories. Assuming it converges (or can be Abel resummed), this inner product is proven to be hermitian and fully gauge-degenerate under spacetime diffeomorphisms. At least for states with a finite past, the inner product is also positive. This allows a Hilbert space of physical states to be constructed.

38 pages, 9 figures, v3 added to exposition and references, v4 expanded prospects section

References in corpus (9)

• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind
• Unitarity and Holography in Gravitational Physics
• Lorentz violation and perpetual motion
• Discreteness without symmetry breaking: a theorem
• Lorentz covariance of loop quantum gravity
• The emergence of a universal limiting speed
• Holographic Thought Experiments
• A Kirchhoff-like conservation law in Regge calculus

Cited by in corpus (4)

• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Emergence of the Circle in a Statistical Model of Random Cubic Graphs
• Spin foam models as energetic causal sets
• Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes