Covariant Macroscopic Quantum Geometry

Details Covariant Macroscopic Quantum Geometry Covariant Macroscopic Quantum Geometry

2012-04-25

arxiv.org/abs/1204.5948v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages, LaTeX

Scientific paper

A covariant noncommutative algebra of position operators is presented, and interpreted as the macroscopic limit of a geometry that describes a collective quantum behavior of the positions of massive bodies in a flat emergent space-time. The commutator defines a quantum-geometrical relationship between world lines that depends on their separation and relative velocity, but on no other property of the bodies, and leads to a transverse uncertainty of the geometrical wave function that increases with separation. The number of geometrical degrees of freedom in a space-time volume scales holographically, as the surface area in Planck units. Ongoing branching of the wave function causes fluctuations in transverse position, shared coherently among bodies with similar trajectories. The theory can be tested using appropriately configured Michelson interferometers.

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