preprints.org > physical sciences > quantum science and technology > doi: 10.20944/preprints201710.0114.v3

Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 17 October 2017 / Approved: 17 October 2017 / Online: 17 October 2017 (11:27:50 CEST)
Version 2 : Received: 2 November 2017 / Approved: 2 November 2017 / Online: 2 November 2017 (06:52:53 CET)
Version 3 : Received: 28 December 2017 / Approved: 28 December 2017 / Online: 28 December 2017 (07:38:53 CET)
Version 4 : Received: 18 March 2018 / Approved: 19 March 2018 / Online: 19 March 2018 (10:33:12 CET)

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model. We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρ_c0 (ρ_c0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term in the effective action; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. We also generalize the equivalence principle to be valid for all quantum phenomenon.

cosmological constant problem; non-linear sigma model; quantum gravity

Physical Sciences, Quantum Science and Technology

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