Dark Energy from Quantum Uncertainty of Distant Clock

Abstract

The observed cosmic acceleration was attributed to an exotic dark energy in the framework of classical general relativity. The dark energy behaves very similar with vacuum energy in quantum mechanics. However, once the quantum effects are seriously taken into account, it predicts a completely wrong result and leads to a severe fine-tuning. To solve the problem, the exact meaning of time in quantum mechanics is reexamined. We abandon the standard interpretation of time in quantum mechanics that time is just a global parameter, replace it by a quantum dynamical variable playing the role of physical clock. We find that synchronization of two spatially separated clocks can not be precisely realized at quantum level. There is an intrinsic quantum uncertainty of distant clock time, which implies an apparent vacuum energy fluctuation and gives an observed dark energy density $\rho_{de}=\frac{6}{\pi}L_{P}^{-2}L_{H}^{-2}$ at tree level approximation, where $L_{P}$ and $L_{H}$ are the Planck and Hubble scale cutoffs. The fraction of the dark energy is given by $\Omega_{de}=\frac{2}{\pi}$, which does not evolve with the internal clock time. The "dark energy" as a quantum cosmic variance is always seen comparable with the matter energy density by an observer using the internal clock time. The corrected distance-redshift relation of cosmic observations due to the distant clock effect are also discussed, which again gives a redshift independent fraction $\Omega_{de}=\frac{2}{\pi}$. The theory is consistent with current cosmic observations.Comment: 7 pages, no figure; v2:added discussion on distance-redshift relation; v3:improved discussion on distance-redshift relation, an independent calculation to the redshift variance over redshift squared is given, dark energy fraction agrees with 2/pi; v4:typos corrected, updated to the final version published in Journal of High Energy Physics, Volume 2015, Issue