MOND from Second-Order Moment Modified Acceleration and Quantum Equivalence Principle

Abstract

This paper proposes a novel non-inertial quantum effect wherein particle spectra show second-order moment extra Gaussian broadening due to local short-time (non-uniform) acceleration, as well as in a deSitter spacetime background. Although the effect is too small to be detected, it provides a mechanism for the cosmological constant to enter the local kinematics of particles in the form of acceleration. The acceleration composition relation of a proper motion acceleration and the cosmological constant playing the role of a background acceleration, which is required in the Modified Newtonian Dynamics (MOND). The origin of acceleration discrepancies lies in the importance of the intrinsic second moment quantum fluctuations in the deSitter background, so that the mean value of derivative (modified effective acceleration) does not equal to the derivative of mean value (the first moment acceleration given by the unmodified Newtonian gravity). Such an interpretation of MOND as a second moment effect necessitates a quantum equivalence principle as its physical foundation, that is, extending the classical equivalence at the level of mean values (first-order moments) to the quantum equivalence at the level of second moment quantum fluctuations. The effective distance quadratic form, effective curvature and effective acceleration, etc., modified by the universal second moments all behave as if they were real geometrical or physical quantities. This effect also offers a unified framework for understanding the accelerated expansion of the universe and the anomalies in galactic rotation curves or radial acceleration.

15 pages, no figure