Modified inertia from extended uncertainty principle(s) and its relation to MoND

Giuseppe Gaetano Luciano,Jaume Giné

doi:10.1140/epjc/s10052-020-08636-x

Abstract

In this paper we show that Modified Inertia, i.e., the modification of inertia predicted by some alternative theories of gravity at cosmic scales, can be naturally derived within the framework of the extended uncertainty principle (EUP). Specifically, we consider two possible extensions of the Heisenberg uncertainty principle (HUP), corresponding to two different deformations of the fundamental commutator: the first one provides the natural generalization of the HUP to the (anti)-de Sitter spacetime and is endowed with only a quadratic correction in the uncertainty position. On the other hand, the second model contains both linear and quadratic extra terms. We prove that modified inertia is a direct consequence of the minimal acceleration experienced by any body due to the cosmic expansion. The obtained results are then discussed in connection with the empirical predictions of Modified Newtonian dynamics (MoND). The requirement of consistency between the two approaches allows us to fix the adjustable constant which marks the transition between the Newtonian and deep-MoND regimes.

Highlights

Negligible when dealing with gravitational phenomena, gravity becomes inconsequential in the quantum realm
In this paper we show that Modified Inertia, i.e., the modification of inertia predicted by some alternative theories of gravity at cosmic scales, can be naturally derived within the framework of the extended uncertainty principle (EUP)
This has been achieved through the prediction of the Hawking [1] and Unruh [2] effects, which emerge from the information loss associated to the appearance of event horizons – the black-hole horizon in the former case, the Rindler horizon in the latter. These two effects are widely accepted, but concerns about their detectability are still being expressed [3,4]. Another fertile arena to explore the interplay between quantum and gravity features is provided by the Generalized Uncertainty Principle (GUP), which accounts for the existence of a minimal length at Planck scale through a suitable modification of the Heisenberg uncertainty principle (HUP) [5,6,7,8,9,10,11]

Summary

Introduction

Among the various attempts to incorporate gravity in the quantum world, the quantum field theory in curved space has yielded great development in recent years This has been achieved through the prediction of the Hawking [1] and Unruh [2] effects, which emerge from the information loss associated to the appearance of event horizons – the black-hole horizon in the former case, the Rindler ( i.e., uniformly accelerated) horizon in the latter. Starting from the outlined picture, in this paper we provide a novel perspective on the phenomenon (1), showing that it arises from the accelerated expansion of the Universe In this sense, it can be naturally derived within the framework of the Extended Uncertainty Principle in de Sitter spacetime, where the correction to the standard inertia is found to be related to the background cosmic acceleration and, to the cosmological constant value.

Quantized inertia from HUP

Case I

Case II

Summary and conclusions