Quantum modified inertia: an application to galaxy rotation curves

TL;DR

This paper introduces a quantum-inspired modified inertia model incorporating acceleration bounds, successfully explaining galaxy rotation curves and reducing dark matter needs while aligning with various astrophysical observations.

Contribution

It develops a novel framework linking quantum acceleration bounds with relativistic inertia, applied to galactic dynamics, offering new insights into galaxy rotation and dark matter reduction.

Findings

Accurately models galaxy rotation curves including Milky Way and DDO 52.

Recovers the Tully-Fisher relation between baryonic mass and velocity.

Predicts a minimal acceleration scale consistent with Solar System constraints.

Abstract

This work explores modified inertia in the context of galactic dynamics by investigating the consequences of introducing quantum-motivated bounds on acceleration. Building on earlier ideas related to maximal acceleration and quantum speed limits, an effective framework is developed in which both upper and lower acceleration bounds are incorporated within special relativity through a correspondence between the proper time of an accelerated object and the quantum speed limit. The resulting modified inertia model is applied to galaxy rotation curves, taking into account the baryonic contributions from stellar disks, gas, and bulges. An analytic expression for the radial acceleration relation is derived within this framework. When confronted with observations, the model provides a good description of several galactic systems, including the Milky Way and the dwarf galaxy DDO 52. It also successfully recovers the Tully-Fisher relation linking the baryonic mass and the terminal speed, with $\mathrm{log}(M) = 4 \, \mathrm{log}(v) + 2.62$. A characteristic minimal acceleration of order $1.8 \times 10^{-11}$ m s$^{-2}$ naturally emerges from the analysis and proves effective in reproducing a wide range of rotation curves. The resulting radial acceleration relation is consistent with Solar System constraints, including the Cassini quadrupole bound, and remains compatible with recent observational results on dwarf spheroidals and ultra-wide binaries. Within this effective description, the presence of a lower acceleration bound significantly reduces the amount of dark matter required to account for galactic rotation curves. Possible implications for the redshift evolution of this minimal acceleration, and for galaxy formation and evolution, are briefly discussed.