Background Independent Quantum Mechanics, Gravity, and Physics at Short Distance: Some Insights

TL;DR

This paper explores a background independent quantum framework, linking quantum state space metrics to Compton wavelength, and discusses implications for gravity and physics at very short distances.

Contribution

It introduces a novel background independent approach to quantum mechanics, expressing the quantum state space metric in terms of the Compton wavelength and analyzing short-distance constraints.

Findings

Quantum state space metric expressed via Compton wavelength.

Insights into neighborhood notions in quantum evolution.

Constraints on minimal distances in quantum limits.

Abstract

In the present discussion Background Independent framework of Quantum Mechanics and its possible implications in the studies of gravity and Physics at short distance are addressed. The expression of the metric of quantum state space $g_{\mu\nu}$ which is intrinsically a quantized quantity, is identified in terms of Compton wavelength as: $[<\partial_\mu\psi\mid\partial_\nu\psi> - <\partial_\mu\psi\mid\psi> <\psi\mid\partial_\nu\psi>] = 1 / \lambdabar_C^2 (=m_0^2c^2 / \hbar^2})$. The discussion also sheds light on the notion of neighborhood in quantum evolution, and various constraints on the possibilities of smallness of distance in the quantum mechanical limits.