On Gravity and the Uncertainty Principle

TL;DR

This paper derives a gravitationally modified uncertainty principle, showing that gravity imposes a fundamental limit on particle position uncertainty, consistent with superstring theory, using basic gravitational theories.

Contribution

It provides a simple, general derivation of the gravitational uncertainty principle without relying on complex string theory frameworks.

Findings

Establishes a minimum position uncertainty of the order of the Planck length.

Shows gravitational effects modify the standard quantum uncertainty principle.

Connects classical gravitational theories with quantum uncertainty concepts.

Abstract

Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of the photon and the particle being observed modifies the uncertainty principle with an additional term. From the modified or gravitational uncertainty principle it follows that there is an absolute minimum uncertainty in the position of any particle, of order of the Planck length. A modified uncertainty relation of this form is a standard result of superstring theory, but the derivation given here is based on simpler and rather general considerations with either Newtonian gravitational theory or general relativity theory.