Scientific value of the quantum tests of equivalence principle in light of Hilbert's sixth problem

TL;DR

This paper critically examines the scientific validity of quantum tests of the equivalence principle through the lens of Hilbert's sixth problem, highlighting logical and semantic issues in current experimental approaches.

Contribution

It provides an axiomatic analysis of quantum tests of the equivalence principle, questioning their scientific value and exposing underlying logical assumptions.

Findings

Quantum tests often implicitly assume the equivalence principle.

Using Planck constant in such tests may lead to tautological conclusions.

Highlights semantic and logical obstacles in uniting quantum mechanics and gravity.

Abstract

In his sixth problem, Hilbert called for an axiomatic approach to theoretical physics with an aim to achieve precision and rigour in scientific reasoning, where logic and language (semantics) of physics play the pivotal role. It is from such a point of view, we investigate the scientific value of the modern experiments to perform quantum tests of equivalence principle. Determination of Planck constant involves the use of acceleration due to gravity of the earth $(g)$ that results in the force on a test mass. The equivalence between inertial mass and gravitational mass of a test object is assumed in the process of logically defining $g$ from the relevant hypotheses of physics. Consequently, if Planck constant is used as input in any experiment (or in the associated theory that founds such an experiment) that is designed to test the equivalence between inertial and gravitational mass, then it is equivalent to establish a scientific truth by implicitly assuming it i.e. a tautology. There are several notable examples which plague the frontiers of current scientific research which claim to make quantum test of equivalence principle. We question the scientific value of such experiments from Hilbert's axiomatic point of view. This work adds to the recently reported semantic obstacle in any axiomatic attempt to put "quantum" and "gravity" together, albeit with an experimental tint.