Flavour-Oscillation Clocks and the Geometricity of General Relativity

TL;DR

This paper critically examines flavour-oscillation clocks and argues that their behavior does not challenge the geometric foundation of general relativity, clarifying misconceptions about gravitational potentials and clock behavior.

Contribution

The paper refutes two claims that flavour-oscillation clocks threaten GR's geometric nature, showing these claims are based on misinterpretations and are consistent with GR.

Findings

Flavour-oscillation clocks do not threaten the geometricity of GR.

The behavior of these clocks can be explained by the violation of the clock hypothesis.

Detection of constant gravitational potentials by such clocks does not imply GR's incompleteness.

Abstract

I look at the 'flavour-oscillation clocks' proposed by D.V. Ahluwalia, and two arguments of his suggesting that such clocks might behave in a way that threatens the geometricity of general relativity (GR). The first argument states that the behaviour of these clocks in the vicinity of a rotating gravitational source implies a non-geometric element of gravity. I argue that the phenomenon is best seen as an instance of violation of the 'clock hypothesis', and therefore does not threaten the geometrical nature of gravitation. Ahluwalia's second argument, for the 'incompleteness' of general relativity, involves the idea that flavour-oscillation clocks can detect constant gravitational potentials. I argue that the purported 'incompleteness-establishing' result is in fact one that applies to all clocks. It is entirely derivable from GR, does not result in the observability of the potential, and is not at odds with any of GR's foundations.