A comparison between models of gravity induced decoherence

TL;DR

This paper compares two models of gravity-induced decoherence, analyzing their assumptions, methods, and noise correlations, and finds that they can be related under certain conditions but require additional criteria for precise predictions.

Contribution

It provides a detailed comparison of the D-model and K-model of gravitational decoherence, clarifying their differences and similarities, especially regarding noise correlation and decoherence calculations.

Findings

Minimal spacetime bounds can be derived from each other under certain conditions

Decoherence time calculation methods are equivalent in both models

K-model exhibits non-white, non-Markovian noise correlation

Abstract

It has been suggested in the literature that spatial coherence of the wave function can be dynamically suppressed by fluctuations in the spacetime geometry. These fluctuations represent the minimal uncertainty that is present when one probes spacetime geometry with a quantum probe. Two similar models have been proposed, one by Di\'osi [D-model] and one by Karolyhazy and collaborators [K-model], based on apparently unrelated minimal spacetime bounds. The two models arrive at somewhat different expressions for the dependence of the localization coherence length on the mass and size of the quantum object. In the present article we compare and contrast the two models from three aspects: (i) comparison of the spacetime bounds, (ii) method of calculating decoherence time, (iii) comparison of noise correlation. We show that under certain conditions the minimal spacetime bounds in the two models can be derived one from the other. We argue that the methods of calculating the decoherence time are equivalent. We re-derive the two-point correlation for the fluctuation potential in the K-model, and confirm the earlier result of Di\'osi and Luk\'acs that it is non-white noise, unlike in the D-model, where the corresponding correlation is white noise in time. This seems to be the origin of the different results in the two models. We derive the non-Markovian master equation for the K-model. We argue that the minimal spacetime bound cannot predict the noise correlation uniquely, and additional criteria are necessary to accurately determine the effects of gravitationally induced decoherence.