A simple gravitational self-decoherence model

TL;DR

The paper introduces a gravitational self-decoherence mechanism that invokes a Heisenberg cut at $M_C \sim M_P$ to separate quantum and classical behavior, positing a gravitational interaction between a particle and a nonphysical virtual clone with a cutoff length $L_C$ that models information transfer to spacetime degrees of freedom. Decoherence is shown to be negligible for $m \ll M_C$ but significant as $m$ approaches the cut, quantified by a purity measure $\eta(t)$ and, in Stern-Gerlach scenarios, by a spin-coherence measure $\xi(t)$; the two-body evolution plus tracing over the clone yields observable mass-dependent deviations from standard QM. The authors connect their model to current experimental capabilities and propose a double Stern-Gerlach-like experiment as a concrete test to distinguish their predictions from QM and Schrödinger-Newton-type models. Overall, the framework provides a falsifiable route to explain the quantum-to-classical transition via gravitational degrees of freedom at the Planck scale, with limited (and fixed) parameter freedom around $M_C \sim M_P$.

Abstract

One of the most significant debates of our time is whether our macroscopic world (i) naturally emerges from quantum mechanics or (ii) requires new physics. We argue for the latter and propose a simple gravitational self-decoherence mechanism. For this purpose, we postulate the existence of a Heisenberg cut such that particles with masses $m$ much smaller and larger than a critical mass $M_{\rm C}$ (of the order of the Planck mass $M_{\rm P}$) would be necessarily treated according to quantum and classical rules, respectively. Our effective model is designed to capture the new physics that free quantum particles would experience as their masses approach $M_{\rm C}$. The purity loss for free quantum particles is evaluated and shown to be highly inefficient for quantum particles with $m \ll M_{\rm C}$ but very effective for those with $m \sim M_{\rm C}$. The physical picture behind it is that coherence would (easily) leak from heavy enough particles to (non-observable) spacetime quantum degrees of freedom. Finally, we contextualize our proposal with state-of-the-art experiments and show how it can be tested in a future Stern-Gerlach-like experiment.

Figures (15)

• Figure 1: The black strip at $L < L_\text{P} \sim 10^{- 35}~m$ veils new physics necessary to probe proper distances smaller than the Planck length $L_\text{P}$, where the spacetime would be described by some (still unknown) quantum spacetime theory (QST). This would jeopardize the existence (or at least, description) of classical particles with lengths $l \ll L_\text{P}$ and quantum particles with wavelengths $\lambdabar \ll L_\text{P}$. In our model, particles with masses much smaller, $m \ll M_\text{P}$, and larger, $m \gg M_\text{P}$, than the Planck mass, $M_\text{P} \sim 10^{- 5}~g$, would necessarily be governed by QM and CM, respectively. The vertical black strip indicates the corresponding Heisenberg cut. Particles with masses $m \sim M_\text{P}$ would require new physics to be described. According to our model, quantum particles, $m \lesssim M_\text{P}$, would experience a significant gravitational self-decoherence as their masses approach the Heisenberg cut, $m \to M_\text{P}$.
• Figure 2: Region II is the allowed parameter subspace. The dark region was excluded since it belongs to the realm of the QST (dark region in Fig. \ref{['fig_manifesto']}). The region below the dashed line ($\sigma / \lambdabar < 1 / 2$) must also be removed because it does not obey the minimum possible value for $\sigma$ according to the Heisenberg uncertainty principle. Finally, region I must be dismissed because it does not satisfy $K / |U| \ll 1$ at $t = 0$. (This plot adopts $L_\text{C} = L_\text{P}$.)
• Figure 3: The time evolution of $\eta(t)$ for a particle with mass $m = M_\text{C} / 2$ ($\lambdabar = 2 L_\text{C}$) is exhibited for $\sigma = 30 \; \sigma_\text{ref}$ (full line) and $\sigma = 60 \; \sigma_\text{ref}$ (dashed line), assuming $L_\text{C} = L_\text{P}$ ($M_\text{C} = M_\text{P}$).
• Figure 4: The purity $\eta(t_\text{ref})$ is exhibited as a function of $\sigma / \lambdabar$ for $m = M_\text{C} / 2$ ($\lambdabar = 2 L_\text{C}$, full line) and $m = M_\text{C}$ ($\lambdabar = L_\text{C}$, dashed line), assuming $L_\text{C} = L_\text{P}$ ($M_\text{C} = M_\text{P}$). The lines have distinct domains to comply with the allowed subspace II in Fig. \ref{['fig_sigma']}. The larger the mass, the larger the decoherence.
• Figure 5: The purity $\eta(t_\text{ref})$ is exhibited as a function of $m / M_\text{C}$ ($= L_\text{C} / \lambdabar$), assuming $L_\text{C} = L_\text{P}$ ($M_\text{C} = M_\text{P}$, solid line) and $L_\text{C} = L_\text{P} / 2$ ($M_\text{C} = 2 M_\text{P}$, dashed line). We note that the larger the mass, the larger the decoherence. Also, larger values of $L_\text{C}$ boost the self-decoherence for the same $m$; e.g, fixing $m = M_\text{P}$, we have $\eta(t_\text{ref}) = 0.90$ for $L_\text{C} = L_\text{P} / 2$ ($M_\text{C} = 2 M_\text{P}$), and $\eta(t_\text{ref}) = 0.84$ for $L_\text{C} = L_\text{P}$ ($M_\text{C} = M_\text{P}$). (We have chosen $\sigma = 30 \; \sigma_\text{ref}$ for every value of $m / M_\text{C}$.)