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arXiv:2305.04780

Probing gravity-related decoherence with a 16 $μ$g Schrödinger cat state

Matteo Fadel

Published May 8, 2023• 1 citation
arXivHTMLPDF

Abstract

The Schrödinger equation predicts the validity of the superposition principle at any scale, yet we do not experience cats being in a superposition of "dead" and "alive" in our everyday lives. Modifications to quantum theory at the fundamental level may be responsible for the objective collapse of the wave function above a critical mass, thereby breaking down the superposition principle and restoring classical behavior at the macroscopic scale. One possibility is that these modifications are related to gravity, as described by the Diósi-Penrose wavefunction collapse model. Here, we investigate this model using experimental measurements on the decoherence of a Schrödinger cat state of a mechanical resonator with an effective mass of 16 micrograms.

DOI
10.48550/arxiv.2305.04780

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Probing gravity-related decoherence with a 16 μμμg Schrödinger cat state
The Schrödinger equation predicts the validity of the superposition principle at any scale, yet we do not experience cats being in a superposition of "dead" and "alive" in our everyday lives. Modifications to quantum theory at the fundamental level may be responsible for the objective collapse of the wave function above a critical mass, thereby breaking down the superposition principle and restoring classical behavior at the macroscopic scale. One possibility is that these modifications are related to gravity, as described by the Diósi-Penrose wavefunction collapse model. Here, we investigate this model using experimental measurements on the decoherence of a Schrödinger cat state of a mechanical resonator with an effective mass of 16 micrograms.
Abstract The possibility that gravity plays a role in the collapse of the quantum wave function has been considered in the literature, and it is of relevance not only because it would provide a solution to the measurement problem in quantum theory, but also because it would give a new and unexpected twist to the search for a unified theory of quantum and gravitational phenomena, possibly overcoming the current impasse. The Diósi–Penrose model is the most popular incarnation of this idea. It predicts a progressive breakdown of quantum superpositions when the mass of the system increases; as such, it is susceptible to experimental verification. Current experiments set a lower bound R 0 ≳ 4 Å for the free parameter of the model, excluding some versions of it. In this work we search for an upper bound, coming from the request that the collapse is effective enough to guarantee classicality at the macroscopic scale: we find out that not all macroscopic systems collapse effectively. If one relaxes this request, a reasonable (although to some degree arbitrary) bound is found to be: R 0 ≲ 10 6 Å. This will serve to better direct future experiments to further test the model.
According to quantum mechanics, a physical system can be in any linear superposition of its possible states. Although the validity of this principle is routinely validated for microscopic systems, it is still unclear why we do not observe macroscopic objects to be in superpositions of states that can be distinguished by some classical property. Here we demonstrate the preparation of a mechanical resonator in Schrödinger cat states of motion, where the ∼10 17 constituent atoms are in a superposition of two opposite-phase oscillations. We control the size and phase of the superpositions and investigate their decoherence dynamics. Our results offer the possibility of exploring the boundary between the quantum and classical worlds and may find applications in continuous-variable quantum information processing and metrology with mechanical resonators.
Physical systems to exist in multiple states simultaneously. While standard quantumtheory permits superposition to persist indefinitely in the absence of mea-surement or environmental decoherence, this work proposes that superpositionstates possess an intrinsic temporal constraint. We argue that quantum super-position cannot remain stable forever and that every superposed system ischaracterized by a finite lifetime, beyond which the superposition inevitablybreaks down and the wave function collapses into a single definite state. Thisproposed time-limited superposition introduces an objective mechanism for wave-function collapse that does not rely on observation or classical interaction.Conceptual arguments, mathematical considerations, and potential experimentalimplications are discussed, including connections to macroscopic quantum lim-its, decoherence timescales, and fundamental temporal structure. If validated,this framework would offer a new perspective on the measurement problem andsuggest that time itself plays an active role in determining quantum outcomes.This perspective is conceptually related to objective collapse models such as theGhirardi–Rimini–Weber (GRW) theory and Penrose’s gravitationally inducedcollapse, while differing in that the collapse mechanism proposed here arisesfrom an intrinsic temporal instability of superposition rather than stochastic orgravity-driven effects.
The Schrödinger cat paradox is often presented as evidence that quantum mechanics fundamentally conflicts with macroscopic reality. This short conceptual paper proposes a resolution based on the TUO–NS (Theory of the Universe as an Operator – Navier–Stokes–like) framework. In this approach, physical states are interpreted as elastic deformations of a coercive vacuum field. The linear superposition principle is shown to be an effective property, valid only in the regime of small, linearized perturbations around a stable background configuration: L[δψ1+δψ2]≈L[δψ1]+L[δψ2]\mathcal{L}[\delta\psi_1 + \delta\psi_2] \approx \mathcal{L}[\delta\psi_1] + \mathcal{L}[\delta\psi_2]L[δψ1​+δψ2​]≈L[δψ1​]+L[δψ2​] At macroscopic scales, the vacuum energy functional E[Ψ]\mathcal{E}[\Psi]E[Ψ] is coercive and admits only isolated local minima. Superpositions of distinct macroscopic configurations correspond to energetically unstable states: E[Ψdead+Ψalive]≫E[Ψdead]+E[Ψalive]\mathcal{E}[\Psi_{dead} + \Psi_{alive}] \gg \mathcal{E}[\Psi_{dead}] + \mathcal{E}[\Psi_{alive}]E[Ψdead​+Ψalive​]≫E[Ψdead​]+E[Ψalive​] These states relax dynamically toward one of the admissible minima. The apparent “collapse of the wave function” is thus reinterpreted as a physical relaxation process, rather than an observer-dependent or probabilistic axiom. This framework provides a physically grounded explanation for the absence of macroscopic superpositions, without invoking external observers, measurement postulates, or modifications of quantum dynamics. This document is intended as a conceptual clarification complementary to the main TUO–NS technical papers, rather than as a replacement for standard quantum mechanics.
For nearly 100 years, the paradox of Schrödinger's Cat has remained unresolved. Why does the world we live in appear classical despite being composed of quantum particles governed by the Schrödinger wave equation? Lajos Diósi and Roger Penrose propose the wavefunction collapses because it describes two incompatible space-times, demonstrating an inconsistency between quantum mechanics and general relativity. To avoid this paradox, collapse must occur within Heisenberg's time-energy uncertainty limit. Subatomic particles with low mass, and correspondingly low energy, collapse in years, while superposed cats would collapse almost instantaneously. We propose a table-top experiment to put two small mirrors into superposition and observe them collapse in a time consistent with the Diósi-Penrose model. We employ two techniques to perform this experiment in ambient laboratory conditions. Most experiments separate a small mass by a large distance. In contrast, we displace a large mass by a small distance where the self-energy follows an inverse square law with correspondingly high collapse times. We further use a symmetrical apparatus, where a break in symmetry indicates collapse independent of decoherence.
We propose that gravitational-wave distinguishability provides a universal, information-theoretic mechanism for decoherence in quantum superpositions involving massive systems. When alternative quantum histories imprint distinguishable gravitational radiation states into spacetime, which-branch information exists in principle even in the absence of measurement. This suppresses interference purely through unitary entanglement with the gravitational field. Unlike collapse models, this framework relies only on standard quantum mechanics and the information-carrying capacity of gravitational radiation. We argue heuristically that the Planck mass emerges as an information-theoretic crossover scale beyond which gravitationally induced decoherence becomes unavoidable. To clarify the conceptual content, we introduce a Schrödinger’s-cat–type thought experiment in which one branch of a quantum superposition produces colliding black holes and gravitational waves, while the other does not. In this limit case, spacetime itself functions as an irreversible which-branch environment. The analysis positions gravity not as a modifier of quantum mechanics, but as a universal information channel contributing to the quantum–classical transition.