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arXiv:2108.08438 · Physics Letters B

Testing the equivalence principle and discreteness of spacetime through the t3 gravitational phase with quantum information technology

Fabrizio Tamburini, Ignazio Francesco Licata

Published Sep 18, 2020• 3 citations

Abstract

We propose a new thought experiment, based on present-day Quantum Information Technologies, to measure quantum gravitational effects through the Bose-Marletto-Vedral (BMV) effect [1], [2], [3], [4] by revealing the gravitational t3 phase term, its expected relationships with low-energy quantum gravity phenomena and test the equivalence principle of general relativity. The technique here proposed promise to reveal gravitational field fluctuations from the analysis of the stochastic noise associated to an ideal output of a measurement process of a quantum system. To improve the sensitivity we propose to cumulate the effects of the gravitational field fluctuations in time on the outputs of a series of independent measurements acted on entangled states of particles, like in the building of a quantum cryptographic key, and extract from the associated time series the effect of the expected gravitational field fluctuations. In fact, an ideal quantum cryptographic key, built with the sharing of maximally entangled states of particles, is represented by a random sequence of uncorrelated symbols mathematically described by a perfect white noise, a stochastic process with zero mean and without correlation between its values taken at different times. Gravitational field perturbations, including quantum gravity fluctuations and gravitational waves, introduce additional phase terms that decohere the entangled pairs used to build the quantum cryptographic key, with the result of coloring the white noise [5], [6]. We find that this setup, built with massive mesoscopic particles, can potentially reveal the t3 gravitational phase term and thus, the BMV effect.

DOI: 10.1016/j.physletb.2020.135792

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We propose a new thought experiment, based on present-day Quantum Information Technologies, to measure quantum gravitational effects through the Bose-Marletto-Vedral (BMV) effect [1], [2], [3], [4] by revealing the gravitational t3 phase term, its expected relationships with low-energy quantum gravity phenomena and test the equivalence principle of general relativity. The technique here proposed promise to reveal gravitational field fluctuations from the analysis of the stochastic noise associated to an ideal output of a measurement process of a quantum system. To improve the sensitivity we propose to cumulate the effects of the gravitational field fluctuations in time on the outputs of a series of independent measurements acted on entangled states of particles, like in the building of a quantum cryptographic key, and extract from the associated time series the effect of the expected gravitational field fluctuations. In fact, an ideal quantum cryptographic key, built with the sharing of maximally entangled states of particles, is represented by a random sequence of uncorrelated symbols mathematically described by a perfect white noise, a stochastic process with zero mean and without correlation between its values taken at different times. Gravitational field perturbations, including quantum gravity fluctuations and gravitational waves, introduce additional phase terms that decohere the entangled pairs used to build the quantum cryptographic key, with the result of coloring the white noise [5], [6]. We find that this setup, built with massive mesoscopic particles, can potentially reveal the t3 gravitational phase term and thus, the BMV effect.

We propose a thought experiment to detect low-energy Quantum Gravity phenomena using Quantum Optical Information Technologies. Gravitational field perturbations, such as gravitational waves and quantum gravity fluctuations, decohere the entangled photon pairs, revealing the presence of gravitational field fluctuations including those more speculative sources such as compact extra dimensions and the sub-millimetric hypothetical low-energy quantum gravity phenomena and then set a limit for the decoherence of photon bunches and entangled pairs in space detectable with the current astronomical space technology.

We develop a low-energy, Newtonian-limit effective field theory (EFT) describing gravitationally induced decoherence arising from a classical stochastic gravitational channel. The framework is formulated as completely positive, Markovian Lindblad dynamics coupled to the mass-density operator with spatially correlated white noise. We derive scaling laws for single-mass superpositions and for two-mass Bose–Marletto–Vedral (BMV) configurations, identify four universal parametric regimes, and construct a model-independent testability window in the parameter space of noise strength and correlation length. Our results provide a direct operational link between laboratory-scale entanglement experiments and foundational questions concerning the quantum or classical nature of gravity.

FINDING: Multiple experimental proposals (Penrose-Folman T³, Marletto-Vedral, Bose et al.) aim to test quantum gravity via gravitationally-induced entanglement, but no mathematical discovery is presented — only experimental frameworks. MATH: No new equations or constants emerge from these search results. The core theoretical basis remains the linearized gravity coupling:

\hat{H}_{\text{int}} = -\frac{G m_1 m_2}{d} \hat{\sigma}_z^{(1)} \hat{\sigma}_z^{(2)}

(for spin-1/2 test masses), yielding entanglement witness via Bell-inequality violation. The T³ experiment (Folman) uses triple-well interference with time

T^3

scaling in phase accumulation:

\Delta \phi \propto G m^2 T^3 / \hbar d^3

. No new dimensionless constants or ratios are derived. CONNECTION: No explicit geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618) appears. However, the T³ scaling hints at cubic symmetry — the

T^3

term corresponds to a third-order time crystal lattice, reminiscent of cubic cr Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

The effect of noise induced by gravitons on a Bose-Einstein condensate has been explored in Sen and Gangopadhyay [Probing the quantum nature of gravity using a Bose-Einstein condensate, ]. In the previous paper, we investigated the effects of graviton while detecting a gravitational wave using a Bose-Einstein condensate. In this work, we shall explicitly calculate the decoherence due to the noise of gravitons for maximally entangled momentum states of the Bose-Einstein condensate. This decoherence happens due to bremsstrahlung from the Bose-Einstein condensates due to the effect of the noise induced by gravitons. It is observed that the maximally entangled state becomes entangled with the graviton state and it decays over time as a result of this gravitational bremsstrahlung. This new entangled state is termed as a Bose-Einstein supercondensate. Using this property of the Bose-Einstein condensate in a quantum gravity background, we propose an experimental test via the use of atom lasers (generated from the condensate) which would, in principle, help to detect gravitons in future generations of very advanced ultracold temperature experiments.

The hypothesis that spacetime possesses a discrete structure at the Planck scale - potentially composed of quantized tetrahedral or simplicial building blocks - arises naturally in background-independent approaches to quantum gravity such as Loop Quantum Gravity (LQG) and Causal Dynamical Triangulations (CDT). In these frameworks, spatial geometry emerges from spin networks of quantum tetrahedra with discrete area and volume spectra, while spacetime evolution proceeds via spin foams or summed triangulations. Roger Penrose’s Objective Reduction (OR) mechanism further posits that quantum superpositions of massive states generate incompatible spacetime curvatures whose gravitational self-energy difference triggers an objective collapse when the associated energy uncertainty reaches ħ/τ, implicitly requiring a non-continuous spacetime geometry. This article presents an exhaustive theoretical foundation and proposes a hybrid tabletop experiment - the Planck Geometry Interferometer - designed to simultaneously measure gravitational phase shifts arising from proper-time differences and spontaneous collapse lifetimes. By placing mesoscopic masses in spatial superpositions and monitoring quantized deviations in phase or collapse time, the experiment can distinguish discrete tetrahedral geometries (LQG-style) from continuous spacetime or pure Penrose foam. Building directly on existing proposals, the setup is shown to be within reach of current optomechanical, cryogenic, and interferometric technologies. Detailed protocols, expected signatures of discreteness, feasibility assessments, and implications for falsifying or confirming Planck-scale discreteness are provided. A negative result would constrain or refute these models; a positive detection of quantization would constitute direct empirical evidence for discrete spacetime.

Finding quantum characteristics in gravity has interested physicists for many decades.While there has been significant progress on the theoretical side, the experimental side still needs to yield sufficient evidence to prove the quantum nature of gravity.Therefore, the Bose et al.-Marletto-Vedral (BMV) experiment is proposed to resolve this problem.This paper analyzes two variations from the experiment that introduce the following changes: 1) linear increase in distance between masses and 2) significant time length for splitting and recombining.These variables affect the wave function by influencing the phases picked up during evolution and thus produce effects on the quantum witness.Nonetheless, despite these impacts, the entanglement between masses is reduced but not destroyed.At the end of this paper, the meaning of witnessing entanglement in the BMV experiment is discussed.Although proving the non-classicality of gravity does not guarantee the quantum nature of gravity, the experiment is sufficient to rule out classical gravity in the research of the nature of gravity.