It has recently been proposed that quantum gravity might lead to the decoherence of superpositions in energy, corresponding to a discretization of time at the Planck scale. At first sight the proposal seems amenable to experimental verification with methods from quantum optics and atomic physics. However, we argue that the predicted decoherence is unobservable in such experiments if it acts globally on the whole experimental setup. This is related to the unobservability of the global phase in interference. We also show how local energy decoherence, which acts separately on system and phase reference, could be detected with remarkable sensitivity and over a wide range of length scales by long-distance Ramsey interferometry with metastable atomic states. The sensitivity of the experiments can be further enhanced using multi-atom entanglement.
Canonical coupling between classical and quantum systems cannot result in reversible equations, rather it leads to irreversible master equations. Coupling of quantized non-relativistic matter to gravity is illustrated by a simplistic example. The heuristic derivation yields the theory of gravity-related decoherence proposed longtime ago by Penrose and the author.
Recent works have proved that semi-classical theories of gravity needed not be fundamentally inconsistent, at least in the Newtonian regime. Using the machinery of continuous measurement theory and feedback, it was shown that one could construct well behaved models of hybrid quantum-classical dynamics at the price of an imposed (non unique) decoherence structure. We introduce a principle of least decoherence (PLD) which allows to naturally single out a unique model from all the available options; up to some unspecified short distance regularization scale. Interestingly, the resulting model is …
In Crull (2015) it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull (2015) concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky (2014), is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergen…
In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity; 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not; 3) Gravitational Decoherence: Derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) M…
We discuss effects of loss of coherence in low energy quantum systems caused by or related to gravitation, referred to as gravitational decoherence. These effects, resulting from random metric fluctuations, for instance, promise to be accessible by relatively inexpensive table-top experiments, way before the scales where true quantum gravity effects become important. Therefore, they can provide a first experimental view on gravity in the quantum regime. We will survey models of decoherence induced both by classical and quantum gravitational fluctuations; it will be manifest that a clear unders…
The experimental observation of a clear quantum signature of gravity is believed to be out of the grasp of current technology. However, several recent promising proposals to test the possible existence of non-classical features of gravity seem to be accessible by the state-of-art table-top experiments. Among them, some aim at measuring the gravitationally induced entanglement between two masses which would be a distinct non-classical signature of gravity. We explicitly study, in two of these proposals, the effects of decoherence on the system's dynamics by monitoring the corresponding degree o…
It is shown that Non-unitary Newtonian Gravity (NNG) model admits a simple interpretation in terms of Feynman path integral, in which the sum over all possible histories is replaced by a summation over pairs of paths. Correlations between different paths are allowed by a fundamental decoherence mechanism of gravitational origin and can be interpreted as a kind of communication between different branches of the wave function. The ensuing formulation could be used in turn as a motivation to introduce Non-unitary Gravity itself.
We give a first principles derivation of a master equation for the evolution of a quantum matter field in a linearly perturbed Minkowski spacetime, based solely on quantum field theory and general relativity. We make no additional assumptions nor introduce extra ingredients, as is often done in alternative quantum theories. When the quantum matter field is projected to a one-particle state, the master equation for a non-relativistic quantum particle in a weak gravitational field predicts decoherence in the energy basis, in contrast to most existing theories of gravitational decoherence. We poi…
In Nature Phys. 11, 668 (2015) (Ref. [1]), a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field is shown to undergo a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's Equivalence Principle to be valid, we demonstrate, first in a Lorentz frame with accelerating detectors, and then directly in the Lab frame with uniform gravity, that the dephasing between the different internal states arise not from gravity but rather from differences in their rest mass, and the mass dependence of the de Br…
We analyze the dynamics of a gravity-induced entanglement for N massive particles. Considering the linear configuration of these particles, we investigate the entanglement between a specific pair of particles under the influence of the gravitational interaction between the massive particles. As the particle number increases, the specific particle pair decoheres more easily due to the gravitational interaction with other particles. The time scale of the gravity-induced decoherence is analytically determined. We also discuss the entanglement dynamics of initially entangled particles, which exemp…
We present a discussion of the fundamental loss of unitarity that appears in quantum mechanics due to the use of a physical apparatus to measure time. This induces a decoherence effect that is independent of any interaction with the environment and appears in addition to any usual environmental decoherence. The discussion is framed self consistently and aimed to general physicists. We derive the modified Schroedinger equation that arises in quantum mechanics with real clocks and discuss the theoretical and potential experimental implications of this process of decoherence.
Erik Verlinde's theory of entropic gravity [arXiv:1001.0785], postulating that gravity is not a fundamental force but rather emerges thermodynamically, has garnered much attention as a possible resolution to the quantum gravity problem. Some have ruled this theory out on grounds that entropic forces are by nature noisy and entropic gravity would therefore display far more decoherence than is observed in ultra-cold neutron experiments. We address this criticism by modeling linear gravity acting on small objects as an open quantum system. In the strong coupling limit, when the model's unitless f…
Recently a theoretical and an experimental protocol known as quantum gravity induced entanglement of masses (QGEM) has been proposed to test the quantum nature of gravity using two mesoscopic masses each placed in a superposition of two locations. If, after eliminating all non-gravitational interactions between them, the particles become entangled, one can conclude that the gravitational potential is induced via a quantum mediator, i.e. a virtual graviton. In this paper, we examine a range of different experimental set-ups, considering different geometries and the number of spatially superpose…
The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the correlation between a system and a clock, where an idealized clock can be modelled as a two level systems. We investigate the dynamics of clocks interacting gravitationally by treating the gravitational interaction as a classical information channel. In particular, we focus on the decoherence rates and temporal resolution of arrays of $N$ clocks showing how the…
Quantum mechanics and the theory of gravity are presently not compatible. A particular question is whether gravity causes decoherence - an unavoidable source of noise. Several models for gravitational decoherence have been proposed, not all of which can be described quantum mechanically. In parallel, several experiments have been proposed to test some of these models, where the data obtained by such experiments is analyzed assuming quantum mechanics. Since we may need to modify quantum mechanics to account for gravity, however, one may question the validity of using quantum mechanics as a calc…
The double slit experiment is iconic and widely used in classrooms to demonstrate the fundamental mystery of quantum physics. The puzzling feature is that the probability of an electron arriving at the detector when both slits are open is not the sum of the probabilities when the slits are open separately. The superposition principle of quantum mechanics tells us to add amplitudes rather than probabilities and this results in interference. This experiment defies our classical intuition that the probabilities of exclusive events add. In understanding the emergence of the classical world from th…
We investigate the dynamics of two quantum mechanical oscillator system-bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar QED. The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence…
Adopting the viewpoint that the standard perturbative quantization of general relativity provides an effective description of quantum gravity that is valid at ordinary energies, we show that gravity as an environment induces the rapid decoherence of stationary matter superposition states when the energy differences in the superposition exceed the Planck energy scale.
Recently, several proposals have been made to test the quantum superposition principle in the mesoscopic regime. Most of these tests consist of a careful measurement of the loss of interference due to decoherence. Here we consider, instead, the spread in position of a freely falling nanosphere. We study in depth the dependence of this spread on self-gravity in the presence of decoherence (exotic and non-exotic). We show that the influence of self-gravity is robust in the presence of weak decoherence, and quantify this robustness by introducing a new parameter, the critical decoherence, aimed a…
Both the additional non-linear term in the Schrödinger equation and the additional non-Hamiltonian term in the von Neumann equation, proposed to ensure localisation and decoherence of macro-objects, resp., contain the same Newtonian interaction potential formally. We discuss certain aspects that are common for both equations. In particular, we calculate the enhancement of the proposed localisation and/or decoherence effects, which would take place if one could lower the conventional length-cutoff and resolve the mass density on the interatomic scale.
Lisi, Marrone, and Montanino have recently proposed a test for quantum gravity induced decoherence effects in neutrino oscillations observed at Super-Kamiokande. We comment here that their equations have the same qualitative form as the energy conserving objective state vector reduction equations discussed by a number of authors. However, using the Planckian parameter value proposed to explain state vector reduction leads to a neutrino oscillation effect many orders of magnitude smaller than would be detectable at Super-Kamiokande. Similar estimates hold for the Ghirardi, Rimini, and Weber spo…
Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schrödinger dynamics based on discrete time intervals with an intrin…
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 Diósi [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 …
Hypothetical models have been proposed in which explicit collapse mechanisms prevent the superposition principle to hold at large scales. In particular, the model introduced by Ellis and co-workers [Phys. Lett. B ${\bf 221}$, 113 (1989)] suggests that quantum gravity might be responsible for the collapse of the wavefunction of massive objects in spatial superpositions. We here consider a recent experiment reporting on interferometry with atoms delocalized over half a meter for timescale of a second [Nature ${\bf 528}$, 530 (2015)] and show that the corresponding data strongly bound quantum gra…
A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary, framework for quantum gravity by assuming that the operators tied to the gravitational degrees of freedom are unobservable and equating physical entropy with matter-gravity entanglement entropy. Here we obtain preliminary results on the extent of decoherence this theory predicts. We treat first a static state which, if one were to ignore quantum gravitational effects, would be a quantum superposition of two spatially displaced states of a sing…
One of the biggest problems faced by those attempting to combine quantum theory and general relativity is the experimental inaccessibility of the unification scale. In this paper we show how incoherent conformal waves in the gravitational field, which may be produced by quantum mechanical zero-point fluctuations, interact with the wavepackets of massive particles. The result of this interaction is to produce decoherence within the wavepackets which could be accessible in experiments at the atomic scale. Using a simple model for the coherence properties of the gravitational field we derive an e…
Evolution of tripartite entanglement in three-qubit Quantum Gravity-Induced Entanglement of Masses (QGEM) with quantum decoherence
Instituto de Física Teórica, UAM-CSIC（理论物理研究所，UAM-CSIC）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）；Departamento de Física Teórica and CIAFF, Universidad Autónoma de Madrid（马德里自治大学理论物理系及CIAFF）
We investigate the meaning of gravity-induced decoherence in quantum theory, known as `intrinsic' or `fundamental' decoherence in the literature. We explore a range of issues relevant to this problem, including the meaning of modified uncertainty relations, the interpretations of the Planck scale, the distinction between quantum and stochastic fluctuations and the role of the time variable in quantum mechanics. We examine the specific physical assumptions that enter into different approaches to the subject. In particular, we critique two representative approaches that identify time fluctuation…
We derive a general quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical external gravitational field. The dynamics predicts decoherence in position, momentum and energy. We show how our master equation reproduces the results present in the literature by taking appropriate limits, thus explaining the apparent contradiction in their dynamical description. Our result is relevant in light of the increasing interest in the low energy quantum-gravity regime.
Differential and Common Decoherence Modes in Witnessing the Quantum Gravity-Induced Entanglement of Matter
University of Groningen（格罗宁根大学）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）；Canadian Institute of Theoretical Astrophysics, University of Toronto（多伦多大学加拿大理论天体物理研究所）
A recent debate has ensued over the claim by Pikovski et al. [Nat. Phys. 11, 668 (2015)] that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical transition. This decoherence is supposed to arise from the different gravitational redshifts experienced by such systems when placed in a superposition of two wave packets at different heights in a gravitational field. Here we investigate some aspects of the discussion with the aid of simple examples. In particular, we first resolve an apparent conflict between th…
Optical lattice clocks can now resolve the height difference below 1 mm within an atomic ensemble by means of gravitational redshift with integration over sufficient amount of time. Further improvement in the stability enables the clocks to resolve the height difference of subsystems within an atomic ensemble that is conventionally interrogated as a single coherent spin state in a single Ramsey sequence, resulting in the dephasing of the coherent spin state. This effect is observable with a clock of a stability of $\lesssim 10^{-21}$ by introducing a single-layer-resolved imaging system for a …
One of the biggest unsolved problems in physics is the unification of quantum mechanics and general relativity. The lack of experimental guidance has made the issue extremely evasive, though various attempts have been made to relate the loss of matter wave coherence to quantum spacetime fluctuations. We present a new approach to the gravitational decoherence near the Planck scale, made possible by recently discovered conformal structure of canonical gravity. This leads to a gravitational analogue of the Brownian motion whose correlation length is given by the Planck length up to a scaling fact…
Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph and coworkers [T C Ralph, G J Milburn, and T Downes, Phys. Rev. A, 79(2):22121, 2009, T C Ralph and J Pienaar, New Journal of Physics, 16(8):85008, 2014], a bipartite entangled system could decohere if each particle traversed …
The Schrödinger-Newton [SN] equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation by itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a s…
We consider the effect of gravity on extended quantum systems (EQS) in the low energy regime. We model the gravitational effect due to a nearby source mass as a redshift in the internal Hamiltonian of the EQS. Due to the dependence of the energy spectrum of the EQS on the position of the massive particle (via the redshift) at zero temperature, our model predicts gravitational decoherence of the massive particle in the position basis. We show that the decoherence effect is multiplicative, in the sense that the increase in number of EQS gravitationally interacting with a single massive particle …
Various models have been proposed in which the Schrödinger equation is modified to account for a decay of spatial coherences of massive objects. While optomechanical systems and matter-wave interferometry with large clusters are promising candidates to test these models, we here show that using available techniques for atoms in optical lattices, some of these models can be efficiently tested. In particular, we compare unconventional decoherence due to quantum gravity as introduced by Ellis and co-workers [Phys. Lett. B ${\bf 221}$, 113 (1989)] and conventional decoherence due to scattering of …
We present a simple calculation leading to the quantum gravitationally-induced decoherence of a spatial superposition of a massive object in the linear coupling regime. The point of this calculation is to illustrate that the gravitationally-induced collapse could be of the same origin as any other collapse, i.e. due to the entanglement between the system (here a massive object) and its environment (in this case gravity, but it could well be the electromagnetic or any other field). We then point out that, in some cases, one has to be careful when concluding that matter-wave interference of larg…
Statistical mechanics explains thermodynamics in terms of (quantum) mechanics by equating the entropy of a microstate of a closed system with the logarithm of the number of microstates in the macrostate to which it belongs, but the question `what is a macrostate?' has never been answered except in a vague, subjective, way. However Hawking's discovery of black hole evaporation led to a formula for black hole entropy with no subjective element. In this letter, we argue from this result, together with the assumption that `black hole thermodynamics is just ordinary thermodynamics applied to black …
It is believed that classical behavior emerges in a quantum system due to decoherence. It has also been proposed that gravity can be a source of this decoherence. We examine this in detail by studying a number of quantum systems, including ultra-relativistic and non-relativistic particles, at low and high temperatures in an expanding Universe, and show that this proposal is valid for a large class of quantum systems.
We show that if a discrete quantum gravity is not classical, then it cannot be generated by an isometric dynamics. In particular, we show that if the quantum measure μ (or equivalently the decoherence functional) is generated by an isometric dynamics, then there is no in- terference between events so the system describing evolving universes is classical. The result follows from a forbidden configuration in the path space of causal sets.
