Quantum Spacetime Research Articles

Shaping Dynamical Casimir Photons

Temporal modulation of the quantum vacuum through fast motion of a neutral body or fast changes of its optical properties is known to promote virtual into real photons, the so-called dynamical Casimir effect. Empowering modulation protocols with spatial control could enable the shaping of spectral, spatial, spin, and entanglement properties of the emitted photon pairs. Space–time quantum metasurfaces have been proposed as a platform to realize this physics via modulation of their optical properties. Here, we report the mechanical analog of this phenomenon by considering systems in which the lattice structure undergoes modulation in space and in time. We develop a microscopic theory that applies both to moving mirrors with a modulated surface profile and atomic array meta-mirrors with perturbed lattice configuration. Spatiotemporal modulation enables motion-induced generation of co- and cross-polarized photon pairs that feature frequency-linear momentum entanglement as well as vortex photon pairs featuring frequency-angular momentum entanglement. The proposed space–time dynamical Casimir effect can be interpreted as induced dynamical asymmetry in the quantum vacuum.

Holographic entanglement negativity and replica symmetry breaking

Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Rényi generalizations in holographic duality. We first review the definition of the Rényi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Rényi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Rényi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.

Symplectic Quantization I: Dynamics of Quantum Fluctuations in a Relativistic Field Theory

We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and thecosmological constant, 2021).

Symplectic Quantization II: Dynamics of Space\u2013Time Quantum Fluctuations and the Cosmological Constant

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor g_{mu nu } on an additional time variable, named intrinsic time at variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of g_{mu nu } quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative {dot{g}}_{mu nu } of the metric field with respect to intrinsic time, corresponding to the conjugated momentum pi _{mu nu }. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional {mathcal {A}}[g_{mu nu },pi _{mu nu }] = {mathcal {K}}[g_{mu nu },pi _{mu nu }] - S[g_{mu nu }], playing formally the role of a Hamilton function, where S[g_{mu nu }] is the standard Einstein–Hilbert action while {mathcal {K}}[g_{mu nu },pi _{mu nu }] is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of g_{mu nu } analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action {mathcal {A}}[g_{mu nu },pi _{mu nu }] and not of energy. Since the Einstein–Hilbert action S[g_{mu nu }] plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of g_{mu nu }. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field pi _{mu nu } gives rise to a cosmological constant term in the path-integral approach.

Schrödinger’s cat for de Sitter spacetime

Quantum gravity is expected to contain descriptions of semiclassical spacetime geometries in quantum superpositions. To date, no framework for modelling such superpositions has been devised. Here, we provide a new phenomenological description for the response of quantum probes (i.e. Unruh–deWitt detectors) on a spacetime manifold in quantum superposition. By introducing an additional control degree of freedom, one can assign a Hilbert space to the spacetime, allowing it to exist in a superposition of spatial or curvature states. Applying this approach to static de Sitter space, we discover scenarios in which the effects produced by the quantum spacetime are operationally indistinguishable from those induced by superpositions of Rindler trajectories in Minkowski spacetime. The distinguishability of such quantum spacetimes from superpositions of trajectories in flat space reduces to the equivalence or non-equivalence of the field correlations between the superposed amplitudes.

Electric dipole interaction in hydrogenic atoms from quantum spacetime

Electric dipole interaction in hydrogenic atoms from quantum spacetime

Nonlocal tidal effects of the moon and numerical estimation of the secular drift rate for a GPS satellite

In this study, we have analyzed several geometrical aspects of the concept of nonlocal-in-time kinetic energy by deriving the extended geodesic and geodesic deviation equations which are the basic stone to analyze tidal and lunar gravitational forces. We have used these equations to study nonlocal tidal effects of the moon. It was observed that nonlocality-in-time generates higher-order corrections to the gravitational tidal field and hence results on a modification of the drift rate of the moon. We have evaluated the maximal secular drift rate for a GPS satellite due to the tidal potential and compared the results with near Earth missions obtained from the Space-Time Explorer and QUantum Equivalence Space Test space mission and some recent relativistic studies. The numerical estimate of nonlocal-in-time parameter is obtained, although it is small, it proves that nonlocality-in-time may have besides the kinetic aspect a geometrical feature.

Dynamics of primordial fields in quantum cosmological spacetimes

Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage of such descriptions is that they are relatively simple and display the classical behavior for large universes. However, they may smooth out an important inner structure and to include it a more detailed treatment is needed. The purpose of the present work is to investigate quantum uncertainty in the basic background variables and its influence on primordial gravitational waves. To this end we quantize a model of the Friedmann-Lemaitre-Robertson-Walker universe filled with a linear barotropic cosmological fluid and with gravitational waves. We carefully derive the dynamical equations for the perturbations in quantum spacetime. The quantization yields an equation of motion for the Fourier modes of gravitational radiation, which is a quantum extension to the usual parametric oscillator equation for gravitational waves propagating in an expanding universe. The two quantum effects from the cosmological background that enter the enhanced equation of motion are (i) a repulsive potential resolving the big bang singularity and replacing it with a big bounce and (ii) uncertainties in the numerical values for the background spacetime dynamical variables. First we study the former effect and its consequences for the primordial amplitude spectrum and carefully discuss the relation between the bounce scale and the physical predictions of the model. Next we investigate the latter effect, in particular the extent to which it may affect the primordial amplitude of gravitational waves. Making use of the WKB approximation we find an analytical formula for the amplitude spectrum as a function of the quantum dispersion of the background spacetime.

A model of spinfoam coupled with an environment

In this paper, an open quantum system theory for spinfoams is developed. This new formalism aims at deriving an effective Lindblad equation to compute the reduced dynamics of a quantum gravitational field. The system parameters are determined from numerical ab initio calculations, based on the spinfoam formalism. This theoretical proposal is illustrated by means of examples. The decoherence effect can induce the relaxation of the quantum gravitational state toward a sate of a small area. This is analogue to the well-known Purcell relaxation of QED, for which the qubits are replaced by the spin-network representation of the gravitational field. Some thermodynamic properties of these systems are computed, and several issues with the thermal time hypothesis are underlined. Moreover, the results suggest that further approximations can be performed to study reduced dynamics of quantum space-time.

Photon helicity and quantum anomalies in curved spacetimes

We compare several definitions of photon helicity (magnetic, electric, electromagnetic) present in literature. In curved spacetime quantum anomalies can spoil helicity conservation inducing - according to these definitions - different effects on photons: either rotation of linear polarization or production of circular polarization. We derive the Noether current associated with duality transformations starting from manifestly invariant Lagrangians in Minkowski spacetime.

Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion

In recent times, there has been considerable interest in scenarios for quantum gravity in which particle kinematics is affected nonlinearly by the Planck scale, with encouraging results for the phenomenological prospects, but also some concerns that the nonlinearities might produce pathological properties for composite/multiparticle systems. We here focus on kinematics in the [Formula: see text]-Minkowski noncommutative spacetime, the quantum spacetime which has been most studied from this perspective and compare the implications of the alternative descriptions of the total momentum of a multiparticle system which have been so far proposed. We provide evidence suggesting that priority should be given to defining the total momentum as the standard linear sum of the momenta of the particles composing the system. We also uncover a previously unnoticed feature concerning some (minute but conceptually important) effects on center-of-mass motion due to properties of the motion of the constituents relative to the center of mass.

Black Holes and Other Clues to the Quantum Structure of Gravity

Bringing gravity into a quantum-mechanical framework is likely the most profound remaining problem in fundamental physics. The “unitarity crisis” for black hole evolution appears to be a key facet of this problem, whose resolution will provide important clues. Investigating this raises the important structural question of how to think about subsystems and localization of information in quantum gravity. Paralleling field theory, the answer to this is expected to be an important ingredient in the mathematical structure of the theory. Perturbative gravity results indicate a structure different from that of quantum field theory, but suggest an avenue to defining subsystems. If black holes do behave similarly to familiar subsystems, unitarity demands new interactions that transfer entanglement from them. Such interactions can be parameterized in an effective approach, without directly addressing the question of the fundamental dynamics, whether that is associated with quantum spacetime, wormholes, or something else. Since such interactions need to extend outside the horizon, that raises the question of whether they can be constrained, or might be observed, by new electromagnetic or gravitational wave observations of strong gravity regions. This note overviews and provides connections between these developments.

BMS algebras in 4 and 3 dimensions, their quantum deformations and duals

BMS symmetry is a symmetry of asymptotically flat spacetimes in vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincaré subalgebras, a fact that has previously been noted in the 3 dimensional case only. Then we use these subalgebras to construct an infinite number of different Hopf algebras being quantum deformations of the BMS algebras. We also discuss different types of twist-deformations and the dual Hopf algebras, which could be interpreted as noncommutative, extended quantum spacetimes.

Ricci Flow Approach to the Cosmological Constant Problem

In order to resolve the cosmological constant problem, the notion of reference frame is re-examined at the quantum level. By using a quantum non-linear sigma model (Q-NLSM), a theory of quantum spacetime reference frame is proposed. The underlying mathematical structure is a new geometry endowed with intrinsic second central moment (variance) or even higher moments of its coordinates, which generalizes the classical Riemannian geometry based on only first moment (mean) of its coordinates. The second central moment of the coordinates directly modifies the quadratic form distance which is the foundation of the Riemannian geometry. At semi-classical level, the second central moment introduces a flow which continuously deforms the Riemannian geometry driven by its classical Ricci curvature, which is known as the Ricci flow. A generalized equivalence principle of quantum version is also proposed to interpret the new geometry endowed with at least second moment. As a consequence, the spacetime is stabilized against quantum fluctuation, and the cosmological constant problem is resolved within the framework. With an isotropic positive curvature initial condition, the long flow time solution of the Ricci flow exists, the accelerating expansion universe at cosmic scale is an observable effect of the spacetime deformation of the normalized Ricci flow. A deceleration parameter − 0.67 consistent with measurement is obtained by using the reduced volume method introduced by Perelman. Effective theory of gravity within the framework is also discussed.

The geometrization of quantum mechanics, the nonlinear Klein–Gordon equation, Finsler gravity and phase spaces

The Geometrization of Quantum Mechanics proposed in this work is based on the postulate that the quantum probability density can curve the classical spacetime. It is shown that the gravitational field produced by smearing a point-mass Mo at r=0 throughout all of space (in a spherically symmetric fashion) can be interpreted as the gravitational field generated by a self-gravitating anisotropic fluid droplet of mass density 4πMor2φ∗(r)φ(r) and which is sourced by the probabilitycloud (associated with a spinless point-particle of mass Mo) permeating a 3-spatial domain region D3=∫4πr2dr at any time t. Classically one may smear the point mass in any way we wish leading to arbitrary density configurations ρ(r). However, Quantum Mechanically this is not the case because the radial mass configuration M(r) must obey a key third order nonlinear differential equation (nonlinear extension of the Klein–Gordon equation) displayed in this work and which is the static spherically symmetric relativistic analog of the Newton–Schrödinger equation. We conclude by extending our proposal to the Lagrange–Finsler and Hamilton–Cartan geometry of (co) tangent spaces and involving the relativistic version of Bohm’s Quantum Potential. By further postulating that the quasi-probability Wigner distribution W(x,p)curves phase spaces, and by encompassing the Finsler-like geometry of the cotangent-bundle with phase space quantum mechanics, one can naturally incorporate the noncommutative and non-local Moyal star product (there are also non-associative star products as well). To conclude, Phase Space is the arena where to implement the space–time–matter unification program. It is our belief this is the right platform where the quantization of spacetime and the quantization in spacetime will coalesce.

Higher-spin kinematics & no ghosts on quantum space-time in Yang–Mills matrix models

Higher-spin kinematics & no ghosts on quantum space-time in Yang–Mills matrix models

Elementary Particles Result from Space-Time Quantization

We justify and extend the standard model of elementary particle physics by generalizing the theory of relativity and quantum mechanics. The usual assumption that space and time are continuous implies, indeed, that it should be possible to measure arbitrarily small intervals of space and time, but we ignore if that is true or not. It is thus more realistic to consider an extremely small “quantum of length” of yet unknown value a. It is only required to be a universal constant for all inertial frames, like c and h. This yields a logically consistent theory and accounts for elementary particles by means of four new quantum numbers. They define “particle states” in terms of modulations of wave functions at the smallest possible scale in space-time. The resulting classification of elementary particles accounts also for dark matter. Antiparticles are redefined, without needing negative energy states and recently observed “anomalies” can be explained.

On the Universality of Hawking Radiation

Abstract A physically consistent semi-classical treatment of black holes requires universality arguments to deal with the ‘trans-Planckian’ problem where quantum spacetime effects appear to be amplified such that they undermine the entire semi-classical modelling framework. We evaluate three families of such arguments in comparison with Wilsonian renormalization group universality arguments found in the context of condensed matter physics. Our analysis is framed by the crucial distinction between robustness and universality. Particular emphasis is placed on the quality whereby the various arguments are underpinned by ‘integrated’ notions of robustness and universality. Whereas the principal strength of Wilsonian universality arguments can be understood in terms of the presence of such integration, the principal weakness of all three universality arguments for Hawking radiation is its absence. 1Introduction2Hawking Radiation and the Trans-Planckian Problem 2.1What is Hawking radiation?2.2Red-shift and robustness2.3Ultraviolet catastrophe3Universality Arguments in Condensed Matter Systems 3.1The Wilsonian approach to critical phenomena3.2The six qualities4Universality Arguments for Hawking Radiation 4.1Arguments from the equivalence principle4.2Arguments from horizon symmetries4.3Arguments from modified dispersion relations5Conclusion

Quantum Spacetime and the Universe at the Big Bang, Vanishing Interactions and Fading Degrees of Freedom

As discussed in Bahns et al. (2015) fundamental physical principles suggests that, close to cosmological singularities, the effective Planck length diverges, hence a “quantum point” becomes infinitely extended. We argue that, as a consequence, at the origin of times spacetime might reduce effectively to a single point and interactions disappear. This conclusion is supported by converging evidences in two different approaches to interacting quantum fields on Quantum Spacetime: (1) as the Planck length diverges, the field operators evaluated at a “quantum point” converge to zero, and so do the lowest order expressions for interacting fields in the Yang Feldman approach; (2) in the same limit, we find convergence of the interacting vacuum to the free one at all perturbative orders. The latter result is obtained using the adaptation, performed in Doplicher et al. (2020), of the methods of perturbative Algebraic Quantum Field Theory to Quantum Spacetime, through a novel picture of the effective Lagrangian, which maintains the ultraviolet finiteness of the perturbation expansion and allows one to prove also the existence of the adiabatic limit. It remains an open question whether the S matrix itself converges to unity and whether the limit in which the effective Planck length diverges is a unique initial condition or an unreachable limit, and only different asymptotics matter.

A geometric picture of quantum mechanics with noncommutative values for observables

We present here what we consider a new picture of quantum mechanics with the position and momentum observables as coordinates of the usual quantum phase space of a single particle, which also serves as the model of the physical space. To minimize the mathematics involved, we stick here to the Hilbert space picture of the phase space. We argue that a quantum observable should be seen as taking noncommutative values each of which can equivalently be represented by an infinite number of real numbers. The six noncommutative values of the position and momentum observables hence serve as an alternative system of coordinates for the Hilbert space. The values can, at least in principle, be experimentally determined. This can be seen as a complete resolution of the Einstein–Bohr debate that Einstein would probably be happy with. What we have is a solid noncommutative geometrical picture of the physical space, or spacetime, beyond the Newtonian and Einsteinian framework that is sure to be relevant to Nature directly coupled with the idea that each physical quantity should better be seen as having a value beyond what can be represented by a number. We finish by sketching some implications of the results for the physics and mathematics of quantum spacetime in general.