Quantum Spacetime Research Articles

Near-horizon aspects of black holes in quantum spacetime

Abstract We give a short introduction to the formalism of noncommutative (twisted) differential geometry that is used to derive the equations of motion for the gravitational perturbation of the Schwarzschild black hole in quantized spacetime. Special attention is given to quantum spacetime arising from r − φ noncommutativity. Tortoise coordinate and near-horizon regions of the effective potentials are analyzed for both polar and axial modes. By carefully examining the associated Schrödinger-type equations, we provide the asymptotic solutions at the horizon and illustrate some differences between the polar and axial modes. These findings give further insight into the polar-axial isospectrality violation in the presence of the quantum structure of spacetime.

Integral quantization in the quantum configuration space

Abstract Quantum spacetime in which time is considered on the same footing as other observables is a part of the quantum configuration space. In such space a natural geometry is generated by the transition amplitudes among quantum configuration space points. It is shown, that a good candidate for quantization of extended (plus time) classical configuration spaces is integral quantization. This quantization is compatible with the notion of quantum time. The most basic features of this quantization are presented.

Spin-Bounded Correlations: Rotation Boxes Within and Beyond Quantum Theory

How can detector click probabilities respond to spatial rotations around a fixed axis, in any possible physical theory? Here, we give a thorough mathematical analysis of this question in terms of “rotation boxes”, which are analogous to the well-known notion of non-local boxes. We prove that quantum theory admits the most general rotational correlations for spins 0, 1/2, and 1, but we describe a metrological game where beyond-quantum resources of spin 3/2 outperform all quantum resources of the same spin. We prove a multitude of fundamental results about these correlations, including an exact convex characterization of the spin-1 correlations, a Tsirelson-type inequality for spins 3/2 and higher, and a proof that the general spin-J correlations provide an efficient outer SDP approximation to the quantum set. Furthermore, we review and consolidate earlier results that hint at a wealth of applications of this formalism: a theory-agnostic semi-device-independent randomness generator, an exact characterization of the quantum (2, 2, 2)-Bell correlations in terms of local symmetries, and the derivation of multipartite Bell witnesses. Our results illuminate the foundational question of how space constrains the structure of quantum theory, they build a bridge between semi-device-independent quantum information and spacetime physics, and they demonstrate interesting relations to topics such as entanglement witnesses, spectrahedra, and orbitopes.

Quantum spacetimes from general relativity?

We introduce a non-commutative product for curved spacetimes, that can be regarded as a generalization of the Rieffel (or Moyal-Weyl) product. This product employs the exponential map and a Poisson tensor, and the deformed product maintains associativity under the condition that the Poisson tensor Θ satisfies Θμν∇νΘρσ=0, in relation to a Levi-Cevita connection. We proceed to solve the associativity condition for various physical spacetimes, uncovering non-commutative structures with compelling properties.

Interactions in the IKKT matrix model on covariant quantum spacetime

We study the interactions of the higher-spin gauge theory arising from the IKKT matrix model on a covariant quantum FLRW quantum space-time MJ1,3, denoted as HS-IKKT. In particular, we elaborate some of the vertices and observe that they are not manifestly Lorentz invariant in the unitary formulation. We argue that Lorentz invariance of HS-IKKT can be recovered since Lorentz transformations are part of the gauge invariance in the covariant formulation. This statement is verified for some vertices with lowest number of derivatives. The lowest-derivative sector of this theory is expected to be governed by an “almost”-Lorentz-invariant Yang-Mills theory coupled to emergent gravity.

Quantum Spacetime: Proposed experiments would search for signs that space and time obey quantum rules.

Quantum Spacetime: Proposed experiments would search for signs that space and time obey quantum rules.

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.

Constraints on quantum spacetime-induced decoherence from neutrino oscillations

We investigate the implications of decoherence induced by quantum spacetime properties on neutrino oscillation phenomena. We develop a general formalism where the evolution of neutrinos is governed by a Lindblad-type equation and we compute the oscillation damping factor for various models that have been proposed in the literature. Furthermore, we discuss the sensitivity to these effects of different types of neutrino oscillation experiments, encompassing astrophysical, atmospheric, solar, and reactor neutrino experiments. By using neutrino oscillation data from long-baseline reactors and atmospheric neutrino observations, we establish stringent constraints on the energy scale governing the strength of the decoherence induced by stochastic metric fluctuations, amounting to, respectively, EQG≥2.6×1034 GeV and EQG≥2.5×1055 GeV. Published by the American Physical Society 2024

Dirac Theory in Noncommutative Phase Spaces

Based on the position and momentum of noncommutative relations with a noncanonical map, we study the Dirac equation and analyze its parity and time reversal symmetries in a noncommutative phase space. Noncommutative parameters can be endowed with the Planck length and cosmological constant such that the noncommutative effect can be interpreted as an effective gauge potential or a (0,2)-type curvature associated with the Plank constant and cosmological constant. This provides a natural coupling between dynamics and spacetime geometry. We find that a free Dirac particle carries an intrinsic velocity and force induced by the noncommutative algebra. These properties provide a novel insight into the Zitterbewegung oscillation and the physical scenario of dark energy. Using perturbation theory, we derive the perturbed and nonrelativistic solutions of the Dirac equation. The asymmetric vacuum gaps of particles and antiparticles reveal the particle–antiparticle symmetry breaking in the noncommutative phase space, which provides a clue to understanding the physical mechanisms of particle–antiparticle asymmetry and quantum decoherence through quantum spacetime fluctuation.

The Einstein–Hilbert action for entropically dominant causal sets

In the path integral formulation of causal set quantum gravity, the quantum partition function is a phase-weighted sum over locally finite partially ordered sets, which are viewed as discrete quantum spacetimes. It is known, however, that the number of ‘layered’ sets—a class of causal sets that look nothing like spacetime manifolds—grows superexponentially with the cardinality n, giving an entropic contribution that can potentially dominate that of the action. We show here that in any dimension, the discrete Einstein–Hilbert action for a typical K-layered causal set reduces to the simple link action to leading order in n. Combined with earlier work, this completes the proof that the layered sets, although entropically dominant, are very strongly suppressed in the path sum of causal set quantum gravity whenever the discreteness scale is greater than or equal to a (mildly dimension-dependent) order one multiple of the Planck scale.

From Snyder space-times to doubly κ-dependent Yang quantum phase spaces and their generalizations

We propose the doubly κ-dependent Yang quantum phase space which describes the generalization of D=4 Yang model. We postulate that such model is covariant under the generalized Born map, what permits to derive this new model from the earlier proposed κ-Snyder model. Our model of D=4 relativistic Yang quantum phase space depends on five deformation parameters which form two Born map-related dimensionful pairs: (M,R) specifying the standard Yang model and (κ,κ˜) characterizing the Born-dual κ-dependence of quantum space-time and quantum fourmomenta sectors; fifth parameter ρ is dimensionless and Born-selfdual. In the last section, we propose the Kaluza-Klein generalization of D=4 Yang model and the new quantum Yang models described algebraically by quantum-deformed oˆ(1,5) algebras.

Unveiling Novel Dark Matter Particles: Insights from Fractal Quantum Gravity Theory

As a promising quantum gravity theory, the newly developed fractal quantum gravity theory (FQG) has introduced the smallest constant of the product of space, time and energy of STQAs (Space-Time Quantum of Action).The product of space, time and energy of every particle is integer times of this smallest constant-STQA. Based on the FQG equation, we have deduced that every physical parameter of existing or possibly existing particle takes some special or limited extrem a values. With the calculation of the minimum value of electric charge that a particle can carry, its magnetic moment, mass, inherent speed, the space size and spin angular momentum, we have discovered a very intriguing brand-new type of particles. Its electric charge is about 1/10 of electrons’, and the magnetic moment is 1.18×10-9 of electrons’. Its mass is 324 times of the mass of the known existing heaviest particle, the top quark. Its inherent speed is about 10-3 of electrons’, space size is about 10-10 of electrons’and its spin is 1.38 times of the spin of electrons. According to the popular thinking about the characteristics of dark matter that are electromagnetically neutral, heavy, slow-moving particles, we believe that this newly discovered particle should be the weakly interacting massive particles (WIMPs), a most promising type of the dark matter particles (DMPs). This is the first time that the specific physical parameters of DMPs have been calculated. These predictions not only provide much insight into the understanding of dark matter, it also makes it possible to explore the experimental verification, possibly using the Large Hadron Collider (LHC) in the future.

Renormalization on the DFR quantum spacetime

An approach to renormalization of scalar fields on the Doplicher–Fredenhagen–Roberts (DFR) quantum spacetime is presented. The effective nonlocal theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singularities associated to the nonlocal kernel that codifies the effects of non-commutativity is analyzed using the tools of microlocal analysis.

Spacetime quantum and classical mechanics with dynamical foliation

Spacetime quantum and classical mechanics with dynamical foliation

Virtual experiment on platonic solids for teaching space-time quantization

The work presents the virtual experiment on Platonic solids in a complementary way, where its importance is crucially used for the treatment of the teaching of the quantization of space-time via loop quantum gravity. The research was part of one of the studies carried out with 23 students in the 3rd year of high school in São Cristóvão, Rio de Janeiro, Brazil. The project is part of several introduced subjects on modern and contemporary physics, as well as frontier research topics. The student starts to have a student-researcher posture and based on Ausubel and Bruner's learning theories, they develop significant learning and receive new information and concepts at the elementary level, conditioning them to a critical and reflective posture. We use the experiment in which students interactively learn three-dimensional shapes, calculate surface area and volume and discover mathematical properties of shapes, necessary knowledge that covers the discussion of the theory. Subsequently, they carried out the skills test and we collected data from the students' operations to present the scenario of innovation and reflection on the possibility of introducing research topics in physics, but with appropriate language for the audience of interest according to Bruner's learning theory.

Traversable wormholes from Loop Quantum Gravity

This study introduces and investigates Lorentzian traversable wormhole solutions rooted in Loop Quantum Gravity (LQG). The static and spherically symmetric solutions to be examined stem from the energy density sourcing self-dual regular black holes discovered by L. Modesto, relying on the parameters associated with LQG, which account for the quantum nature of spacetime. We specifically focus on macroscopic wormholes characterized by small values of these parameters. Our analysis encompasses zero-tidal solutions and those with non-constant redshift functions, exploring immersion diagrams, curvatures, energy conditions, equilibrium requirements, and the requisite quantity of exotic matter to sustain these wormholes. The investigation underscores the influence of LQG parameters on these features, highlighting the pivotal role of spacetime's quantum properties in shaping such objects and governing their behavior.

Matter Is the Representation of Space-Time

The continuous flowing spacetime forms a spacetime group _G_, one of its fundamental groups is the Poincare group _PO(1,3)_, and the matter and interaction fields are representations of its intrinsic spacetime group. As a kind of quantized space-time unit, space-time group elements generate both space-time manifolds and matter. Matter and fields are aggregates of the quantum space-time within them and determine their type: the Lorentz group _SO(1,3)_ represents a rotating spacetime corresponding to visible matter and the translation group _P1,3_ represents a translational spacetime corresponding to dark matter and dark energy. The aggregation mode of space-time degrees of freedom in matter reveals that charge conjugation symmetry is the inverse symmetry of internal time of charged particles, and the external parity breaking of neutrinos is also due to their internal spatial aggregation mode.

Extracting electromagnetic signatures of spacetime fluctuations

We present a formalism to discern the effects of fluctuations of the spacetime metric on electromagnetic radiation. The formalism works via the measurement of electromagnetic field correlations, while allowing a clear assessment of the assumptions involved. As an application of the formalism, we present a model of spacetime fluctuations that appear as random fluctuations of the refractive index of the vacuum in single, and two co-located Michelson interferometers. We compare an interferometric signal predicted using this model to experimental data from the Holometer and aLIGO. We show that if the signal manifests at a frequency at which the interferometers are sensitive, the strength and scale of possible spacetime fluctuations can be constrained. The bounds, thus obtained, on the strength and scale of the spacetime fluctuations, are also shown to be more stringent than the bounds obtained previously using astronomical observation at optical frequencies. The formalism enables us to evaluate proposed experiments such as QUEST for constraining quantum spacetime fluctuations and to design new ones.

Neutron Star in Quantized Space-Time

We construct and analyze a model of a neutron star in a κ-deformed space-time. This is conducted by first deriving the κ-deformed generalization of the Einstein tensor, starting from the non-commutative generalization of the metric tensor. By generalizing the energy-momentum tensor to the non-commutative space-time and exploiting the κ-deformed dispersion relation, we then set up Einstein’s field equations in the κ-deformed space-time. As we adopt a realization of the non-commutative coordinates in terms of the commutative coordinates and their derivatives, our model is constructed in terms of commutative variables. Using this, we derive the κ-deformed generalization of the Tolman–Oppenheimer–Volkoff equation. Now, by treating the interior of the star as a perfect fluid as in the commutative space-time, we investigate the modification of the neutron star’s mass due to the non-commutativity of space-time, valid up to first order in the deformation parameter. We show that the non-commutativity of space-time enhances the mass limit of the neutron star. We show that the radius and maximum mass of the neutron star depend on the deformation parameter. Further, our study shows that the mass increases as the radius increases for fixed values of the deformation parameter. We show that maximum mass and radius increase as the deformation parameter increases. We find that the mass varies from 0.26M⊙ to 3.68M⊙ as the radius changes from 8.45 km to 18.66 km. Using the recent observational limits on the upper bound of the mass of a neutron star, we find the deformation parameter to be |a|∼10−44 m. We also show that the compactness and surface redshift of the neutron star increase with its mass.

One-loop effective action of the IKKT model for cosmological backgrounds

We study cosmological solutions of the IKKT model with k = –1 FLWR geometry, taking into account one-loop corrections. A previously discussed covariant quantum spacetime is found to be stabilized through one-loop effects at early times, without adding a mass term to the model. At late times, this background is modified and goes through a period of acceleration, before settling down to a coasting FLRW geometry with scale parameter a(t) ~ t. This is qualitatively close to observation without any fine-tuning, irrespective of the detailed matter content of the universe.