Quantum Spacetime Research Articles

Causality, Uncertainty Principle, and Quantum Spacetime Manifold in Planck Scale

In causal set theory, there are three ambiguous concepts that this article tries to provide a solution to resolve these ambiguities. These three ambiguities in Planck's scale are: the causal relationship between events, the position of the uncertainty principle, and the kinematic. Assuming the interaction between events, a new definition of the causal relationship is presented. Using the principle of superposition, more than one world line are attributed to two events that are interacting with each other to cover the uncertainty principle. Using these achievements, it is shown that kinematics has no place in the Planck dimension and that quantum spacetime manifold should be used instead.

On the propagation across the big bounce in an open quantum FLRW cosmology

The propagation of a scalar field in an open FLRW bounce-type quantum spacetime is examined, which arises within the framework of the IKKT matrix theory. In the first part of the paper, we employ general-relativity tools to study null and timelike geodesics at the classical level. This analysis reveals that massless and massive non-interacting particles can travel across the big bounce. We then exploit quantum-field-theory techniques to evaluate the scalar field propagator. In the late-time regime, we find that it resembles the standard Feynman propagator of flat Minkowski space, whereas for early times it governs the propagation across the big bounce and gives rise to a well-defined correlation between two points on opposite sheets of the spacetime.

Atomic Spacetime Model Based on Atomic AString Functions

A novel model of spacetime and fields atomization based on Atomic Series over finite Atomic AString Functions is offered. Formulated Atomization Theorems allow representing polynomials, analytic functions, and solutions of field equations including General Relativity via superposition of solitonic atoms which can be associated with flexible spacetime quantum, metriants, or elementary distortions. Spacetime is conceptualized as a lattice of flexible Atomic Solitons adjusting locations to reproduce different metrics and other physical fields. It may offer the variants of unified field theory based on Atomic Solitons where, like in string theory, fields become interconnected having a common mathematical ancestor.

Study of Quantization of Space-Time Explains Matter and Its Aspects

By quantizing space-time in such a way that I can calculate all of the constants of physics and derive and explain every equation therein. The magnetic field appears when the electric field seems to travel faster than c. The same way an “anti-gravity” perpendicular field appears, totally depended on relative velocities, since the electric and gravitational forces are made of the micro field lines and are different aspects of the same force [1]. The “gravitational” perpendicular force can be repellant, when masses travel in the same direction, (massive distant galaxies repel enlarging the universe, new current mass just being released) and it can be attractive (opposite spiral arms moving in opposite directions, combined with a super-massive black hole). The recent detection of gravity waves, is clear evidence for all of this since these waves need a perpendicular field, like electro-magnetic waves. The magnetic style of the perpendicular field, at extremely high can cause matter and dark to interact

Quantum discrete levels of the Universe from the early trans-Planckian vacuum to the late dark energy

The standard model of the universe is further completed back in time before inflation in agreement with observations, classical-quantum gravity duality and quantum space-time. Quantum vacuum energy bends the space-time and produces a constant curvature de Sitter background. We link de Sitter universe and the cosmological constant to the (classical and quantum) harmonic oscillator. Quantum discrete cosmological levels are found: size, time, vacuum energy, Hubble constant and gravitational (Gibbons-Hawking) entropy from the very early trans-planckian vacuum to the classical today vacuum energy. For each level $n = 0, 1, 2,...$, the two: post and pre (trans)-planckian phases are covered: In the post-planckian universe, the levels (in planck units) are: Hubble constant $H_{n} = {1}/\sqrt{(2n + 1)}$, vacuum energy $\Lambda_{n} = 1/(2n + 1)$, entropy $S_n = (2n + 1)$. As $n$ increases, radius, mass and $S_n$ increase, $H_n$ and $\Lambda_n$ decrease and {\it consistently} the universe {\it classicalizes}. In the pre-planckian (trans-planckian) phase, the quantum levels are: $H_{Qn} = \sqrt{(2n + 1)},\; \Lambda_{Qn} = (2n + 1)/1,\; S_{Qn} = 1/(2n + 1)$, $Q$ denoting quantum. The $n$-levels cover {\it all} scales from the far past highest excited trans-planckian level $n = 10^{122}$ with finite curvature, $\Lambda_Q = 10^{122}$ and minimum entropy $S_Q = 10^{-122}$, $n$ decreases till the planck level $(n = 0)$ and enters the post-planckian phase e.g: $n = 1, 2,...,n_{inflation} = 10^{12},... ,n_{cmb} = 10^{114},...,n_{reoin} = 10^{118},...,n_{today} = 10^{122}$ with the most classical value $H_{today} = 10^{-61}$, $\Lambda_{today} = 10^{-122}$, $S_{today} = 10^{122}$. We implement the Snyder-Yang algebra in this context yielding a consistent group-theory realization of quantum discrete de Sitter space-time, classical-quantum gravity duality symmetry and a clarifying unifying picture.(Abridged)

Quantum gravity with THESEUS

In this paper we explore the possibility to search for a dispersion law for light propagation in vacuo with a sample of Gamma-Ray Bursts detected by the THESEUS satellite. Within Quantum Gravity theories, different models for space-time quantization predict relative discrepancies of the speed of photons w.r.t. the speed of light that (in a series expansion) depend on a given power of the ratio of the photon energy to the Planck energy. This ratio is as small as 10− 23 for photons in the soft γ −ray band (100 keV). The dominant effect is determined by the first significant term of this expansion. If the first order in this expansion is relevant, these theories imply a Lorentz Invariance Violation (LIV hereafter) and are generally dubbed LIV-theories. Therefore, to detect this effect, light must propagate over enormous distances and the experiment must have extraordinary sensitivity. Gamma-Ray Bursts, occurring at cosmological distances, could be used to detect this tiny signature of space-time granularity. Once the photons of a Gamma-Ray Burst are emitted at a given (cosmological) distance, they arrive on the detector with relative delays that linearly depends on the energy differences and on the distance travelled, that, given a set of cosmological parameters, is a unique function of the redshift. The strong temporal variability of the Gamma-Ray Bursts light-curves allows, with different techniques (e.g. cross-correlations), to compute these delays by comparing light-curves of Gamma-Ray Bursts for which the redshift is known, in adjacent energy bands covering a sufficiently wide energy range. In this way, LIV-theories can be effectively constrained. THESEUS offers the opportunity to collect a homogeneous set of GRBs for which the redshift is known, with a signal to background ratio sufficient to compute delays through cross correlation techniques, and covering an energy band (from few keV to few MeV) wide enough to produce significant delays. In this article we explore the possibility to constrain LIV-theories with THESEUS by means of Monte Carlo simulations. In summary, within the nominal duration of 3 years, THESEUS could constrain (or detect) Quantum Gravity Lorentz Invariance Violation effects at al level of 17 times the Planck Length (1.6 × 10− 33 cm); if the mission is extended up to 7 years, this constrain is improved down to a level of 11 times the Planck Length.

Spinorial Snyder and Yang models from superalgebras and noncommutative quantum superspaces

The relativistic Lorentz-covariant quantum space-times obtained by Snyder can be described by the coset generators of (anti) de-Sitter algebras. Similarly, the Lorentz-covariant quantum phase spaces introduced by Yang, which contain additionally quantum curved fourmomenta and quantum-deformed relativistic Heisenberg algebra, can be defined by suitably chosen coset generators of conformal algebras. We extend such algebraic construction to the respective superalgebras, which provide quantum Lorentz-covariant superspaces (SUSY Snyder model) and indicate also how to obtain the quantum relativistic phase superspaces (SUSY Yang model). In last Section we recall briefly other ways of deriving quantum phase (super)spaces and we compare the spinorial Snyder type models defining bosonic or fermionic quantum-deformed spinors.

Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection

We explore emergent geometry of the spacetime at the microscopic scale by adiabatic transport of a quasi-coherent state of a fermionic string, with quantum spacetime described by the matrix theory (BFSS matrix model). We show that the generator of the Berry phase is the shift vector of the spacetime foliation by spacelike surfaces associated with the quasi-coherent state. The operator-valued generator of the geometric phase of weak adiabatic transport is the Lorentz connection of the emergent geometry which is not torsion free at the microscopic scale. The effects of the torsion seem consistent with the usual interpretation of the Berry curvature as a pseudo magnetic field.

Spin‐Spacetime Censorship

AbstractQuantum entanglement and relativistic causality are key concepts in theoretical works seeking to unify quantum mechanics and gravity. In this article, a gedanken experiment that couples the spin to spacetime is proposed, and is then analyzed in the context of quantum information by using different approaches to quantum gravity. Both classical gravity theory and certain quantum theories predict that around a spin‐half particle, the spherical symmetry of spacetime is broken by its magnetic field or merely by its intrinsic angular momentum. It is asserted that any spin‐related deviation from spherical symmetry, upon appropriate measurement, can violate relativistic causality and quantum no‐cloning. To avoid these violations, the measurable spacetime around the particle's rest frame shall typically remain spherically symmetric, potentially as a back‐action by the act of a covariant measurement, or due to a quantized spin‐dependence of the magnetic field. This way, this gedanken experiment suggests a censorship mechanism preventing the possibility of spacetime‐based spin detection, which can shed light on the interface between quantum mechanics and gravity. Since this proposed gedanken experiment is independent of any specific theory, it is suitable for testing the coupling of quantum matter and spacetime in present and future candidate theories of quantum gravity.

Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus

We consider space-time quantum fields with exponential/trigonometric interactions. In the context of Euclidean quantum field theory, the former and the latter are called the Hoegh-Krohn model and the Sine-Gordon model, respectively. The main objective of the present paper is to construct infinite dimensional diffusion processes which solve modified stochastic quantization equations for these quantum fields on the two-dimensional torus by the Dirichlet form approach and to prove strong uniqueness of the corresponding Dirichlet operators.

World quantum gravity: quantum test objects and Synge’s world function

A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity could be technically simpler to work with than variant quantities such as the metric tensor. It also could facilitate the studies of matter coupling and quantum spacetime causal structures. In contrast to approaches based on piecewise linear geometries, here gravity is captured by its effects on quantum test particles and fields. By an observation of Parker, under a Feynman sum a gravitational phase can be traded into a Van Vleck–Morette determinant term. This leads to a new candidate path integral for gravity, which in certain special cases can be computed efficient in the Lorentzian signature. We discuss some ambiguities left in the path integral measure, which invite further clarifications.

PARTS OF SPACETIME

Abstract Consider the following pair of theses: (i) all fundamental physical objects are spatiotemporal and (ii) all non-fundamental physical objects are ultimately composed of fundamental objects. Work on the physics of quantum gravity suggests that spacetime is a non-fundamental, emergent phenomenon and thus that thesis (i) is false. The fundamentals are non-spatiotemporal in nature. This paper will argue against (ii) on the grounds that non-fundamental spatiotemporal objects cannot be composed of fundamental non-spatiotemporal objects. So, assuming that spacetime is emergent, new metaphysical resources are needed to explain the relationship between the fundamental objects posited by quantum gravity and spacetime.

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Study on the Relationship between Quantum Entanglement and Spacetime

Quantum entanglement and spacetime are strongly associated fields in modern physics. This paper investigated the connection between quantum entanglement and spacetime, particularly focusing on how they mutually form one another. The quantum mechanics and relativity theory cannot peacefully coexist in some cases, so it is difficult to combine them together. This article analyzes studies which suggest quantum entanglement can fabricate the continuous spacetime, and studies that imply spacetime geometry can explain quantum entanglement. These findings may bring us a better vision of the relation between quantum mechanics and relativity, as well as pave a path to the unification of quantum mechanics and relativity.

Emergent geometry through quantum entanglement in Matrix theories

In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to light-cone M-theory in a PP-wave background, we compute the Von Neumann entanglement entropy between a probe giant graviton and a source. We demonstrate that this entanglement entropy is directly and generally related to the local tidal acceleration experienced by the probe. This establishes a new map between local spacetime geometry and quantum entanglement, suggesting a mechanism through which geometry emerges from Matrix quantum mechanics. We extend this setting to light-cone M-theory in flat space, or the Banks-Fischler-Shenker-Susskind Matrix model, and we conjecture a new general relation between a certain measure of entanglement in Matrix theories and local spacetime geometry. The relation involves a ‘c-tensor’ that measures the evolution of local transverse area and relates to the local energy-momentum tensor measured by a probe.

Quantization of inhomogeneous spacetimes with cosmological constant term

We show that the Szekeres system with cosmological constant admits a sufficient number of conservation laws, which allow to claim the integrability of the system. The main novelty in this investigation is that we find that the unique attractor of the Szekeres system is the isotropic inhomogeneous de Sitter (-like) Universe, contrary to the original system in which the attractors describe Kantowski–Sachs (-like) spacetimes. We also study the existence of quantum corrections and the emergence of classicality by considering the linear and quadratic conserved quantities at the quantum level. We perform an analysis considering different approaches, involving the Bohmian quantum potential and a probability analysis. The result is that there are no quantum corrections for the quadratic integrals, while there exists a linear case for which we find quantum corrections.

Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale

Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared to other schemes of gravitational decoherence, we find that the decoherence rate predicted by our model is extremal, being minimal in the deep quantum regime below the Planck scale and maximal in the mesoscopic regime beyond it. We discuss possible experimental tests of our model based on cavity optomechanics setups with ultracold massive molecular oscillators and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.

Spacetime Quantum Reference Frames and superpositions of proper times

In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.

Space-Time Quantum Metasurfaces

Metasurfaces have recently entered the realm of quantum photonics, enabling manipulation of quantum light using a compact nanophotonic platform. Realizing the full potential of metasurfaces at the deepest quantum level requires the ability to tune coherent light-matter interactions continuously in space and time. Here, we introduce the concept of space-time quantum metasurfaces for arbitrary control of the spectral, spatial, and spin properties of nonclassical light using a compact photonic platform. We show that space-time quantum metasurfaces allow on-demand tailoring of entanglement among all degrees of freedom of a single photon. We also show that spatiotemporal modulation induces asymmetry at the fundamental level of quantum fluctuations, resulting in the generation of steered and vortex photon pairs out of vacuum. Space-time quantum metasurfaces have the potential to enable novel photonic functionalities, such as encoding quantum information into high-dimensional color qudits using designer modulation protocols, sculpting multispectral and multispatial modes in spontaneous emission, and generating reconfigurable hyperentanglement for high-capacity quantum communications.

Quantum gravity phenomenology in the infrared

Quantum gravity effects are traditionally tied to short distances and high energies. In this essay, we argue that, perhaps surprisingly, quantum gravity may have important consequences for the phenomenology of the infrared. We center our discussion around a conception of quantum gravity involving a notion of quantum spacetime that arises in metastring theory. This theory allows for an evolution of a cosmological Universe in which string-dual degrees of freedom decouple as the Universe ages. Importantly, such an implementation of quantum gravity allows for the inclusion of a fundamental length scale without introducing the fundamental breaking of Lorentz symmetry. The mechanism seems to have potential for an entirely novel source for dark matter/energy. The simplest observational consequences of this scenario may very well be residual infrared modifications that emerge through the evolution of the Universe.