Space-time Description Research Articles

Do regular quantum black holes exist?

Abstract Regular black holes do not exist in any classical theory of gravity including Einstein's general relativity. This unappealing feature owes to the appearance of a singularity in the interior of the black hole described by any classical theory. As Hawking argued, all known laws of physics must break down at the singularity. It is thus an important question whether this singularity can disappear in a quantum mechanical description of spacetime. In this Letter, we therefore quantize the black hole interior in a Kantowski-Sachs minisuperspace representation in the presence of spontaneous Klein-Gordon matter field fluctuations. This leads to a Wheeler-DeWitt equation whose solution yields the interior wave function of the black hole. The regular part of this wave function satisfies the DeWitt boundary condition in that it vanishes at the singularity. Moreover, the wave function is regular and well-behaved in the region around the singularity. These features of the wave function suggest that regular black holes do exist in quantum gravity.

Quantum nature of spacetime near the black hole singularity

The concept of spacetime loses its usual interpretation at the essential singularity of a black hole. In consequence, all laws of physics must fail at this classical singularity. This unphysical behavior of spacetime at the singularity originates from general relativity. In order to have a consistent description of spacetime, this singularity must disappear in a quantum mechanical description of spacetime which is expected to be given by a quantum theory of gravity. In this paper, we therefore attempt to describe the quantum nature of spacetime in the vicinity of the (classical) singularity of a black hole. We take the Kantowsi–Sachs representation for the interior spacetime of a black hole and include inevitable vacuum fluctuations of matter field in the Klein–Gordon representation. Hence we obtain the Wheeler–DeWitt equation for the black hole interior and solve this equation exactly yielding a general expression for the interior wave function of the black hole. Admissible wave functions consistent with the DeWitt boundary condition implies that the Hilbert space has three nonoverlapping sectors distinguished by the relative character of the eigenvalues. Regular quantum black holes with admissible and well-behaved wave function having no singularity can exist only in two of those sectors. However, the remaining sector does not contain any regular quantum black hole.

Space-time description of atoms, part I: Electronic structures, dark matter, and g-factors of electron, muon and tau

The description of atoms is based on 3D time and some relativistic effects about spinning bodies have been published previously. The time displacement of the electrons also plays an important role. While the principal quantum number [Formula: see text] refers to the angular momentum [Formula: see text] observed by external observer, the azimuth quantum number [Formula: see text] refers to the angular momentum [Formula: see text] observed from the electron itself. The intrinsic angular momentum observed by the electron is [Formula: see text] according to Stern–Gerlach experiment, but the angular momentum observed by external observer is about [Formula: see text]. The magnetic quantum numbers are deduced from the mentioned effects and the trajectories of electrons are non-probabilistic and geometrically well determined. The spin quantum number indicates the time arrow toward the future or toward the past. So, the electrons with opposite time arrows can be grouped in pairs, where the nucleus is in the middle. Descriptions of the dark matter particles and the electrons are given. Using the value [Formula: see text] suggested from the QED, the [Formula: see text]-factors of the electron and muon are [Formula: see text]; [Formula: see text], which give excellent agreements with the experiments. So, if we equalize the formulas for [Formula: see text]-factor from QED and this approach, it determines the theoretical value of [Formula: see text], without experiment.

T-Minkowski Noncommutative Spacetimes I: Poincaré Groups, Differential Calculi, and Braiding

Abstract This paper introduces and investigates a class of noncommutative spacetimes that I will call “T-Minkowski,” whose quantum Poincaré group of isometries exhibits unique and physically motivated characteristics. Notably, the coordinates on the Lorentz subgroup remain commutative, while the deformation is confined to the translations (hence the T in the name), which act like an integrable set of vector fields on the Lorentz group. This is similar to Majid’s bicrossproduct construction, although my approach allows the description of spacetimes with commutators that include a constant matrix as well as terms that are linear in the coordinates (the resulting structure is that of a centrally extended Lie algebra). Moreover, I require that one can define a covariant braided tensor product representation of the quantum Poincaré group, describing the algebra of N-points. This also implies that a 4D bicovariant differential calculus exists on the noncommutative spacetime. The resulting models can all be described in terms of a numerical triangular R-matrix through RTT relations (as well as RXX, RXY, and RXdX relations for the homogeneous spacetime, the braiding, and the differential calculus). The R-matrices I find are in one-to-one correspondence with the triangular r-matrices on the Poincaré group without quadratic terms in the Lorentz generators. These have been classified, up to automorphisms, by Zakrzewski, and amount to 16 inequivalent models. This paper is the first of a series, focusing on the identification of all the quantum Poincaré groups that are allowed by my assumptions, as well as the associated quantum homogeneous spacetimes, differential calculi, and braiding constructions.

A new teaching-learning sequence to promote secondary school students’ learning of quantum physics using Dirac notation

This paper describes the design of a new teaching-learning sequence on quantum physics aimed at upper secondary school students. In this teaching-learning sequence, GeoGebra simulations and interactive screen experiments are used to investigate the behaviour of a single photon at beam splitter and single photon interference in a Michelson interferometer. We propose a minimal formalism using Dirac notation, which avoids complex numbers and elaborate vector calculus, to make a quantitative description of the quantum optics experiments accessible to secondary school students. With this new educational pathway, we take into account findings from physics education research, which suggest that the introduction of a mathematical formalism tailored to students’ abilities might help them to overcome naive-realist views of quanta or space-time descriptions of quantum phenomena, while at the same time facilitating a transition to a functional understanding of quantum models.

Quantum-Spacetime Symmetries: A Principle of Minimum Group Representation

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum spacetime: this is the principle of minimal group representation, which allows us to consistently and simultaneously obtain a natural description of spacetime’s dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the metaplectic group Mp(n), the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the metaplectic-group symmetry generators and the physical states (the mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov–Klauder type defined by the action of the metaplectic group that divides the Hilbert space into even and odd states that are mutually orthogonal. They carry spin weight of 1/4 and 3/4, respectively, from which two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4- and 3/4-spin-weight states, plus their symmetric and antisymmetric combinations, have spin contents s=0,1/2,1,3/2 and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) spacetime for n→∞. (vii) There emerges a relation between the eigenvalue α of our coherent-state metric solution and the black-hole area (entropy) as Abh/4lp2=α, relating the phase space of the metric found, gab, and the black hole area, Abh, through the Planck length lp2 and the eigenvalue α of the coherent states. As a consequence of the lowest level of the quantum-discrete-spacetime spectrum—e.g., the ground state associated to n=0 and its characteristic length—there exists a minimum entropy related to the black-hole history.

COSMOLOGICAL SCALE FACTOR IN THE RELATIONAL APPROACH

In recent years, within the framework of the relational approach to the description of space-time and physical interactions, a number of studies have been carried out to substantiate the observed cosmological effects. In particular, it has been shown that the cosmological redshift described by the linear part of the Hubble law and the cosmic microwave background can be the result of contributions from emitted but not absorbed electromagnetic radiation. To describe the nonlinear part of the Hubble law, a logarithmic coordinate transformation was used, associated with the existence of a limiting observed distance, expressed by the gravitational radius of the observable Universe. The use of such a transformation must be justified by showing how it can be obtained in the derivation of space-time concepts for a system of a large number of emitters and absorbers. The article provides this rationale: it is shown that when deriving classical distances in the relational approach, there are two possibilities for determining the distance scale, they correspond to the scales of comoving and proper distances in cosmology, while the scale factor is expressed through the partition function of the configurations of emitters and absorbers.

The tensor of the exact circle: reconstructing geometry

Developing a theory for quantum gravity is one of the big open questions in theoretical high-energy physics. Recently, a tensor model approach has been considered that treats tensors as the generators of commutative non-associative algebras, which might be an appropriate interpretation of the canonical tensor model. In this approach, the non-associative algebra is assumed to be a low-energy description of the so-called associative closure, which gives the full description of spacetime including the high-energy modes. In the previous work it has been shown how to (re)construct a topological space with a measure on it, and one of the prominent examples that was used to develop the framework was the exact circle. In this work we will further investigate this example, and show that it is possible to reconstruct the full Riemannian geometry by reconstructing the metric tensor. Furthermore, it is demonstrated how diffeomorphisms behave in this formalism, firstly by considering a specific class of diffeomorphisms of the circle, namely the ellipses, and subsequently by performing an explicit diffeomorphism to ‘smoothen’ sets of points generated by the tensor rank decomposition.

Limits of a non-local quantum spacetime

A generic implication of incorporating gravitational effects in the analysis of quantum measurements is the existence of a zero-point length of spacetime. This requires an inherently non-local description of spacetime, beyond the usual one based on metric [Formula: see text] etc. The quantum spacetime should instead be reconstructed from non-local bi-tensors of the form [Formula: see text]. A deeper look then reveals a subtle interplay between non-locality and the limit [Formula: see text]. In particular, the so-called emergent gravity paradigm — in which gravitational dynamics/action/spacetime are emergent and characterized by an entropy functional — arises as the Cheshire grin of a fundamentally non-local quantum spacetime. This paper describes the flow of metric with respect to Planck length, and proposes a novel action for the same.

Space-time behavior of the compressible Navier-Stokes equations with hyperbolic heat conduction

We consider compressible Navier-Stokes equations with hyperbolic heat conduction in R3. A space-time description of the classical solution is given when the initial perturbation is suitable small. The result implies that all of the unknowns obey the generalized Huygens’ principle as the classical compressible Navier-Stokes equations in Liu and Wang [Commun. Math. Phys. 196, 145–173 (1998)]. Additionally, we show that the decay of the flux q is faster than the other unknowns.

On de Sitter spacetime and string theory

We review various aspects of de Sitter spacetime in string theory: its status as an Effective Field Theory spacetime solution, its relation to the vacuum energy problem in string theory, its (global) holographic definition in terms of two entangled and noncanonical conformal field theories as well as a realization of a realistic de Sitter universe endowed with the observed visible matter and the necessary dark sector in order to reproduce the realistic cosmological structure. In particular, based on the new insight regarding the cosmological constant problem in string theory, we argue that in a doubled, [Formula: see text]-duality-symmetric, phase-space-like and noncommutative generalized-geometric formulation, string theory can naturally lead to a small and positive cosmological constant that is radiatively stable and technically natural. Such a formulation is fundamentally based on a quantum spacetime, but in an effective spacetime description of this general formulation of string theory, the curvature of the dual spacetime is the cosmological constant of the observed spacetime, while the size of the dual spacetime is the gravitational constant of the same observed spacetime. Also, the three scales associated with intrinsic noncommutativity of string theory, the cosmological constant scale, the Planck scale as well as the Higgs scale, can be arranged to satisfy various seesaw-like formulae. Along the way, we show that these new features of string theory can be implemented in a particular deformation of cosmic-string-like models.

Tunneling wave function proposal with loop quantum geometry effects

In Vilenkin's tunneling wave function proposal our expanding Universe is born via a tunneling through a barrier from nothing at the zero scale factor. We explore the viability of this proposal for the spatially-closed Friedmann-Lema\^{\i}tre-Robertson-Walker model with a positive cosmological constant including quantum gravity modifications in the Planck regime. Our setting is the effective spacetime description of loop quantum cosmology (LQC) which is known to replace the big bang singularity with a bounce due to the holonomy modifications. Due to the bounce, the barrier potential of the Wheeler-DeWitt theory is replaced by a steplike potential which makes the tunneling proposal incompatible. But for a complete picture of singularity resolution, inverse scale-factor modifications from quantum geometry must be included which play an important role at very small scale factors in the spatially closed models. We show that with inclusion of inverse scale-factor modifications the resulting potential is again a barrier potential. The Universe at the vanishing scale factor is dynamically nonsingular and in an Einstein staticlike phase. We show that quantum geometric effects in LQC provide a nonsingular completion of Vilenkin's tunneling proposal. We also find that quantum geometric effects result in a possibility of a tunneling to a quantum cyclic universe albeit for a very large value of cosmological constant determined by the quantum geometry.

The balance In the six dimensions of space-time description of quantum mechanics phenomena and nature of time

<p>This study presents a theory with a six-dimensional space-time structure, R^6, in order to describe quantum mechanic phenomena, the time arrow and quantum gravity. The interpretation of quantum world phenomena using four-dimensional space-time would be a very complicated and indescribable task. The dual wave-particle behavior, entanglement, quantum corridors, etc., represent the complex space-time structure. Previous studies indicate that complicated behaviors of particles in quantum mechanics are basically considered as the inherent behavior of those particles. The theoretical framework of the balance is the transformation of imaginary dimensions into geometric dimensions and the description of quantum mechanical phenomena using external Euclidean geometry. The six-dimensional space-time structure consists of three space and three time dimensions and the time arrow is the result of the impossibility of the existence of matter in six space-time dimensions, and the direction of the arrow is aligned with the expansion of the universe.</p>

«МАНАСТЫ» ИЛИМИЙ ИЗИЛДӨӨНҮН ФИЛОСОФИЯЛЫК- МЕТОДОЛОГИЯЛЫК ТҮПТҮҮ МАСЕЛЕЛЕРИ

The article analyzes the philosophical and methodological problems of studying the epic "Manas". The study of the epic within the framework of the materialist-Marxist methodological paradigm has made a certain contribution, but in the current conditions, the need to study such cultural phenomena in the context of new philosophical and methodological paradigms and concepts is becoming increasingly obvious. In addition to the relevance of the research problem, the article raises such questions as - is the epic "Manas" a work of art or contains a partial historical truth? What are the reasons for the creation of "Manas" as a heroic epic poem? Within the framework of another philosophical and methodological paradigm. The speech form, style, structure of the text of "Manas", the meaning of words, in general, linguistic features were formed on a historical basis, over a very long period of time. Modern postmodernism as a phenomenon in culture and literature in many of its features in style, comprehension, description of space-time, in the structure of text form, etc., has similarities with folklore, the Manas epic.

Black hole and de Sitter microstructures from a semiclassical perspective

We describe two different, but equivalent semiclassical views of black hole physics in which the equivalence principle and unitarity are both accommodated. In one, unitarity is built-in, while the black hole interior emerges only effectively as a collective phenomenon involving horizon (and possibly other) degrees of freedom. In the other, more widely studied approach, the existence of the interior is manifest, while the unitarity of the underlying dynamics can be captured only indirectly by incorporating certain nonperturbative effects of gravity. These two pictures correspond to a distant description and the description based on entanglement islands/replica wormholes, respectively. We also present a holographic description of de Sitter spacetime based on the former approach, in which the holographic theory is located on the stretched horizon of a static patch. We argue that the existence of these two approaches is rooted in the two formulations of quantum mechanics: the canonical and path integral formalisms.

Pointwise space-time estimates of compressible Oldroyd-B model

In this paper, we investigate pointwise space-time behavior of the compressible Oldroyd-B model in R3 based on Green's function method. We first give the representations of two Green's matrices in the Fourier space: one is a 7×7 matrix for the compressible part and the other is a 6×6 matrix for the incompressible part. Then by using high-medium-low frequency analysis together with real analysis and Fourier analysis we get the pointwise estimates for each entry in these Green's matrices. Finally, we deal with the nonlinear problem and obtain the pointwise space-time description of the solution. It shows that the fluid density ρ, momentum m and the symmetric tensor of constrains T obey the generalized Huygens' principle as the compressible Navier-Stokes equations. As a byproduct, we extend L2-estimate in [47] to Lp-estimate with p>1. Moreover, the decay of T is faster than those of (ρ,m), which also refine the result in [47].

Novel relationship between shear and energy density at the bounce in nonsingular Bianchi I spacetimes

In classical Bianchi I spacetimes, underlying conditions for what dictates the singularity structure---whether it is anisotropic shear or energy density, can be easily determined from the generalized Friedmann equation. However, in nonsingular bouncing anisotropic models these insights are difficult to obtain in the quantum gravity regime where the singularity is resolved at a nonvanishing mean volume which can be large compared to the Planck volume, depending on the initial conditions. Such nonsingular models may also lack a generalized Friedmann equation making the task even more difficult. We address this problem in an effective spacetime description of loop quantum cosmology (LQC) where energy density and anisotropic shear are universally bounded due to quantum geometry effects, but a generalized Friedmann equation has been difficult to derive due to the underlying complexity. Performing extensive numerical simulations of effective Hamiltonian dynamics, we bring to light a surprising, seemingly universal relationship between energy density and anisotropic shear at the bounce in LQC. For a variety of initial conditions for a massless scalar field, an inflationary potential, and two types of ekpyrotic potentials we find that the values of energy density and the anisotropic shear at the quantum bounce follow a novel parabolic relationship which reveals some surprising results about the anisotropic nature of the bounce, such as that the maximum value of the anisotropic shear at the bounce is reached when the energy density reaches approximately half of its maximum allowed value. The relationship we find can prove very useful for developing our understanding of the degree of anisotropy of the bounce, isotropization of the postbounce universe, and discovering the modified generalized Friedmann equation in Bianchi I models with quantum gravity corrections.

Black holes in dS3

In three-dimensional de Sitter space classical black holes do not exist, and the Schwarzschild-de Sitter solution instead describes a conical defect with a single cosmological horizon. We argue that the quantum backreaction of conformal fields can generate a black hole horizon, leading to a three-dimensional quantum de Sitter black hole. Its size can be as large as the cosmological horizon in a Nariai-type limit. We show explicitly how these solutions arise using braneworld holography, but also compare to a non-holographic, perturbative analysis of backreaction due to conformally coupled scalar fields in conical de Sitter space. We analyze the thermodynamics of this quantum black hole, revealing it behaves similarly to its classical four-dimensional counterpart, where the generalized entropy replaces the classical Bekenstein-Hawking entropy. We compute entropy deficits due to nucleating the three-dimensional black hole and revisit arguments for a possible matrix model description of dS spacetimes. Finally, we comment on the holographic dual description for dS spacetimes as seen from the braneworld perspective.

Untying the Gordian Knot: Process, Reality, and Context

Untying the Gordian Knot: Process, Reality, and Context

Dark energy star in gravity's rainbow

The concept of dark energy can be a candidate for preventing the gravitational collapse of compact objects to singularities. According to the usefulness of gravity's rainbow in UV completion of general relativity (by providing a new description of spacetime), it can be an excellent option to study the behavior of compact objects near phase transition regions. In this work, we obtain a modified Tolman-Openheimer-Volkof (TOV) equation for anisotropic dark energy as a fluid by solving the field equations in gravity's rainbow. Next, to compare the results with general relativity, we use a generalized Tolman-Matese-Whitman mass function to determine the physical quantities such as energy density, radial pressure, transverse pressure, gravity profile, and anisotropy factor of the dark energy star. We evaluate the junction condition and investigate the dynamical stability of dark energy star thin shell in gravity's rainbow. We also study the energy conditions for the interior region of this star. We show that the coefficients of gravity's rainbow can significantly affect this non-singular compact object and modify the model near the phase transition region.