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10 pages, 259 KiB

Open AccessArticle

On the Hilbert Space in Quantum Gravity

by Ednardo Paulo Spaniol, Ronni Geraldo Gomes Amorim and Sergio Costa Ulhoa

Universe 2022, 8(8), 413; https://doi.org/10.3390/universe8080413 - 5 Aug 2022

Viewed by 1381

Abstract

This article deals with the fractional problem of Sturm–Liouville and the Hilbert space associated with the solutions of this differential equation. We apply a quantization procedure to Schwarzschild space–time and obtain a fractional differential equation. The Hilbert space for these solutions is established. [...] Read more.

This article deals with the fractional problem of Sturm–Liouville and the Hilbert space associated with the solutions of this differential equation. We apply a quantization procedure to Schwarzschild space–time and obtain a fractional differential equation. The Hilbert space for these solutions is established. We used equations arising from quantization for the FRW and Reissner–Nordstron metrics to build the respective Hilbert spaces. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

26 pages, 366 KiB

Open AccessArticle

A Unified Quantization of Gravity and Other Fundamental Forces of Nature

by Claus Gerhardt

Universe 2022, 8(8), 404; https://doi.org/10.3390/universe8080404 - 1 Aug 2022

Cited by 1 | Viewed by 1670

Abstract

We quantized the interaction of gravity with Yang–Mills and spinor fields; hence, offering a quantum theory incorporating all four fundamental forces of nature. Let us abbreviate the spatial Hamilton functions of the standard model by

H_{S M}

and the Hamilton function of [...] Read more.

We quantized the interaction of gravity with Yang–Mills and spinor fields; hence, offering a quantum theory incorporating all four fundamental forces of nature. Let us abbreviate the spatial Hamilton functions of the standard model by

H_{S M}

and the Hamilton function of gravity by

H_{G}

. Working in a fiber bundle E with base space

S_{0} = R^{n}

, where the fiber elements are Riemannian metrics, we can express the Hamilton functions in the form

H_{G} + H_{S M} = H_{G} + t^{- \frac{2}{3}} {\tilde{H}}_{S M}

, if

n = 3

, where

{\tilde{H}}_{S M}

depends on metrics

σ_{i j}

satisfying

det σ_{i j} = 1

. In the quantization process, we quantize

H_{G}

for general

σ_{i j}

but

{\tilde{H}}_{S M}

only for

σ_{i j} = δ_{i j}

by the usual methods of QFT. Let v resp.

ψ

be the spatial eigendistributions of the respective Hamilton operators, then, the solutions u of the Wheeler–DeWitt equation are given by

u = w v ψ

, where w satisfies an ODE and u is evaluated at

(t, δ_{i j})

in the fibers. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

8 pages, 1202 KiB

Open AccessCommunication

Analogue Quantum Gravity in Hyperbolic Metamaterials

by Igor I. Smolyaninov and Vera N. Smolyaninova

Universe 2022, 8(4), 242; https://doi.org/10.3390/universe8040242 - 14 Apr 2022

Cited by 3 | Viewed by 2388

Abstract

It is well known that extraordinary photons in hyperbolic metamaterials may be described as living in an effective Minkowski spacetime, which is defined by the peculiar form of the strongly anisotropic dielectric tensor in these metamaterials. Here, we demonstrate that within the scope [...] Read more.

It is well known that extraordinary photons in hyperbolic metamaterials may be described as living in an effective Minkowski spacetime, which is defined by the peculiar form of the strongly anisotropic dielectric tensor in these metamaterials. Here, we demonstrate that within the scope of this approximation, the sound waves in hyperbolic metamaterials look similar to gravitational waves, and therefore the quantized sound waves (phonons) look similar to gravitons. Such an analogue model of quantum gravity looks especially interesting near the phase transitions in hyperbolic metamaterials where it becomes possible to switch quantum gravity effects on and off as a function of metamaterial temperature. We also predict strong enhancement of sonoluminescence in ferrofluid-based hyperbolic metamaterials, which looks analogous to particle creation in strong gravitational fields. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

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19 pages, 454 KiB

Open AccessArticle

Lorentzian Vacuum Transitions in Hořava–Lifshitz Gravity

by Hugo García-Compeán and Daniel Mata-Pacheco

Universe 2022, 8(4), 237; https://doi.org/10.3390/universe8040237 - 12 Apr 2022

Cited by 13 | Viewed by 1693

Abstract

The vacuum transition probabilities for a Friedmann–Lemaître–Robertson–Walker universe with positive curvature in Hořava–Lifshitz gravity in the presence of a scalar field potential in the Wentzel–Kramers–Brillouin approximation are studied. We use a general procedure to compute such transition probabilities using a Hamiltonian approach to [...] Read more.

The vacuum transition probabilities for a Friedmann–Lemaître–Robertson–Walker universe with positive curvature in Hořava–Lifshitz gravity in the presence of a scalar field potential in the Wentzel–Kramers–Brillouin approximation are studied. We use a general procedure to compute such transition probabilities using a Hamiltonian approach to the Wheeler–DeWitt equation presented in a previous work. We consider two situations of scalar fields, one in which the scalar field depends on all the spacetime variables and another in which the scalar field depends only on the time variable. In both cases, analytic expressions for the vacuum transition probabilities are obtained, and the infrared and ultraviolet limits are discussed for comparison with the result obtained by using general relativity. For the case in which the scalar field depends on all spacetime variables, we observe that in the infrared limit it is possible to obtain a similar behavior as in general relativity, however, in the ultraviolet limit the behavior found is completely opposite. Some few comments about possible phenomenological implications of our results are given. One of them is a plausible resolution of the initial singularity. On the other hand, for the case in which the scalar field depends only on the time variable, the behavior coincides with that of general relativity in both limits, although in the intermediate region the probability is slightly altered. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

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4 pages, 192 KiB

Open AccessArticle

Considerations on Quantum Gravity Phenomenology

by Carlo Rovelli

Universe 2021, 7(11), 439; https://doi.org/10.3390/universe7110439 - 15 Nov 2021

Cited by 7 | Viewed by 2099

Abstract

I describe two phenomenological windows on quantum gravity that seem promising to me. I argue that we already have important empirical inputs that should orient research in quantum gravity. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

7 pages, 371 KiB

Open AccessCommunication

Spin Distribution for the ’t Hooft–Polyakov Monopole in the Geometric Theory of Defects

by Mikhail O. Katanaev

Universe 2021, 7(8), 256; https://doi.org/10.3390/universe7080256 - 21 Jul 2021

Cited by 4 | Viewed by 1622

Abstract

Recently the ’t Hooft–Polyakov monopole solutions in Yang–Mills theory were given new physical interpretation in the geometric theory of defects describing the continuous distribution of dislocations and disclinations in elastic media. It means that the ’t Hooft–Polyakov monopole can be seen, probably, in [...] Read more.

Recently the ’t Hooft–Polyakov monopole solutions in Yang–Mills theory were given new physical interpretation in the geometric theory of defects describing the continuous distribution of dislocations and disclinations in elastic media. It means that the ’t Hooft–Polyakov monopole can be seen, probably, in solids. To this end we need to compute the corresponding spin distribution on lattice sites of crystals. The paper describes one of the possible spin distributions. The Bogomol’nyi–Prasad–Sommerfield solution is considered as an example. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

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Review

Jump to: Research

45 pages, 3799 KiB

Open AccessReview

Torsion at Different Scales: From Materials to the Universe

by Nick E. Mavromatos, Pablo Pais and Alfredo Iorio

Universe 2023, 9(12), 516; https://doi.org/10.3390/universe9120516 - 14 Dec 2023

Cited by 7 | Viewed by 1743

Abstract

The concept of torsion in geometry, although known for a long time, has not gained considerable attention from the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of contexts of physical interest. These range from [...] Read more.

The concept of torsion in geometry, although known for a long time, has not gained considerable attention from the physics community until relatively recently, due to its diverse and potentially important applications to a plethora of contexts of physical interest. These range from novel materials, such as graphene and graphene-like materials, to advanced theoretical ideas, such as string theory and supersymmetry/supergravity, and applications thereof in terms of understanding the dark sector of our Universe. This work reviews such applications of torsion at different physical scales. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

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22 pages, 536 KiB

Open AccessReview

Hunting Quantum Gravity with Analogs: The Case of High-Energy Particle Physics

by Paolo Castorina, Alfredo Iorio and Helmut Satz

Universe 2022, 8(9), 482; https://doi.org/10.3390/universe8090482 - 13 Sep 2022

Cited by 2 | Viewed by 1618

Abstract

In this review, we collect, for the first time, old and new research results, and present future perspectives on how hadron production, in high-energy scattering processes, can experimentally probe fundamental questions of quantum gravity. The key observations that ignited the link between the [...] Read more.

In this review, we collect, for the first time, old and new research results, and present future perspectives on how hadron production, in high-energy scattering processes, can experimentally probe fundamental questions of quantum gravity. The key observations that ignited the link between the two arenas are the so-called “color-event horizon” of quantum chromodynamics, and the (de)accelerations involved in such scattering processes. Both phenomena point to the Unruh (and related Hawking)-type effects. After the first pioneering investigations, such research studies continued, including studies of the horizon entropy and other “black-hole thermodynamical” behaviors, which incidentally are also part of the frontier of the analog gravity research itself. It has been stressed that the trait d’union between the two phenomenologies is that in both hadron physics and black hole physics, “thermal” behaviors are more easily understood, not as due to real thermalization processes (sometimes just impossible, given the small number of particles involved), but rather to a stochastic/quantum entanglement nature of such temperatures. Finally, other aspects, such as the self-critical organizations of hadronic matter and of black holes, have been recently investigated. The results of those investigations are also summarized and commented upon here. As a general remark, this research line shows that we can probe quantum gravity theoretical constructions with analog systems that are not confined to only the condensed matter arena. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

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23 pages, 970 KiB

Open AccessReview

Hunting Quantum Gravity with Analogs: The Case of Graphene

by Giovanni Acquaviva, Alfredo Iorio, Pablo Pais and Luca Smaldone

Universe 2022, 8(9), 455; https://doi.org/10.3390/universe8090455 - 30 Aug 2022

Cited by 16 | Viewed by 2105

Abstract

Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of the classical or quantum gravity of quantum fields in curved space or of other high-energy scenarios on lower-energy corresponding systems. The “reverse way” consists [...] Read more.

Analogs of fundamental physical phenomena can be used in two ways. One way consists in reproducing specific aspects of the classical or quantum gravity of quantum fields in curved space or of other high-energy scenarios on lower-energy corresponding systems. The “reverse way” consists in building fundamental physical theories, for instance, quantum gravity models, inspired by the lower-energy corresponding systems. Here, we present the case of graphene and other Dirac materials. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

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18 pages, 720 KiB

Open AccessReview

Maximal Kinematical Invariance Group of Fluid Dynamics and Applications

by V. V. Sreedhar and Amitabh Virmani

Universe 2022, 8(6), 319; https://doi.org/10.3390/universe8060319 - 7 Jun 2022

Cited by 2 | Viewed by 1624

Abstract

The maximal kinematical invariance group of the Euler equations of fluid dynamics for the standard polytropic exponent is larger than the Galilei group. Specifically, the inversion transformation [...] Read more.

The maximal kinematical invariance group of the Euler equations of fluid dynamics for the standard polytropic exponent is larger than the Galilei group. Specifically, the inversion transformation

(Σ : t \to - 1 / t, \vec{x} \to \vec{x} / t)

leaves the Euler equation’s invariant. This duality has been used to explain the striking similarities observed in simulations of the supernova explosions and laboratory implosions induced in plasma by intense lasers. The inversion symmetry extends to discontinuous fluid flows as well. In this contribution, we provide a concise review of these ideas and discuss some applications. We also explicitly work out the implosion dual of the Sedov’s explosion solution. Full article

(This article belongs to the Special Issue Quantum Gravity Phenomenology)

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