scholarly journals From the black hole conundrum to the structure of quantum gravity

2021 ◽  
pp. 2130007
Author(s):  
Yasunori Nomura
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Quantum System ◽  
Path Integral ◽  
Recent Progress ◽  
Black Hole Physics ◽  
Interior Volume

We portray the structure of quantum gravity emerging from recent progress in understanding the quantum mechanics of an evaporating black hole. Quantum gravity admits two different descriptions, based on Euclidean gravitational path integral and a unitarily evolving holographic quantum system, which appear to present vastly different pictures under the existence of a black hole. Nevertheless, these two descriptions are physically equivalent. Various issues of black hole physics — including the existence of the interior, unitarity of the evolution, the puzzle of too large interior volume, and the ensemble nature seen in certain calculations — are addressed very differently in the two descriptions, still leading to the same physical conclusions. The perspective of quantum gravity developed here is expected to have broader implications beyond black hole physics, especially for the cosmology of the eternally inflating multiverse.

scholarly journals A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

2010 ◽  
Vol 19 (12) ◽  
pp. 2003-2009 ◽  
Author(s):  
POURIA PEDRAM
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Uncertainty Principle ◽  
Deformed Algebra ◽  
Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

scholarly journals Violation of unitarity in gravitational subregions

2021 ◽  
Author(s):  
Aron C. Wall
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Path Integral ◽  
Cpt Symmetry ◽  
Negative Norm ◽  
Trapped Surfaces ◽  
Negative Probability

This essay contends that in quantum gravity, some spatial regions do not admit a unitary Hilbert space. Because the gravitational path integral spontaneously breaks CPT symmetry, “states” with negative probability can be identified on either side of trapped surfaces. I argue that these negative norm states are tolerable, by analogy to quantum mechanics. This viewpoint suggests a resolution of the firewall paradox, similar to black hole complementarity. Implications for cosmology are briefly discussed.

scholarly journals Ontology in Quantum Mechanics

2021 ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Evolution Equations ◽  
Black Hole Physics ◽  
Special Kind ◽  
Quantum Evolution ◽  
The Standard Model ◽  
Low Energies

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is given by elements of the permutation group. This would restore an ontological interpretation. It is shown how, at low energies per particle degree of freedom, almost any quantum system allows for such a transformation. This contradicts Bell’s theorem, and we emphasise why some of the assumptions made by Bell to prove his theorem cannot hold for the models studied here. We speculate how an approach of this kind may become helpful in isolating the most likely version of the Standard Model, combined with General Relativity. A link is suggested with black hole physics.

DIMENSION EMERGENCE, HOLOGRAPHY AND QUANTUM GRAVITY

2011 ◽  
Vol 26 (21) ◽  
pp. 3679-3696
Author(s):  
YU-LEI FENG ◽  
LI-XIN XU ◽  
YU-TING WANG
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Quantum System ◽  
Alternative Interpretation ◽  
Reduction Mechanism ◽  
Dimensional Theory ◽  
Shift Vector ◽  
Higher Dimensional ◽  
Holography Principle

In this paper, we try to give an alternative interpretation of the holography principle. We argue that the space or time may be regarded as emerging from quantum mechanics as an evolutive parameter. The lower D-dimensional theory is related to a corresponding (D+1)-theory by a mysterious quantum system. Then from the higher-dimensional theory, under a new dimension reduction mechanism we obtain the corresponding results. We also try to incorporate the gauge field into the reduction, roughly identifying Aμ with Nμ which is the shift vector in the ADM-like decomposition of space–time metric. In the end, we extend to the gravitational field, and obtain a relation [Formula: see text] with a cutoff factor κ, from a different view.

scholarly journals MASSIVE ELEMENTARY PARTICLES AND BLACK HOLE PHYSICS IN RESUMMED QUANTUM GRAVITY

2005 ◽  
Vol 20 (14) ◽  
pp. 3128-3131 ◽  
Author(s):  
B. F. L. WARD
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Black Hole Physics ◽  
Elementary Particles ◽  
Exact Results ◽  
New Approach

We use exact results in a new approach to quantum gravity to discuss some issues in black hole physics.

scholarly journals Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study

2015 ◽  
Vol 24 (10) ◽  
pp. 1550073 ◽  
Author(s):  
Giovanni Amelino-Camelia ◽  
Valerio Astuti
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Recent Progress ◽  
Covariant Formulation ◽  
Specific Context ◽  
Intrinsic Interest ◽  
Alternative Approaches

Alternative approaches to the study of the quantum gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics, suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetime, which is also of some intrinsic interest, since hundreds of studies were devoted to its analysis. We show that empty Snyder spacetime, described in terms of a suitable kinematical Hilbert space, is discrete, but this is only a formal artifact: the discreteness leaves no trace on the observable properties of particles on the physical Hilbert space.

scholarly journals Fuzzy Instantons in Landscape and Swampland: Review of the Hartle–Hawking Wave Function and Several Applications

Universe ◽  
2021 ◽  
Vol 7 (10) ◽  
pp. 367
Author(s):  
Dong-han Yeom
Keyword(s):  
Black Hole ◽  
Wave Function ◽  
Path Integral ◽  
Initial Conditions ◽  
Black Hole Physics ◽  
Slow Roll ◽  
Potential Shape ◽  
Euclidean Wormholes ◽  
The Universe ◽  
Origin Of The Universe

The Euclidean path integral is well approximated by instantons. If instantons are dynamical, they will necessarily be complexified. Fuzzy instantons can have multiple physical applications. In slow-roll inflation models, fuzzy instantons can explain the probability distribution of the initial conditions of the universe. Although the potential shape does not satisfy the slow-roll conditions due to the swampland criteria, the fuzzy instantons can still explain the origin of the universe. If we extend the Euclidean path integral beyond the Hartle–Hawking no-boundary proposal, it becomes possible to examine fuzzy Euclidean wormholes that have multiple physical applications in cosmology and black hole physics.

Black-hole Information Loss Problem: Past, Present, and Future

2020 ◽  
Vol 29 (11) ◽  
pp. 17-25
Author(s):  
Sang-Heon YI ◽  
Dong-han YEOM
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Hawking Radiation ◽  
Recent Progress ◽  
Information Loss ◽  
Future Perspectives ◽  
Black Hole Information ◽  
Information Loss Problem

In this article, we discuss the information loss problem of black holes and critically review candidate resolutions of the problem. As a black hole evaporates via Hawking radiation, it seems to lose original quantum information; this indicates that the unitarity of time evolution in quantum mechanics and the fundamental predictability of physics are lost. We categorized candidate resolutions by asking (1) where information is and (2) which principle of physics is changed. We also briefly comment on the recent progress in the string theory community. Finally, we present several remarks for future perspectives.

scholarly journals Path Integral Implementation of Relational Quantum Mechanics

2021 ◽  
Author(s):  
Jianhao M. Yang
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Path Integral ◽  
Measurement Theory ◽  
Entanglement Entropy ◽  
Quantum Probability ◽  
Probability Amplitude ◽  
Path Integral Representation ◽  
Relational Quantum Mechanics ◽  
Influence Functional

Abstract Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In the recent works (J. M. Yang, Sci. Rep. 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born's Rule, Schr\"{o}dinger Equations, and measurement theory. This paper gives a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifies the physical meaning of the relational probability amplitude, but also gives several important applications. For instance, the double slit experiment can be elegantly explained. A path integral representation of the reduced density matrix of the observed system can be derived. Such representation is shown valuable to describe the interaction history of the measured system and a series of measuring systems. More interestingly, it allows us to develop a method to calculate entanglement entropy based on path integral and influence functional. Criteria of entanglement is proposed based on the properties of influence functional, which may be used to determine entanglement due to interaction between a quantum system and a classical field.

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