scholarly journals DIMENSIONFUL DEFORMATIONS OF POINCARÉ SYMMETRIES FOR A QUANTUM GRAVITY WITHOUT IDEAL OBSERVERS

1998 ◽  
Vol 13 (16) ◽  
pp. 1319-1325 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Theoretical Framework ◽  
Ideal Observers

Quantum mechanics is revisited as the appropriate theoretical framework for the description of the outcome of experiments that rely on the use of classical devices. In particular, it is emphasized that the limitations on the measurability of (pairs of conjugate) observables encoded in the formalism of quantum mechanics reproduce faithfully the "classical-device limit" of the corresponding limitations encountered in (real or gedanken) experimental setups. It is then argued that devices cannot behave classically in quantum gravity, and that this might raise serious problems for the search of a class of experiments described by theories obtained by "applying quantum mechanics to gravity." It is also observed that using heuristic/intuitive arguments based on the absence of classical devices one is led to consider some candidate quantum gravity phenomena involving dimensionful deformations of the Poincaré symmetries.

scholarly journals Quantum gravity, shadow states and quantum mechanics

2003 ◽  
Vol 20 (6) ◽  
pp. 1031-1061 ◽  
Author(s):  
Abhay Ashtekar ◽  
Stephen Fairhurst ◽  
Joshua L Willis
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity

Polymer quantization effects on gauge-flation

2018 ◽  
Vol 15 (10) ◽  
pp. 1850169
Author(s):  
M. Mardaani ◽  
K. Nozari
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Gauge Field ◽  
Quantum Cosmology ◽  
Loop Quantum Gravity ◽  
Loop Quantum Cosmology ◽  
Abelian Gauge ◽  
Friedmann Equations ◽  
Cosmological Inflation

Polymer quantum mechanics, as a non-standard representation of quantum mechanics, is based on a symmetric sector of loop quantum gravity known as loop quantum cosmology. In this work, by analyzing the Hamiltonian and Friedmann equations in the standard Hilbert space and polymer Hilbert space, we show that polymer quantization is a successful formalism for a non-Abelian gauge field driving the cosmological inflation, the so-called gauge-flation, in order to remove initial singularity and also keeping the inflationary trajectories in this model as attractors of dynamics after the bounce.

Conditional interpretation of time in quantum gravity and a time operator in relativistic quantum mechanics

2020 ◽  
Vol 35 (21) ◽  
pp. 2050114
Author(s):  
M. Bauer ◽  
C. A. Aguillón ◽  
G. E. García
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Relativistic Quantum ◽  
Canonical Quantization ◽  
Time Operator ◽  
Relativistic Quantum Mechanics ◽  
Problem Of Time ◽  
Quantization Of Gravity ◽  
Dynamical Time ◽  
Spatial Coordinates

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger’s equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus “time” in QM and “time” in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter [Formula: see text] (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed.

scholarly journals Indistinguishability and the origins of contextuality in physics

2019 ◽  
Vol 377 (2157) ◽  
pp. 20190150 ◽  
Author(s):  
J. Acacio de Barros ◽  
Federico Holik ◽  
Décio Krause
Keyword(s):  
Quantum Mechanics ◽  
Set Theory ◽  
Physical Quantity ◽  
Theoretical Framework ◽  
Quantum Systems ◽  
Strong Sense ◽  
Theme Issue ◽  
Identity Of Indiscernibles ◽  
Theoretical Structure

In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernibles. This framework allows us to consider a new ontology in order to study the properties of quantum systems. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

scholarly journals Emergence of Time in Quantum Gravity: Is Time Necessarily Flowing?

KronoScope ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Pierre Martinetti
Keyword(s):  
Quantum Mechanics ◽  
Quantum Gravity ◽  
Proper Time ◽  
Dimensional Space ◽  
Thermal Time ◽  
List Type ◽  
State Dependent ◽  
Dimensional Space Time ◽  
Flow Of Time ◽  
Time In Quantum Mechanics

Abstract We discuss the emergence of time in quantum gravity and ask whether time is always “something that flows.” We first recall that this is indeed the case in both relativity and quantum mechanics, although in very different manners: time flows geometrically in relativity (i.e., as a flow of proper time in the four dimensional space-time), time flows abstractly in quantum mechanics (i.e., as a flow in the space of observables of the system). We then ask the same question in quantum gravity in the light of the thermal time hypothesis of Connes and Rovelli. The latter proposes to answer the question of time in quantum gravity (or at least one of its many aspects) by postulating that time is a state-dependent notion. This means that one is able to make a notion of time as an abstract flow—that we call the thermal time—emerge from the knowledge of both: the algebra of observables of the physical system under investigation; a state of thermal equilibrium of this system. Formally, the thermal time is similar to the abstract flow of time in quantum mechanics, but we show in various examples that it may have a concrete implementation either as a geometrical flow or as a geometrical flow combined with a non-geometric action. This indicates that in quantum gravity, time may well still be “something that flows” at some abstract algebraic level, but this does not necessarily imply that time is always and only “something that flows” at the geometric level.

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 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 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.

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