scholarly journals The Quantum Cosmological Constant

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1130 ◽  
Author(s):  
Stephon Alexander ◽  
Joao Magueijo ◽  
Lee Smolin
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Uncertainty Relation ◽  
Time Variable ◽  
Transition Functions ◽  
New Interpretation ◽  
Chern Simons

We present an extension of general relativity in which the cosmological constant becomes dynamical and turns out to be conjugate to the Chern–Simons invariant of the Ashtekar connection on a spatial slicing. The latter has been proposed Soo and Smolin as a time variable for quantum gravity: the Chern–Simons time. In the quantum theory, the inverse cosmological constant and Chern–Simons time will then become conjugate operators. The “Kodama state” gets a new interpretation as a family of transition functions. These results imply an uncertainty relation between Λ and Chern–Simons time; the consequences of which will be discussed elsewhere.

scholarly journals QUANTUM GRAVITY, DYNAMICAL ENERGY–MOMENTUM SPACE AND VACUUM ENERGY

2010 ◽  
Vol 25 (35) ◽  
pp. 2947-2954 ◽  
Author(s):  
LAY NAM CHANG ◽  
DJORDJE MINIC ◽  
TATSU TAKEUCHI
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Cosmological Constant ◽  
Momentum Space ◽  
Vacuum Energy

We argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy–momentum space. We discuss the freezing of vacuum energy in such a dynamical energy–momentum space and present a phenomenologically viable seesaw formula for the cosmological constant in this context.

“Prehistoric” Quantum Gravity

2020 ◽  
pp. 41-70
Author(s):  
Dean Rickles
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Quantum Gravity ◽  
Philosophical Nature

In this chapter we examine the very earliest work on the problem of quantum gravity (understood very liberally). We show that, even before the concept of the quantization of the gravitational field in 1929, there was a fairly lively investigation of the relationships between gravity and quantum stretching as far back as 1916, and certainly no suggestion that such a theory would not be forthcoming. Indeed, there are, rather, many suggestions explicitly advocating that an integration of quantum theory and general relativity (or gravitation, at least) is essential for future physics, in order to construct a satisfactory foundation. We also see how this belief was guided by a diverse family of underlying agendas and constraints, often of a highly philosophical nature.

scholarly journals WHY THERE IS SOMETHING SO CLOSE TO NOTHING: TOWARDS A FUNDAMENTAL THEORY OF THE COSMOLOGICAL CONSTANT

2007 ◽  
Vol 22 (10) ◽  
pp. 1797-1818 ◽  
Author(s):  
VISHNU JEJJALA ◽  
DJORDJE MINIC
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Cosmological Constant ◽  
Vacuum Energy ◽  
Uncertainty Relation ◽  
Space Time ◽  
Large Size ◽  
Minkowski Space Time ◽  
The Universe ◽  
Canonical Quantum

The cosmological constant problem is turned around to argue for a new foundational physics postulate underlying a consistent quantum theory of gravity and matter, such as string theory. This postulate is a quantum equivalence principle which demands a consistent gauging of the geometric structure of canonical quantum theory. We argue that string theory can be formulated to accommodate such a principle, and that in such a theory the observed cosmological constant is a fluctuation about a zero value. This fluctuation arises from an uncertainty relation involving the cosmological constant and the effective volume of space–time. The measured, small vacuum energy is dynamically tied to the large "size" of the universe, thus violating naive decoupling between small and large scales. The numerical value is related to the scale of cosmological supersymmetry breaking, supersymmetry being needed for a nonperturbative stability of local Minkowski space–time regions in the classical regime.

scholarly journals On the emergence of the structure of physics

2018 ◽  
Vol 376 (2118) ◽  
pp. 20170231 ◽  
Author(s):  
S. Majid
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Recent Work ◽  
Space Time ◽  
Quantum Space ◽  
Conceptual Level ◽  
Theme Issue ◽  
Self Duality ◽  
Born Reciprocity

We consider Hilbert’s problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space–time as motivated by this non-standard philosophy, including a new toy model of gravity on a space–time consisting of four points forming a square. This article is part of the theme issue ‘Hilbert’s sixth problem’.

scholarly journals On the Minimal Length Uncertainty Relation and the Foundations of String Theory

2011 ◽  
Vol 2011 ◽  
pp. 1-30 ◽  
Author(s):  
Lay Nam Chang ◽  
Zachary Lewis ◽  
Djordje Minic ◽  
Tatsu Takeuchi
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
String Theory ◽  
Momentum Space ◽  
Vacuum Energy ◽  
Uncertainty Relation ◽  
Minimal Length

We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of nonperturbative string theory.

scholarly journals Renormalizable and Unitary Lorentz Invariant Model of Quantum Gravity

2021 ◽  
Author(s):  
S. A. Larin
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Curvature Tensor ◽  
Quantum Theory Of Gravitation ◽  
Proper Choice ◽  
Invariant Model ◽  
Self Consistent ◽  
Theory Of Gravitation

We analyze the R + R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

The Problem of Quantum Gravity: From Feelings to Phenomena

2020 ◽  
pp. 1-16
Author(s):  
Dean Rickles
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
New Phenomena

This chapter provides a simple, schematic introduction to the problem of quantum gravity. The problem of quantum gravity spent much of its earliest history at the mercy of wider changes with respect to the ingredient theories, general relativity and quantum theory. Even once those theories settled down, quantum gravity remained firmly detached from experiments. This situation has only recently changed and promises to offer new phenomena to test proposed solutions to the problem which will enable us to make firmer statements about the more physical implications of these proposed solutions. However, we see that we may still face a problem of polysemicity stemming from the very differing interpretations and formulations that the ingredient theories allow, as well as differing motivations for pursuing quantum gravity.

scholarly journals FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY

2007 ◽  
Vol 16 (09) ◽  
pp. 1397-1474 ◽  
Author(s):  
MUXIN HAN ◽  
YONGGE MA ◽  
WEIMING HUANG
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Dynamics ◽  
Loop Quantum Gravity ◽  
Hamiltonian Constraint ◽  
Dimensional Manifold ◽  
Fundamental Structure ◽  
Fundamental Scale

In the recent twenty years, loop quantum gravity, a background independent approach to unify general relativity and quantum mechanics, has been widely investigated. The aim of loop quantum gravity is to construct a mathematically rigorous, background independent, non-perturbative quantum theory for a Lorentzian gravitational field on a four-dimensional manifold. In the approach, the principles of quantum mechanics are combined with those of general relativity naturally. Such a combination provides us a picture of, so-called, quantum Riemannian geometry, which is discrete on the fundamental scale. Imposing the quantum constraints in analogy from the classical ones, the quantum dynamics of gravity is being studied as one of the most important issues in loop quantum gravity. On the other hand, the semi-classical analysis is being carried out to test the classical limit of the quantum theory. In this review, the fundamental structure of loop quantum gravity is presented pedagogically. Our main aim is to help non-experts to understand the motivations, basic structures, as well as general results. It may also be beneficial to practitioners to gain insights from different perspectives on the theory. We will focus on the theoretical framework itself, rather than its applications, and do our best to write it in modern and precise langauge while keeping the presentation accessible for beginners. After reviewing the classical connection dynamical formalism of general relativity, as a foundation, the construction of the kinematical Ashtekar–Isham–Lewandowski representation is introduced in the content of quantum kinematics. The algebraic structure of quantum kinematics is also discussed. In the content of quantum dynamics, we mainly introduce the construction of a Hamiltonian constraint operator and the master constraint project. At last, some applications and recent advances are outlined. It should be noted that this strategy of quantizing gravity can also be extended to obtain other background-independent quantum gauge theories. There is no divergence within this background-independent and diffeomorphism-invariant quantization program of matter coupled to gravity.

Black to white hole tunneling: An exact classical solution

2015 ◽  
Vol 30 (28n29) ◽  
pp. 1545015 ◽  
Author(s):  
Hal M. Haggard ◽  
Carlo Rovelli
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Quantum Theory ◽  
Quantum Gravity ◽  
Quantum Tunneling ◽  
Einstein Equations ◽  
White Hole ◽  
Small Quantum ◽  
Pile Up ◽  
Over Time

We present a metric that describes conventional matter collapsing into a black hole, bouncing and emerging from a white hole, and that satisfies the vacuum Einstein equations everywhere, including in the interior of the black hole and the subsequent white hole, except for a small compact 4d “quantum tunneling” zone. This shows that a black hole can tunnel into a white hole without violating classical general relativity where this can be trusted. We observe that quantum gravity can affect the metric in a region outside the horizon without violating causality because small quantum effects might pile up over time. We study how quantum theory can determines the bouncing time.

scholarly journals Uncertainty relation for quantum gravity

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645028
Author(s):  
Ya. I. Azimov
Keyword(s):  
Quantum Theory ◽  
Quantum Gravity ◽  
Uncertainty Relation ◽  
Physical Realization ◽  
Non Local ◽  
Theory Of Gravity ◽  
The Physical Realization

Discussion of the physical realization of coordinates demonstrates that the quantum theory of gravity (still absent) should be non-local and, probably, non-commutative as well.

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