scholarly journals An Entropic Dynamics Approach to Geometrodynamics

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 13
Author(s):  
Selman Ipek ◽  
Ariel Caticha
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
First Principles ◽  
Scalar Fields ◽  
Poisson Brackets ◽  
Classical Approach ◽  
Quantum Domain ◽  
Physical Information ◽  
Entropic Dynamics

In the Entropic Dynamics (ED) framework quantum theory is derived as an application of entropic methods of inference. The physics is introduced through appropriate choices of variables and of constraints that codify the relevant physical information. In previous work, a manifestly covariant ED of quantum scalar fields in a fixed background spacetime was developed. Manifest relativistic covariance was achieved by imposing constraints in the form of Poisson brackets and of intial conditions to be satisfied by a set of local Hamiltonian generators. Our approach succeeded in extending to the quantum domain the classical framework that originated with Dirac and was later developed by Teitelboim and Kuchar. In the present work the ED of quantum fields is extended further by allowing the geometry of spacetime to fully partake in the dynamics. The result is a first-principles ED model that in one limit reproduces quantum mechanics and in another limit reproduces classical general relativity. Our model shares some formal features with the so-called “semi-classical” approach to 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.

scholarly journals MINIMUM LENGTH FROM FIRST PRINCIPLES

2005 ◽  
Vol 14 (12) ◽  
pp. 2195-2199 ◽  
Author(s):  
XAVIER CALMET ◽  
MICHAEL L. GRAESSER ◽  
STEPHEN D. H. HSU
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Gravitational Collapse ◽  
First Principles ◽  
Minimal Length ◽  
Minimum Length ◽  
Position Operator ◽  
Planck Length ◽  
Gedanken Experiment ◽  
Hoop Conjecture

We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the eigenvalues of the position operator to within that accuracy. The only assumptions in our argument are causality, the uncertainty principle from quantum mechanics and a dynamical criteria for gravitational collapse from classical general relativity called the hoop conjecture. The inability of any gedanken experiment to measure a sub-Planckian distance suggests the existence of a minimal length.

The Shock of the New

2020 ◽  
pp. 71-118
Author(s):  
Dean Rickles
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Particle Production ◽  
Mechanical Systems ◽  
Quantum Mechanical ◽  
Uncertainty Relations ◽  
Mathematical Structures ◽  
Quantum Mechanical Systems ◽  
Concrete Representations

In this chapter, we show how the newest developments in quantum mechanics of the late 1920s were very quickly compared with general relativity, with attempts made to demonstrate their mutual coherence. This involved focusing on the basic mathematical structures that formed the first concrete representations of quantum mechanical systems. The aim was structural harmonisation, rather than quantization. Likewise, we will find that conceptual debates, especially having to do with measurement and the uncertainty relations, as well as new cosmological discoveries (based on applications of general relativity) were also quickly compared, often with surprising results such as explanations of discreteness and predictions of particle production in curved spaces. We see two primary motivations pushing this research forward: coherence (into which the more formal approaches also fit) and utility (that is attempting to gain a better grip on the quantum theory).

Atoms of Space and Time

2020 ◽  
pp. 135-151
Author(s):  
Demetris Nicolaides
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Physics ◽  
Space Time ◽  
Heisenberg Uncertainty Principle ◽  
Quantum Jump ◽  
Time And Motion ◽  
Scientific Hypothesis ◽  
Heisenberg Uncertainty

Epicurus argued that the Democritean atoms couldn’t move, unless space, time, and motion were radically reimagined. In addition to material atoms (smallest cuts of matter), there exist space “atoms” (smallest spatial expanses) and time “atoms” (smallest time intervals)! Also, he thought an atom’s motion is quantum! It moves from here to there without passing through the points in between—exactly the meaning of a quantum jump in quantum physics (presuming motion does occur). An atom spontaneously swerves (creating uncertainty in its whereabouts), a feature added by Epicurus in a first-ever attempt to escape Democritean determinism and subject human free will to a scientific hypothesis. Space atoms are required by loop quantum gravity (which unifies quantum theory with general relativity). The cause of the most consequential premise of quantum mechanics—the Heisenberg uncertainty principle—will be cautiously speculated with an original idea, using the Epicurean theory of space, time, and motion.

Quantum Becoming?

2017 ◽  
Author(s):  
Craig Callender
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Quantum Time ◽  
Quantum Non Locality ◽  
Time Quantum ◽  
Temporal Becoming ◽  
Non Locality ◽  
Quantum Wavefunction

Two of quantum mechanics’ more famed and spooky features have been invoked in defending the idea that quantum time is congenial to manifest time. Quantum non-locality is said by some to make a preferred foliation of spacetime necessary, and the collapse of the quantum wavefunction is held to vindicate temporal becoming. Although many philosophers and physicists seek relief from relativity’s assault on time in quantum theory, assistance is not so easily found.

Surfing the Quantum World

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Musical Instrument ◽  
Popular Science ◽  
Quantum Spin ◽  
Exclusion Principle ◽  
Maximum Height ◽  
Core Concepts ◽  
The Many ◽  
The One

Surfing the Quantum World bridges the gap between in-depth textbooks and typical popular science books on quantum ideas and phenomena. Among its significant features is the description of a host of mind-bending phenomena, such as a quantum object being in two places at once or a certain minus sign being the most consequential in the universe. Much of its first part is historical, starting with the ancient Greeks and their concepts of light, and ending with the creation of quantum mechanics. The second part begins by applying quantum mechanics and its probability nature to a pedagogical system, the one-dimensional box, an analog of which is a musical-instrument string. This is followed by a gentle introduction to the fundamental principles of quantum theory, whose core concepts and symbolic representations are the foundation for most of the subsequent chapters. For instance, it is shown how quantum theory explains the properties of the hydrogen atom and, via quantum spin and Pauli’s Exclusion Principle, how it accounts for the structure of the periodic table. White dwarf and neutron stars are seen to be gigantic quantum objects, while the maximum height of mountains is shown to have a quantum basis. Among the many other topics considered are a variety of interference phenomena, those that display the wave properties of particles like electrons and photons, and even of large molecules. The book concludes with a wide-ranging discussion of interpretational and philosophic issues, introduced in Chapters 14 by entanglement and 15 by Schrödinger’s cat.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

scholarly journals On Russell’s 1927 Book The Analysis of Matter

Philosophies ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 40
Author(s):  
Said Mikki
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Building Blocks ◽  
Bertrand Russell ◽  
Important Work ◽  
Philosophy Of Nature ◽  
Foundations Of Physics ◽  
The World ◽  
Ordinal Space ◽  
Historical Fact

The goal of this article is to bring into wider attention the often neglected important work by Bertrand Russell on the philosophy of nature and the foundations of physics, published in the year 1927. It is suggested that the idea of what could be named Russell space, introduced in Part III of that book, may be viewed as more fundamental than many other types of spaces since the highly abstract nature of the topological ordinal space proposed by Russell there would incorporate into its very fabric the emergent nature of spacetime by deploying event assemblages, but not spacetime or particles, as the fundamental building blocks of the world. We also point out the curious historical fact that the book The Analysis of Matter can be chronologically considered the earliest book-length generic attempt to reflect on the relation between quantum mechanics, just emerging by that time, and general relativity.

scholarly journals Experimental test of the Greenberger–Horne–Zeilinger-type paradoxes in and beyond graph states

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zheng-Hao Liu ◽  
Jie Zhou ◽  
Hui-Xian Meng ◽  
Mu Yang ◽  
Qiang Li ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Success Probability ◽  
Quantum Foundations ◽  
Mixed States ◽  
Graph States ◽  
Hardy Type ◽  
Realistic Description ◽  
Entanglement Detection ◽  
Quantum Paradoxes

AbstractThe Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks.

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