scholarly journals The de Broglie–Bohm Quantum Theory and Its Application to Quantum Cosmology

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 134
Author(s):  
Nelson Pinto-Neto
Keyword(s):  
Quantum Theory ◽  
Configuration Space ◽  
Physical System ◽  
Quantum Cosmology ◽  
Dynamical Theory ◽  
Cosmological Models ◽  
Cosmological Perturbations ◽  
Alternative Description ◽  
Quantum Phenomena ◽  
De Broglie Bohm

We review the de Broglie–Bohm quantum theory. It is an alternative description of quantum phenomena in accordance with all the quantum experiments already performed. Essentially, it is a dynamical theory about objectively real trajectories in the configuration space of the physical system under investigation. Hence, it is not necessarily probabilistic, and it dispenses with the collapse postulate, making it suitable to be applied to cosmology. The emerging cosmological models are usually free of singularities, with a bounce connecting a contracting era with an expanding phase, which we are now observing. A theory of cosmological perturbations can also be constructed under this framework, which can be successfully confronted with current observations, and can complement inflation or even be an alternative to it.

scholarly journals Bouncing Quantum Cosmology

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 110
Author(s):  
Nelson Pinto-Neto
Keyword(s):  
Dark Matter ◽  
Quantum Theory ◽  
Dark Energy ◽  
Quantum Cosmology ◽  
Canonical Quantization ◽  
Quantization Scheme ◽  
Physical Effects ◽  
Planck Energy ◽  
De Broglie Bohm

The goal of this contribution is to present the properties of a class of quantum bouncing models in which the quantum bounce originates from the Dirac canonical quantization of a midi-superspace model composed of a homogeneous and isotropic background, together with small inhomogeneous perturbations. The resulting Wheeler-DeWitt equation is interpreted in the framework of the de Broglie-Bohm quantum theory, enormously simplifying the calculations, conceptually and technically. It is shown that the resulting models are stable and they never get to close to the Planck energy, where another more involved quantization scheme would have to be evoked, and they are compatible with present observations. Some physical effects around the bounce are discussed, like baryogenesis and magnetogenesis, and the crucial role of dark matter and dark energy is also studied.

BOUNCING AND QUANTUM THEORY

2011 ◽  
Vol 03 ◽  
pp. 183-194
Author(s):  
NELSON PINTO-NETO
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Power Spectrum ◽  
Quantum Cosmology ◽  
Cosmological Perturbations ◽  
Simple Equations ◽  
The Universe ◽  
Inflationary Models

In this contribution I will present a review about bouncing models arriving from quantum cosmology and show how one can describe the evolution of quantum cosmological perturbations on them. I will discuss the important role played by the choice of the precise quantum theory one selects to interpret the wave function of the Universe in order to obtain simple equations for the evolution of quantum perturbations on these quantum cosmological backgrounds. I will present the predictions of these models concerning the power spectrum of cosmological perturbations and how they can be compared with the usual results obtained from inflationary models. Finally, I will present the new implications of these results for quantum theory.

BOUNCING AND QUANTUM THEORY

2011 ◽  
Vol 26 (22) ◽  
pp. 3801-3812
Author(s):  
NELSON PINTO-NETO
Keyword(s):  
Wave Function ◽  
Quantum Theory ◽  
Power Spectrum ◽  
Quantum Cosmology ◽  
Cosmological Perturbations ◽  
Simple Equations ◽  
The Universe ◽  
Inflationary Models

In this contribution I will present a review about bouncing models arriving from quantum cosmology and show how one can describe the evolution of quantum cosmological perturbations on them. I will discuss the important role played by the choice of the precise quantum theory one selects to interpret the wave function of the Universe in order to obtain simple equations for the evolution of quantum perturbations on these quantum cosmological backgrounds. I will present the predictions of these models concerning the power spectrum of cosmological perturbations and how they can be compared with the usual results obtained from inflationary models. Finally, I will present the new implications of these results for quantum theory.

Entanglement

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
Physical Condition ◽  
Physical System ◽  
Polarization State ◽  
Quantum Systems ◽  
Ghz State ◽  
Mathematical Representation ◽  
Entangled State ◽  
Physical Relation

Often a pair of quantum systems may be represented mathematically (by a vector) in a way each system alone cannot: the mathematical representation of the pair is said to be non-separable: Schrödinger called this feature of quantum theory entanglement. It would reflect a physical relation between a pair of systems only if a system’s mathematical representation were to describe its physical condition. Einstein and colleagues used an entangled state to argue that its quantum state does not completely describe the physical condition of a system to which it is assigned. A single physical system may be assigned a non-separable quantum state, as may a large number of systems, including electrons, photons, and ions. The GHZ state is an example of an entangled polarization state that may be assigned to three photons.

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

scholarly journals p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

2002 ◽  
Vol 17 (10) ◽  
pp. 1413-1433 ◽  
Author(s):  
GORAN S. DJORDJEVIĆ ◽  
BRANKO DRAGOVICH ◽  
LJUBIŠA D. NEŠIĆ ◽  
IGOR V. VOLOVICH
Keyword(s):  
Quantum Mechanics ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Quantum Effects ◽  
De Sitter Space ◽  
Cosmological Models ◽  
De Sitter ◽  
Adelic Quantum Mechanics ◽  
Matter Fields

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

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