scholarly journals The simplest possible bouncing quantum cosmological model

2016 ◽  
Vol 31 (21) ◽  
pp. 1640006 ◽  
Author(s):  
Patrick Peter ◽  
Sandro D. P. Vitenti
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Cosmological Model ◽  
Functional Form ◽  
Initial Conditions ◽  
Wave Functions ◽  
General Situation ◽  
Spatial Curvature ◽  
Bianchi I ◽  
Contracting Phase

We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler–De Witt equation) in the Friedmann–Lemaître–Robertson–Walker (FLRW) minisuperspace without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a nonsingular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non-symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperspace.

scholarly journals The Strange (Hi)story of Particles and Waves

2016 ◽  
Vol 71 (3) ◽  
pp. 195-212
Author(s):  
H. Dieter Zeh
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Excited States ◽  
Configuration Space ◽  
Historical Context ◽  
Quantum States ◽  
Wave Functions ◽  
General Readership ◽  
Boson Fields

AbstractThis is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are “occupied once” (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the “configuration” space of fundamental fields, or on another, as yet elusive, fundamental local basis.

EPR Elements of Physical Reality in Quantum Mechanics

1997 ◽  
Vol 12 (29) ◽  
pp. 5289-5303
Author(s):  
V. K. Thankappan ◽  
Ravi K. Menon
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Singlet State ◽  
Physical Reality ◽  
The State ◽  
Wave Functions ◽  
Definition Of

The concept of elements of physical reality (e.p.r.) in quantum mechanics as defined by Einstein, Podolsky and Rosen (EPR) is discussed in the context of the EPR–Bohm and the EPR–Bell experiments on a pair of spin 1/2 particles in the singlet state. It is argued that EPR's definition of e.p.r. is appropriate to the EPR–Bell experiment rather than to the EPR–Bohm experiment, and that Bohr's interpretation of e.p.r. is also consistent with such a viewpoint. It is shown that the observed correlation between the spins of the two particles in the EPR–Bell experiment is just a manifestation of the correlation that exists between the wave functions of the particles in the singlet state and a consequence of the fact that a Stern–Gerlach magnet does not change the state of a particle but only transforms its wave function into a representation defined by the axis of the magnet. As such, the correlation is suggested to be an affirmation of Einstein's concept of locality, and not an evidence for nonlocality.

scholarly journals QUANTUM RAINBOW COSMOLOGICAL MODEL WITH PERFECT FLUID

2013 ◽  
Vol 22 (13) ◽  
pp. 1350079 ◽  
Author(s):  
BARUN MAJUMDER
Keyword(s):  
Quantum Mechanics ◽  
Cosmological Model ◽  
Perfect Fluid ◽  
Fluid Model ◽  
Cosmic Time ◽  
Wave Functions ◽  
Interpretation Of Quantum Mechanics ◽  
Many Worlds ◽  
The Many

Isotropic quantum cosmological perfect fluid model is studied in the formalism of Rainbow gravity. It is found that the only surviving matter degree of freedom played the role of cosmic time. With the suitable choice of the Rainbow functions it is possible to find the wave packet naturally from the superposition of the wave functions of the Schrödinger–Wheeler–deWitt equation. The many-worlds interpretation of quantum mechanics is applied to investigate the behavior of the scale factor and the behavior is found to depend on the operator ordering. It is shown that the model in the Rainbow framework may avoid singularity yielding a bouncing nonsingular universe.

scholarly journals Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 594
Author(s):  
Antoine Tilloy ◽  
Howard M. Wiseman
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Hidden Variables ◽  
Bohmian Mechanics ◽  
Primitive Ontology ◽  
Collapse Model ◽  
Collapse Models

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.

scholarly journals On the Quantum Mechanical Wave Function as a Link Between Cognition and the Physical World: A Role for Psychology

2020 ◽  
Author(s):  
Douglas Michael Snyder
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Physical World ◽  
Wave Functions ◽  
Human Cognition ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Empirical Level ◽  
And Behavior ◽  
Empirical Demonstration

A straightforward explanation of fundamental tenets of quantum mechanics concerning the wave function results in the thesis that the quantum mechanical wave function is a link between human cognition and the physical world. The reticence on the part of physicists to adopt this thesis is discussed. A comparison is made to the behaviorists’ consideration of mind, and the historical roots of how the problem concerning the quantum mechanical wave function arose are discussed. The basis for an empirical demonstration that the wave function is a link between human cognition and the physical world is provided through developing an experiment using methodology from psychology and physics. Based on research in psychology and physics that relied on this methodology, it is likely that Einstein, Podolsky, and Rosen’s theoretical result that mutually exclusive wave functions can simultaneously apply to the same concrete physical circumstances can be implemented on an empirical level. Original article in The Journal of Mind and Behavior is on JSTOR at https://www.jstor.org/stable/pdf/43853678.pdf?seq=1 . Preprint on CERN preprint server at https://cds.cern.ch/record/569426 .

scholarly journals THE EQUIVALENCE POSTULATE OF QUANTUM MECHANICS

2000 ◽  
Vol 15 (13) ◽  
pp. 1869-2017 ◽  
Author(s):  
ALON E. FARAGGI ◽  
MARCO MATONE
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Bound States ◽  
Initial Conditions ◽  
Hidden Variables ◽  
Direct Consequence ◽  
Self Energy ◽  
Trajectory Representation ◽  
Relativistic Extension ◽  
Linear Differential

The removal of the peculiar degeneration arising in the classical concepts of rest frame and time parametrization is at the heart of the recently formulated equivalence principle (EP). The latter, stating that all physical systems can be connected by a coordinate transformation to the free one with vanishing energy, univocally leads to the quantum stationary HJ equation (QSHJE). This is a third order nonlinear differential equation which provides a trajectory representation of quantum mechanics (QM). The trajectories depend on the Planck length through hidden variables which arise as initial conditions. The formulation has manifest p-q duality, a consequence of the involutive nature of the Legendre transformation and of its recently observed relation with second order linear differential equations. This reflects in an intrinsic ψD-ψ duality between linearly independent solutions of the Schrödinger equation. Unlike Bohm's theory, there is a nontrivial action even for bound states and no pilot waveguide is present. A basic property of the formulation is that no use of any axiomatic interpretation of the wave function is made. For example, tunneling is a direct consequence of the quantum potential which differs from the Bohmian one and plays the role of particle's self-energy. Furthermore, the QSHJE is defined only if the ratio ψD/ψ is a local homeomorphism of the extended real line into itself. This is an important feature as the L2(ℝ) condition, which in the Copenhagen formulation is a consequence of the axiomatic interpretation of the wave function, directly follows as a basic theorem which only uses the geometrical gluing conditions of ψD/ψ at q=±∞ as implied by the EP. As a result, the EP itself implies a dynamical equation that does not require any further assumption and reproduces both tunneling and energy quantization. Several features of the formulation show how the Copenhagen interpretation hides the underlying nature of QM. Finally, the nonstationary higher dimensional quantum HJ equation and the relativistic extension are derived.

Multiscalar field models: Interaction potentials, wave functions and cosmological solutions

2020 ◽  
Vol 29 (07) ◽  
pp. 2050046
Author(s):  
Sameerah Jamal
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Scalar Interaction ◽  
Coordinate Transformations ◽  
Spatial Curvature ◽  
Field Equations ◽  
Interaction Potentials ◽  
Cosmological Solutions ◽  
The Universe ◽  
Friedmann Robertson Walker

We consider a multiscalar tensor cosmology model described by Friedmann–Robertson–Walker (FRW) spacetime with zero spatial curvature. Three specific scalar interaction potentials that characterize the model are analyzed under a set of coordinate transformations. By implication, we solve for the wave function of the universe, reduce the dimension of the underlying Hamiltonian system and consequently, establish analytical solutions of the multiscalar model’s field equations.

scholarly journals The “noncausal causality” of quantum information

2021 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Information ◽  
Wave Functions ◽  
Probability Density Distribution ◽  
Information Function ◽  
Classical Physics ◽  
Physical Description ◽  
Probabilistic Causality ◽  
Random Probability

The paper is concentrated on the special changes of the conception of causalityfrom quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by the conservation of quantum information and in accordance with Born’s interpretation; (3) it introduces inverse causality, “backwards in time”, observable “forwards in time” as the fundamentally random probability density distribution of all possible measurements of any physical quantity in quantum mechanics; (4) it involves a kind of “bidirectional causality” unifying (4.1) the classical determinism of cause and effect, (4.2) the probabilistic causality of quantum mechanics, and (4.3) the reversibility of any coherent state; (5) it identifies determinism with the function successor in Peano arithmetic, and its proper generalized causality with the information function successor in Hilbert arithmetic.

Unified theory of classic mechanics and quantum mechanics

2020 ◽  
Vol 35 (38) ◽  
pp. 2030022
Author(s):  
Hong-Xing Li
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Fuzzy Systems ◽  
Mass Point ◽  
Wave Functions ◽  
Unified Theory ◽  
Countably Infinite

In this paper, I review one of the most important and interesting parts of my new book “Fuzzy Systems to Quantum Mechanics” (see Ref. 1). Several conclusions in this part are worth introducing here. First of all, the motion of a mass point in classic mechanics has also waviness and the wave function of the motion of a mass point is composed of wave functions of countably infinite microscopic particles. Secondly, based on the waviness of the motion of a mass point we surely know the new conclusion described as the wave-mass-point dualism in classic mechanics. And thirdly, by using the closed relation between the wave-mass-point dualism in classic mechanics and the wave-particle dualism in quantum mechanics, unified theory of classic mechanics and quantum mechanics is naturally formed.

scholarly journals Relational Quantum Mechanics and the PBR Theorem: A Peaceful Coexistence

2021 ◽  
Vol 51 (4) ◽  
Author(s):  
Andrea Oldofredi ◽  
Caludio Calosi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Functions ◽  
Type Result ◽  
Relational Quantum Mechanics ◽  
Formal Result ◽  
Underlying Reality ◽  
Physical Item ◽  
Interpretative Framework ◽  
Epistemic View

AbstractAccording to Relational Quantum Mechanics (RQM) the wave function $$\psi$$ ψ is considered neither a concrete physical item evolving in spacetime, nor an object representing the absolute state of a certain quantum system. In this interpretative framework, $$\psi$$ ψ is defined as a computational device encoding observers’ information; hence, RQM offers a somewhat epistemic view of the wave function. This perspective seems to be at odds with the PBR theorem, a formal result excluding that wave functions represent knowledge of an underlying reality described by some ontic state. In this paper we argue that RQM is not affected by the conclusions of PBR’s argument; consequently, the alleged inconsistency can be dissolved. To do that, we will thoroughly discuss the very foundations of the PBR theorem, i.e. Harrigan and Spekkens’ categorization of ontological models, showing that their implicit assumptions about the nature of the ontic state are incompatible with the main tenets of RQM. Then, we will ask whether it is possible to derive a relational PBR-type result, answering in the negative. This conclusion shows some limitations of this theorem not yet discussed in the literature.

Sign in / Sign up

Export Citation Format

Share Document