scholarly journals Generalized Probabilistic Theories in a New Light

2021 ◽  
Author(s):  
Raed Shaiia
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Quantum Mechanical ◽  
Infinite Dimensional ◽  
Classical Systems ◽  
Generalized Probabilistic Theories ◽  
Deterministic Description ◽  
New Formulation ◽  
The Universe ◽  
Probabilistic Theories

Abstract In this paper we will present a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, and give the guidelines to how to extend this work to infinite dimensional Hilbert spaces. Moreover, this new formulation which we will call extended operational-probabilistic theories, applies not only to quantum systems, but also equally well to classical systems, without violating Bell’s theorem, and at the same time solves the measurement problem. This is why we will see that the question of why our universe is quantum mechanical rather than classical is misplaced. The only difference that exists between a classical universe and a quantum mechanical one lies merely in which observables are compatible and which are not. Besides, this extended probability theory which we present in this paper shows that it is non-determinacy, or to be more precise, the non-deterministic description of the universe, that makes the laws of physics the way they are. In addition, this paper shows us that what used to be considered as purely classical systems and to be treated that way are in fact able to be manipulated according to the rules of quantum mechanics –with this new understanding of these rules- and that there is still a possibility that there might be a deterministic level from which our universe emerges, which if understood correctly, may open the door wide to applications in areas such as quantum computing. In addition to all that, this paper shows that without the use of complex vector spaces, we cannot have any kind of continuous evolution of the states of any system.

scholarly journals IMPLICATIONS OF A QUANTUM MECHANICAL TREATMENT OF THE UNIVERSE

1998 ◽  
Vol 13 (05) ◽  
pp. 347-351 ◽  
Author(s):  
MURAT ÖZER
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Early Universe ◽  
Mechanical Treatment ◽  
Correspondence Principle ◽  
Scale Factor ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment ◽  
The Standard Model ◽  
The Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

scholarly journals TOWARDS A DEFINITION OF QUANTUM INTEGRABILITY

2009 ◽  
Vol 06 (01) ◽  
pp. 129-172 ◽  
Author(s):  
JESÚS CLEMENTE-GALLARDO ◽  
GIUSEPPE MARMO
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Degrees Of Freedom ◽  
Complete Integrability ◽  
Infinite Dimensional ◽  
Quantum Integrability ◽  
Classical Systems ◽  
Definition Of ◽  
Geometrical Formulation ◽  
Quantum Framework

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to the quantum framework would not work because all infinite dimensional Hilbert spaces are unitarilly isomorphic and, as a consequence, it would not be easy to define degrees of freedom. We argue that a geometrical formulation of quantum mechanics might provide a way out.

Quantum transition between spaces in a multidimensional Universe and spatial unconnectivity explain free will and solve the measurement problem of quantum mechanics

2020 ◽  
Vol 33 (1) ◽  
pp. 34-37
Author(s):  
José M. Frade
Keyword(s):  
Quantum Mechanics ◽  
Free Will ◽  
Measurement Problem ◽  
Fundamental Property ◽  
Quantum Transition ◽  
Observable Universe ◽  
Temporal Dimension ◽  
Spatial Dimensions ◽  
Future Events ◽  
The Universe

Spacetime is deterministic, but the Universe appears to be stochastic. How to reconcile free will with the determinism inherent to the Universe? In this essay, we postulate that free will can only emanate from the existence of multiple additional spatial dimensions constituting the Universe. As our space displaces through the temporal dimension, we can choose any of the infinite possibilities defined by the additional spatial dimensions, through a process we refer to as quantum transition between spaces. Reality would emerge from the specific materialization of this quantum transition, resulting in a time series of events. This materialization is based on a fundamental property of any space, independently of its dimensions, which we refer to as spatial unconnectivity. This property implies the inability of the constituents of a particular space to observe spaces located in other dimensions. Therefore, the unconnectivity between spaces would prevent the simultaneous observation of all possible events at a specific time point, as well as past and future events, resulting in a unique reality. It would be the observers who determine the temporal trajectory of events, thus providing themselves with free will. In the absence of observers, all possibilities are feasible, thus explaining the quantum properties of elementary particles when they are not directly observed. Our model reconciles quantum mechanics with relativistic physics and is the easiest way to understand how reality arises in our observable Universe.

scholarly journals A glance beyond the quantum model

2009 ◽  
Vol 466 (2115) ◽  
pp. 881-890 ◽  
Author(s):  
Miguel Navascués ◽  
Harald Wunderlich
Keyword(s):  
General Relativity ◽  
Quantum Mechanics ◽  
Physical Theory ◽  
Quantum Mechanical ◽  
Quantum Model ◽  
Microscopic Structure ◽  
Quantum Mechanical System ◽  
Classical Physics ◽  
Quantum Limits ◽  
The Universe

One of the most important problems in physics is to reconcile quantum mechanics with general relativity, and some authors have suggested that this may be realized at the expense of having to drop the quantum formalism in favour of a more general theory. Here, we propose a mechanism to make general claims on the microscopic structure of the Universe by postulating that any post-quantum theory should recover classical physics in the macroscopic limit. We use this mechanism to bound the strength of correlations between distant observers in any physical theory. Although several quantum limits are recovered, such as the set of two-point quantum correlators, our results suggest that there exist plausible microscopic theories of Nature that predict correlations impossible to reproduce in any quantum mechanical system.

scholarly journals The universe from a single particle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Michael Freedman ◽  
Modjtaba Shokrian Zini
Keyword(s):  
Quantum Mechanics ◽  
Single Particle ◽  
Quantum Mechanical ◽  
Local Minima ◽  
Quantum Mechanical System ◽  
Many Body ◽  
Gaussian Unitary Ensemble ◽  
Interacting Systems ◽  
The Universe ◽  
Unitary Ensemble

Abstract We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to a random quantum mechanical system (the Gaussian unitary ensemble), but also less symmetrical local minima corresponding to interacting systems at the level of operators.

scholarly journals Random World and Quantum Mechanics

2021 ◽  
Author(s):  
Jerzy Król ◽  
Krzysztof Bielas ◽  
Torsten Asselmeyer-Maluga
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Infinite Sequence ◽  
Quantum Limit ◽  
Random Real ◽  
Practical Applications ◽  
Infinite Dimensional ◽  
Structural Resemblance ◽  
Random Forcing ◽  
The Universe

Abstract Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin-Löf. We extend this result and demonstrate that QM is algorithmic ω-random and generic precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo-Fraenkel Solovay random on infinite dimensional Hilbert spaces. Moreover it is more likely that there exists a standard transitive model of ZFC M where QM is expressed in reality than in the universe V of sets. Then every generic quantum measurement adds the infinite sequence, i.e. random real r ∈ 2ω, to M and the model undergoes random forcing extensions, M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit. This shows the structural resemblance of both in the limit. We discuss several questions regarding measurability and eventual practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC, however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself the issues considered here become mostly hidden.

scholarly journals The Surjective Mapping Conjecture and the Measurement Problem in Quantum Mechanics

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2155
Author(s):  
Fritz Wilhelm Bopp
Keyword(s):  
Quantum Mechanics ◽  
Measurement Problem ◽  
Complex Conjugate ◽  
Arbitrary Boundary ◽  
Quantum Time ◽  
Symmetric Quantum ◽  
Surjective Mapping ◽  
Measurement Path ◽  
The Universe ◽  
Selection Of

Accepting a time-symmetric quantum dynamical world with ontological wave functions or fields, we follow arguments that naturally lead to a two-boundary interpretation of quantum mechanics. The usual two boundary picture is a valid superdeterministic interpretation. It has, however, one unsatisfactory feature. The random selection of a chosen measurement path of the universe is far too complicated. To avoid it, we propose an alternate two-boundary concept called surjective mapping conjecture. It takes as fundamental a quantum-time running forward like the usual time on the wave-function side and backward on the complex conjugate side. Unrelated fixed arbitrary boundary conditions at the initial and the final quantum times then determine the measurement path of the expanding and contracting quantum-time universe in the required way.

scholarly journals Random World and Quantum Mechanics

2021 ◽  
Author(s):  
Jerzy Król ◽  
Krzysztof Bielas ◽  
Torsten Asselmeyer-Maluga
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Infinite Sequence ◽  
Quantum Limit ◽  
Random Real ◽  
Practical Applications ◽  
Infinite Dimensional ◽  
Entire Process ◽  
The Universe ◽  
Infinite Sequences

Abstract Quantum mechanics (QM) predicts probabilities on the fundamentallevel which are, via Born probability law, connected to the formal randomnessof infinite sequences of QM outcomes. Recently it has been shown thatQM is algorithmic 1-random in the sense of Martin-L¨of. We extend this resultand demonstrate that QM is algorithmic ω-random and generic, precisely asdescribed by the ’miniaturisation’ of the Solovay forcing to arithmetic. Thisis extended further to the result that QM becomes Zermelo–Fraenkel Solovayrandom on infinite-dimensional Hilbert spaces. Moreover, it is more likely thatthere exists a standard transitive ZFC model M, where QM is expressed in reality,than in the universe V of sets. Then every generic quantum measurementadds to M the infinite sequence, i.e. random real r ∈ 2ω, and the model undergoesrandom forcing extensions M[r]. The entire process of forcing becomesthe structural ingredient of QM and parallels similar constructions applied tospacetime in the quantum limit, therefore showing the structural resemblanceof both in this limit. We discuss several questions regarding measurability andpossible practical applications of the extended Solovay randomness of QM.The method applied is the formalization based on models of ZFC; however,this is particularly well-suited technique to recognising randomness questionsof QM. When one works in a constant model of ZFC or in axiomatic ZFCitself, the issues considered here remain hidden to a great extent.

scholarly journals Random World and Quantum Mechanics

2021 ◽  
Author(s):  
Jerzy Król ◽  
Krzysztof Bielas ◽  
Torsten Asselmeyer-Maluga
Keyword(s):  
Quantum Mechanics ◽  
Hilbert Spaces ◽  
Infinite Sequence ◽  
Quantum Limit ◽  
Random Real ◽  
Practical Applications ◽  
Infinite Dimensional ◽  
Structural Resemblance ◽  
Random Forcing ◽  
The Universe

Abstract Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin-Löf. We extend this result and demonstrate that QM is algorithmic ω-random and generic precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo-Fraenkel Solovay random on infinite dimensional Hilbert spaces. Moreover it is more likely that there exists a standard transitive model of ZFC M where QM is expressed in reality than in the universe V of sets. Then every generic quantum measurement adds the infinite sequence, i.e. random real r ∈ 2ω , to M and the model undergoes random forcing extensions, M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit. This shows the structural resemblance of both in the limit. We discuss several questions regarding measurability and eventual practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC, however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself the issues considered here become mostly hidden.

scholarly journals Signatures of Quantum Mechanics in Chaotic Systems

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 618 ◽  
Author(s):  
Kevin M. Short ◽  
Matthew A. Morena
Keyword(s):  
Quantum Mechanics ◽  
Quantum Entanglement ◽  
Chaotic Systems ◽  
Measurement Problem ◽  
Quantum Systems ◽  
Analytical Tool ◽  
Quantum Mechanical ◽  
Unstable Periodic Orbits ◽  
Classical Correspondence ◽  
Quantum Mechanical Systems

We examine the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic system’s set of cupolets, which are highly-accurate stabilizations of its unstable periodic orbits. Our discussion is motivated by the bound or entangled states that we have recently detected between interacting chaotic systems, wherein pairs of cupolets are induced into a state of mutually-sustaining stabilization that can be maintained without external controls. This state is known as chaotic entanglement as it has been shown to exhibit several properties consistent with quantum entanglement. For instance, should the interaction be disturbed, the chaotic entanglement would then be broken. In this paper, we further describe chaotic entanglement and go on to address the capacity for chaotic systems to exhibit other characteristics that are conventionally associated with quantum mechanics, namely analogs to wave function collapse, various entropy definitions, the superposition of states, and the measurement problem. In doing so, we argue that these characteristics need not be regarded exclusively as quantum mechanical. We also discuss several characteristics of quantum systems that are not fully compatible with chaotic entanglement and that make quantum entanglement unique.

Sign in / Sign up

Export Citation Format

Share Document