Epilogue A Game of Theories

2020 ◽  
pp. 265-268
Author(s):  
Jim Baggott
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Historical Context ◽  
Basic Knowledge ◽  
Scientific Theories ◽  
To Come

The Quantum Cookbook shows that whilst quantum mechanics is mathematically challenging, some basic knowledge and a bit of effort will carry you a long way. It also explains how quantum mechanics was derived from the physics. The abstract formalism based on state vectors in Hilbert space was introduced only when it was deemed desirable to lend the theory greater mathematical consistency, and to reject some of its historical baggage. The best way to come to terms with this formalism is to understand how and why it came about. Debates about interpretation continue to this day and, by providing some historical context, you should get the impression that any lack of comprehension of its meaning on your part is absolutely not your fault. Quantum mechanics challenges our comprehension of what any (and all) scientific theories are meant to be telling us about the nature of reality. It’s okay to have doubts.

Nonlinear quantum mechanics in a q-deformed Hilbert space

2019 ◽  
Vol 383 (23) ◽  
pp. 2729-2738 ◽  
Author(s):  
Bruno G. da Costa ◽  
Ernesto P. Borges
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

THE UNREASONABLE EFFECTIVENESS OF EXPONENTIALLY SUPPRESSED CORRECTIONS IN PRESERVING INFORMATION

2013 ◽  
Vol 22 (12) ◽  
pp. 1342030 ◽  
Author(s):  
KYRIAKOS PAPADODIMAS ◽  
SUVRAT RAJU
Keyword(s):  
Hilbert Space ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Nonperturbative Effects ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Information Theoretic ◽  
Black Hole Evaporation ◽  
Strong Subadditivity ◽  
Unreasonable Effectiveness

We point out that nonperturbative effects in quantum gravity are sufficient to reconcile the process of black hole evaporation with quantum mechanics. In ordinary processes, these corrections are unimportant because they are suppressed by e-S. However, they gain relevance in information-theoretic considerations because their small size is offset by the corresponding largeness of the Hilbert space. In particular, we show how such corrections can cause the von Neumann entropy of the emitted Hawking quanta to decrease after the Page time, without modifying the thermal nature of each emitted quantum. Second, we show that exponentially suppressed commutators between operators inside and outside the black hole are sufficient to resolve paradoxes associated with the strong subadditivity of entropy without any dramatic modifications of the geometry near the horizon.

scholarly journals Is Overtourism Overused? Understanding the Impact of Tourism in a City Context

2018 ◽  
Vol 10 (12) ◽  
pp. 4384 ◽  
Author(s):  
Ko Koens ◽  
Albert Postma ◽  
Bernadett Papp
Keyword(s):  
Historical Context ◽  
Popular Media ◽  
Current Paper ◽  
Qualitative Investigation ◽  
Tourism Impacts ◽  
European Cities ◽  
To Come ◽  
The Impact

In less than two years, the concept of overtourism has come to prominence as one of the most discussed issues with regards to tourism in popular media and, increasingly, academia. In spite of its popularity, the term is still not clearly delineated and remains open to multiple interpretations. The current paper aims to provide more clarity with regard to what overtourism entails by placing the concept in a historical context and presenting results from a qualitative investigation among 80 stakeholders in 13 European cities. Results highlight that overtourism describes an issue that is multidimensional and complex. Not only are the issues caused by tourism and nontourism stakeholders, but they should also be viewed in the context of wider societal and city developments. The article concludes by arguing that while the debate on overtourism has drawn attention again to the old problem of managing negative tourism impacts, it is not well conceptualized. Seven overtourism myths are identified that may inhibit a well-rounded understanding of the concept. To further a contextualized understanding of overtourism, the paper calls for researchers from other disciplines to engage with the topic to come to new insights.

scholarly journals Periodicity of functionals and representations of normed algebras on reflexive spaces

1976 ◽  
Vol 20 (2) ◽  
pp. 99-120 ◽  
Author(s):  
N. J. Young
Keyword(s):  
Hilbert Space ◽  
Continuous Homomorphism ◽  
Linear Operators ◽  
The Other ◽  
Continuous Linear ◽  
Normed Algebra ◽  
Reflexive Space ◽  
To Come ◽  
Algebra Of Operators ◽  
Continuous Linear Operators

It is a well-known fact that any normed algebra can be represented isometrically as an algebra of operators with the operator norm. As might be expected from the very universality of this property, it is little used in the study of the structure of an algebra. Far more helpful are representations on Hilbert space, though these are correspondingly hard to come by: isometric representations on Hilbert space are not to be expected in general, and even continuous nontrivial representations may fail to exist. The purpose of this paper is to examine a class of representations intermediate in both availability and utility to those already mentioned—namely, representations on reflexive spaces. There certainly are normed algebras which admit isometric representations of the latter type but have not even faithful representations on Hilbert space: the most natural example is the algebra of all continuous linear operators on E where E = lp with 1 < p ≠ 2 < ∞, for Berkson and Porta proved in (2) that if E, F are taken from the spaces lp with 1 < p < ∞ and E ≠ F then the only continuous homomorphism from into is the zero mapping. On the other hand there are also algebras which have no continuous nontrivial representation on any reflexive space—for example the algebra of finite-rank operators on an irreflexive Banach space (see Berkson and Porta (2) or Barnes (1) or Theorem 3, Corollary 1 below).

scholarly journals Ontology in Quantum Mechanics

2021 ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Hilbert Space ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Mechanics ◽  
Evolution Equations ◽  
Black Hole Physics ◽  
Special Kind ◽  
Quantum Evolution ◽  
The Standard Model ◽  
Low Energies

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is given by elements of the permutation group. This would restore an ontological interpretation. It is shown how, at low energies per particle degree of freedom, almost any quantum system allows for such a transformation. This contradicts Bell’s theorem, and we emphasise why some of the assumptions made by Bell to prove his theorem cannot hold for the models studied here. We speculate how an approach of this kind may become helpful in isolating the most likely version of the Standard Model, combined with General Relativity. A link is suggested with black hole physics.

scholarly journals Nonlinear Generalisation of Quantum Mechanics

2021 ◽  
Author(s):  
Alireza Jamali
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Lorentz Invariance ◽  
Current Theory ◽  
Quantum Mechanical ◽  
Dynamical Condition ◽  
Current Definition ◽  
Klein Gordon ◽  
Definition Of ◽  
Mechanical Momentum

It is known since Madelung that the Schr&ouml;dinger equation can be thought of as governing the evolution of an incompressible fluid, but the current theory fails to mathematically express this incompressibility in terms of the wavefunction without facing problem. In this paper after showing that the current definition of quantum-mechanical momentum as a linear operator is neither the most general nor a necessary result of the de Broglie hypothesis, a new definition is proposed that can yield both a meaningful mathematical condition for the incompressibility of the Madelung fluid, and nonlinear generalisations of Schr&ouml;dinger and Klein-Gordon equations. The derived equations satisfy all conditions that are expected from a proper generalisation: simplification to their linear counterparts by a well-defined dynamical condition; Galilean and Lorentz invariance (respectively); and signifying only rays in the Hilbert space.

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