scholarly journals IS PT -SYMMETRIC QUANTUM THEORY FALSE AS A FUNDAMENTAL THEORY?

2016 ◽  
Vol 56 (3) ◽  
pp. 254 ◽  
Author(s):  
Miloslav Znojil
Keyword(s):  
Quantum Theory ◽  
Fundamental Theory ◽  
Model Based ◽  
Symmetric Quantum ◽  
Present Text ◽  
Recent Extension

Yi-Chan Lee et al. claim (cf. Phys. Rev. Lett. 112, 130404 (2014)) that the “recent extension of quantum theory to non-Hermitian Hamiltonians” (which is widely known under the nickname of “<em>PT</em>-symmetric quantum theory”) is “likely false as a fundamental theory”. By their opinion their results “essentially kill any hope of <em>PT</em>-symmetric quantum theory as a fundamental theory of nature”. In our present text we explain that their toy-model-based considerations are misleading and that they do not imply any similar conclusions.

scholarly journals Generation of families of spectra in PT -symmetric quantum mechanics and scalar bosonic field theory

2013 ◽  
Vol 371 (1989) ◽  
pp. 20120049 ◽  
Author(s):  
Steffen Schmidt ◽  
S. P. Klevansky
Keyword(s):  
Field Theory ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Complex Analysis ◽  
One Dimension ◽  
Quantum Mechanical ◽  
Bosonic Field ◽  
Symmetric Quantum ◽  
The Difference ◽  
Do So

This paper explains the systematics of the generation of families of spectra for the -symmetric quantum-mechanical Hamiltonians H = p 2 + x 2 (i x ) ϵ , H = p 2 +( x 2 ) δ and H = p 2 −( x 2 ) μ . In addition, it contrasts the results obtained with those found for a bosonic scalar field theory, in particular in one dimension, highlighting the similarities to and differences from the quantum-mechanical case. It is shown that the number of families of spectra can be deduced from the number of non-contiguous pairs of Stokes wedges that display symmetry. To do so, simple arguments that use the Wentzel–Kramers–Brillouin approximation are used, and these imply that the eigenvalues are real. However, definitive results are in most cases presently only obtainable numerically, and not all eigenvalues in each family may be real. Within the approximations used, it is illustrated that the difference between the quantum-mechanical and the field-theoretical cases lies in the number of accessible regions in which the eigenfunctions decay exponentially. This paper reviews and implements well-known techniques in complex analysis and -symmetric quantum theory.

scholarly journals Uncertainty Relations: Curiosities and Inconsistencies

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1640
Author(s):  
Krzysztof Urbanowski
Keyword(s):  
Quantum Theory ◽  
Lower Bound ◽  
Uncertainty Relation ◽  
Quantum Particle ◽  
Uncertainty Relations ◽  
Rigorous Analysis ◽  
Special Cases ◽  
The Status ◽  
Symmetric Quantum ◽  
Standard Deviations

Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: ΔA·ΔB≥0. Here we discuss examples of such cases and some other inconsistencies which can be found performing a rigorous analysis of the uncertainty relations in some special cases. As an illustration of such cases matrices (2×2) and (3×3) and the position–momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in PT–symmetric quantum theory and the problems associated with it are also studied.

Interlude: Some Alternative Interpretations

2017 ◽  
Author(s):  
Richard Healey
Keyword(s):  
Decision Making ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Bohmian Mechanics ◽  
Natural Phenomena ◽  
Fundamental Theory ◽  
Relativistic Invariance ◽  
The World ◽  
And Control ◽  
Non Locality

An understanding of quantum theory is manifested by the ability successfully and unproblematically to use it to further the scientific goals of prediction, explanation, and control of natural phenomena. An Interpretation seeks further to formulate or reformulate it as a fundamental theory that provides a self-contained description of the world. I critically review three prominent but radically different Interpretations of quantum theory (Bohmian mechanics, non-linear theories, Everettian quantum mechanics) and give my reasons for rejecting each as a way of understanding quantum theory. These include problems associated with non-locality, failure of relativistic invariance, empirical inaccessibility, and decision-making. We can achieve a satisfactory understanding of quantum theory and how it successfully advances the goals of science without providing an Interpretation of the theory.

Conventional Bell Basis in PT-symmetric Quantum Theory

2018 ◽  
Vol 57 (12) ◽  
pp. 3839-3849
Author(s):  
Xiang-yu Zhu ◽  
Yuan-hong Tao
Keyword(s):  
Quantum Theory ◽  
Symmetric Quantum ◽  
Bell Basis

scholarly journals An algebraic PT-symmetric quantum theory with a maximal mass

2016 ◽  
Vol 47 (2) ◽  
pp. 135-156 ◽  
Author(s):  
V. N. Rodionov ◽  
G. A. Kravtsova
Keyword(s):  
Quantum Theory ◽  
Symmetric Quantum ◽  
Maximal Mass

scholarly journals A no-go theorem for theories that decohere to quantum mechanics

2018 ◽  
Vol 474 (2214) ◽  
pp. 20170732 ◽  
Author(s):  
Ciarán M. Lee ◽  
John H. Selby
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Incomplete Information ◽  
Experimental Evidence ◽  
Fundamental Theory ◽  
Classical Physics ◽  
Lack Of Information ◽  
The World ◽  
Physical Principles ◽  
Effective Description

To date, there has been no experimental evidence that invalidates quantum theory. Yet it may only be an effective description of the world, in the same way that classical physics is an effective description of the quantum world. We ask whether there exists an operationally defined theory superseding quantum theory, but which reduces to it via a decoherence-like mechanism. We prove that no such post-quantum theory exists if it is demanded that it satisfy two natural physical principles: causality and purification . Causality formalizes the statement that information propagates from present to future, and purification that each state of incomplete information arises in an essentially unique way due to lack of information about an environment. Hence, our result can be viewed either as evidence that the fundamental theory of Nature is quantum or as showing in a rigorous manner that any post-quantum theory must abandon causality, purification or both.

scholarly journals Embedding, simulation and consistency ofPT-symmetric quantum theory

2018 ◽  
Vol 382 (36) ◽  
pp. 2578-2585 ◽  
Author(s):  
Minyi Huang ◽  
Asutosh Kumar ◽  
Junde Wu
Keyword(s):  
Quantum Theory ◽  
Symmetric Quantum
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