Alternatives to standard quantum theory ruled out

Nature ◽  
2021 ◽  
Author(s):  
William K. Wootters
Keyword(s):  
Quantum Theory ◽  
Standard Quantum

scholarly journals Local Realistic Theory for PDC Experiments Based on the Wigner Formalism

2001 ◽  
Vol 56 (1-2) ◽  
pp. 178-181 ◽  
Author(s):  
Alberto Casado ◽  
Ramón Risco-Delgado ◽  
Emilio Santos
Keyword(s):  
Quantum Theory ◽  
Radiation Field ◽  
Hidden Variables ◽  
Standard Quantum ◽  
Realistic Theory ◽  
Photon Pairs ◽  
Parametric Down Conversion ◽  
Wigner Representation ◽  
Down Conversion ◽  
Made In

Abstract In this article we present a local hidden variables model for all experiments involving photon pairs produced in parametric down conversion, based on the Wigner representation of the radiation field. A modification of the standard quantum theory of detection is made in order to give a local realistic explanation of the counting rates in photodetectors. This model involves the existence of a real zeropoint field, such that the vacumm level of radiation lies below the threshold of the detectors.

scholarly journals Symmetries in Foundation of Quantum Theory and Mathematics

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 409 ◽  
Author(s):  
Felix M. Lev
Keyword(s):  
Quantum Theory ◽  
Dark Energy ◽  
Lie Algebra ◽  
De Sitter ◽  
Classical Level ◽  
Standard Quantum ◽  
Background Space ◽  
Classical Mathematics ◽  
Formal Limit ◽  
And Mathematics

In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite—background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare symmetry can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario in which the phenomenon of cosmological acceleration can be explained by proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic p and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

Quantum theory from quantum information: the purification route

2013 ◽  
Vol 91 (6) ◽  
pp. 475-478 ◽  
Author(s):  
Giulio Chiribella ◽  
Xiao Yuan
Keyword(s):  
Quantum Mechanics ◽  
Information Processing ◽  
Quantum Theory ◽  
Quantum Information ◽  
Foundations Of Quantum Mechanics ◽  
Mathematical Structure ◽  
Mathematical Language ◽  
Standard Quantum ◽  
Information Theoretic

Quantum information provided a new angle on the foundations of quantum mechanics, where the emphasis is placed on operational tasks pertaining to information-processing and computation. In this spirit, several authors have proposed that the mathematical structure of quantum theory could (and should) be rebuilt from purely information-theoretic principles. Here we review the particular route proposed by D'Ariano, Perinotti, and one of the authors (Chiribella et al. Phys. Rev. A, 84, 012311 (2011)), with the purpose of giving a synopsis of the informational principles therein, along with a translation of those principles into the mathematical language of standard quantum theory.

scholarly journals Lectures on dynamical models for quantum measurements

2014 ◽  
Vol 28 (21) ◽  
pp. 1430014
Author(s):  
Theo M. Nieuwenhuizen ◽  
Marti Perarnau-Llobet ◽  
Roger Balian
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Density Matrix ◽  
Quantum Measurements ◽  
Quantum Spin ◽  
Spin Component ◽  
Time Interval ◽  
Large Set ◽  
Standard Quantum ◽  
The One

In textbooks, ideal quantum measurements are described in terms of the tested system only by the collapse postulate and Born's rule. This level of description offers a rather flexible position for the interpretation of quantum mechanics. Here we analyse an ideal measurement as a process of interaction between the tested system S and an apparatus A, so as to derive the properties postulated in textbooks. We thus consider within standard quantum mechanics the measurement of a quantum spin component ŝz by an apparatus A, being a magnet coupled to a bath. We first consider the evolution of the density operator of S + A describing a large set of runs of the measurement process. The approach describes the disappearance of the off-diagonal terms ("truncation") of the density matrix as a physical effect due to A, while the registration of the outcome has classical features due to the large size of the pointer variable, the magnetization. A quantum ambiguity implies that the density matrix at the final time can be decomposed on many bases, not only the one of the measurement. This quantum oddity prevents to connect individual outcomes to measurements, a difficulty known as the "measurement problem". It is shown that it is circumvented by the apparatus as well, since the evolution in a small time interval erases all decompositions, except the one on the measurement basis. Once one can derive the outcome of individual events from quantum theory, the so-called collapse of the wavefunction or the reduction of the state appears as the result of a selection of runs among the original large set. Hence nothing more than standard quantum mechanics is needed to explain features of measurements. The employed statistical formulation is advocated for the teaching of quantum theory.

scholarly journals Examples of Non-Constructive Proofs in Quantum Theory

2015 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Arkady Bolotin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Infinite Number ◽  
Physical Science ◽  
Physical Theory ◽  
Quantum States ◽  
Standard Quantum ◽  
Macroscopic Quantum ◽  
Quantum Formalism ◽  
Constructive Proofs

<p class="1Body">Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is exactly that: algorithmic procedures (built on a certain mathematical formalism) for obtaining verifiable conclusions from a set of basic hypotheses. By admitting non-constructivist statements, a physical theory loses its concrete applicability and thus verifiability of its predictions. Accordingly, the requirement of constructivism must be indispensable to any physical theory. Nevertheless, in at least some physical theories, and especially in quantum mechanics, one can find examples of non-constructive statements. The present paper demonstrates a couple of such examples dealing with macroscopic quantum states (i.e., with the applicability of the standard quantum formalism to macroscopic systems). As it is shown, in these examples the proofs of the existence of macroscopic quantum states are based on logical principles allowing one to decide the truth of predicates over an infinite number of things.</p>

PRINCIPLES OF A NEW QUANTUM THEORY

1998 ◽  
Vol 13 (21) ◽  
pp. 1675-1688 ◽  
Author(s):  
C. SYROS
Keyword(s):  
Quantum Theory ◽  
Time Evolution ◽  
Evolution Operator ◽  
Quantization Rule ◽  
Time Evolution Operator ◽  
Standard Quantum ◽  
Time Space ◽  
Field Action ◽  
Time Quantum ◽  
Time’S Arrow

The principles of a random quantum theory (R-QT) which is alternatively time-asymmetric or time-symmetric if the quantization is Fermi–Dirac or Bose–Enstein, respectively are presented. Bohr's quantization rule is applied on the field-action integral. A time topological space, [Formula: see text], is mathematically defined in which the paradoxes in standard quantum theory are solved. The time "quantum", is created as a regular, positive into-map of an observed observable's change resulting from a fundamental interaction process. [Formula: see text] is constructed as the union of time elements and can be embedded disconnectedly in the continuous Newtonian universal time, [Formula: see text]. Six axioms are formulated characterizing the space–time and R-QT. The disconnectedness of the (κ×λκ)-fold time-space, [Formula: see text], imparts a kind of disconnectedness to the κ×λκ-fold space–times, [Formula: see text], and induces the chrono-topology. In chrono-topology the unitary, U, or non-measure preserving, R, dynamics, is implemented by means of a time evolution, "complex" operator, [Formula: see text]. It breaks down by means of Bohr quantization into: [Formula: see text][Formula: see text] coincides formally — apart from the spontaneous renormalization — with the time evolution operator in the standard QFT. [Formula: see text] is a novum and produces the Maxwell–Boltzmann energy level distribution in a non-Euclidean QFT. Compatibility between time-reversal invariance of the standard QT equations and irreversibility of some phenomena both in microcosmos and macrocosmos is obtained. The [Formula: see text]-evolution leads to a time's arrow on quantum-scale systems.

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