Non-Deterministic Semantics for Quantum States

In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.

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NONLOCAL MEASUREMENTS IN THE TIME-SYMMETRIC QUANTUM MECHANICS

International Journal of Modern Physics B ◽

10.1142/s0217979206034108 ◽

2006 ◽

Vol 20 (11n13) ◽

pp. 1528-1535 ◽

Cited By ~ 5

Author(s):

LEV VAIDMAN ◽

IZHAR NEVO

Keyword(s):

Quantum Mechanics ◽

Quantum Systems ◽

Quantum Measurements ◽

Quantum States ◽

Standard Quantum ◽

Time Direction ◽

Quantum Formalism ◽

Symmetric Quantum ◽

Time Symmetric Quantum Mechanics

Although for some nonlocal variables the standard quantum measurements which are reliable, instantaneous, and nondemolition, are impossible, demolition reliable instantaneous measurements of all variables are possible. It is shown that this is correct also in the framework of the time-symmetric quantum formalism, i.e. nonlocal variables of composite quantum systems with quantum states evolving both forward and backward in time are measurable in a demolition way. The result follows from the possibility to reverse with certainty the time direction of backward evolving quantum states.

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‘Space is blue and birds fly through it’

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2017.0312 ◽

2018 ◽

Vol 376 (2123) ◽

pp. 20170312 ◽

Cited By ~ 13

Author(s):

Carlo Rovelli

Keyword(s):

Quantum Mechanics ◽

Foundations Of Quantum Mechanics ◽

Quantum States ◽

Contemporary Society ◽

Physical Variables

Quantum mechanics is not about ‘quantum states’: it is about values of physical variables. I give a short fresh presentation and update on the relational perspective on the theory, and a comment on its philosophical implications. This article is part of a discussion meeting issue ‘Foundations of quantum mechanics and their impact on contemporary society’.

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Examples of Non-Constructive Proofs in Quantum Theory

Applied Physics Research ◽

10.5539/apr.v8n1p1 ◽

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>

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COMPLEMENTARY HISTORIES AND COLLAPSE INTO THE PAST IN STANDARD QUANTUM MECHANICS

International Journal of Modern Physics B ◽

10.1142/s0217979299002551 ◽

1999 ◽

Vol 13 (20) ◽

pp. 2629-2636

Author(s):

YURI F. ORLOV

Keyword(s):

Quantum Mechanics ◽

Quantum States ◽

Standard Quantum ◽

Quantum Formalism ◽

The Past ◽

Interpretations Of Quantum Mechanics ◽

Single State ◽

Standard Formalism ◽

Faster Than Light

It follows from the standard quantum formalism that in the time between any two noncommuting measurements there are two quantum states of the same system representing two complementary, forward and backward histories, histories that may be observed in two complementary experiments. It follows from this in turn that all interpretations of quantum mechanics based on the idea of a single state between measurements should be rejected. The non-existence of a faster-than-light nonlocality and of paradoxes in EPR-type experiments1 can be proved in the frame of the standard formalism when the reality of backward histories is taken into account.

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Quantum Theory

10.1093/oso/9780198808275.003.0009 ◽

2017 ◽

Author(s):

Frank S. Levin

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Uncertainty Principle ◽

Quantum Spin ◽

Quantum States ◽

Wave Functions ◽

Symbolic Representations ◽

Quantum Numbers ◽

The Subject ◽

Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

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