scholarly journals Quantum Contextuality and Indeterminacy

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 867
Author(s):  
Gregg Jaeger
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables ◽  
Equivalence Classes ◽  
Measuring Apparatus ◽  
Classical Physics ◽  
Quantum Contextuality ◽  
Natural Feature ◽  
Classical Models ◽  
Quantum Behavior ◽  
Quantum Observables

The circumstances of measurement have more direct significance in quantum than in classical physics, where they can be neglected for well-performed measurements. In quantum mechanics, the dispositions of the measuring apparatus-plus-environment of the system measured for a property are a non-trivial part of its formalization as the quantum observable. A straightforward formalization of context, via equivalence classes of measurements corresponding to sets of sharp target observables, was recently given for sharp quantum observables. Here, we show that quantum contextuality, the dependence of measurement outcomes on circumstances external to the measured quantum system, can be manifested not only as the strict exclusivity of different measurements of sharp observables or valuations but via quantitative differences in the property statistics across simultaneous measurements of generalized quantum observables, by formalizing quantum context via coexistent generalized observables rather than only its subset of compatible sharp observables. Here, the question of whether such quantum contextuality follows from basic quantum principles is then addressed, and it is shown that the Principle of Indeterminacy is sufficient for at least one form of non-trivial contextuality. Contextuality is thus seen to be a natural feature of quantum mechanics rather than something arising only from the consideration of impossible measurements, abstract philosophical issues, hidden-variables theories, or other alternative, classical models of quantum behavior.

Quantum contextuality in the Copenhagen approach

2019 ◽  
Vol 377 (2157) ◽  
pp. 20190025 ◽  
Author(s):  
Gregg Jaeger
Keyword(s):  
Quantum Mechanics ◽  
Experimental Situation ◽  
Hidden Variables ◽  
Theme Issue ◽  
Standard Quantum ◽  
Von Neumann ◽  
Physical Description ◽  
Quantum Contextuality ◽  
Quantum Observables

The origin and basis of the notion of quantum contextuality is identified in the Copenhagen approach to quantum mechanics, where context is automatically invoked by its requirement that the experimental arrangement involved in any measurements or set of measurements be taken into account while, in general, the outcome of a measurement may depend on other measurements immediately preceding or jointly performed on the same system. For Bohr, the specification of the experimental situation of any measurement is essential to its significance in light of complementarity and the omnipresence of the quantum of action in physics; for Heisenberg, the incompatibility of pairs of sharp measurements belonging to different situations coheres with both the completeness of the quantum state as an objective physical description and the principle of indeterminacy. Here, context in the Copenhagen approach is taken to be the equivalence class of experimental arrangements corresponding to a set of compatible measurements of quantum observables in standard quantum mechanics; the associated form of contextuality in quantum mechanics arises via the non-commutativity in general of sharp observables, proven by von Neumann, that can appear, providing different contexts. This notion is related to theoretical situations explored later by Bell, by Kochen and Specker, and by others in relation to the classification of hidden-variables theories and elsewhere in physics. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

PROBING BELL'S INEQUALITY WITH CLASSICAL SYSTEMS

2010 ◽  
Vol 09 (04) ◽  
pp. 395-402 ◽  
Author(s):  
D. K. FERRY
Keyword(s):  
Quantum Mechanics ◽  
Bell Inequality ◽  
Hidden Variables ◽  
Optical Polarization ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Quantum Theories ◽  
Considerable Evidence ◽  
Classical Systems ◽  
Quantum Behavior

From the early days of quantum mechanics, there has been a discussion on the concept of reality, exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell inequality. Yet, there remains considerable evidence that this inequality can be violated even by classical systems, so that experiments showing quantum behavior and the violation of the inequality must be questioned. Here, we demonstrate that classical optical polarization experiments can be shown to violate the Bell inequality. Hence, such experiments cannot be used to distinguish between classical and quantum theories.

scholarly journals The indeterminist objectivity of quantum mechanics versus the determinist subjectivity of classical physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Free Will ◽  
Hidden Variables ◽  
Classical Mechanics ◽  
Niels Bohr ◽  
Necessary Condition ◽  
Human Beings ◽  
Classical Physics ◽  
Physical Universe ◽  
Max Born

Indeterminism of quantum mechanics is considered as an immediate corollary from the theorems about absence of hidden variables in it, and first of all, the Kochen – Specker theorem. The base postulate of quantum mechanics formulated by Niels Bohr that it studies the system of an investigated microscopic quantum entity and the macroscopic apparatus described by the smooth equations of classical mechanics by the readings of the latter implies as a necessary condition of quantum mechanics the absence of hidden variables, and thus, quantum indeterminism. Consequently, the objectivity of quantum mechanics and even its possibility and ability to study its objects as they are by themselves imply quantum indeterminism. The so-called free-will theorems in quantum mechanics elucidate that the “valuable commodity” of free will is not a privilege of the experimenters and human beings, but it is shared by anything in the physical universe once the experimenter is granted to possess free will. The analogical idea, that e.g. an electron might possess free will to “decide” what to do, scandalized Einstein forced him to exclaim (in a letter to Max Born in 2016) that he would be а shoemaker or croupier rather than a physicist if this was true. Anyway, many experiments confirmed the absence of hidden variables and thus quantum indeterminism in virtue of the objectivity and completeness of quantum mechanics. Once quantum mechanics is complete and thus an objective science, one can ask what this would mean in relation to classical physics and its objectivity. In fact, it divides disjunctively what possesses free will from what does not. Properly, all physical objects belong to the latter area according to it, and their “behavior” is necessary and deterministic. All possible decisions, on the contrary, are concentrated in the experimenters (or human beings at all), i.e. in the former domain not intersecting the latter. One may say that the cost of the determinism and unambiguous laws of classical physics, is the indeterminism and free will of the experimenters and researchers (human beings) therefore necessarily being out of the scope and objectivity of classical physics. This is meant as the “deterministic subjectivity of classical physics” opposed to the “indeterminist objectivity of quantum mechanics”.

Quantum mechanics, «First kind» states and local hidden variables: Three experimentally distinguishable situations

1978 ◽  
Vol 43 (1) ◽  
pp. 65-72 ◽  
Author(s):  
A. Baracca ◽  
A. Cornia ◽  
R. Livi ◽  
S. Ruffo
Keyword(s):  
Quantum Mechanics ◽  
Hidden Variables

scholarly journals Free Will in Human Behavior and Physics

2020 ◽  
Author(s):  
Vasil Dinev Penchev
Keyword(s):  
Quantum Mechanics ◽  
Quantum Information ◽  
Free Will ◽  
Human Behavior ◽  
Physical World ◽  
Classical Physics ◽  
Quantum Bit ◽  
The Past ◽  
The Mean ◽  
The One

If the concept of “free will” is reduced to that of “choice” all physical world share the latter quality. Anyway the “free will” can be distinguished from the “choice”: The “free will” involves implicitly a certain goal, and the choice is only the mean, by which the aim can be achieved or not by the one who determines the target. Thus, for example, an electron has always a choice but not free will unlike a human possessing both. Consequently, and paradoxically, the determinism of classical physics is more subjective and more anthropomorphic than the indeterminism of quantum mechanics for the former presupposes certain deterministic goal implicitly following the model of human freewill behavior. Quantum mechanics introduces the choice in the fundament of physical world involving a generalized case of choice, which can be called “subjectless”: There is certain choice, which originates from the transition of the future into the past. Thus that kind of choice is shared of all existing and does not need any subject: It can be considered as a low of nature. There are a few theorems in quantum mechanics directly relevant to the topic: two of them are called “free will theorems” by their authors (Conway and Kochen 2006; 2009). Any quantum system either a human or an electron or whatever else has always a choice: Its behavior is not predetermined by its past. This is a physical law. It implies that a form of information, the quantum information underlies all existing for the unit of the quantity of information is an elementary choice: either a bit or a quantum bit (qubit).

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