On the reality of the quantum state once again: A no-go theorem for $ψ$-ontic models

Carcassi, Gabriele; Oldofredi, Andrea; Aidala, C.

doi:10.48550/arxiv.2201.11842

Cited by 3 publications

(2 citation statements)

References 27 publications

(29 reference statements)

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“…It is important, however, that also arguments against a realistic interpretation of quantum states are given in the literature [66,67].…”

Section: Interpretation Of Quantum Mechanicsmentioning

confidence: 99%

An alternative foundation of quantum theory

Helland

2023

Preprint

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A new approach to quantum theory is proposed in this paper. The basis is first taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an actor to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an actor or to some communicating actors. Group actions are defined on these variables, and group representation theory is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. To focus only on physical variables rather than mathematical variables, the concept of inaccessible variables is then replaced by the concept of notions, and in this connection, aspects of category theory partly replace group theory. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations.

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“…It is important, however, that also arguments against a realistic interpretation of quantum states are given in the literature [66,67].…”

Section: Interpretation Of Quantum Mechanicsmentioning

confidence: 99%

An alternative foundation of quantum theory

Helland

2023

Preprint

View full text Add to dashboard Cite

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“…Other authors use language in a way that, intentionally or otherwise, suggests that the mathematical state is also ontological. Attempts to narrow the range of possibilities are ongoing [ 65 , 66 ], but there is little agreement in this area [ 67 ]. Thus, it remains true that“there do not yet appear to be clear grounds to accept any simple relationship between the quantum mechanical state and independent reality” [ 1 ] (p. 401) [ 40 ] (p. 6) [ 64 ] (Section 2) [ 68 ] (p. 3) [ 69 ] (Sections 20.3–20.5).…”

Section: Statistical Balancementioning

confidence: 99%

Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications

Drummond

2022

Entropy

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Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical states, and not yet explained. The concept of “statistical balance” is here explored, comparing its meaning since 2019 with its original meaning in 2001. Statistical balance now refers to a feature of contexts in which: (a) there is a prescribed probability other than 0 or 1 for the collective response of an ensemble to one measurement type; and (b) the collective response of the same ensemble to another measurement type demonstrates that no well-defined value can be attributed, for the property relevant to the original measurement type, to individual members of the ensemble. In some unexplained way, the outcomes of single runs of a measurement of the original type “balance” each other to give an overall result in line with the prescribed probability. Unexplained statistical balance prompts caution in assessing the conceptual implications of entanglement, measurement, uncertainty, and two-slit and Bell-type analyses. Physicists have a responsibility to the wider population to be conceptually precise about quantum mechanics, and to make clear that many possible conceptual implications are uncertain.

show abstract

An alternative foundation of quantum theory

Helland

2023

Preprint

View full text Add to dashboard Cite

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The essential use of inaccessible variables can be avoided by basing the approach on some simple category theory.The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations.

show abstract

On the reality of the quantum state once again: A no-go theorem for $ψ$-ontic models

Cited by 3 publications

References 27 publications

An alternative foundation of quantum theory

An alternative foundation of quantum theory

Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications

An alternative foundation of quantum theory

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