Nonexistence of Quantum Nonlocality

Griffiths, Robert B.

doi:10.48550/arxiv.1304.4425

Cited by 2 publications

(2 citation statements)

References 15 publications

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“…Also, as argued by Griffiths (see Ref. [28] and references therein), with a consistent interpretation of quantum theory there are no nonlocality and superluminal interactions. In Sec.…”

Section: Position Operator In Relativistic Quantum Mechanicssupporting

confidence: 52%

A new look at the position operator in quantum theory

Lev

2015

Phys. Part. Nuclei

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Abstract:The postulate that coordinate and momentum representations are related to each other by the Fourier transform has been accepted from the beginning of quantum theory by analogy with classical electrodynamics. As a consequence, an inevitable effect in standard theory is the wave packet spreading (WPS) of the photon coordinate wave function in directions perpendicular to the photon momentum. This leads to several paradoxes. The most striking of them is that coordinate wave functions of photons emitted by stars have cosmic sizes and strong arguments indicate that this contradicts observational data. We argue that the above postulate is based neither on strong theoretical arguments nor on experimental data and propose a new consistent definition of the position operator. Then WPS in directions perpendicular to the particle momentum is absent and the paradoxes are resolved. Different components of the new position operator do not commute with each other and, as a consequence, there is no wave function in coordinate representation. Implications of the results for entanglement, quantum locality and the problem of time in quantum theory are discussed.

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“…Also, as argued by Griffiths (see Ref. [28] and references therein), with a consistent interpretation of quantum theory there are no nonlocality and superluminal interactions. In Sec.…”

Section: Position Operator In Relativistic Quantum Mechanicssupporting

confidence: 52%

A new look at the position operator in quantum theory

Lev

2015

Phys. Part. Nuclei

View full text Add to dashboard Cite

show abstract

“…Also, as argued by Griffiths (see Ref. [65] and references therein), with a consistent interpretation of quantum theory there are no nonlocality and superluminal interactions. In Sec.…”

Section: Position Operator In Relativistic Quantum Mechanicssupporting

confidence: 52%

Finite Mathematics, Finite Quantum Theory and Applications to Gravity and Particle Theory

Lev

2011

Preprint

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We argue that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete and even finite, is described by continuous mathematics. Moreover, no ultimate physical theory can be based on continuous mathematics because, as follows from Gödel's incompleteness theorems, any mathematics involving the set of all natural numbers has its own foundational problems which cannot be resolved. In the first part of the work we discuss inconsistencies in standard quantum theory and reformulate the theory such that it can be naturally generalized to a formulation based on finite mathematics. It is shown that: a) as a consequence of inconsistent definition of standard position operator, predictions of the theory contradict the data on observations of stars; b) the cosmological acceleration and gravity can be treated simply as kinematical manifestations of de Sitter symmetry on quantum level (i.e. for describing those phenomena the notions of dark energy, space-time background and gravitational interaction are not needed). In the second part we consider a quantum theory based on finite mathematics with a large characteristic p. In this approach the de Sitter gravitational constant depends on p and disappears in the formal limit p → ∞, i.e. gravity is a consequence of finiteness of nature. The application to particle theory gives that: a) no neutral elementary particles can exist; b) the electric charge and the baryon and lepton quantum numbers can be only approximately conserved (i.e. the notion of a particle and its antiparticle is only approximate). We also consider a possibility that only Dirac singletons can be true elementary particles.

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Nonexistence of Quantum Nonlocality

Abstract: What violations of Bell inequalities teach us is that the world is quantum mechanical, i.e., nonclassical. Assertions that they imply the world is nonlocal arise from ignoring differences between quantum and classical physics.

Cited by 2 publications

References 15 publications

A new look at the position operator in quantum theory

A new look at the position operator in quantum theory

Finite Mathematics, Finite Quantum Theory and Applications to Gravity and Particle Theory

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