Year 2024

• Bell-Type Inequalities from the Perspective of Non-Newtonian Calculus

  Publication

  • M. P. Piłat

  - Foundations of Science - Year 2024

  A class of quantum probabilities is reformulated in terms of non-Newtonian calculus and projective arithmetic. The model generalizes spin-1/2 singlet state probabilities discussed in Czachor (Acta Physica Polonica:139 70–83, 2021) to arbitrary spins s. For s → ∞ the formalism reduces to ordinary arithmetic and calculus. Accordingly, the limit “non-Newtonian to Newtonian” becomes analogous to the classical limit of a quantum theory

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• Imitating Quantum Probabilities: Beyond Bell’s Theorem and Tsirelson Bounds

  Publication

  • M. Czachor
  • K. Nalikowski

  - Foundations of Science - Year 2024

  Local hidden-variable model of singlet-state correlations discussed in M. Czachor, Acta Phys. Polon. A 139, 70, is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a `confusion of languages' problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring...

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Year 2023

• Consistency of Quantum Computation and the Equivalence Principle.

  Publication

  • M. Nowakowski

  - Foundations of Science - Year 2023

  The equivalence principle, being one of the building blocks of general relativity, seems to be crucial for analysis of quantum effects in gravity. In this paper we consider the relation between the equivalence principle and the consistency of quantum information processing in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame....

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Year 2021

• Non-Newtonian Mathematics Instead of Non-Newtonian Physics: Dark Matter and Dark Energy from a Mismatch of Arithmetics

  Publication

  • M. Czachor

  - Foundations of Science - Year 2021

  Newtonian physics is based on Newtonian calculus applied to Newtonian dynamics. New paradigms such as ‘modified Newtonian dynamics’ (MOND) change the dynamics, but do not alter the calculus. However, calculus is dependent on arithmetic, that is the ways we add and multiply numbers. For example, in special relativity we add and subtract velocities by means of addition β1⊕β2=tanh(tanh−1(β1)+tanh−1(β2)), although multiplication β1⊙β2=tanh(tanh−1(β1)⋅tanh−1(β2)),...

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Year 2020

• A Loophole of All ‘Loophole-Free’ Bell-Type Theorems

  Publication

  • M. Czachor

  - Foundations of Science - Year 2020

  Bell’s theorem cannot be proved if complementary measurements have to be represented by random variables which cannot be added or multiplied. One such case occurs if their domains are not identical. The case more directly related to the Einstein–Rosen–Podolsky argument occurs if there exists an ‘element of reality’ but nevertheless addition of complementary results is impossible because they are represented by elements from different...

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Year 2019

• Systems, Environments, and Soliton Rate Equations: Toward Realistic Modeling

  Publication

  • M. Kuna

  - Foundations of Science - Year 2019

  In order to solve a system of nonlinear rate equations one can try to use some soliton methods. The procedure involves three steps: (1) find a ‘Lax representation’ where all the kinetic variables are combined into a single matrix ρ, all the kinetic constants are encoded in a matrix H; (2) find a Darboux–Bäcklund dressing transformation for the Lax representation iρ˙=[H,f(ρ)], where f models a time-dependent environment; (3) find...

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