Product associativity in scator algebras and the quantum wave function collapse

Year 2018, Volume: 1 Issue: 2, 80 - 88, 26.06.2018

Manuel Fernandez-guasti

https://doi.org/10.32323/ujma.423045

Cited By: 10

Abstract

The scator product in $1+n$ dimensions for $n>1$, is associative if all possible product pairs have a non vanishing additive scalar component. The product is in general, not associative in the additive representation whenever the additive scalar component of a product pair is zero. A particular case of this statement is non associativity due to zero products of non zero factors. These features of scator algebra could be used to model the quantum wave function evolution and collapse in a unified description.

Keywords

Commutative algebras, Hypercomplex numbers, Non associative algebras, Quantum measurement problem

References

• [1] M. Fernández-Guasti. A non-distributive extension of complex numbers to higher dimensions. Adv. Appl. Clifford Algebras, 25:829–849, Oct. 2015.
• [2] A. Kobus and J. L. Cieśliński. On the Geometry of the Hyperbolic Scator Space in 1+2 Dimensions. Advances in Applied Clifford Algebras,27(2):1369–1386, 2017.
• [3] M. Fernández-Guasti and F. Zaldívar. A hyperbolic non distributive algebra in 1+2 dimensions. Adv. Appl. Clifford Algebras, 23(3):639–653, 2013.
• [4] M. Fernández-Guasti and F. Zaldívar. Multiplicative representation of a hyperbolic non distributive algebra. Adv. Appl. Clifford Algebras, 24(3):661–674,2014.
• [5] M. Fernández-Guasti and F. Zaldívar. An elliptic non distributive algebra. Adv. Appl. Clifford Algebras, 23(4):825–835, 2013.
• [6] W. E. Baylis and J. D. Keselica. A classical spinor approach to the quantum/classical interface. Canadian Journal of Physics, 86(4):629–634, 2008.
• [7] D. Hestenes. New foundations for classical mechanics. Kluwer, 1990.
• [8] F. Catoni, D. Boccaletti, R. Cannata, V. Catoni, E. Nichelatti, and P. Zampetti. The Mathematics of Minkowski Space-Time. Number 2 in Frontiers inMathematics. Birkhauser Verlag, 2008.
• [9] M. Fernández-Guasti. Time and space transformations in a scator deformed Lorentz metric. European Physical Journal - Plus, 129(195):1–10, 2014.
• [10] M. Fernández-Guasti and F. Zaldívar. Hyperbolic superluminal scator algebra. Adv. Appl. Clifford Algebras, 25(2):321–335, 2015.
• [11] V. Allori, S. Goldstein, R. Tumulka, and N. Zanghì. On the Common Structure of Bohmian Mechanics and the Ghirardi–Rimini–Weber Theory. BritishJournal for the Philosophy of Science, 59(3):353–389, 2008.
• [12] A. Bassi and G. C. Ghirardi. Dynamical reduction models. Physics Reports, 379(5–6):257–426, 2003.
• [13] R. Penrose. The Road to reality. Knopf, 2005.
• [14] M. Fernández-Guasti. Imaginary Scators Bound Set Under The Iterated Quadratic Mapping In 1+2 Dimensional Parameter Space. Int. J. of Bifurcationand Chaos, 26(1):1630002, 2016.