The Geometric Algebra lift of qubits and beyond

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

The Geometric Algebra lift of qubits and beyond

Postby gill1109 » Tue Feb 09, 2021 3:20 am

I’m reading a fascinating book about a GA approach to QM, by Alexander M. Soiguine (2020). Here’s the “Foreward”.

Feasible Formalism to Replace Conventional Quantum Mechanics ... and_Beyond

Following the B. Hiley belief [1] that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical stricture I address with my work first of all to those who are not brainwashed by N. Bohr and his adepts into thinking that the question of quantum mechanics is solved, and to young brave students not zombied-out yet with Hilbert space formalism of quantum mechanics and not being afraid to be considered as heretics, pariahs by the physicists majority. I know that the set of such people is not empty. I do also encourage all of them by saying that physical phenomena are happening in real world not in Hilbert space. It is also good to remember Max Planck’s words: “A scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die and a new generation grows up that is familiar with it.”
Quantum computers and quantum cryptography, being maybe the first potential commercial applications of quantum physics, will get their practical implementation if only described in terms of adequate mathematical structure. That will open a way for, particularly, creating secure quantum communication channels, critical components of future global system that will replace Internet.
Nothing is more practically valuable than good theory.
The suggested formalism demonstrates, for example, that the core of future quantum computing should not be in entanglement, as common wisdom reads, which only formally follows in conventional quantum mechanics from representation of the many particle states as tensor products of individual states. The core of quantum computing scheme should be in manipulation and transferring of quantum states as operators acting on observables and formulated in terms of geometrical algebra. In this way quantum computer will be a kind of analog computer keeping and processing information by sets of objects possessing infinite number of degrees of freedom, contrary to the two value bits or two- dimensional Hilbert space elements, qubits.
I prefer not using highly compromised term “hidden variables”. I will talk and deal with objects unspecified in conventional quantum mechanics. The beginning of our long journey starts with generalization of complex numbers the seminal idea of which is explicit introduction of a variable “complex” plane in three dimensions that immediately eliminates all questions like “Why do we need imaginary unit in quantum mechanics?”

[1] B. J. Hiley, "Structure Proceses, Weak Values and Local Momentum," Journal of Physics: Conference Series, vol. 701, no. 1, 2016.
[2] D. Hestenes, New Foundations for Classical Mechanics, Dordrecht/Boston/London: Kluwer Academic Publishers, 1999.
[3] C. Doran and A. Lasenby, Geometric Algebra for Physicists, Cambridge: Cambridge University Press, 2010.
[4] A. Soiguine, Geometric Phase in Geometric Algebra Qubit Formalism, Saarbrucken: LAMBERT Academic Publishing, 2015.
[5] A. Soiguine, "Anyons in three dimensions with geometric algebra," July 2016. [Online]. Available:
[6] A. M. Soiguine, "Complex Conjugation - Relative to What?," in Clifford Algebras with Numeric and Symbolic Computations, Boston, Birkhauser, 1996, pp. 284-294.
[7] A. Soiguine, "State/observable interactions using basic geometric algebra solutions of the Maxwell equation," 07 July 2018. [Online]. Available: arXiv:1807.08603.
[8] A. Soiguine, Geometric Phase in Geometric Algebra Qubit Formalism, Saarbrucken: Lambert Academic Publishing, 2015.
[9] A. Soiguine, "Scattering of Geometric Algebra Wave Functions and Collapse in Measurements," Journal of Applied Mathematics and Physics, vol. 8, pp. 1838-1844, 2020.
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