On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra: A Proof that Quantum Interference Arises in a Clifford Algebraic Formulation of Quantum Mechanics

We review a rough scheme of quantum mechanics using the Clifford algebra. Following the steps previously published in a paper by another author [31], we demonstrate that quantum interference arises in a Clifford algebraic formulation of quantum mechanics. In 1932 J. von Neumann showed that projection operators and, in particular, quantum density matrices can be interpreted as logical statements. In accord with a previously obtained result by V. F Orlov , in this paper we invert von Neumann’s result. Instead of constructing logic from quantum mechanics , we construct quantum mechanics from an extended classical logic. It follows that the origins of the two most fundamental quantum phenomena , the indeterminism and the interference of probabilities, lie not in the traditional physics by itself but in the logical structure as realized here by the Clifford algebra. c © Electronic Journal of Theoretical Physics. All rights reserved.