# On the logical origins of quantum mechanics demonstrated by using Clifford algebra

*Electronic Journal of Theoretical Physics*8 (25):109-126 (2011)

**Abstract**

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 Neumannâ€™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.

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