


Volume 9 No 2 (2011)
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On the Logical Origins of Quantum Mechanics Demonstrated By Using Clifford Algebra
Elio Conte
Abstract
Recently we have given proof of two theorems characterizing the Clifford algebra. By
using such two theorems we have reformulated the well known von Neumann
postulate on quantum measurements giving evidence of the algebraic manner in which
quantum wave function collapse of quantum mechanics happens. In the present paper
we introduce logic in Clifford algebra interpreting its idempotent as logical statements.
Using the previously mentioned theorems we demonstrate that the two basic
foundations of quantum mechanics, as the indeterminism and the quantum
interference, do not arise from physics itself but from logic. We advance the principles
that there are levels of our reality in which we lose our possibility of unconditionally
define the truth. At this level of reality we cannot separate matter per se from the
basic foundations of the logic that we use to describe it. This logical relativism does not
characterize classical mechanics but quantum physics. According to Y.F. Orlov, at
quantum level the truths of logical statements about dynamic variables become
dynamic variables themselves.
Keywords
quantum cognition, quantum Clifford algebra, quantum mechanics of mental entities, quantum interference, quantum interference of logical statements, von Neumann theorem, interference of quantum logical statements.
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