Louis H. Kauffman. Non-commutative Worlds and Classical Constraints
Submitted on: Sep 18, 2012, 07:12:18
Natural Sciences / Physics / Mathematical Physics
Description: This paper shows how discrete measurement leads to commutators and how discrete derivatives are naturally represented by commutators in a non-commutative extension of the calculus in which they originally occurred. We show how the square root of minus one (i) arises naturally as a time-sensitive observable for an elementary oscillator. In this sense the square root of minus one is a clock and/or a clock/observer. This sheds new light on Wick rotation, which replaces t (temporal quantity) by it. In this view, the Wick rotation replaces numerical time with elementary temporal observation. The relationship of this remark with the Heisenberg commutator [P,Q]=ihbar is explained in the Introduction. After a review of previous work, the paper begins with a section of iterants - a generalization of the complex numbers as described above. This generalization includes all of matrix algebra in a temporal interpretation. We then give a generalization of the Feynman-Dyson derivation of electromagnetism in the context of non-commutative worlds.
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