Abstract—The concept of mutual independence is related to basic topics of science as such and especially to relativity and quantum theory. Under which circumstances can something be treated as being free from any influence, guidance or control of another? In fact, can something be 'absolutely' independent of another or of itself at all? Is the concept of independence reference-frame dependent? While the probability based concept of independence is solved in a logically consistent way, the relationship between independence and commutativity is still a matter of dispute. This publication will make the proof that commutativity and independence are equivalent.

Index Terms—Independence, dependence, commutativity, non-commutativity, causality.

Ilija Barukčić is with Horandstrasse, Jever, Germany (e-mail: Barukcic@t-online.de).

Cite: Ilija Barukčić, "The Equivalence of Commutativity and Independence," International Journal of Applied Physics and Mathematics vol. 3, no. 6, pp. 370-372, 2013.