Deterministic Elaboration of Heisenberg's Uncertainty Relation

Details Deterministic Elaboration of Heisenberg's Uncertainty Relation Deterministic Elaboration of Heisenberg's Uncertainty Relation

2012-04-06

arxiv.org/abs/1204.1877v1

Mathematics

General Mathematics

14 pages, 1 figure

Scientific paper

In this paper we provide a new derivation of the Heisenberg's uncertainty principle without using the quantum physics framework, the uncertainty principle is found via characteristics of continuous and nowhere differentiable functions. We prove that any physical system that has a continuous and nowhere differentiable position function is subject to an uncertainty in the simultaneous determination of values of its physical properties. The uncertainty in the simultaneous knowledge of the position deviation and the average rate of change of this deviation is found to be governed by a relation equivalent to the one discovered by Heisenberg in 1925. Conversely, we prove that any continuous position function that is subject to an uncertainty relation must be nowhere differentiable.

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