The certainty principle I

  D. A. Arbatsky

June, 2005

Abstract

The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics are studied. The certainty principle for quantum systems is formulated and proved. It turns out that the certainty principle is closely connected with the Heisenberg uncertainty principle (it presents, in some sense, an opposite point of view). But at the same time the certainty principle allows to give rigorous formulations for wider class of problems (it allows to rigorously interpret and ground the analogous inequalities for the pairs of quantities like time - energy, angle - angular momentum etc.).
Note:
This original paper is given here for people interested in the history of the certainty principle. People, who just want to get acquainted with a scientific view of the question, should read The certainty principle (review), where a more systematic explanation is given.

The certainty principle II
Proof of the uncertainty principle

  D. A. Arbatsky

March, 2006

Abstract

A more detailed derivation of the Heisenberg uncertainty principle from the certainty principle is given.
Note:
This original paper is given here for people interested in the history of the certainty principle. People, who just want to get acquainted with a scientific view of the question, should read The certainty principle (review), where a more systematic explanation is given.

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