Geometric derivation of quantum uncertainty

Abstract

Quantum observables can be identified with vector fields on the sphere of normalized states. Consequently, the uncertainty relations for quantum observables become geometric statements. In the Letter the familiar uncertainty relation follows from the following stronger statement: Of all parallelograms with given sides the rectangle has the largest area.

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References in corpus (3)

• Stochastic Reduction in Nonlinear Quantum Mechanics
• On the measurement problem for a two-level quantum system
• Quantum mechanics on Hilbert manifolds: The principle of functional relativity

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• A possible mathematics for the unification of quantum mechanics and general relativity
• Geometric uncertainty relation for quantum ensembles
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• Functional methods underlying classical mechanics, relativity and quantum theory
• Emergence of Classical Dynamics from a Random Matrix Schrödinger Model