Foundations of Physics

, Volume 39, Issue 2, pp 194–214 | Cite as

The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?

Article

Abstract

We show that the strong form of Heisenberg’s inequalities due to Robertson and Schrödinger can be formally derived using only classical considerations. This is achieved using a statistical tool known as the “minimum volume ellipsoid” together with the notion of symplectic capacity, which we view as a topological measure of uncertainty invariant under Hamiltonian dynamics. This invariant provides a right measurement tool to define what “quantum scale” is. We take the opportunity to discuss the principle of the symplectic camel, which is at the origin of the definition of symplectic capacities, and which provides an interesting link between classical and quantum physics.

Keywords

Uncertainty principle Symplectic non-squeezing Symplectic capacity Hamiltonian mechanics 

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Faculty of Mathematics, NuHAGUniversity of ViennaViennaAustria

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