The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?
- Maurice A. de GossonAffiliated withFaculty of Mathematics, NuHAG, University of Vienna Email author
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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.
KeywordsUncertainty principle Symplectic non-squeezing Symplectic capacity Hamiltonian mechanics
- The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?
Foundations of Physics
Volume 39, Issue 2 , pp 194-214
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- Springer US
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- Uncertainty principle
- Symplectic non-squeezing
- Symplectic capacity
- Hamiltonian mechanics
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- Author Affiliations
- 1. Faculty of Mathematics, NuHAG, University of Vienna, Nordbergstrasse 15, 1090, Vienna, Austria