Foundations of Physics 39 (2):194-214 (2009)

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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DOI 10.1007/s10701-009-9272-2
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The Emperor’s New Mind.Roger Penrose - 1989 - Oxford University Press.
The Quasiclassical Realms of This Quantum Universe.James B. Hartle - 2011 - Foundations of Physics 41 (6):982-1006.

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