Hamburg 2016 – scientific programme

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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 3: Philosophy of Physics 3

AGPhil 3.1: Invited Talk

Tuesday, March 1, 2016, 13:15–14:00, VMP6 HS G

Individuation, Entanglement and Composition for Fermions — •Adam Caulton — MCMP, LMU Munich, Germany

Permutation symmetry in many-particle quantum mechanics can take one of two interpretations. According to the first interpretation, the transformations under which physical quantities (such as the joint Hamiltonian) are invariant represent a literal permutation of the constituent particles. According to the second interpretation, those transformations are construed as ``gauge", i.e. a reshuffling of non-representative elements in the mathematical formalism. My talk explores the consequences of taking this second interpretation, especially for fermions.

The first consequence I will explore concerns the individuation of particles. I show how single-particle quantities may be found, and even reduced density operators may be defined, in a permutation-invariant way.

The second consequence concerns entanglement. In particular, non-separability of the joint state can no longer be taken as a sufficient condition for entanglement between the constituent systems. A natural surrogate may be defined, which agrees with the proposals of Ghirardi, Marinatto and Weber (2002). This surrogate is further justified by an analogue of Gisin's theorem for permutation-invariant systems.

The third and final consequence, which is a little more metaphysical, concerns the composition of fermionic joint systems. I argue that fermionic systems disobey classical mereology, the theory of parts and wholes developed by Leśniewski and Leonard & Goodman.