Symmetries and quantum indiscernibility

null, Tomasz Bigaj (University of Warsaw)

Abstract: There is an entrenched view in philosophy of physics, according to which the symmetry (resp. permutation-invariance) of the many-particle quantum states implies the absolute indiscernibility of those particles. This claim seems to be confirmed by an elementary fact, provable in model theory, that in symmetric languages there is no formula which absolutely discerns objects in the domain. The only type of discernibility apparently available in symmetric languages is so-called weak discernibility. In my talk I will discuss a relatively less-well known theorem, due to Simon Saunders, to the effect that even in symmetric languages it is possible to formulate a sentence which, in models of a given cardinality, is equivalent with the sentence stating the absolute discernibility of the elements of the domain. This opens the possibility of distinguishing quantum particles of the same type with the help of their measurable properties, despite adopting the symmetrization postulate. I will show how to express such distinguishability facts in terms of appropriate symmetric projectors.

Link to MS Teams: 

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