The Case Against Factorism: On the Labels of
⊗-Factor Hilbert-Spaces of Similar Particles in Quantum Mechanics
Abstract We discuss the case against Factorism , which is the standard assumption in quantum mechanics that the labels of the
⊗ ⊗ -factor Hilbert-spaces in direct-product Hilbert-spaces of composite physical systems of similar particles refer to particles, either directly or descriptively . We distinguish different versions of Factorism and argue for their truth or falsehood. In particular, by introducing the concepts of snapshot Hilbert-space and Schrödinger-movie , we demonstrate that there are Hilbert-spaces and
⊗ ⊗ -factorisations where the labels do refer, even descriptively, to similar particles, which renders them probabilistically absolutely discernible.