The orthodox debate on state symmetrization in QM is, in my view, divorced from the actual physics involved. I attempt to rectify this situation in my recent publication (accepted in Entropy, Special Issue: “Quantum Mereologies and Quantum Inspired Set Theories and Logics.). Briefly, a ‘symmetrized state’ is a state in which there is no ‘fact of the matter’ about which particle is in which state (whether momentum, spin, etc.). An example is the ‘singlet state’ for electrons:
|Psi> = (1/sqrt 2) [ |up> |down> – |down> |up>].
The conventional debate on this topic in philosophy of physics circles has long assumed that lack of empirical access to a particular state, such as |up>|down> or |down>|up>, implies a “representational redundancy” (i.e., it claims that these states refer to “the same physical situation”). This leads to inconsistencies, which need to be “corrected” by imposing symmetrization. I argue in a new paper (below) that this is not what symmetrization really comes from, since the two situations are independently physically meaningful–thus don’t have the same physical referent.
The fallacy in equating empirical inaccessibility to a redundancy (i.e. the same physical situation described two different ways) is evident as follows: Of course I cannot distinguish between a black object and a white object if I cannot see either object. But this does not demonstrate representational redundancy of the terms “black” and “white.”
Transactional Interpretation 