I have come to the conclusion that socks are fermions, and that this explains much of the behavior of disappearing socks. (There may be other factors at play, of course) Clearly they are not bosons; you cannot make two socks occupy the same space: Put two socks on the same foot and they wll be layered, and there is a finite number you can fit into a washing machine or a dryer. Socks worn in the normal fashion are distinguishable by being on the left or right foot (or hand, in the case of the sock puppet effect; I won’t be discussing the very interesting Lamb-Chop-shift one can observe). The individual socks in a pair, however, are indistinguishable and they must have an antisymmetric wave function and thus obey Fermi-Dirac statistics and follow the Pauli exclusion principle.
Put two socks comprising a pair into the wash and occasionally only one will be there at the end of the cycle. Why? Two socks can clearly exist in a system, thus there must be at least two sock states. Let’s assume two, making them sock spin one-half states, and call these “sock up” and “sock down” (and not confuse this with the sock-it-to-me state, the investigation of which was popular in the late 60s)
The socks are in the dryer system and one of them is sock-up with the other being sock-down, in perfect accordance with the Pauli exclusion principle. However, occasionally there will be an interaction with the dryer (I call this the argyle sock-flip interaction, which should be mediated by the Lint boson) which is very strong; the socks cannot remain confined to the dryer, and one sock is expelled by the degenerate Fermi sock pressure. This is seen more at high temperatures where the thermodynamic pressure is also high, and where the containment of the dryer is insufficient. This can also happen with socks in a hamper or clothes pile, but since there is no true confinement, one might just see that the socks have migrated elsewhere in the room, or be on the lip of the hamper (or floor next to it); this is enough to break any possible degeneracy in the sock states.
This expulsion can be by tunneling, in which case the sock may be found nearby; often covered in residual lint from the interaction. It is also possible that the sock is simply disintegrated; sockiness may not be a strictly conserved quantity, or there may be a sock one-half particle (the socktrino) that is ejected while the rest of the sock is carried off as Lintons, some of which may be captured in the lint tray. High energy Lintons would escape and disintegrate into Dustyons in the surrounding region. Clearly there is some more theoretical and experimental work to be done here to confirm the existence of the socktrino; some holes in the theory must be darned and most facilities are not up to the task of detecting this signal amidst the large background lint and dust signals.
More complicated behaviors exist as well, in the guise of condensed-sockmatter physics. What if one were to place more than two identical socks into the wash? This is clearly an important avenue of investigation; procuring multiple pairs of identical socks allows one to combat the prevalence of sock loss and the resulting uselessness of the remaining sock. There is also the advantage in the pairing of the socks afterward, because, interestingly, free socks tend to repel in the clean-clothes pile of multiple paris of different sock patterns, and considerable work must be done to decrease their entropy. (There is some very interesting behavior to investigate here, as well, but sock-sorting dynamics is beyond the scope of this discussion). With multiple pairs of identical socks in the dryer, a band structure is now formed to lift the degeneracy of the individual socks, reducing the strength of the argyle sock-flip by the apathy factor (measured in Mehs), which scales with the number of socks, which makes the loss of any one sock less important. Whether this scaling is linear is as yet undetermined.
Clearly this is a very rich field of further inquiry for the budding scientist hoping to get his or her work published in the esteemed Journal of Irreproducible Results. There is the very exciting prospect of investigating a four-sock interaction to see if one can make two socks disappear, and see if there is a sharp division between the individual quantum and the condensed-sockmatter reactions. If adequate funding could be procured, one might also envision the construction of a sockcellerator, to look at higher-energy sock interactions to investigate the vector and scalar nature of the lint boson and to pursue the detection of evidence for the socktrino.