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Will two freely rotatable linear polarizers (placed in sequence and at some angular offset less than, say, 45 degrees) eventually align if you shine (plenty of) unpolarized light at the first one?

If so, will the second polarizer align itself with the first one, or will both of them start to rotate towards alignment (although perhaps not necessarily equally quick)?

Edit. There are over 400 views and five answers now (one at +1, the others at 0), which are all highly appreciated. However, I thought it might be useful to provide a bit of my initial intuition with regards to the first part of the question.

I am assuming that the light is polarized vertically after passing the first polarizer and that the second polarizer (pictured) is slightly offset.

To represent the vertical polarization I give a single photon some vertical extent (possibly in terms of probability amplitude). This the segment A-B. I am not at all sure that such representation is allowed or misguided.

Now the observation is that a collision (absorption or reflection) at B will produce more angular momentum (of the polarizer) than a collision at A.