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I am somewhat confused about this topic.

It is usually explained how magnetic fields avoid break*ing* time reversal symmetry by the example of a field produced by a circulating charge current - run time backwards, the current direction is reversed and so is the field.

But what about the moment associated with the electron spin? Is the spin of an electron not an intrinsic property? So why (if indeed it does) would running time backwards change the sign of the spin?

EDIT: I appreciate all of your comments below, but I feel this question has got away from me somewhat. I should have added more information at first.

I am wondering about Anderson's description of a dirty superconductor where the pairing is between so-called time-reversed states. In Tinkham it says that these states are only degenerate in the absence of magnetic or other time-reversal noninvariant terms. This makes the previous edit (now in italics) a little confusing to me.

Back to the loop of current: Surely if you switch the charge and the direction of flow then the magnetic field stays pointing in the same direction. Where is the inconsistency here?

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    $\begingroup$ Time reversal turns an electron into a positron $\endgroup$ Sep 12 '14 at 11:28
  • $\begingroup$ @JohnRennie: Are you sure? Charge is an invariant under T-symmetry (so electrons stay electrons), and to make out of a electron travelling forward in time a positron going backward in time we would have to apply at least the combined CT-symmetry, if not the whole CPT. $\endgroup$
    – ACuriousMind
    Sep 12 '14 at 13:59
  • $\begingroup$ @ACuriousMind: hmm slightly dubious wording. I meant that an electron travelling backwards in time looks like a positron. $\endgroup$ Sep 12 '14 at 14:54
  • $\begingroup$ Speaking of how to interpret reversed videos in terms of real physics, I've always been amused by how we casually accept that we would even be able to see them. After all, the photons involved would need to reverse direction also, traveling from our retinas to the viewed objects. Bottom line, classical time doesn't reverse well, regardless of how well time reversal at the particle level works. $\endgroup$ Sep 13 '14 at 0:13
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    $\begingroup$ @TerryBollinger: This old question (or rather, the answers, especially by DavidZ and Ron Maimon) seems to back my case that is it indeed CPT-symmetry and not just time reversal that we have to look at. The notion that "antimatter is matter going backwards" arises from CPT being a symmetry of every conceivable theory, so that antimatter going backwards (i.e. the state after CPT was applied) is indistinguishable from matter going forwards, but this does not imply that the time reversal alone turns matter into antimatter. $\endgroup$
    – ACuriousMind
    Sep 13 '14 at 13:26
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Yes, spin direction is also reversed. An "up" electron spin state simply becomes a "down" spin state. Electron spin remains fundamentally a type of angular momentum, even though the rules get a bit odder at the quantum scale.

Incidentally, when time is reversed all particles also turn into their antimatter equivalents. So a bit of safety advise: Never, ever shake hands with the other you that you see in a reverse video...

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    $\begingroup$ Now all you have to do, to convince me, is to run time in reverse. :-) $\endgroup$
    – CuriousOne
    Sep 13 '14 at 0:20

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