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The title summarizes it. I'm confused as to how the anti-unitary operators work. If it inverts the signal of the angular momentum and conjugates the rotation operator, I can see why the rotation operator is invariant by time-reversal. However, if the operator acts like that, then the time progression operator is also invariant and we won't get the reversal of time as we should. Can anyone briefly explain how it acts?

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The sign of the magnitude is not preserved in reversed-time; only the magnitude itself is unchanged in 4D during acceleration.

Flipping the sign of the magnitude is what makes it reverse time.

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