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Right-hand rules are, of course, merely convention; however, if we are to decide upon using a right-hand rule to obtain directions in one coordinate space, then why should we not use the left-hand rule to obtain the same directions when we mirror that coordinate space. Surely that seems a consistent approach? The thing that has confused me is that axial vectors (pseudovectors), if they are to remain in the same direction in the mirror world, must use the same handed rule as in the original, non-mirrored world.

P0W8J6
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  • A bit confused on your last sentence, but pseudovectors (axial vectors) do not change direction upon parity operation, by definition. Think of a (psuedo)vector sitting on $\hat{z}$-axis. Flipping $\hat{x}$- and $\hat{y}$-axes (applying parity) does not change aforementioned (pseudo)vector. – Jacob A Sep 03 '21 at 17:45
  • My thinking was that, taking current in a coil as an example, and holding the coil horizontally to a mirror, the current would be 'rotating', so to speak, in the same direction in the mirror as it is in our world. We know that magnetic field is an axial vector and so must not change direction in the mirror and, if it is to not change direction in the mirror, it must be determined using the same handed rule as was used in the original world, since the current is rotating in the same direction in both worlds. So in this context, it seems that the same-handed rule must be used in both worlds. – P0W8J6 Sep 03 '21 at 17:56
  • Check out https://physics.stackexchange.com/questions/138558/is-this-an-example-of-parity-violation Does this help? – Jacob A Sep 03 '21 at 18:08
  • It hasn't given me an adequately satisfying answer to.my question unfortunately. – P0W8J6 Sep 04 '21 at 20:37

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