What does a Mirror Flip?

I recently was asked a question about mirrors which has been asked a million times before: Why does a mirror flip the left and right side of a face, but not up and down? There is, after all, no reason for the mirror to prefer the horizontal axis when it flips something. How do we explain this correctly?

Imagine standing in front of a mirror, or actually do it. Now point with your arm sideways in any direction, or up, or down. You will notice that the mirror image points into the same direction. Your conclusion should be that the mirror does not flip sides, nor does it flip up and down.

But if you point towards the mirror, the mirror image will point into the other direction! So the mirror really exchanges front and back, not any other axis.

Why then do we think that the sides of our faces are flipped? This happens because we imagine the person in the mirror to step out of its mirror world and turn around to look into the same direction as we do. If it jumped out of the mirror and stood on its head where we stand, it would flip the up and down axis. So it is really our imagination which makes us think that the mirror changes left to right.

But it is worth noting that the mirror does indeed flip one direction. The world in the mirror is fundamentally different from ours. Students of physics learn how to determine the magnetic field of a changing current with their right hand. If they used the left hand, they’d get it wrong. For another example, molecules can turn polarized light, and they do it only in one direction depending on the molecule.

This raises the question how we could explain with words alone what left and right means to us to someone living in another world, possibly a mirror world. The magnetic field is not useful because we had to tell the poles of a magnet first. From what I heard, it turns out that our world prefers one of the two mirror types of some molecules. An anti-matter world would prefer the other. But I do not know the details of this phenomenon. Maybe, you can find more about this question.