I want to get a basic idea of some symmetries in nature and one that I have across is parity. I have read on the internet that parity transformation can be thought of as a mirror transformation.
However I have stumbled across two different sources which directly contradict one another and so has me confused. If anyone could explain to me which one is correct that would be helpful.
Source 2https://galileospendulum.org/tag/parity-violation/
The second source essentially says its not really a micror transformation.
Best Answer
A mirror reflection flips just one of the three components of the
position vector ($x, y, z$).
A parity transformation flips all three components of the position vector:
($x, y, z$) becomes ($-x, -y, -z$).
Now suppose the velocity has only one component. Then the parity operator becomes equal to a mirror reflection. In this case, the parity operation becomes equal to the mirror reflection, after which the handedness for the particle is reversed. The same holds for the parity transformation, which is a combined reversal of all three position components, so also, in this case, the handedness changes.
This is clearly visible in the last picture: turn the velocity of the right particle upside-down, and you have a particle with an opposite handedness from the original particle (just as in the picture where "they" perform a mirror reflection). So the statement that the spin remains untouched (with respect to the velocity of the particle) is not true. In other words, the handedness is reversed.
In the last picture, the spin does remain untouched, but the velocity is reversed, so also the handedness is reversed.