Why do mirrors reverse left and right? Is nature mirror symmetric?

The image you see in a mirror is not real - quite obviously so since it will have a watch on its right arm if you have a watch on your left arm! It is what is called a virtual image. Your brain interprets the light reaching your eyes as having travelled in a straight line from its source, when in fact it has travelled along a 'crooked' line - it has been reflected from the surface of the mirror. So your brain 'sees' an image the same distance 'inside' (or behind) the mirror as you are standing from the mirror. The fact that the reflected light is interpreted as having travelled in a straight line from 'inside' the mirror is what changes the handedness of the image your brain 'sees'.

Before the mid 1950's, scientists believed that nature was 'mirror symmetric' - that the laws of physics should not have an intrinsic handedness. In other words, they believed that if you were viewing an elementary particle interaction in a darkened room, you could not tell whether you were viewing the real process, or the image of the real process in a mirror. However, evidence emerged to suggest that one of the four fundamental interactions between elementary particles, namely the weak interaction, could in fact distinguish left from right.

An experiment confirming this suspicion was carried out in 1958 by a female physicist, Chien-Shiung Wu. Prior to the experiment, the Nobel Prize winning Italian physicist Wolfgang Pauli had stated, "I do not believe that the Lord is a weak left-hander, and I am ready to bet a very high sum that the experiments will give symmetric results." He lost his money!
By mahesh saagr khanal for scientific nepal

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