In the Dark

I’ve had these pictures for quite a while and can’t remember where I got them from, but I used them in my lectures on Theoretical Particle Physics when I was in Nottingham to illustrate CP-violation.

The following picture by M.C. Escher is called Day and Night:

If you look at it you can see two kinds of symmetry emerging. One is a kind of reflection symmetry about a vertical axis drawn through the centre of the picture that applies to shapes but not to colour. The other is between black and white. But it is obvious that the picture doesn’t display these symmetries separately: to get a picture unchanged from the original you would have to do the mirror reflection and change black to white (and vice-versa).

The mirror reflection in the image can be taken to represent parity (P). Strictly speaking parity refers to a reflection through the origin in 3D rather than a mirror reflection, but it’s just for illustration. We know that a parity symmetry is violated in weak interactions just as it is in the picture.

The other possible symmetry, between black and white can be taken to represent charge-conjugation (C), the operation that converts particles into anti-particles and vice-versa.

While P is not an exact symmetry of weak interactions, it was long thought that the combination of C and P (CP) would be. Actually it isn’t. The story of the discovery of CP-violation is fascinating but I don’t have time to go into it here. It suffices to say that the Escher print also displays CP violation.

First lets do `C’, i.e. convert black to white and vice-versa. The result is:

Now reflect about the vertical mid-line to illustrate `P’:

If `CP’ were an exact symmetry then that image would be identical to the original, which I reproduce here:

You can see, however, that while some elements of the picture do look the same after this combined operation (e.g. the birds), others (e.g. the buildings at the bottom) do not.