Archive for M.C. Escher

Day and Night and CP Violation

Posted in Art, The Universe and Stuff with tags , , , on July 4, 2018 by telescoper

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.


Cosmology, Escher and the Field of Screams

Posted in Art, Education, The Universe and Stuff with tags , , , , , on March 20, 2012 by telescoper

Up early this morning for yet another busy day I thought I’d post a quick follow-up to my recent item about analogies for teaching physics (especially cosmology).

Another concept related to the cosmic microwave background that people sometimes have problems understanding is that of last scattering surface.

Various analogies are useful for this. For example, when you find yourself in thick fog you may have the impression that you are surrounded by an impenetrable wall at some specific distance around you. It’s not a physical barrier, of course, it’s just the distance at which there sufficient water droplets in the air to prevent light from penetrating further. In more technical terms the optical depth of the fog exceeds unity at the distance at which this wall is seen.

Another more direct analogy is provided by the Sun. Here’s a picture of said object, taken through an H-α filter..

What’s surprising to the uninitiated about an image such as this is that the Sun appears to have a distinct edge, like a solid object. The Sun, however, is far from solid. It’s just a ball of hot gas whose density and temperature fall off with distance from its centre. In the inner parts the Sun is basically opaque, and photons of light diffuse outwards extremely slowly because they are efficiently scattered by the plasma. At a certain radius, however, the material becomes transparent and photons travel without hindrance. What you see is the photosphere which is a sharp edge defined by this transition from opaque to transparent.

The physics defining the Sun’s photosphere is much the same as in the Big Bang, except that in the case of the Sun we are outside looking in whereas we are inside the Universe trying to look out. Take a look at this image from M.C. Escher:

The universe isn’t actually made of Angels and Demons – at least not in the standard model – but if you imagine you are in the centre of the picture  it nicely represents what it is like looking out through an expanding cosmology. Since light travels with finite speed, the further you look out the further you look back into the past when things were denser (and hotter). Eventually you reach a point where the whole Universe was as hot as the surface of a star, this is the cosmic photosphere or the last scattering surface, which is a spherical surface centred on the observer. We can’t see any further than this because what’s beyond is hidden from us by an impenetrable curtain,  but if we could just a little bit further we’d see the Big Bang itself where the density is infinite, not as a point in space but all around us.

Although it looks like we’re in a special place (in the middle) of the image, in the Big Bang theory everywhere is equivalent; any observer would see a cosmic photosphere forming a sphere around them.

And while I’m on about last scattering, here’s another analogy which might be useful if the others aren’t. I call this one the Field of Screams.

Imagine you’re in the middle of a very large, perhaps infinite, field crammed full of people, furnished with synchronised watches, each of whom is screaming at the top of their voice. At a certain instant, say time T, everyone everywhere stops screaming.

What do you hear?

Well , you’ll obviously  notice that it gets quieter straight away as the people closest to you have stopped screaming.  But you will still hear a sound because some of the sound entering your ear set out at a time before t=T. The speed of sound is 300 m/s or so, so after 1 second you will still hear the sound arriving from people further than 300 metres away. It might be faint, but it would be there. After two seconds you’d still be hearing from people further than 600 metres away,. and so on. At any time there’ll be circle around you, defined by the distance sound can have travelled since the screaming stopped – the Circle of Last Screaming. It would appear that you are in the centre of this circle, but anyone anywhere in the field would form the same impression about what’s happening around them.

Change sound to light, and move from two dimensions to three, and you can see how last scattering produces a spherical surface around you. Simples.