Billiards and Symmetry


Billiards and why we are here

Many years ago one of my teachers told me that playing billiards would teach me a lot about Physics. I thought at the time that this would be to do with things like the conservation of momentum,kinetic energy and so on. With a few assumptions it does this very well. Half a century on the billiard table still yields new insights. One of the things which seems a bit of a puzzle is to do with particles and anti-particles (An electron is negatively charged,it’s anti particle is the positron which has the same mass but a positive charge).Why are there more particles than anti-particals ?. You would expect them to exist in the same quantity,you put a lot of energy into the vacuum and you create an election-positron pair. ( The positron hangs a round for a bit before it annihilates with an electron,and this is used for medical imaging Positron Emission Tomography otherwise called PET scan)).Physicists like the things to be symmetrical and this is a a massive asymmetry and its a problem . .
What has this to do with billiards ?.To make things simple let’s think of a billiard table without pockets ,and imagine a simple shot bouncing off three cushions.Imagine now a perfect mirror and how the shot would look .If the shot heads towards the left hand cushion,in the mirror it would got toward the right and so on(it is laterally inverted).

The really interesting thing is if I were to show you a series of shots and ask you which ones are real and which ones are mirror images you couldn’t tell,the mirror image is a perfectly possible shot. Contrast this with bowling where the ball is biased ,shots in the real world curve to the right in the mirror thy would curve to the left.( I might have this the wrong way round I don’t play bowls).Until sometime in the late 1950’s physicists thought that if you looked at any natural process what you see in the mirror is equally possible. They technically described this as “parity” being conserved.The reason they thought this is that they didn’t think the universe (or God) should be left or right handed.In the 1950’s experiments were carried out looking at one of the forces of nature (weak nuclear force) which showed electrons behaving in a way that gave a result which changed if you look at the mirror image in a process called beta decay this led to the famous remark “Who would have thought that God is left handed” it was that shocking .To fix this up Physicists decided that to preserve symmetry the charge should change sign when you look in the mirror,this would mean if you multiplied the charge by the parity (which is always +1 or -1) then you wouldn’t be able to tell if you we’re looking at an electron or a positron in a mirror.This was known as Charge Parity conservation.This worked for a while until processes were discovered which violated this principle.

I know that we have a picture of a snooker table and up to now the everything I’ve said still applies to the snooker shot,When it come to time reversal we need to be careful and this is because the table starts off ordered and becomes disorded which gives the game away ( this is the subject of another discussion about heat and time)

“Back to the billiard table ” If you were to film the shot and run the film backwards then what you see is also a perfectly allowed trajectory .Just like the mirror ,if I ask which way is time going you can’t really say . So we now say that the charge changes sign and time run backwards in the mirror .All is well ,as far as we know in all processes charge ,parity and time are conserved ,this is known as CPT conservation. So there is no need for there to equal numbers of particles and anti-particles because the fundamental process just needs to conserve CPT ,if it was just charge there would have to be as many positrons as there are electrons . Which is why we are here because all the electrons didn’t annihilate all the positrons .

Things which I didn’t do properly,Parity .If you ;look in the mirror one of two things can happen. Things look exactly the same (+1) or they are inverted (-1). Depending which behaviour they exhibit they are either “Fermions” or “Bosons” . Time runs forwards (+1) or backwards(-1) and charge is positive (+1) or negative (-1). So you have three numbers to multiply together and the answer is all ways +1 or -1. CPT tells us that if start out with the vacuum, then you get two particles one with CPT +1 and the other with CPT-1 which added to gather is zero which is where we started .
In nature there are left handed a right handed crystals ,not thought through how this happens, I’ve got a few ideas though.

Finally, I didn’t talk about the experiment which violated charge parity conservation. I don’t know ¬†about it will get back when I’ve found out .Also this is not really my field so all this could be nonsense.
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