Relativistic billiard problems

September 18, 2013 at 7:57 AMMichele Mottini

I did not find anything ‘pre cooked’ to convert my billiard simulator to use special relativity, so I started to work on the necessary math from scratch – that turned out to be problematic (to say the least).

For example, the collision of a ball with the side of the table become something like this:


because – in the frame of reference of the table – the ball contracts along its direction of motion. This deformation affects the computation of the collision time and changes the dynamic of the collision. The same collision seen in the frame of reference of the ball becomes instead:


because now it is the distance from the ball to the side that contracts, changing the collision angle.

A ball-ball collision is even worse, being something like this (in the table frame of reference):


I found some pretty good notes on relativistic dynamics by an Oberlin college professor. The last chapter has a section about ‘hard sphere forces’ – e.g. billiard balls – that concludes that the whole idea of handling them within special relativity is ‘ludicrous’. At the same  time I found one article about rigid bodies in special relativity. I think that some kind of solution should be possible, but I have to study more.

For the moment being I am going through the relativistic dynamics notes (including the exercises!) and then I’ll have a look at the rigid body article.

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