Rugby and Relativity

Rugby football is a game I can’t claim absolutely to understand in all its niceties, if you know what I mean. I can follow the broad, general principles, of course. I mean to say, I know that the main scheme is to work the ball down the field somehow and deposit it over the line at the other end and that, in order to squalch this programme, each side is allowed to put in a certain amount of assault and battery and do things to its fellow man which, if done elsewhere, would result in 14 days without the option, coupled with some strong remarks from the Bench.P.G. Wodehouse, Very Good, Jeeves 

Relativity of motion need not be a problem only for Einstein. Who has not had the experience of sitting in a stationary railway carriage at a station, then suddenly getting the sensation of being in motion, only to recognise that a train on the parallel track has just moved off in the other direction and your train is not moving at all?

Here is another example. Five years ago I spent two weeks visiting the University of New South Wales in Sydney during the time that the Rugby World Cup was dominating the news media and public interest. Watching several of these games on television I noticed an interesting problem of relativity that was unnoticed by the celebrities in the studio. What is a forward pass relative to? The written rules are clear: a forward pass occurs when the ball is thrown towards the opposing goal line. But when the players are moving the situation becomes more subtle for an observer to judge due to relativity of motion.

Imagine that two attacking players are running (up the page) in parallel straight lines 5 metres apart at a speed of 8 metres per sec towards their opponents’ line. One player, the ‘receiver’, is a metre behind the other, the ‘passer’, who has the ball. The passer throws the ball at 10 metres per sec towards the receiver. The speed of the ball relative to the ground is actually √(102 + 82) = 12.8 metres per sec and it takes a time of 0.4 sec to travel the 5 metres between the players. During this interval the receiver has run a further distance of 8 × 0.4 = 3.2 metres. 

When the pass was thrown he was 1 metre behind the passer but when he catches the ball he is 2.2 metres in front of him from the point of view of a touch judge standing level with the original pass. He believes there has been a forward pass and waves his flag. But the referee is running alongside the play, doesn’t see the ball go forwards, and so waves play on!