Relativity trick slashes computing times
Apr 5, 2007
Simulating the interactions between relativistic objects -- those travelling close to the speed of light -- can take enormous amounts of computer time. But according to Jean-Luc Vay of Lawrence Berkeley National Laboratory in the US, this time can be slashed enormously by considering how the interactions occur from the point of view of a fast-moving observer -- a short cut made possible by Einstein's century-old theory of relativity that no one seems to have noticed before (Phys. Rev. Lett. 98 130405).
"There's no such thing as a free lunch" is the usual response Vay receives when he tells his particle-physicist colleagues how to speed-up computer simulations a thousand times over by making a simple mathematical transformation. And it's hardly surprising: many physicists use relativity theory routinely, and think they already know how to simplify calculations by considering relativistic interactions from the perspective of an observer in a convenient "reference frame" where many tricky factors cancel-out.
Although such reference frames help the human brain to get to grips with the interactions, Vay says they do no favours for computer programs. In a particle accelerator, for example, a centimetre-wide pulse can cover distances of many kilometres – and this huge difference in length scales makes computer simulations very time consuming. Instead, he says that if the reference frame itself is moving relativistically compared to the interaction, the difference in scales becomes much less significant.
"The first time I noticed it my reaction was to think that I had made a mistake in my calculations," Vay told Physics Web. "After I checked them, I assumed that it was probably known already and I used it without reporting it formally. Only last year I realized it was largely unknown."
Vay's method of choosing reference frames works because of a familiar effect of relativity known as length contraction. If an observer is in a reference frame that is moving fast compared to an object – and the closer to the speed of light the better – the length of that object appears to be shorter. Vay realized, however, that not only do individual lengths reduce, but also the difference between them. This means that simulations run from the perspective of a relativistic reference frame are much less complex, and therefore take much less time to compute.
Vay has tried his method on several examples of relativistic interactions including a free-electron laser, a laser-plasma accelerator, and a particle beam colliding with an electron cloud. For the particle beam example, the simulation in a typical reference frame took over a week to run, whereas in Vay's relativistic, "ideal" reference frame it took just half an hour.
Groups at the University of California in Los Angeles and Tech-X Corporation in the US are already exploring Vay's time-saving method for simulating relativistic experiments. Nevertheless, the question remains of why such a simple consequence of relativity has never surfaced. "Computer simulations didn't exist when relativity was invented," said Vay. "It's plausible that the effect was identified early on by the founders of relativity, but didn't lead them to any interesting applications."
About the author
Jon Cartwright is a reporter for Physics Web