Earlier quoted context omitted.
Currently, very little. According to the article, you need crazy particle-accelerator-levels of energy to have them happen at all. However, by studying and understanding such events, we can test and improve our theories of physics, which may lead to breakthroughs in technology we can only dream of. For example, general relativity would have been considered completely useless knowledge for any practical purpose when i…
I've heard people make the argument about GR being essential to the GPS system before, but the skeptic in me has doubts. I don't deny that it's useful to have a correction derived from relativity, but is it really as essential as people make it out to be? If we hadn't known about GR when we built the GPS system, wouldn't we have realised there was an unexpected drift in the clocks and found a way to recalibrate them…
A quick note from: (i'm too lazy to do the calculations right now) http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....
If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.