Some of the swimming events have very close finishes, for example in the 200m butterfly Chad le Clos beat Michael Phelps by 0.05s. This is pretty close but not the closest.  In the 1972 Olympics in Munich Karl Gunnar Larsson of Sweden beat Tim McKee of the US by 0.002s in the 400m medley. After that they stopped using thousandths of a second so this will never be bettered. I was listening to an interview with Karl Gunnar on TV and he had calculated what distance must have separated the swimmers. The race was 400m and the time close to 4:32 so the average speed was 1.5ms^-1. So in 0.002s the distance travelled would be 3mm. I’m sure he said it was 0.3mm on the TV which doesn’t seem to be correct. (source: yahoo.com/news)