Asimov's response: http://chem.tufts.edu/answersinscience/relativityofwrong.htm

It is rather easy to collect sufficient evidence to conclude that the earth is not flat. The people who thought the earth was flat put very little effort into determining the shape of the earth.

Modern scientists have put a great deal of effort into determining the fundamental laws of physics. They have done a proper job of looking for evidence that the laws of physics can vary with location, and they've found none.

The most obvious check would be to go somewhere else and run some experiments. We have not done that.