It would mean that the theory of relativity is not 100% correct (in much the same way as Newtonian physics are not 100% correct). It wouldn't have any direct i

It would mean that the theory of relativity is not 100% correct (in much the same way as Newtonian physics are not 100% correct). It wouldn't have any direct impact on anything (because relativity still makes correct predictions the vast majority of the time), but it would create the opportunity for new theories which can explain everything that relativity does plus this new experiment to be created. That new theory could have significant ramifications, or it could be a minor adjustment to current theory that changes nothing.