The most counter-intuitive realm of physics, to me, is quantum mechanics. It is chock full of things that have made folks say "That can't possibly be true, because if that were true, this absurd thing would be the case." Then folks finally get around to testing it, and they find that the absurd thing is actually the case.
Einstein, the man behind relativity (and, interestingly, behind some work that contributed to the early development of quantum mechanics), famously was not an admirer of quantum mechanics.