Roger Penrose, in The Road to Reality, section 16.7 (size of infinity in physics) writes:
"...It is perhaps remarkable, in view of the close relationship between mathematics and physics, that issues of such basic importance in mathematics as transfinite set theory and computability have as yet had a very limited impact on our description of the physical world. It is my own personal opinion that we shall find that computability issue will eventually be found to to have a deep relevance to future physical theory, but very little use of these ideas has so far been made in mathematical physics".
I personally think that concept of time my be described better using objects in set theory: today we use real numbers as mathematical model for describing time, but maybe (some time!) physicist use a more complicated order, like objects we deal with them in set theory and other branches of mathematical logic, as a more accurate model for time. But, of course, its only an imagination!...