Can you study and contribute to physics if you are a mathematician? I'm an undergraduate student majoring in mathematics; I totally love it and I want to get Ph.D in pure mathematics. 

I'm also interested in physics, especially the theoretical field; my favorite areas are relativity and quantum theory. Of course, I'm more into mathematics than physics, that is why I majored in math; plus I don't get as high grades in physics as I do in math. 

Now here is my question, if I became a mathematician, can I switch to physics easily if I wanted to? I heard a lot about mathematicians contributing to string theory and other areas. I guess what I'm looking for is not a total switch to another field; rather it's more like the ability to learn more about physics easily and being able to contribute to the theories.

What I meant was that I want my Ph.D to be in pure math; in essence my focus would be on math. But also I want to study the stuff that interests me in physics, e.g. GR, String theory, etc. I'm asking if it's possible for a professional mathematician to 


study these subjects in depth without much difficulties; and I'm referring to difficulties in getting enrolled in classes and being able to handle them, and
be able to contribute to these fields  


I'm sorry English isn't my first language, I hope I made my question clear.
Yes, technically speaking, you can cross the fence -- either direction -- between those two disciplines, but be aware of their different agendas.

Physics uses the language of mathematics to construct mathematical models of reality, but the physics is really contained in the following three non-mathematical tasks:


Establishing the association between mathematical symbols and reality (interpretation of the mathematical models).
Verifying the validity of the conceived mathematical models (physical theory verification). 
Establishing their limits of validity.


You can be a great mathematician, but if you fail in understanding the above not-so-easy tasks, you will be a bad physicist.