Can a PhD thesis consist of "exploratory research"? I am a physics graduate student at the stage where I need to come up with a PhD thesis proposal.

I have an idea for a thesis project that I think is very interesting and has not been explored in the literature. Specifically, the idea is to take a powerful new numerical technique that was developed in a completely different field and try to apply it to problems in my own field. If it works, it could greatly impact the field by drastically reducing the computational cost of calculations, which is one of the biggest limitations of current research.

The problem I face is that this research would be exploratory in nature. By this I mean that I do not have a well-defined problem to solve beyond "attempt to adapt it to my field and establish how well it works on some basic problems". In contrast, every thesis I have read has consisted of applying known techniques to new problems. My approach would be to do the opposite: apply a new technique to known problems to establish whether it could be feasible as a new tool in my field. 

So my question is: can exploratory studies such as this one constitute a PhD thesis? In my experience, I have never seen a thesis of this type, and I am worried that this is because it is a bad idea.
Yes.  A PhD thesis that introduces new methods to old problems can be an excellent thesis if:


The new methods are in some way better than old methods.
The new methods are widely adopted.  


Some of the most successful physicists work in this way.