Physicist, currently at CERN

I believe nothing to be true (clearly real) if it cannot be proved.

I'll take the question and make a pseudo-invariant transformation that makes it more apt to my brain. When Bohr was asked what is the complementary variable of "truth" (Wirklichkeit) he replied with no hesitation "clarity" (Klarheit). Contrary to Bohr, and since neither truth nor clarity are quantum mechanical variables, real truth and comprehensive clarity should be simultaneously achievable given rigorous experimental evidence. [In particular since "Wirklichkeit" means reality, and "Klarheit" is clarity in the sense of good understanding.]

In fact I will use clarity (as in "clear reality"), in the place of truth.

I will also invent equivalents for proof and for belief. Proof will be interchangeable with "experimental scientific evidence". Belief is more tricky given that it has to do with complex carbonic life. It can be interchangeable with "theoretical assessment" or "assessment by common sense" (depending on the scale and the available technology). In this process (no doubt in a path full of traps and pitfalls) I have cannibalized the original question to the following:

What do you (commonsensical/theoretically) assess to be clearly real even though you have no experimental scientific evidence for it?

Now this is hard: there are many theoretical assessments for the explanation of the natural phenomena at the extreme energy scales (from the subnuclear to the supercosmic), that possess a degree of clarity. But all of them are inspired by the vast collection of conciliatory data that scale by scale speak of Nature's works. This is so even for string theory. 

So the answer is still...nothing.

Following Bohr's complementarity I would spot that belief and proof are in some way complementary: if you believe you don't need proof, and (arguably) if you have proof you don't need to believe.(I would assign the hard-core string theorists who do not really care about experimental scientific evidence in the first category).

But Edge wants us to identify the equivalent(s) of the general theory of relativity in today's scientific thinking(s). Or a prediction of what are the big things in science that come at us unexpectedly. In my field, even frameworks that explain the world using extra dimensions of space (in extreme versions) are not unexpected. As a matter of fact we are preparing to discover or exclude them using the data. My hunch (and wish) is that in the laboratory we will be able to segment spacetime so finely that gravity will be studied and understood in a controlled environment, and that gravitational particle physics will be a new field.