As for the forces, electromagnetism and gravity we experience in everyday life. But the weak and strong forces are beyond our ordinary experience. So in physics, lots of the basic building blocks take 20th- or perhaps 21st-century equipment to explore.
There is a difference between knowing what is true and knowing why it is true.
One very important aspect of string theory is definitely testable. That was the prediction of supersymmetry, which emerged from string theory in the early ’70s.
Quantum mechanics brought an unexpected fuzziness into physics because of quantum uncertainty, the Heisenberg uncertainty principle. String theory does so again because a point particle is replaced by a string, which is more spread out.
Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle.
Im actually, for the most part, a complete agnostic politically.
So when you ask me how string theory might be tested, I can tell you what’s likely to happen at accelerators or some parts of the theory that are likely to be tested.
As far as extra dimensions are concerned, very tiny extra dimensions wouldn’t be perceived in everyday life, just as atoms aren’t: we see many atoms together but we don’t see atoms individually.