I am convinced that quantum mechanics is not a final theory. I believe this because I have never encountered an interpretation of the present formulation of quantum mechanics that makes sense to me. I have studied most of them in depth and thought hard about them, and in the end I still can't make real sense of quantum theory as it stands. Among other issues, the measurement problem seems impossible to resolve without changing the physical theory.
Quantum mechanics must then be an approximate description of a more fundamental physical theory. There must then be hidden variables, which are averaged over to derive the approximate, probabilistic description which is quantum theory. We know from the experimental falsifications of the Bell inequalities that any theory which agrees with quantum mechanics on a range of experiments where it has been checked must be non-local. Quantum mechanics is non-local, as are all proposals for replacing it with something that makes more sense. So any additional hidden variables must be non-local. But I believe we can say more. I believe that the hidden variables represent relationships between the particles we do see, which are hidden because they are non-local and connect widely separated particles.
This fits in with another core belief of mine, which derives from general relativity, which is that the fundamental properties of physical entities are a set of relationships, which evolve dynamically. There are no intrinsic, non-relational properties, and there is no fixed background, such as Newtonian space and time, which exists just to give things properties.
One consequence of this is that the geometry of space and time is also only an approximate, emergent description, applicable only on scales too large to see the fundamental degrees of freedom. The fundamental relations are non-local with respect to the approximate notion of locality that emerges at the scale where it becomes sensible to talk about things located in a geometry.
Putting these together, we see that quantum uncertainty must be a residue of the resulting non-locality, which restricts our ability to predict the future of any small region of the universe. Hbar, the fundamental constant of quantum mechanics that measures the quantum uncertainty, is related to N, the number of degrees of freedom in the universe. A reasonable conjecture is that hbar is proportional to the inverse of the square root of N.
But how are we to describe physics, if it is not in terms of things moving in a fixed spacetime? Einstein struggled with this, and my only answer is the one he came to near the end of his life: fundamental physics must be discrete, and its description must be in terms of algebra and combinatorics.
Finally, what of time? I have been also unable to make sense of any of the proposals to do away with time as a fundamental aspect of our description of nature. So I believe in time, in the sense of causality. I also doubt that the "big bang" is the beginning of time, I strongly suspect that our history extends backwards before the big bang.
Finally, I believe that in the near future, we will be able to make predictions based on these ideas that will be tested in real experiments.