Quantum physics has to deal with this problem because of the issue of observation of basic particles. To observe an event you have to use a constant stream of colliding particles. To see a cup of tea on the table, the photons have to hit the cup and reflect into your eye. But what if the cup was so small or the photon is so big, that when they collide the position and velocity of the cup has already changed way before the photon comes back to the retina? This is a fundamental problem in quantum interactions as the particles used to observe are at a comparable size to the particles observed. In other words, it's hard to say if there is a way to firmly determine positions of small particles (at least for me, as I'm not a physicist), so that is your prime candidate in nature for the third option.