This is a complicated question, but I will try to answer a small part of it.
I think that the answer is that, first of all, cause-and-effect or 'causality', does not apply to all physical systems. In the world of quantum mechanics, the 'motion' of an electron is not completely a causal process because of the nature of the wave function. Although the wave function is completely specified by the potential energy of the atom, and the various quantum numbers of the electron, it is not possible to follow the electron in a causal chain of events as it 'orbits' the nucleus. To make matters worse, because of the Heisenberg Uncertainty Principle, the 'motion' of the electron can actually exceed the speed of light because although the instantaneous 'light cone' of the electron is well-defined by relativity, you cannot simultaneously know both the position and velocity of the electron with absolute certainty. This means its speed during some of its 'jumps' can be greater than the speed of light, and so it is free to create non-causal events by re-visiting its own past and interacting with itself!!!
At the quantum scale, the physical world is indeed 'random' but still obeys certain well-defined laws. These laws are only partially 'causal'.