Incoming links: Schrödinger picture
In simple terms, if you believe in the Schrödinger equation and its modern probabilistic interpretation as described in the Schrödinger picture, then at first it seem that there is no strict causality to the outcome of experiments.
People have then tried to recover that by assuming that there is some inner sate beyond the Schrödinger equation, but these ideas are refuted by Bell test experiments, unless we give up the principle of locality, which feels more important, especially in special relativity, where faster-than-light implies time travel, which breaks causality even more dramatically.
The de Broglie-Bohm theory is a deterministic but non-local formulation of quantum mechanics.
These are the key mathematical ideas to understand!!
There are actually a few formulations out there. By far the dominant one as of 2020 has been the Schrödinger picture, which contrasts notably with the Heisenberg picture.
Another well known one is the de Broglie-Bohm theory, which is deterministic, but non-local.
Schrödinger picture example: quantum harmonic oscillator Updated 2024-12-15 +Created 1970-01-01
TODO: use the results from the quantum harmonic oscillator solution to precisely illustrate the discussion at Schrödinger picture with a concrete example.