You don’t even need to go down to quantum mechanics. I am hard pressed to think of an energy scale in which physics have the kind of determinism and predictability that is required for Eric’s formulation. From highest to lowest energy scale (handwavy rankings for some):
- Quantum gravity is presumably only deterministic up to a wavefunction level and therefore has determinism problem
- GR+QFT has both determinism problem (from both GR and QFT) and predictability problem (from GR)
- GR+quantum mechanics has determinism problem (from QM and GR) and predictability problem (from GR)
- QFT has determinism problem due to its quantum nature
- QM alone has determinism problem
- GR+Classical mechanics: Has both determinism and predictability problems from GR
- Special Relativity+Classical mechanics: Has predictability problem from SR
- Classical mechanics: Has determinism problem without SR
Edit: Quantum mechanics can be made deterministic, but one has to give up locality.