Silas: The uncertainty principle comes from the fact that position and momentum are related by Fourier transform. Or, in laymans terms, the fact that particles act like waves. This is one of the fundamental principles of QM, so yeah, it sort of does depend on the validity thereof. Not the Schrodinger equation itself perhaps, but other concepts.
As for whether QM proves that all probabilities are inherent in a system, it doesn’t. It just prevents mutual information in certain situations. In coin flips or dice rolls, theoretically you could predict the outcome with enough information. Most probabilistic situations are that way; they’re probabilistic because you don’t have that info. QM is a bit different, and scientists still argue about it, but the fine detail of behavior of atoms doesn’t have any effect on a poker game.
Silas: The uncertainty principle comes from the fact that position and momentum are related by Fourier transform. Or, in laymans terms, the fact that particles act like waves. This is one of the fundamental principles of QM, so yeah, it sort of does depend on the validity thereof. Not the Schrodinger equation itself perhaps, but other concepts.
As for whether QM proves that all probabilities are inherent in a system, it doesn’t. It just prevents mutual information in certain situations. In coin flips or dice rolls, theoretically you could predict the outcome with enough information. Most probabilistic situations are that way; they’re probabilistic because you don’t have that info. QM is a bit different, and scientists still argue about it, but the fine detail of behavior of atoms doesn’t have any effect on a poker game.