> Quantum mechanics tells us that, in order to predict the outcome of a measurement, we have to compute a specific probability based on the amplitude of the wavefunction
Even this is already wading into interpretational waters. The math says nothing about whether a given POVM should be thought of as a measurement or an interaction (or both, or neither).
Sure, it's not part of the math, but it is part of the physics. There is a very clear distinction in the theory between "interactions", governed entirely by the Schrodinger equation (or its relativistic versions, or QFT), and a "measurement", where you have the apply the Born rule not only to predict what the measurement device will show, but also to correctly predict what will happen in a subsequent experiment on the same particle.
Without the Born rule, QM makes nonsensical predictions that don't explain what happens. Decoherence helps explain certain things directly from the math without appealing to the extra Born rule, but not fully, and not quantitatively (not the specific probabilities).
> Sure, it's not part of the math, but it is part of the physics.
"the physics" here is a specific interpretation
> Decoherence helps explain certain things directly from the math without appealing to the extra Born rule, but not fully, and not quantitatively (not the specific probabilities).
No, "the physics" here is the way we are supposed to tie the math to physical observations. You can't explain all of our experiments if you don't make a distinction between interactions which preserve quantum properties and measurements which lead to classical observations. For a specific example, you can't explain the double-slit experiment with a detector at one slit if you don't make this distinction.
> You can derive the Born rule using decoherence
No, you can't. I have actively looked for such derivations and found none (at least none that are considered credible), and there is literature that explicitly says that this hasn't been convincingly done, e.g. [0]:
> My main conclusion is that there is no way to derive the Born rule without
additional assumptions. It is true both in the framework of collapse theories and,
more surprisingly, in the framework of the MWI. The main open question is not the
validity of various proofs, but what are the most natural assumptions we should add
for proving the Born rule.
> Again, that's a matter of interpretation. The different quantum interpretations say different things here.
In my view, a physical theory has two parts: a mathematical model, and a series of rules to relate the model physical experiments. For example, the theory of Newtonian mechanics isn't just F=m×a, it also includes the observation of how to measure the mass of an object and its speed etc.
Without these extra rules, you just have a mathematical theory, not a physical theory.
> Yes, you can. Look up Quantum Darwinism.
I did, and as far as I understand (e.g. from here [0]), it is an exciting candidate for explaining the Born rule based only on the other equations, but it's not fully accepted and it has its own limitations so far. Still, very interesting, thanks for pointing me to it.
> PS. throwing "nuh uhs" back to a professional in the field is not appropriate. Get your respect in order.
I did not throw a "nuh uh", I explained what I looked for and why I came to my conclusion, including a citation from a professor in the field. I think that's about as far from disrespecting you as I can get, while still disagreeing. Not to mention, I didn't know you were a professional in the field.
Even this is already wading into interpretational waters. The math says nothing about whether a given POVM should be thought of as a measurement or an interaction (or both, or neither).