The mathematical structure in common is called a “measure.”
I agree that there’s something mysterious-feeling about probability in QM, though I mostly think that feeling is an illusion. There’s a (among physicists) famous fact that the only way to put a ‘measure’ on a wavefunction that has nice properties (e.g. conservation over time) is to take the amplitude squared. So there’s an argument: probability is a measure, and the only measure that makes sense is the amplitude-squared measure, therefore if probability is anything it’s the amplitude squared. And it is! Feels mysterious.
But after getting more used to anthropics and information theory, you start to accumulate more arguments for the same thing that take it from a different angle, and it stops feeling so mysterious.
The mathematical structure in common is called a “measure.”
I agree that there’s something mysterious-feeling about probability in QM, though I mostly think that feeling is an illusion. There’s a (among physicists) famous fact that the only way to put a ‘measure’ on a wavefunction that has nice properties (e.g. conservation over time) is to take the amplitude squared. So there’s an argument: probability is a measure, and the only measure that makes sense is the amplitude-squared measure, therefore if probability is anything it’s the amplitude squared. And it is! Feels mysterious.
But after getting more used to anthropics and information theory, you start to accumulate more arguments for the same thing that take it from a different angle, and it stops feeling so mysterious.