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My mental model is that complex numbers are the first of the basic number systems that no longer has a total ordering. That alone is super useful for it. Quan
by taeric 1y ago
My mental model is that complex numbers are the first of the basic number systems that no longer has a total ordering. That alone is super useful for it.
Quantum is an odd one, as the name indicates that it deals in quantums. Minimum values that can't be divided. The difficult parts seems more to be in systems that have a probability space more than an analytical model that describes them. Which, fair, it is not a number system.
- CGMthrowaway 1y agoThe loss of ordering is what makes complex numbers unique and useful for describing systems like rotations and probabilities. Classical probability works with real numbers (probabilities between 0 and 1). Quantum probability involves amplitudes represented by complex numbers. These amplitudes can wave-interfere with each other, leading to superposition and entanglement
- ogogmad 1y agoThe phase space formulation of QM still only uses REAL-valued probabilities, but outside the interval [0,1]. I'm not sure I agree with the rest of your comment either.