This doesn’t really help. How is this amplitude different from traditional probability? How can an event have negative amplitude? What does it even mean?

Amplitudes were needed to easily describe wave-like behavior. To produce an interference pattern, we need something like a probability that can be negative to represent the negative half of a wave.

Amplitudes are like probabilities that can destructively interfere when added. With traditional probabilities, if P(A) > 0 and P(B) > 0 the sum of the probabilities P(A)+P(B) cannot be zero. However, we needed to model observations like the two slit experiment where we observed that a location on the target that had positive probability of being hit by a photon in the two single-slit-only situations, that became zero when both slits were open.

Isn’t it P(A|C) = P(B|C) = 0 where C is both slits are open? P(A)+P(B) is still > 0. The condition C modifies the marginal probabilities of A and B, does it not?

This was a very effective way to describe it, I've read a great deal about QM and you made it click much better.

Ok, so an "amplitude" is just like a PDF, only that it can also take on negative values and that adding "amplitudes" is a meaningful operation?

Quantum mechanics makes a lot more sense if you don’t care about what it means and just learn the math.

Look at frequency and amplitude in sound, how different sound waves of different amplitudes interfere with each other. That'll help.

Came across this while looking for an example: https://www.youtube.com/watch?v=CAe3lkYNKt8

The traditional probability = amplitude squared. An event can have negative amplitude, but due to the square the probability cannot be negative.

I'm not sure why they don't just say that, it is the most straightforward part of QM.

Amplitudes can be non-real, so simply squaring them doesn't ensure that you have a (non-negative) probability; you have to also take the absolute value. It's still a pretty straightforward process to derive a probability from an amplitude, but fully explaining that process is a bit of a distraction from making the point that amplitudes really aren't probabilities and shouldn't be thought of as equivalent to or even intuitively similar to probabilities.

To be more pedantic, it's actually the product of [amplitude] times [complex conjugate of amplitude][0]. Confusingly, this is sometimes called the "square" of a value - usually in contexts where complex-element vectors and matrices are involved, since most[1] real-element formulas calling for matrix transpose (dot products[2] are a special case of this) actually want conjugate transpose[3] but didn't notice because conjugate is identity on reals.

0: zz* = (z)·(z*) = (a+bi)·(a-bi)

1: Possibly all - I have yet to happen across a counterexample.

2: https://en.wikipedia.org/wiki/Dot_product#Algebraic_definiti...

3: https://en.wikipedia.org/wiki/Conjugate_transpose