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Configurations and Amplitude

So from what I understand:

A photon is merely our way of interpreting an amplitude wave in 3d-space. Such a 3d amplitude can be described by an x,y vector or (to simplify things), a x+yi complex number. (The complex number multiplied by i is really just a way of getting the same result as an x,y vector, due to the properties of complex numbers.)

Correct me if I am wrong so far, because I am about to get a bit fuzzy.

From what I see, the half-silvered mirror sends the amplitude wave in both directions, and is capable of reversing the phase of the amplitude -- thus, it is possible for amplitudes to intersect and cancel out. When an amplitude gets to a detector, we can see its magnitude, and count that as 'a certain number of photons'. This is why 'origin of the photon' is inconsequential (as discussed in the next article', because a 'photon' is a factor of our reading the amplitudes.

That's what I got from the article, is that a correct conclusion?

I think that I must be missing something here, because I have a few questions.

How does the half silvered mirror split the amplitude? Is the 'wave' split into two sub-waves with half the amplitude, and we just send 'photons' in bulk so it looks like 'half of the photons' got to one detector and 'half' to the other, when really each wave is split and gets to both?

Which seems like just treating photons as waves... Furthermore, as far as my understanding goes, waves are a result of particle transmission. What I'm getting at is, what is 'causing' these amplitudes, or how can an 'amplitude' be measured (and what medium is the wave measured in)?