The key to understanding configurations, and hence the key to understanding quantum mechanics, is realizing on a truly gut level that configurations are about more than one particle.

Continuing from the previous essay, Figure 1 shows an altered version of the experiment where we send in two photons toward D at the same time, from the sources B and C.

The starting configuration then is:

“a photon going from B to D,

and a photon going from C to D.”

Again, let’s say the starting configuration has amplitude $(- 1 + 0 i)$ .

And remember, the rule of the half-silvered mirror (at D) is that a right-angle deflection multiplies by i, and a straight line multiplies by 1.

So the amplitude flows from the starting configuration, separately considering the four cases of deflection/non-deflection of each photon, are:

The “B to D” photon is deflected and the “C to D” photon is deflected. This amplitude flows to the configuration “a photon going from D to E, and a photon going from D to F.” The amplitude flowing is $(- 1 + 0 i) \times i \times i = (1 + 0 i)$ .
The “B to D” photon is deflected and the “C to D” photon goes straight. This amplitude flows to the configuration “two photons going from D to E.” The amplitude flowing is $(- 1 + 0 i) \times i \times 1 = (0 - i)$ .
The “B to D” photon goes straight and the “C to D” photon is deflected. This amplitude flows to the configuration “two photons going from D to F.” The amplitude flowing is $(- 1 + 0 i) \times 1 \times i = (0 - i)$ .
The “B to D” photon goes straight and the “C to D” photon goes straight. This amplitude flows to the configuration “a photon going from D to F, and a photon going from D to E.” The amplitude flowing is $(- 1 + 0 i) \times 1 \times 1 = (- 1 + 0 i)$ .

Now—and this is a very important and fundamental idea in quantum mechanics—the amplitudes in cases 1 and 4 are flowing to the same configuration. Whether the B photon and C photon both go straight, or both are deflected, the resulting configuration is one photon going toward E and another photon going toward F.

So we add up the two incoming amplitude flows from case 1 and case 4, and get a total amplitude of $(1 + 0 i) + (- 1 + 0 i) = 0$ .

When we wave our magic squared-modulus-ratio r...

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