The experiment in the previous essay carried two key lessons:

First, we saw that because amplitude flows can cancel out, and because our magic measure of squared modulus is not linear, the identity of configurations is nailed down—you can’t reorganize configurations the way you can regroup possible worlds. Which configurations are the same, and which are distinct, has experimental consequences; it is an observable fact.

Second, we saw that configurations are about multiple particles. If there are two photons entering the apparatus, that doesn’t mean there are two initial configurations. Instead the initial configuration’s identity is “two photons coming in.” (Ideally, each configuration we talk about would include every particle in the experiment—including the particles making up the mirrors and detectors. And in the real universe, every configuration is about all the particles… everywhere.)

What makes for distinct configurations is not distinct particles. Each configuration is about every particle. What makes configurations distinct is particles occupying different positions—at least one particle in a different state.

To take one important demonstration…

Figure 1 is the same experiment as Figure 2 in Configurations and Amplitude, with one important change: Between A and C has been placed a sensitive thingy, S. The key attribute of S is that if a photon goes past S, then S ends up in a slightly different state.

Let’s say that the two possible states of S are Yes and No. The sensitive thingy S starts out in state No, and ends up in state Yes if a photon goes past.

Then the initial configuration is:

“photon heading toward A; and S in state No,” $(- 1 + 0 i)$

Next, the action of the half-silvered mirror at A. In the previous version of this experiment, without the sensitive thingy, the two resultant configurations were “A to B” with amplitude −i and “A to C” with amplitude −1. Now, though, a new element has been introduced into the system, and all configurations are about all particles, and so every configuration mentions the new element. So the amplitude flows from the initial configuration are to:

“photon from A to B; and S in state No,” $(0 - i)$

“photon from A to C; and S in state Yes,” $(-$

... ,,,,,,,,