[varsigma]

I'll go over what I was attempting to do.

I made an assumption about light, particles of light, and that this meant I could "decompose" a beam of light, into half-beams until there was no beam.  A naive algorithm that assumed something about an algebra and linearity.

Now I see that I need to refine this idea considerably, perhaps not looking at intensities, but polarization angles as the basis of a linear system. A measurement basis. This set of angles and positions for polarizing filters is the physical basis. Now I need to characterize the Hilbert space, and if linearity is somehow a necessary condition, then I will be using a complex vector space. Who cares why, it works.

. . . another detail is that your observables are equivalent to what you can do to the equipment. Operators and observables are now in the same set. Sometimes quanta will delay this, and ignore what you've done to the positions of say, optical filters, even if you know what the angle is, so you have information about half the state of each input beam.

The other half seems to be sort of up for grabs, somehow . . .