Quantum reality 101 --- living in a real Fock space

I have pushed hard to ask for new experiments to test my new theory of quantum electrodynamics, MQED, against the best standard mainstream version of QED most widely used today in predicting real experiments. I call that mainstream version ρQED, because it makes heavy use of "density matrices" ρ. 

However... not everyone knows what practical, mainstream quantum mechanics really says, today. 

There are hundreds of philosophies and beliefs out there about what quantum mechanics actually is; that's why I am doing this blog post on "quantum realism 101," explaining what ρQED is. When I ran the NSF research program ("QMHP") to support quantum modeling for practical use in electronics and photonics, the practical work was mostly all based on ρQED in practice (though they didn't spend a lot of time on the philosophy of what they were doing). 

So... in quantum realism 101, in ρQED , we always assume a distinction between what the state of the cosmos actually IS at any time, the wave function ψ, and the state of our knowledge,  represented by the density matrix ρ. That's difference from the old 1920's version, when they thought that the wave function ψ represents all of our knowledge; turns out, that didn't really work. (I got to see that ever so vividly in NSF reviews of ideas for quantum computing.) 

In ρQED, we assume that the "law of everything," the dynamic equation which governs everything in the cosmos, is just dψ/dt=iHψ, the usual "Schrodinger equation", where H is the usual normal Hamiltonian operator well-known in QED. That IS unitary. We often think of the wave function ψ as a vector in Fock-Hilbert space (the Hilbert space of functions like ψ defined over Fock space, over "the multiverse.") 

But the big problem lies in how we model actual measurement processes.  

What happens when we put two or three polarizers between a source of entangled photons and the detectors behind them? Many philosophers believe that this is where God, free will, or metaphysical consciousness intervene and perform a miracle in the real world. Sometimes I call it "looking for the soul in your sunglasses" (if you have polarizing sunglasses). Many mezzo people believe that the polarizers perform a UNITARY TRANSFORMATION, that they input one definite wave function ψ and output another definite wave function, according to a well-known formula, their version of the "Born rule."

But in ρQED, we assume that the polarizer is a stochastic object, somewhat unpredictable to us human experimenters because we DON'T KNOW the state of every atom and electron in the polarizer. Thus when a definite known wave function ψ comes into the polarizer, we use the modern version of the "Born rule" to tell us what MIGHT come out, with what probability. If the incoming wave function represents just one photon reaching the polarizer, then there are only two possibilities for what might come out: (1) nothing, represented by the wave function ψ=0, the vacuum state; and (2) a photon aligned to the polarization angle which that polarizer supports. 

(I think that good ordinary sunglasses just pass through photons polarized sideways, so as to protect you from the up-and-down photons coming from the sun. Zielinger's group in Austria -- the worlds leader in this entangled photon stuff -- writes the wave function for a horizontal photon, what the sunglasses pass through, as ψ=|H>, where "H" means horizontal.)

And so, ρQED predicts that the output of the polarizer is a stochastic mix of the wave function 0 and the wave function |H>. That is NOT a unitary model of the polarizer!!!

The density matrix   ψ   for a definite known state ψ is defined simply as

(ψ)(ψ-transpose), where ψ is considered as a vector. The density matrix coming out of the polarizer is predicted to be  ρ=a*ρ0+b*ρH, where a and b are just scalars, and where ρ0 and ρH are the density matrices representing the vacuum state 0 and the horizontal state |H> respectively.

In summary, ρQED models the polarizer as a stochastic input-output process, not unitary -- as an ordinary Markov process. This kind of input-output behavior cannot be the result of a unitary Schrodinger equation by itself; it requires that we assume some kind of stochastic noise in the polarizer itself. But modern ρQED also includes lots of work on "master equations," equations for describing what happens to density matrices inside of solid objects. They are not unitary over Fock-Hilbert space; they are usually written in "Lindblad form," which makes them linear in the density matrix. 

So all of that is ρQED. My modified version, MQED, still assumes that the state of the cosmos at time t is defined by the wave function ψ. It still assumes that the cosmos is governed by the same Schrodinger equation. The underltying dynamics of the cosmos are still unitary The only difference lies in how measurement devices like polarizers are modelled. MQED requires that ALL passive macroscopic objects (objects which do not channel free energy from some source other than the light or electricity we are modeling explicitly) have a time-symmetric stochastic model. That means that complicated experiments or devices, which involve more than one macroscopic object, must be modeled as a kind of MARKOV RANDOM FIELD over time, rather than a Markov process. 

In theory, this is a bit more complicated than ρQED. However, in practice, the predictions of MQED are easier to calculate than the predictions of ρQED for many experiments, like the classic experiments with entangled photons. MQED predicts that we can use a simple lumped input-output analysis to predict those experiments, without even using wave functions at all. 

I have a new paper in draft which gives a nice example of this, with supporting data, but for now I must hold it in confidence, for many reasons (not least of them the terrible political sensitivities and activist groups emerging in the world lately).