Maaneli said:
Andy,
Did you read any of those links? Barut does say what he thinks about the configuration space formulation. That's why I posted them for you.
I did read the links, and what Barut says, does not make clear what he thinks, sorry.
Maaneli said:
He also says it is necessary for accounting for nonlocal correlations.
I have not found the word "nonlocal". He does mention "long-range quantum correlations". I'm not sure this is the same thing.
Maaneli said:
Mathematically, this is no different from what is done in standard QM for entangled wavefunctions. So nothing really changes there except now you have the self-field interaction which makes the wave equation nonlinear. In fact, he is not at all linearizing the Dirac equation by constructing that 16-component nonlocal wavefunction. The Dirac equation is still a nonlinear integro-differential equation, but now with a nonlocal self-field. In fact, what Barut does here is exactly what I proposed one would do in constructing the SFED version of the singlet state in an earlier post. Nightlight's comments seem misguided to me. He was incorrectly mixing up the Hartree-Fock approximation for separable wavefunctions, with nonlocality in Barut's SFED.
When I was talking about linearization, I did not mean that specific equation. I meant that "underoptimization" and the configuration space in general may appear as a result of linearization. nightlight cites the results from K. Kowalski and W.-H. Steeb, Nonlinear Dynamical Systems and Carleman Linearization (World Scientific, Singapore, 1991) (brief outline in
http://arxiv.org/abs/hep-th/9212031 ): if we have a nonlinear differential equation in an (s+1)-dimensional space-time {\partial_t}u(x,t) = F(u,{D^\alpha}u) , where {D^\beta}={\partial^{|\beta|}}/\partial x_1^{\beta_1}\ldots<br />
\partial<br />
x_s^{\beta_s}, |\beta|=\sum\limits_{i=1}^{s}\beta_i , we can introduce a normalized functional
coherent state |u\rangle =\exp\left(-\frac{1}{2}\int<br />
d^sx|u|^2\right)\exp\left(\int<br />
d^sxu(x)a^\dagger(x)\right)|0\rangle (so a(x)|u\rangle =u(x)|u\rangle, where {a^\dagger}(x) and a(x) are the standard Bose operators of creation and annihilation) and a boson operator M = \int {d^s}x{a^\dagger}(x)F(a(x),{D^\alpha}a(x)) , and then we have a linear evolution equation in Hilbert
space \frac{d}{dt}|u,t\rangle = M|u,t\rangle, where |u,t\rangle = \exp\left[\frac{1}{2}\left(\int {d^s}xu^2<br />
-\int {d^s}xu_0^2\right)\right]|u\rangle and \qquad<br />
|u,0\rangle=|u_0\rangle (I did cut some corners; you can find the details in the Kowalski's work). Thus, a less than exciting nonlinear differential equation can be linearized using 2nd quantization. If we did not know the equation for what it was, we could start talking about the configuration space, entangled wavefunctions, and so on. Are you sure we should do just that? I am not. I am not trying to convince you that entangled wavefunctions are just an artifact of linearization, but I believe this is a possibility.
Maaneli said:
How can you still not see it? We've just been over the fact that entangled wavefunctions are not only possible in SFED, but that it would be necessary to consistently predict the current quantum entanglement correlations for electrons, even though none of them VBI quite yet (because the seperability condition hasn't been implemented yet). Otherwise, the theory wouldn't even be able to match these nonideal correlations. You would have to construct some additional ad-hoc mechanism to do this. And you couldn't use stochastic optics to do it, since there are no ZPF fields in SFED. So I don't know what else would be availabe. And, honestly, what seems more natural, using the entanglement of the wavefunctions in configuration space which the theory permits or something entirely new and ad-hoc?
Frankly, a straight-forward nonlinear differential equation seems much more natural. Whether such a minimalist theory is possible, I don't know, but so far I don't see any fundamental difficulties, theoretical or experimental.
Just a few more words. I can live without locality. I can live without reality. I can live without causality. But not until I am absolutely sure I do have to go to such extremes.