In QED, the angular momentum of a pure momentum state is explicitly *undefined*, where the photon's spin in this state is 1.
Then a pure momentum state, pure or intrinsic angular momentum isn't explicitly defined in QED. Spin is intrinsic angular momentum in any quantized theory including electrodynamics. Therefore spin is not defined so even assigning Planck integral units to it would be meaningless. QED.
When QM says a particle is spread out, it's understood to mean that at any given time, there is a non-zero probability of detecting that particle at many places.
This is a semi-classical attempt to marry field theory and QM. It works reasonably well in some places and fails miserably in others. QED would like to quantize a field, e.g. the electric field associated with particulate electron. Particulization implies extension. The electron is precluded from having any spacetime extension because the extension makes QED non-renormalizable, that is, the field necessarily has infinite density at least in one point. The problem lies in imposing a classical spacetime point conceptualization, or to say there is a certain probability of locating a point at a certain time which is defined in a region of probability space. This is a heuristic or epistemological device. It almost allows an adequate characterization of outcome of experiments.
Now clearly, if we set up many detectors, only one of them will indicate the presence of the particle
No. The right way to say it is "some one of them should indicate a response that purportedly evidences the particle" because the integral of the probability density function is 1, surety, since outcomes of experiments which are local are assumed to be local. However this makes an assumption not formally supported in QM. And that is that outcomes are local. There are assumptions about local and global spacetime topology made also. Hidden assumptions. The photon may be connected to every point in the universe and only appear to act in particulate behavior by our anthropomorphic designs. QM provides for the possibility that there is no spacetime extension, no continuum, only the Baer Space of points and that such 0 dimensional space is absolutely indeterminate as to whether it exists.
The angular momentum that extended ED, non-linear Maxwell, talks about and which is applicable to a soliton-like discretization of the photon, is simply E x B, the electric and magnetic field vectors' cross product which has a tensor density character. It is an area with orientation orthogonal to these vectors. The area per unit volume rotates and progresses in Planck units in the helical direction of the wave front expansion. I had used this device to explain the Gaussian modes because it seemed similar to what Palmer was doing with Laguerre's modes. Maybe this is all relevant, but on examining the SR device, it also seems superfluous.
I want to emphasize that for 30 years I have been intimately involved in GR, QC, hep, and QM, and I assure you that what you are saying is simply some various models that have been cooked over the years. These models work only up to a point, and then they are useless. What we have been doing is just giving up at that point and going on to something else. Example: what is a magnetic field? No one knows. We know a lot about what it does, but trying to decompose it into bits has been out of the question. No, it is not virtual photons. What are they? Irrationalizations. Usually when someone has tried to find a mechanism, they end up saying something like "and inside the mechanism is a magnetic field which..." This recurs everywhere in physics. It seems impossible to separate definiens and definiendum, so physics is relative, subjective, and creative, and so is inherently ambiguous.
What I do is exchange equations with colleagues. We do the word game too, but it is only the equations that matter. |
