DrChinese said:
With all of this, there are so many nuances that the language and specific words can get in the way. We tend to debate this stuff around and around, as within the scientific community there are a variety of opinions.
1. You can have single photons propagating in space. One, and only one (as you mention above, a Fock state). And you can localize it to block of spacetime. You can manipulate it in many ways, and then detect it where you would expect to find it. See details here, for one example which goes far past the photoelectric effect:
http://people.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf
Of course one can prepare single photons, e.g., by using parametric down-conversion an using one photon as a "signal photon" to "herald" the other single "idler" photon. You can even determine the polarization state of the idler photon when doing a polarization measurement on the signal photon thanks to the entanglement of the photon pair.
It's, however indeed not simply a massless point-like classical particle. It's not only not localizable but doesn't even have a position observable at all. All you can know, given its state ("preparation procedure") are the probabilities for detecting it at a given time and at the position of the detector. This is encoded in the autocorrelation functions ("Green's functions") of the em. field's energy density. It's nicely described in the quoted paper.
DrChinese said:
2. With due respect to PeterDonis' always correct answers: a photon may or may not be considered a local object depending on the experimental setup. And also depends what you call "local".
Not again ;-). But here I agree. Photons are not localizable. All you can observe are "detection events" at a certain time and position of the corresponding detector. Of course, the QED as the paradigmatic example of a local relativistic QFT is, well, local in the very clear and specific sense it is by construction:
(a) The local observables are built by field operators that transform locally under Poincare transformations
(b) The Hamilton density commutes with all local observables at space-like distances (microcausality)
(c) This implies that the S-matrix (transition-probability densities) obeys the cluster-decomposition principle, is unitary and Poincare invariant.
DrChinese said:
The main idea of this thread is that photons don't have something that corresponds to a position in the same manner that an electron does. There are a number of reasons for this, and generally within QFT the explanation is not dependent on the Uncertainty Principle.
Of course, the uncertainty principle holds also in QFT. It's a mathematical property following from the very basic rules of any QT. If there is a position and a momentum observable they fulfill the corresponding uncertainty principle ##\Delta x_j \Delta p_k\geq \hbar/2 \delta_{jk}##. Photons have no position observable though. "Localizability" of photons must thus be a derived concept, i.e., rely on the observables, like detection probabilities.
DrChinese said:
One problem is that single photons cannot be easily be created on demand in the very specific sense that emission/absorption times are precise and knowable. In an attosecond (10^-18 seconds), a photon will travel roughly 5 times the radius of a hydrogen atom (just to put in perspective). There are not many experiments running at that level of accuracy, and in fact single photon experiments often resolve photons not much better than to the femtosecond to nanosecond scales (which are a thousand to a billion times less resolution). You also have the problem that the wavelength of the photon may be larger than the spacetime block you are trying to localize the photon to, which leads to more difficulty. So you can't push a button and know the extremely precise time of photon creation. Ergo, you could never use a standard approach to assessing its position at some precise point in time.
That precisely goes in the direction I mentioned above.
DrChinese said:
So if it cannot have a position, how can it be considered local to anything? Again, this is a point that is hotly debated. I think the best one can say is that QFT makes predictions as to what a specific experimental setup will demonstrate about a photon, and the results match the predictions. That's impressive. I don't think the English language conveys the issues well in the context of some of the thread answers.
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Does a photon have a position, or can it be considered localized in a meaningful manner? Apparently, it depends.
As you say it depends on what you mean by "localized". It cannot be in the sense of a position observable as for massive particles but only in terms of detection at a certain time and space with a detector, and these quantities have of course a finite resolution only, where particularly the temporal resolution is also to be considered separately, because the related "energy-time uncertainty relation" is not of the usual kins of uncertainty relations between observables since time never is an observable (i.e., neither in non-relativistic QM nor in relativistic QFT), but that's another story.