DrChinese said:
Good point AndresB, I wouldn't always take this position. But these are entangled particles. They do not produce double slit interference.
It depends, of course, on the setup. Recently we have discussed a nice double-double-slit experiment with entangled photons, demonstrating the original EPR debate about entanglement in momentum/position space (open-access article):
Kaur, M., Singh, M. Quantum double-double-slit experiment with momentum entangled photons. Sci Rep 10, 11427 (2020).
https://doi.org/10.1038/s41598-020-68181-1
DrChinese said:
But even in the double slit, with a normal photon, I would say it took a "path". Being a quantum particle, it did not take one specific path in an experiment designed to highlight this quantum behavior. I point out another such in post #41 above, point 4: where light does not take classical paths.
Come on! That's at the very fundamentals of all quantum theory that there is no classical path. You cannot understand the diffraction pattern in experiments like that with single particles nor single photons. It's fasterfully explained in the introductory chapter of the Feynman lectures vol. 3.
DrChinese said:
But in an instance where such properties can be neglected - which was the case in the thread where this originated - of course I would talk about a photon's path. Virtually all photons that arrive anywhere do so upon what is almost perfectly a classical path - that is easily demonstrated by blocking anywhere along the most likely path. Should we need factor in the effect of gravity on light when we discuss how light moves? I would not mention that gravity bends light when discussing photon path unless there are large objects involved. To recap my position (from another post of mine above):
Entangled photons travel on paths whether or not they are in fiber. They almost exactly follow classical trajectories. They are NOT classical paths however, for a lot of reasons. The main reason is that photons are quantum particles, not classical particles. I don't know if an individual photon travels on one path, many paths (path integral concept), different paths in different MWI worlds, exact Bohmian trajectories, are continuous or not, etc. They can do lots of things when not being observed. (Nobody I aware of on this planet has any superior understanding of the "truth" of what happens.)
Photons don't take paths in the sense of classical particles. The classical limit of the quantized electromagnetic field is not a point-particle theory but classical Maxwell theory. AFAIK there is no satisfactory Bohmian interpretation of relativistic QFT.
DrChinese said:
And yet: every experimentalist does all test calibration as if they are observing entangled photons moving on their precisely desired "classical" path with a classically expected arrival time relative to the entangled partner. Let's just call that a path, like everyone else does.
No! When taking the effort to use entangled photon pairs usually researchers are after quantum effects, where a classical particle picture is inapplicable. Particularly photons don't even have a position observable. All that is physical are detection probabilities at positions defined by the detector at times measured by a clock.
DrChinese said:
Guess what? All of the above is also true about momentum, position, etc. of any quantum particle. And yet we use the words momentum and position to discuss such particles. Obviously, if I choose to place these attributes in superposition, those words can become meaningless. So I would say there is context to consider, just as when answering a question on any subject.
For massive particles there exists a position observable, a non-relativistic approximation, and a classical point-particle limit, but not for photons. It is important to use the words "position" and "momentum" in the right way, when it comes to quantum properties of particles and photons, particularly in cases, which are not describable in terms of the classical point-particle picture, and particles or photons in entangled states are the extreme example for a situation, where the classical point-particle picture and even the classical theory of "local realism" a la EPR fails.
Parametric downconversion to prepare entangled photon pairs is also a characteristic example: The entanglement comes from the fact that you select such pairs via phase matching that you
can't know in principle which "path" each of the photons took, and that's why you have a superposition that is not a product state, like the type-II case
$$|\Psi_{\pm} \rangle=\frac{1}{\sqrt{2}} [\hat{a}(\vec{k}_1,H) \hat{a}(\vec{k}_2,V) \pm \hat{a}(\vec{k}_1,V) \hat{a}(\vec{k}_2,H)]|\Omega \rangle.$$
As an example, see the paper with the theory about it you quoted yourself yesterday, where the state of the created pairs is treated in great detail including all the deviations from the above quoted idealized example:
https://arxiv.org/abs/quant-ph/0103168v1
