Demystifier said:
No, classical waves could never do that. You need quantum waves, which differ from quantum ones by having a probabilistic interpretation.
Gee. I'm confused now of what Ken was talking about. The following is the complete context of what he was describing. Do you know what he was talking about when he talked about "detection densities", "divergence-free field", etc. which he claimed was related to the experiment?
(the rest is Ken comment, what part is wrong?)
Ken G: "It doesn't mean that... Nothing in that experiment is the trajectory of an individual photon, instead, what they have seems to me is equivalent to what you'd get if you put the detecting screen at various different places and create a field of detection densities, attribute the detection densities to trajectory densities such as could be done with any divergence-free field, and draw the "field lines" and call them average trajectories. I'll wager doing that would generate precisely the same figure. Much ado about nothing.
What they seem to be missing is that the classical picture of waves going through two slits could generate the same figure. What makes the quantum realm so weird is the quantization-- not the averaged behavior. I really don't see what "weak measurement" is adding to the question, it still is not true that you can say which slit any of those electrons went through."
"What I'm saying is, I'm not convinced that "weak measurement" is any different from "compiling average trajectories from treating the wave energy flux like a divergenceless scalar field and drawing 2D lines of force for that field." I maintain you could get that exact same picture by measuring the energy flux of a classical wave passing between two slits, and drawing trajectories such that the line density is proportional to the energy flux density. This would be completely consistent with a macroscopic treatment of an energy flux as a photon number flux. Those trajectories don't really mean anything beyond a statistical treatment of where photons go in large aggregations, that they could get the same picture with "weak measurement" of "one photon at a time" doesn't strike me as being at all profound.
Let me put it another way. The key statement that we don't know the trajectory of an individual photon is that we cannot know which slit it went through, and still have that photon participate in an interference pattern. Does this experiment tell us which slit any of those photons went through? No. So what? There are still no trajectories in the physical reality of what happened to those photons, and it's not at all clear that an "average trajectory" is anything different from the usual macro aggregate measurement in the classical limit. To me, all this experiment is is a kind of consistency check that "weak measurement" can recover statistical aggregates, but I see no threat to the CI interpretation that the reality is still only what you measure and not what happens between the measurements. So they can create weak measurements that don't completely collapse the wave function, then recover the aggregate behavior in the same way that complete measurements that do collapse the wavefunction could easily do also. What does that tell us? That weak measurements don't mess up aggregate results? Why should we be surprised-- the weak measurements don't tell us the trajectories of any of those particles."
