You are saying a classical wave (without any particle) can also produce the same results. Ok.I know they are using a subtle approach to their weak measurements, that's not the point I'm making. I'm saying that no matter how they do it, the "average trajectories" they get are obviously the same as the streamlines of what we would call the "photon fluxes" in a completely classical limit where they are just the energy flux in a classical wave going between two slits. So I could easily draw their exact same figure with entirely classical measurements of an entirely classical wave. So their result (that figure) is nothing the least bit surprising. So what is their claim? That somehow the "weak measurements" are telling us something more than the exact same figure made purely classically? I see no evidence for that claim at all, if you have the exact same output as a classical approach, you don't have any additional information there, you just have a much more complicated way of extracting the same information.
The other way to get that same figure is to send one photon through at a time, and just let it hit a detector on a wall that is at variable distances from the slits, running the experiment over and over. Normalize the patterns on all those walls to have zero divergence, and draw the stream lines. Same picture again, still no trajectories of any individual photons, just an aggregate of different detector realities uniting to make a pretty picture.
Try to use pure wave on the following description (see below). What is counterpart to "photon polarization" or "Photons that enter the calcite perpendicular to the surface pass straight through" or "Photons that enter at a shallower angle follow a longer path through the calcite". Can you put pure wave into a calcite? See below:
Excerpt from http://scienceblogs.com/principles/2011/06/watching_photons_interfere_obs.php [Broken]
"How do you only measure a tiny bit of the momentum? Isn't that a "little bit pregnant" sort of contradiction? The system they used for this is really ingenious: they use the photon polarization as a partial indicator of the momentum. They send their original photons in in a well-defined polarization state, then pass them through a calcite crystal. Calcite is a "birefringent" material, which changes the polarization by a small amount depending on the amount of material the photon passes through.
Photons that enter the calcite perpendicular to the surface pass straight through, and travel a distance equal to the thickness of the calcite. Photons that enter at a shallower angle follow a longer path through the calcite (think of it like cutting a loaf of French bread on the bias-- the angle-cut pieces are longer than the thickness of the loaf), and thus experience a greater change in polarization. The polarization of an individual photon then depends on the angle it took through the calcite, which tells you the direction of its momentum. The magnitude of the momentum is determined by the wavelength, which is the same for all the photons, so this gives you the information you need for the trajectory."
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