Please don't go there, Peter. We both know that there is just such a null hypothesis, and the inappropriateness of that one was the very reason I used it.
One thing that may help here: It's one thing to compare a measurement to its uncertainty. (A tape measure says my desk is 48 inches wide, and the uncertainty on that is well under 0.1 inch, so this is a "480 sigma" result.) It's quite another to translate that into a probability.
The...
I am very familiar with MATLAB and with PCA, but not with MATLAB's PCA. (I use the SVD functions.) Which toolbox is PCA in?
I ask because I'm not sure if you have small syntactic problem with the PCA function or a deeper problem (which is being exposed by the difficulties with the PCA...
As I, too, think aloud here, it seems to me that -
1. The diffuse output from a flat surface will transfer momentum into the surface normal (average across all outgoing photons), as stated above.
2. However, the light source will transfer momentum into it in the direction of the source, as you...
Ah - yes, if you are thinking of dust, then of course thermal emission can occur in all directions (if the dust is either thermally conductive or spinning rapidly), including "out the back", away from the light source. And I believe that emission would indeed be considered diffuse. However, it...
Yes, indeed! The same is true in acoustics, and for the same reason. The closest we can come in optics is probably holography, because that provides at least some phase information. But optical frequencies are simply to high to sample the waveform in real time and construct the phase information.
BTW, I am assuming here that the surface is nearly flat. If it's significantly concave, the result might be the same, but the proof modestly more complicated. If it's not concave everywhere, my guess is that (a) it's still true provided that there is a well-defined normal (untrue for a sphere...
My technical background on the practical optical physics includes (ancient) techniques for producing diffuse reflectants, as for calibrations. Those relied on a crystalline powder -- likely TiO2, though I don't recall. The crystals therefore perform as phase-randomizers: both tiny prisms and...
By diffuse, you presumably mean that the mirror consists of a distribution of randomly orientated, small reflecting regions (facets), whose mean normals are the same as the normal of the mirror as a whole, right? In that case, each facet's momentum transfer is along its own normal. (Note that...
The Sun, along with the rest of the Solar System, orbits the Milky Way in a somewhat complicated orbit: more or less circular around the center, with a period ~ 220 MYr. But it also oscillates above and below the MW's spiral arms and disk with a period ~ 30 MYr. (FWIW, we are headed in the...