The point is that noise acts to dither the levels. Suppose the true signal is some value X between zero and one, over a patch of the image (we are going to ignore natural scene variation for the purpose of answering your question). Suppose the noise is of strength N, for example let N be one level. The noise adds a random number roughly between -N and N to X, so that the pixel wants to record some number between X-N and X+N. Of course, the resulting signal plus noise is digitized so the output is either 0 or 1; if the noise is random (uncorrelated from pixel to pixel), the value of X is reflected in the percentage of 1's vs 0's in the patch -- a fraction X of the pixels will be 1 and the rest 0. If we average the levels over a large enough patch, we recover the original signal, even though each individual pixel only recorded 0 or 1.
This is the basic idea that allows one to trade resolution for noise -- and why downsampled images look less noisy. Note also that while the average is more finely graded than steps of one, that doesn't mean we buy anything by making individual pixels record values more finely spaced than the level of noise, because the individual values are jumping around randomly by an amount between -N and N.
Thanks for attempting the explanation, Emil, even though I have to admit it is not all totally clear.
Nevertheless, I can see with my own eyes that noisy images after downsampling exhibit less noise. A similar effect can be achieved simply by viewing the image from a greater distance.
What still puzzles me is that a 14 bit A/D converter in a camera with a good dynamice range, such as the D7000, will not provide any IQ advantages in the deepest shadows, compared with 12 bit.
However, I can understand this might be the case with a Canon camera which doesn't go beyond 12 stops of DR.
I've gone back to the RAW files and created crops of the 12th, 13th and 14th stops, which show a clear improvement in IQ in the 12th stop.
Now, you seem to be claiming that such improvement in that 12th stop is entirely due to the greater quantity of light resulting in an improved SNR (1/500th sec as opposed to 1/2000th for the 14th stop).
Of course, I am able to appreciate that 4x the number of photons will improve the SNR and the IQ as a result.
I'm just a bit skeptical that the image quality in that 12th stop, as shown in my attached image, could be achieved with just the one level per channel of a 12 bit converter, as opposed to the 4 levels per channel of the 14 bit converter.
Normally, I would just repeat the test in 12 bit and 14 bit modes. If I see a difference at the same very low exposures, then there's a difference, depite any theory from an eminent Physicist.
Unfortunately, my D7000 is in for repair due to its inability to autofocus in cold weather. It looks as though I won't get it back for a while because it is now Spring in Australia, and the Nikon repair agent is unable to duplicate the problem in the artificially cold environments he has created.
Tell me now whether I can expect to see the same image quality in that 12th stop with the D7000 set to 12 bit mode, and when I get the camera back, or a new replacement, I'll carry out the tests and tell you whether you are right or wrong.