TerryW said:
Summary:: Is the size of a star image determined by pixels in the camera or by Feynman's paths
Images of stars taken by Earth based telescopes can be enlarged by atmospheric fluctuations, but images of bright stars taken by Hubble are also large. Is this the result of some electronic effect in the camera pixels whereby the intensity of light falling on a pixel can cause adjacent pixels to record light, or is the image enlarged by lots of photons traveling on nearby Feynman paths which result in them being spread out. Or is this a daft question?
All telescopes, even those in space, have limits to their resolving power based on the wavelength of light being observed and the aperture (a.k.a size of diameter) of the telescope.
Even an ideal telescope, perfect in every way although having a finite aperture, will not resolve far away stars to a point. The star (or any point source) will instead form an "Airy disk."
https://en.wikipedia.org/wiki/Airy_disk
There are a couple of fourmulas and "limits" as to how to characterize the resolving power of a telescope: namely the
Rayleigh criterion and the
Dawes' limit, which both describe the same sort of thing.
This diffraction limit is the best it can get. Other imperfections (atmospheric aberrations, optical aberrations, sensor limitations, etc., only make it worse. But just know that space telescopes such as Hubble (HST) and James Webb (JWST) are pretty darned close to being diffraction limited. Larger, Earth based telescopes that employ adaptive optics can also get pretty close. Even my backyard telescope, when imaging brighter planets such as Venus, Mars and Jupiter, can get surprisingly close to its diffraction limit when employing lucky imaging techniques.
So, to your original question: Do you need Feynman's paths to show this? No. All you need is the wave theory of light (i.e., light is a wave), and some physics courses. You can sufficiently derive all of this with first year physics course that touches on diffraction theory. (Although if you wanted to derive the full shape of the Airy disk, it requires knowledge of Bessel functions, so there's some math involved.)
That said, you
can use quantum electrodynamics (QED) explain diffraction, if you really wanted to. The classical solutions will match the quantum. I'm just saying that it's not necessary to use the quantum approach. It would be like trying to kill a mosquito with a rocket propelled grenade. It might work, but it's overkill.
