system
Given the following post, respond as if you're commenting on Reddit:
human
Can you tell the / is there a the difference between redshifted EM radiation and EM radiation of a longer wavelength?

If you were to generate a photon from a relatively stationary point on a planet and observe it, it has a certain wavelength.  If you were to do the same thing on a ship that is traveling at a constant velocity apparently near lightspeed from your stationary point, the photon on the ship would appear to have a certain wavelength, which would be shorter than the wavelength would appear if we observed it from the planet.

My question is, if we were to generate a photon on Earth that was the same wavelength as the photon we detect from the ship, is there any way we could tell that the one from the ship was emitted from something moving away from us?  

For instance, when we see red-shifted stars, we know they are traveling away from us because we know what wavelength we expect the light to be, and we see that it is longer.  But if we didn't know that, if we just saw some light without context, would we have any way of telling whether the light was red-shifted or if it was the same wavelength as it was in a frame stationary relative to the emitter?
gpt
No. There is no difference. Photons in the exact same state are indistinguishable. This concept is actually true of all fundamental particles. 

At the heart of your question is the fundamental nature of relativity: there are no preferred or special reference frames. All reference frames are equally valid and "real". A photon that is redshifted is really just a photon that is being observed from a different reference frame. Since all reference frames are equally valid, observing a photon from a certain reference frame does not make it different or special aside from the effects of the frame switch itself. 

With respect to astronomy, the reason we can tell the light is red-shifted is because the spectral pattern for a certain element in a star is the same as the spectral pattern of the same element as measured on Earth, except it is shifted to the red. We can't tell that the light is red-shifted just by looking at individual photons and seeing them as somehow different.