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Can one physically distinguish a photon of frequency $\omega$, generated by a stationary laser, from a photon generated by a mechanically moving laser (a different laser from the first one) which, due to the Doppler shift, has the same frequency $\omega$?

Note that the two lasers have different frequencies: The first laser (stationary) emits photons of frequency $\omega$. The second laser (moving) would emit photons of frequency $\omega^\prime$ if it were stationary. However, due to its motion (at a certain velocity) and the ensuing Doppler shift, it emits photons of frequency $\omega$ (the same as the first stationary laser). In all cases, the observer is also stationary.

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  • $\begingroup$ I think the answer is no. It's not possible to physically distinguish between photons of the same frequency based on their generation type. Photons carry no information about how their frequency has changed, making photons with the same frequency indistinguishable to an observer regardless of their source's motion. $\endgroup$
    – Omid
    Mar 12 at 7:24
  • $\begingroup$ The same also applies to polarization. There's no way to distinguish a photon that has been generated, for example, as linearly-polarized directly by a laser from a photon that has become linearly-polarized by passing through a polarizer. $\endgroup$
    – Omid
    Mar 12 at 7:34

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Electromagnetic Doppler shift can only be detected only with additional knowledge. For example, knowing what the frequency (or wavelength) would be without such a shift enables velocity determination.

In astronomy, the wavelengths used for velocity measurement correspond to lines in the spectra of various materials. These wavelengths are known from laboratory observations on Earth, and are presumed to be the same throughout the universe.

Accordingly, displacement of spectral lines from their known wavelengths is interpreted as Doppler shift.

Without a priori knowledge of the "at rest" wavelength, Doppler measurement of the velocity component is not possible.

If there are 2 lasers emitting at the same wavelength, their relative speeds (radially with respect to an observer) can be determined using the Doppler method.

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  • $\begingroup$ Thanks for your response. So, are you suggesting that it's impossible to distinguish without prior knowledge of the source motion? $\endgroup$
    – Omid
    Mar 12 at 5:34
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    $\begingroup$ No, please carefully read the last sentence. In astronomy there was no prior knowledge of galactic velocities - the Doppler shifts were seen first, and the velocities inferred from them. $\endgroup$
    – MarkH
    Mar 12 at 5:42
  • $\begingroup$ Thanks. But in the question I explicitly said that the two lasers are not the same (in the frequency I meant). $\endgroup$
    – Omid
    Mar 12 at 5:44
  • $\begingroup$ When the relationship between the source wavelengths is unknown, Doppler can't per se reveal relative motion. $\endgroup$
    – MarkH
    Mar 12 at 5:47
  • $\begingroup$ I added an extra piece of information. Please kindly read the question again with the new information. Thanks anyway for your comments! $\endgroup$
    – Omid
    Mar 12 at 5:56

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