Q:

Doppler Shift & Light Quanta

I have a couple of (noob) questions regarding Doppler Shift and light from a quantum physics perspective:
a) Since different observers will see the light at different frequencies depending on their reference frame / velocity thus resulting in Doppler Shift, does that mean that any light emitted exists in an infinite variation / probability of frequencies, and only the "observed" / measured frequencies will materialize?
b) If there are an infinite / very large number of observers, would the emitted light (say a very brief burst) run out of observable light? Because if a single photon is emitted, then even if there are 2 detectors, only one will fire. Likewise, if an emitted light burst contains only say 1 million photons, does that mean the 1,000,001th observer (or detector) will not see anything?
Thank you for "shedding light on the matter". :)

A:

A) Yes and No. Doppler shift is about apparent changes in frequency. Emphasis on apparent changes.The relative frequency of the light depends on the observer. Frequency is not, however, an inherent quality of the light. You may be conflating frequency and wavelength-a common error.
B) Perhaps. If you are firing them sequentially onto a different detector each time, and you cease firing photons (you've fired your quota of 1,000,000) then the 1,000,001st detector will probably not detect a photon. If you fire 1,000,000 photons all at once, or in some other grouping,  then it depends on your setup. Depending on the setup you could get all sorts of bizarre interference and data. It's possible under some setups for it to appear that your 1,000,000 photons registered in more than 1,000,000 places. It's also possible that with 1,000,000 photons and 1,000,001 simultaneous observers there will be one that doesn't get a photon to observe.

