Doppler Shift and Light Quanta: Questions on the Nature of Light and Observation

[Andy_K]

Dear All,

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". :)

 

[PeterDonis]

does that mean that any light emitted exists in an infinite variation / probability of frequencies, and only the "observed" / measured frequencies will materialize?

No, it means that the state of the light alone is not enough to determine what its measured frequency will be; you also need to know the state of the measuring device (or at least enough of it to determine the Doppler shift). This is not an issue specific to QM.

If there are an infinite / very large number of observers, would the emitted light (say a very brief burst) run out of observable light?

It depends on what measurement you make and how the observers get the results. Yes, if you make a measurement that counts photons, you will only count a finite number and then there will be no more. But there is no reason why any given observer can only know the result of his own counter. And you can also make other measurements that don't count photons (they measure other observables).

 

[Andy_K]

Thank you for your clarifications. Let's say if we are solely looking at "visual" measurements, i.e. with humans seeing the light, where the underlying process is similar to counting photons.

Does that mean there is a theoretical limit as to how many people can visually observe a burst of light, due to a finite number of photons / energy emitted?

Consequently, does that mean that a faraway observer could potentially visually observe an event that a nearer observer may not see, since the light can take on any path (though with differing probabilities)?

It depends on what measurement you make and how the observers get the results. Yes, if you make a measurement that counts photons, you will only count a finite number and then there will be no more. But there is no reason why any given observer can only know the result of his own counter. And you can also make other measurements that don't count photons (they measure other observables).

 

[PeterDonis]

Let's say if we are solely looking at "visual" measurements, i.e. with humans seeing the light, where the underlying process is similar to counting photons.

Sort of.

Does that mean there is a theoretical limit as to how many people can visually observe a burst of light, due to a finite number of photons / energy emitted?

In principle there could be, yes. But you might want to try estimating how likely it would be for such a limit to be reached in practice.

does that mean that a faraway observer could potentially visually observe an event that a nearer observer may not see, since the light can take on any path (though with differing probabilities)?

Again, in principle this could happen (with sufficiently faint light emitted from the event), but you might want to try estimating how likely it would be in practice for a typical amount of light emitted from a typical event.

The short answer is that the everyday light we see can be treated classically; the quantum aspects of light take much more precise experiments to probe.