Where is a Photon? Understanding Light and Momentum

[wotanub]

I've been thinking about this for a while. I believe I have some misconceptions about light.

Let's say we have a photon that is emitted from some atom as it de-exictes. It has definite momentum since it is of a specific energy. Where is it located? Let's ignore the issue of trying to pin down a photon without using a photon. Since the uncertainty of momentum is 0, the position is infinitely uncertain.

Okay. One explanation I thought up for this is the photon's postion is a superposition of postion states from x=0 to x = ct, where t is the time since the photon was emitted. I can't think of how exactly one would write down a wavefunction for a photon though. Maybe that means the particle interpretation of a photon fails for this problem and I should interpret it as a wave instead. Maybe a standing wave in a "cavity" of length ct.

Even if my little guess is right, it isn't very satisfying because the photon has to be somewhere definitely, I think. For example, if we intend to have it incident on a detector 1 light-seconds away. After a second passes, the detector will go off, so it was obviously at the detector. How how can we know it was at the detector and know its momentum? I suppose the argument could be made that we didn't actually mesure the momentum, we just "guessed" the right one because we knew about the energy levels of the atom beforehand.

Can the momentum (wavelength, energy) of a photon be know exactly? If this is impossible, I'll easily accept that we can know where it is.

 

[Vanadium 50]

Why do you think you know the momentum exactly? (Even if you knew its magnitude exactly, which you don't, you have no idea of its direction)

 

[Cthugha]

Let's say we have a photon that is emitted from some atom as it de-exictes. It has definite momentum since it is of a specific energy. Where is it located? Let's ignore the issue of trying to pin down a photon without using a photon. Since the uncertainty of momentum is 0, the position is infinitely uncertain.

As you seem to try to think about it yourself, two comments as a kind of stimulation:

1. Besides momentum-position uncertainty, consider also energy-time uncertainty. How well can you know the time of emission if you really have a specific well defined energy or (going away from photons for a moment) the duration of a classical pulse of perfectly defined energy?

2. Does a specific energy really give you all the information about momentum? Energy is scalar. Momentum is a vector.

Even if my little guess is right, it isn't very satisfying because the photon has to be somewhere definitely, I think.

Localizing photons ends up pretty badly. Considering tightly localized polychromatic photons, you will end up having the largest probability for detection at a different position than the position of highest energy density. The Mandel/Wolf, the 'bible' of quantum optics has a whole section on this. Photons are not particles in the classical sense of the word.

 

[wotanub]

I read some more about spontaneous emission and I knew we couldn't know the energy exactly for a laser pulse, but what is a single photon? Doesn't a single photon only have one energy? Or is it in some superposition of energy states? I think that has to be true, or else I have to go back to thinking definte energy implies frequency impies wavelength implies magnitude of momentum, and since photons go in a straight line, you can tell the direction from where it hits the detector and where the atom is.

 

[wotanub]

Yes I think I've got it now. When you quantize the field, you have to use coherent states like a harmonic oscillator, which is a superposition.