# Photon formation

Thanks to some answers in another thread, I’ve now formulated a more specific question dealing with the formation of photons. As I understand it, an atom emits a photon whenever its electrons collapse from one level to another.

My question deals with the mechanics of this process.

Is the frequency of the photon proportional to the amount of time it takes for the electron’s level to change, thus sort of “building” the photon from energy? Or is the photon formed all at once upon completion of the collapse?

What is the energy that propels the photon away from the atom? Does the gravity or structure of the atom affect the photon’s vector?

Finally, if the electron cloud is globular, what is the mechanism that determines from what point on the globe the photon will emit? Or does it emit as a three-dimensional wave from all points of the cloud?

The frequency of a photon is related to the energy of each photon. The higher the frequency, the higher the energy of each photon. When an electron drops from one level to another, it loses a certain amount of energy, so that energy goes into creating one photon. Therefore it’s the energy level difference that determines the photon frequency (i.e. photon energy). You can think of it as an instantaneous process, there’s never a half-photon floating around being constructed. (At least you won’t be able to observe such a thing.)

Once a photon is created, it travels at, um, the speed of light. It’ll fly away on its own. Emission direction is pretty much random, though some emission mechanisms are directional.

Is the available energy of a photon always constant? That is, is there any entropy?

I feel I have an obligation to address this. But you might want to read some introductory books on quantum theory. Good science popularizing seems to be going the way of the dodo, though.

1. Photon emission is essentially instantaneous (within uncertainty limits). The frequency of the emitted light is determined by the energy difference between the starting and the final state of the atom. The frequency is that energy difference divided by Planck’s constant.

2. Photons are packets of electromagnetic energy that travel at the speed of light in that medium, and neither faster nor slower. It therefore doesn’t need to be propelled away from the atom. Gravity will certainly affect the path of the photon, since it distorts spacetime, but an atom is extremely light, so the effect is pretty small.

3. All electron clouds are not globular. In fact, most of them have pretty exotic and interesting shapes. Some look downright obscene. Again, look at a good book on quantum mechanics. Only the “s” levels are spherically symmetric.

4. Nevertheless, photon emission from an atom is equally probably in all directions. It’s the assumption I’ve made in a lot of scattering/absorption/emission calculations, and it fits the observations.

A photon is the smallest possible amplitude increment of an electromagnetic field. It’s like one notch on the volume knob of your stereo.
So a photon can’t be built up, gradually increase in energy, because a photon is the smallest possible energy increment.

Your questions about where the photon starts and ends up traveling suggest you are imagining a trajectory for the photon. There is no such animal. One way to think about it is that when the atom emits a single, pure photon, the probability amplitude of electric field intensity over a certain volume of space suddenly jumps up one notch. When the photon is observed, the probability amplitude suddenly concentrates at whatever place the photon was observed.

What happened in between? That is not knowable, since no observations were made, and knowledge without observation is logically contradictory.

The mechanics of which you speak, the exact details of photon emission from an atom, would involve very complicated relativistic calculations, because an infinite number of complicated processes involving the electron(s), the final (real) photon, and an infinite number of virtual photons must all be considered. Even calculating in complete detail what happens when a single isolated electron is coupled to the radiation field (i.e. allowed to interact with virtual photons) is a problem for which Julian Schwinger and Richard Feynmann jointly received a Nobel Prize. And the problem was not entirely solved.

A photon does not expend energy to travel. This reflects Aristotelian physics, not Newtonian. You need to consider the meaning of inertia.

Entropy is not like energy. It is not a physical measurable quantity. Entropy is a measure of the ignorance implied by your definition of the state of a system. Hence depending on how you define the state of the system you are considering, you may have different values of the entropy. Generally most physicists interested in a simple treatment of photon emission would work with a single wavefunction, for which the entropy would be and remain zero.

I might be wrong on this but I’m reasonably certain an electron changes levels instantly. It does not ‘travel’ down (or up) a level such that at some point it is in between two shells. Rather, it is in one shell at one moment and in the next shell the next (hopefully that’ll get you around the notion of a photon being ‘built’ even if the notion of popping from one shell to the next with travesing the space inbetween is somehwhat difficult to believe).

Oops…

Make that “without traversing”.

You’re not wrong, but it’s better to say the electron cannot be observed in transition. CalMeacham’s description “Photon emission is essentially instantaneous (within uncertainty limits)” is also a better way to say it.

You must have better knowledge in this field, but I had always assumed that the direction and polarization of emitted photons depended on the exact state the electron was in. So you’re saying that even if the electron is in some funky hybridized state, the emission angle is always uniform distributed? What about the polarization?

There’s also momentum to consider. The photon’s momentum is proportional to its frequency (and to its energy). When an atom emits a photon, its momentum changes by opposite the momentum of the photon (action/reaction).

Yes, with some qualifications. Different frames of reference will measure different frequencies (and energy, momentum, etc). This is the Doppler shift. A photon emitted from a moving atom will be frequency-shifted.

There are also gravitational shifts. This effect is described by General Relativity. A photon climbing out of a gravity well will be red-shifted.