I What is the true nature of a photon's collapse?

[wavepax]

Here is my answer. Add any clarifications you might have..

Since the photon is a wave, the answer is similar to the answer to the question, "What is the size of a wave?" The size of a photon depends on how precisely you know the photon's momentum, or equivalently, by deBroglie's relations, how precisely you know the photon's spatial frequency (= f = 1 / λ). This is true of all waveforms/signals, and is summarized by the Δx × Δf = constant theorem.

What if a photon imparts it's energy to an electron in an atom? The photon will then had to of transferred all of its energy to the electron wave, Standard quantum mechanics states that the photon wave function collapses, but gives no explanation as to how this happens. Standard quantum mechanics regards the waveform as giving only probabilistic information, and that modeling is content with only knowing the probability that a collapse will happen, not how it happens.

 

[Simon Bridge]

Here is my answer. Add any clarifications you might have..

Since the photon is a wave,...

Can you support this assertion? A photon is usually described either as a quanta of light or the particle that mediates the electromagnetic interaction ... either way, it is a particle and obeys the laws of particle physics. The question of whether a photon is a particle or a wave is well discussed by Feynman (see bottom).

... the answer is similar to the answer to the question, "What is the size of a wave?" The size of a photon depends on how precisely you know the photon's momentum, or equivalently, by deBroglie's relations, how precisely you know the photon's spatial frequency (= f = 1 / λ). This is true of all waveforms/signals, and is summarized by the Δx × Δf = constant theorem.

In QM it is not useful to describe the size of an object in terms of it's spatial extent ... but that would be a naive lay definition of size. To work out a photon's spatial extent, however, you'd have to look for the smallest volume that a photon has been confined to. The photon itself would be smaller than that.

Note: the $\Delta x$ and $\Delta f$ are, properly, the statistical uncertainties on position and frequency, not the spatial extent and bandwidth. That is, they don't tell you the size.

What if a photon imparts it's energy to an electron in an atom? The photon will then had to of transferred all of its energy to the electron wave, ...

Technically it has been destroyed, it's energy going to the atomic state.
You appear to be thinking of deBroglie matter waves. This is an outdated concept no longer used except as a stepping-stone for students.
It is hard to tell though, because you seem to be confusing them with the wave-function in the wave mechanics formulation of quantum mechanics and also with electromagnetic light waves ... from the wave model of light. In other words, it looks like you are trying to use three different ways to model nature at the same time. This never ends well.

Standard quantum mechanics states that the photon wave function collapses, but gives no explanation as to how this happens. Standard quantum mechanics regards the waveform as giving only probabilistic information, and that modeling is content with only knowing the probability that a collapse will happen, not how it happens.

This bit is besides the point - the question you are trying to answer is "how big is a photon".

You have not actually answered the question... except maybe to say "it depends on how well you know the spatial frequency".
Well, "it depends" is pretty good:

I was at a lecture where the subject of "size" was being demonstrated ... the prof held up a variety of different shaped objects and asked the students to vote for which they thought was the smallest. There were all kinds, including a 1m long rod, a cube, a basket ball etc. Once the votes were in (the smallest being a ping pong ball) the prof held up a garden sieve and announced that to count as "small" it had to fit through that. The only object that qualified was the long rod.

The point being that size depends on context. This is true in particle physics ... something is usefully big or small according to what size sieve it fits through ... this is usually described using the probability of a particular interaction: called a "cross-section" because it turns out to have units of area and is similar to the macroscopic idea of an "impact parameter".

You should tackle the question again: it's the sort of thing physicists get asked a lot. This time start out by figuring what the questioner means by "size" - since what counts depends on what the questioner want to use the photon for.

To get a better idea about how photons are treated, I would suggest the, very accessible, old but still relevant, Feynman QED lectures.
http://www.vega.org.uk/video/subseries/8

 

[vanhees71]

Argh. I should really try to finish my Insights article on photons...

First of all a photon is not a particle in the usual sense. It's represented by a one-quantum Fock state of the electromagnetic quantum field. It's not possible to boil this very abstract concept to something simpler, because then it gets wrong.

Second, a photon doesn't even have an observable that resembles all properties of a position observable which exists for massive quanta (and also for massless scalar and spin-1/2 but not for massless quanta for spin $\geq 1$).

Third, to define an extension of a quantum is non-trivial in any case. You have to define it as a property in terms of observables. E.g., the radius of a proton is usually given as the charge radius, which is defined through the electromagnetic form factors to be determined by scattering of electrons on protons or by "hydrogen bound states". Note that there is some unsolved riddle concerning the charge radius of the proton, because the value differs between the one defined by the usual electronic hydrogen and the muonic hydrogen-like bound states. For photons, I don't think that one has a meaningful definition of its extension at all!

 

[Nugatory]

Since the photon is a wave...

Although you'll find stuff in the pop-sci press that might mislead you into thinking that, it is not true. A thread that starts with a false premise is unlikely to turn out well, so this thread is closed.

If you search this forum you'll find a number of other threads discussing what a photon is and is not.