Photon Width: What Have I Missed?

[padraighaz]

Thanks Edgardo for your post. This is the kind of analysis I vaguely remember learning decades ago and the coherence length is what I had in mind for the scale length in the direction of motion, where you needed a superposition of components to generate a finite wavepacket.

My original question concerned transverse scales since I was wondering how wide is a photon and couldn't remember having learned anything about this. If it can be as wide as the slit separation, it's no big deal to point out single photon interference requires a photon to go through both slits at once etc. etc. Couldn't one argue that a double-slit single photon experiment is a detector of transverse scales? There might not be a single unique scale; there might be a distribution - in which case interference will still occur over a range of slit separations - but the existence of the distribution is interesting in and of itself, and so is the fact (if this interpretation it correct) that the photons in this case have transverse macroscopic physical dimensions. This passing through both slits at once issue becomes less so under these circumstances.

 

[ZapperZ]

Unfortunately, one needs to look at those papers cited by Edgardo VERY carefully to know what is the "wavepacket" being mentioned there. Keep in mind one very important difference here:

The "wavefuction" as obtained out of the Schrodinger equation is NOT the same "wave" that we describe light with! The schrodinger wavefuction exists in "configuration space", whereas the "wave" that we associate light with (as when you solve Maxwell equation) is a REAL wave. One can put an antenna or a pickup probe and literally see this oscillation.

Thus, it is STILL wrong to say that a photon is made up of wavepackets of light! No where in those papers will you see such a description. What is being done instead is to designate a photon as a "particle" similar to the way you solve the Schrodinger Equation for a "free particle". When you do that, you can see that you don't have any restriction on the "k" values of your solution. To make some form of "localization" of that photon, you make a superposition of wavefunction with different k. Using a priori knowledge of the source, one can make a reasonable guess at what k values one can use.

However, after you get such a "wavepacket", do you actually know the size of a photon? You don't. All the wavefuction that is represented by your wavepacket is saying is that if you make a single measurement, this is where you will find the photon. If you make another single measurement of the identical system, this is where you will find a photon... etc.. etc. In other words, the $\Delta(x)$ is the SPREAD in the statistics of finding where that photon is! It does not correspond to the width of the photon anymore than the standard deviation of how often the number 3 comes up in a throw of a dice is the "width" of number 3!

As Mies van de Rohe used to say "God is in the details"...

Zz.

 

[markyannone]

One photon

Given the difficulty in sizing a photon, how can you send just one? The beginning is easily determined by the start of the event . . . but the end of the transmission? When is that?

 

[ZapperZ]

Given the difficulty in sizing a photon, how can you send just one? The beginning is easily determined by the start of the event . . . but the end of the transmission? When is that?

You let mother nature take care of it. Single photon sources basically are photo emitters that are "slow", or http://physics.nist.gov/Divisions/Div844/facilities/cprad/PhotonSource.htm" .

Zz.

 

[Chaos' lil bro Order]

Unfortunately, one needs to look at those papers cited by Edgardo VERY carefully to know what is the "wavepacket" being mentioned there. Keep in mind one very important difference here:

The "wavefuction" as obtained out of the Schrodinger equation is NOT the same "wave" that we describe light with! The schrodinger wavefuction exists in "configuration space", whereas the "wave" that we associate light with (as when you solve Maxwell equation) is a REAL wave. One can put an antenna or a pickup probe and literally see this oscillation.

Thus, it is STILL wrong to say that a photon is made up of wavepackets of light! No where in those papers will you see such a description. What is being done instead is to designate a photon as a "particle" similar to the way you solve the Schrodinger Equation for a "free particle". When you do that, you can see that you don't have any restriction on the "k" values of your solution. To make some form of "localization" of that photon, you make a superposition of wavefunction with different k. Using a priori knowledge of the source, one can make a reasonable guess at what k values one can use.

However, after you get such a "wavepacket", do you actually know the size of a photon? You don't. All the wavefuction that is represented by your wavepacket is saying is that if you make a single measurement, this is where you will find the photon. If you make another single measurement of the identical system, this is where you will find a photon... etc.. etc. In other words, the $\Delta(x)$ is the SPREAD in the statistics of finding where that photon is! It does not correspond to the width of the photon anymore than the standard deviation of how often the number 3 comes up in a throw of a dice is the "width" of number 3!

As Mies van de Rohe used to say "God is in the details"...

Zz.

This might be a stupid question, but can you put a maximum contraint on the size of a photon?

 

[christianjb]

This thread seems a bit tense to me. Some people need to calm down.

I think part of the confusion is what do you define to be a photon? Is it the wave-function or is it the the result of a position measurement on that wave-function?

A photon is a point, in the sense that one photon can only set off one photo-multiplier at one point in space. However, the wave-function of a photon is presumably massively delocalized.

 

[ZapperZ]

This thread seems a bit tense to me. Some people need to calm down.

Note that this is a rather "old" thread, the last post was in Oct. 2006 before being resurrected today.

Zz.

 

[jackiefrost]

Having read through this whole thread with interest, please forgive me for keeping it alive when maybe y'all would rather it evaporate. I'm only (very slowly) working my way through classical electrodynamics ala Griffith and various other sources and I only know the very basics regarding QM. Having said that, my question is this: how should I blend the notion of a single photon in the QM sense while still regarding what I've learned about the electromagnetic field in the Maxwellian sense [and I probably make no sense ]? Thanks if anyone has a clue as to my confusion.

jf

 

[Mentz114]

Trying to define a size for the photon can lead to some weird conclusions. Consider a very high Q single mode cavity with a volume V, with a EM field inside that has the energy of just one photon. So far everything is classical. We introduce an atom into the cavity that has a suitable resonant transition, which absorbs one photon. At the time of the absorption, where was the photon and how big was it ? It must have been close to the atom one supposes. Classically energy was everywhere in volume, but in photon terms where was it before absorption ?

I'd also like to add that interference of light can be explained as a purely classical wave phenomemon with actual interference in normal 3D space, but interference of matter waves takes place in configuration space.

So the 2 slit experiment is not a good place to start.

 

[jtbell]

I'd also like to add that interference of light can be explained as a purely classical wave phenomemon with actual interference in normal 3D space,

Even at the level of single photons, going through the apparatus one at a time?

 

[christianjb]

Trying to define a size for the photon can lead to some weird conclusions. Consider a very high Q single mode cavity with a volume V, with a EM field inside that has the energy of just one photon. So far everything is classical. We introduce an atom into the cavity that has a suitable resonant transition, which absorbs one photon. At the time of the absorption, where was the photon and how big was it ? It must have been close to the atom one supposes. Classically energy was everywhere in volume, but in photon terms where was it before absorption ?

I'd also like to add that interference of light can be explained as a purely classical wave phenomemon with actual interference in normal 3D space, but interference of matter waves takes place in configuration space.

So the 2 slit experiment is not a good place to start.

OK, I need to learn something. What's the difference between 3D space and configuration space for one particle? Isn't configuration space of one particle just x-y-z?

 

[Mentz114]

jtbell

Even at the level of single photons, going through the apparatus one at a time?

There's probably no classical explanation for that, as you know, because the photon is not a classical concept. Even stranger is the Hong-Ou-Mandel experiment.

It seems though, that to model a single photon one needs a wave packet, which is a mixture of modes and seems a sort of compromise to get some kind of localisation.

Apart from the single-photon stuff, light only gets quantised when interacting with matter at which time it is also localised.

As has been pointed out already in this thread, there is no property of the photon which corresponds to the classical idea of 'size'.

Christian, I would say that configuration space never coincides with real space. Phase space and configuration space are ideas.