# Do single photons disperse like a wave?

Hi,

if an electron and a positron collide and annihilate they will produce two gamma photons departing from the collision point in opposite directions at the speed of light, right ?
Now since there is this wave/particle duality problem I was wondering if in a vacuum in this particular scenario there is evidence for a particle-like behaviour (so seemingly a departing point of constant amplitude - so the energy stays in that moving "point") or wave-like behaviour (so seemingly a departing wave whose area increases with distance and amplitude decreases proportionally - so the energy is "spread out" or "diffuses" with time).

 regarding the title: "disperse" is actually the wrong term. i mean "diffuse".

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Well, I guess I've found an answer in wiki...
"However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter."

So I'd restate my question to: What is the difference between a photon and electromagnetic radiation ? And does the latter exist at all ?

kith
If you have a single photon, the classical electromagnetic field can be seen as roughly analoguous to the wavefunction ψ(x) of the electron: it gives you the probability to detect the photon at a certain position (however, this should be taken with a grain of salt because of some mathematical difficulties).

In many situations, you don't need the photon picture at all. For typical light sources like a laser or a gas at a certain temperature, the so-called "semiclassical" approach is used. There, matter is described by quantum mechanics and light by classical electrodynamics and wave optics.

Only special situations where we can track the emission of single photons force us to use quantum optics. Examples are entanglement and photon-antibunching, where we cannot explain the statistical distributions of photon detection events by classical theories.

Nugatory
Mentor
Well, I guess I've found an answer in wiki...
"However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter."

So I'd restate my question to: What is the difference between a photon and electromagnetic radiation ? And does the latter exist at all?
That wiki quote isn't exactly wrong (a single photon doesn't spread out, and it doesn't divide into two when it encounters a beam splitter) but it is very misleading.

The right way to really understand the relationship between photons and electromagnetic radiation is to learn QED (after you've learned basic QM). But if you're just after an intuitive picture, try this:

Electromagnetic radiation always behaves like a wave, spreading out as it propagates, going two directions at beam splitters, bending when it's refracted, and generally acting like a solution to the electromagnetic wave equations from Maxwell.... With one exception.

That one exception is that when EM radiation is absorbed by matter, the energy it carries is deposited at single points, and the location of these points is more or less random within the area illuminated by the radiation. We call the lump of energy deposited at each point a "photon". In this picture, it doesn't make a lot of sense to talk about what the photon is doing before it's detected at a single point.

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Thanks for the replies.
Could you name experiments in which we can actually observe the photon nature of EM radiation (the more the better ? i know the photo-electric effect and the change of electron orbitals in atoms. Can you name a few others in which a wave-like behaviour cannot account for the observation ?

Nugatory
Mentor
Thanks for the replies.
Could you name experiments in which we can actually observe the photon nature of EM radiation (the more the better ? i know the photo-electric effect and the change of electron orbitals in atoms. Can you name a few others in which a wave-like behaviour cannot account for the observation ?
The photoelectric effect is, of course, behind my answer above.

Beyond that, the interference patterns built up a single spot at a time when the double-slit experiment is run at very low intensities are very convincing.

There's also Compton scattering, the observation that pair production appears to happen at a point, and plenty more that other posters wll be able to add.

regarding the single spot on the screen experiment i'd have some questions (even without the double slit).
imagine you have a device which is able to emit single photons. The possible direction of each photon is within a certain angle, so many of these would assemble a "light-cone".
Now I put a photon-detector-screen at a certain distance in this "cone" and since we're emitting only single photons, a single spot should randomly show up on the detector-screen. My question regarding this setup are:
(1) Is every emitted photon being detected (in a random location on the detector-screen) ?
(2) Is it at all possible to know if we have emitted a photon without it being detected at the screen (otherwise (1) would be a self-fulfilling prophecy) ?
(3) Does the distance of the detector-screen to the photon-source make a difference in the number of detected photons (in relation to the actually emitted ones) ?

Nugatory
Mentor
regarding the single spot on the screen experiment i'd have some questions....

The mental model of a single source firing photons like little bullets on a specific trajectory is just plain bogus (and that's why the wiki quote you found is so misleading even if it's not false - it tempts you into thinking of photons as little bullets following paths through space).

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Okay, so let's restate: If we dim down the light-source enough such that only a single spot appears on the film at any given moment. Now we could count how many spots per second appear on the screen. Now I vary the distance of the screen to the emitter. Does the number of detected spots per second change (assuming the detector-screen is always completely covering the lightcone of course) ?

Nugatory
Mentor
Okay, so let's restate: If we dim down the light-source enough such that only a single spot appears on the film at any given moment. Now we could count how many spots per second appear on the screen. Now I vary the distance of the screen to the emitter. Does the number of detected spots per second change (assuming the detector-screen is always completely covering the lightcone of course) ?
No, but the average distance between them increases, so the number of spots per square centimeter goes down.

No, but the average distance between them increases, so the number of spots per square centimeter goes down.
okay, that makes sense. thank you very much :)

Cthugha
Could you name experiments in which we can actually observe the photon nature of EM radiation (the more the better ? i know the photo-electric effect and the change of electron orbitals in atoms. Can you name a few others in which a wave-like behaviour cannot account for the observation ?

Create a single photon state and direct it towards a 50/50 beam splitter. Place a detector at each output port of the beam splitter. You will notice that each detector will fire from time to time, but the two detectors will never fire simultaneously. This cannot be explained using wave-like behaviour. However, it works only for "true" single photons, not for light sources which just have a mean photon number of less than 1.

However, it works only for "true" single photons, not for light sources which just have a mean photon number of less than 1.
Hmm, but are single photons now bogus or not ? How would you create "true" single photons ? I'm confused... :/

Cthugha
Single photons do exist, but "single" just tells you about the photon number. There is exactly one excitation present. That does not mean it will behave like a tiny bullet.

One way to create a "true" single photon is simply by using a single atom. Get it to the excited state and it will emit a photon. As it is now in the ground state, it cannot emit a second photon for some time as you have to get it to the excited state again before you can do so.

It is just important to stress again that this photon is not a tiny bullet. You start with an atom in the excited state and you end up with a photon getting detected somewhere. You do not know much about what happens in between. Most importantly, usually you cannot figure out a clear cut time when a photon is emitted or things like that.

WannabeNewton
Hmm, but are single photons now bogus or not ? How would you create "true" single photons ? I'm confused... :/
Do you know the formalism of the quantum harmonic oscillator?

vanhees71