Photon Divergence: Questions & Answers

[Rattus_norveg]

I've been told time and again that any beam of light (think laser) exhibits divergence no matter how perfect. This prompts three questions:

1) Theoretically, if a laser beam is emitted such that each photon is exactly parallel, (obviously more perfect than can be achieved in reality) does the beam still diverge?

2) Consider a single photon propagating through space. Does it still exhibit divergence?

3) Consider two coherent photons emitted exactly at the same time along exactly the same axis, do they exhibit divergence? If so, why?

[a note to those who will undoubtedly say the situation is impossible, and not worth considering: you're missing the point]

 

[pallidin]

Good questions.
Unlike charged particles(say, a stream of electrons), photons do not repel each other, so the photons divergence can not be associated with them repelling each other.

I heard once that two strictly parallel lines will eventually diverge. So, perhaps this phenomenon is related to space/time divergence. Not sure though.

 

[Dmitry67]

Claiming that 2 photons are EXACTLY parralel means that you know EXACTLY their momentum. Then, based on HUP, you can't know their position and the beam diverges!

If narrower the beam you make (you know the position), the faster it diverges (more uncertanity in momentum)

Only infinitely wide beam does not diverge.

 

[Rattus_norveg]

My interpretation of the HUP is that there is a fundamental uncertainty (with regards to position and momentum) that can be measured experimentally -- if one is measured the other is perturbed by the measurement, thus both cannot be known experimentally. However, this is not to say that a photon does not have position and momentum, only that we can't know them both by measurement. For example, imagine you're looking at someone across the street and then a bus pulls in front of you, occluding your view. Now you can no longer see the person but it is safe to say they still exist. Can you be certain of the person's position? No, because they could walk away and you wouldn't know, but they do in fact have position even if you don't know what it is.

 

[Dmitry67]

No, your interpretation (instrumental) is wrong.
This is not an issue how we measure these properties.
They just don't exist at the same time - mathematically.

 

[sheaf]

What about the single photon case ? If we look at the propagation amplitude in the path integral picture, then the most of the amplitudes cancel except for the classical path (straight line). Most, but perhaps not all ?

 

[Dmitry67]

Single photon will hit a single point. In that sense, it does not diverge
However, it can hit a point away from the axis of the beam. In that sense, it diverges.

 

[jostpuur]

It would be lot easier to discuss this topic, if the mainstream quantum literature actually had told us what kind of equation to use for the wave function of a photon

 

[Rattus_norveg]

I agree that a single photon can interact with a point away from the axis of travel. But isn't this because both the electric and magnetic field vectors have an amplitude (strongest perpendicular to the axis of travel) and therefor the photon has a certain minimum "width" in a sense. So if you could see the electric and magnetic fields, then sighting down the axis of travel would not reduce the photon to a single point.

 

[Dmitry67]

No, you can locate a photon of any wavelength in any arbitrary small region of space.
Talking about HUP you can't use Maxwell equations (talking about electric and magnetic fields etc), you should use QM instead. Maxwell equations are just approximations of QFT

 

[LostConjugate]

Single photon will hit a single point. In that sense, it does not diverge
However, it can hit a point away from the axis of the beam. In that sense, it diverges.

Seems more like your talking about the curl of the field here. The divergence of a field is the change in flux over the entire surface of a sphere, so the direction should not matter.

 

[glengarry]

It would be lot easier to discuss this topic, if the mainstream quantum literature actually had told us what kind of equation to use for the wave function of a photon

So then let's go back to the 19th century when they actually spoke intellegently about the nature of EM radiation! (Seriously... I'm not being sarcastic.)

 

[LostConjugate]

So then let's go back to the 19th century when they actually spoke intellegently about the nature of EM radiation! (Seriously... I'm not being sarcastic.)

as opposed to uncertainly certain measurements where continuation requires an infinite dimensional space, and every value is an expectation in a world where not everything commutes?

 

[Antiphon]

(single even) Photons don't travel in strait lines. They obey Maxwells equations which means they diverge.

edit: Actually, I'll qualify this as follows: you can create a photon that moves in strait line using an infinitly large current plane to launch it. Any finite sized source of the photon will create a quantum (whose probability of detection) spreads out.

 

[glengarry]

as opposed to uncertainly certain measurements where continuation requires an infinite dimensional space, and every value is an expectation in a world where not everything commutes?

It's hard to fathom how we got to this point, all because of one seemingly harmless little h!

 

[jostpuur]

(single even) Photons don't travel in strait lines. They obey Maxwells equations which means they diverge.

Maxwell's equation describe classical electromagnetic fields only, not wave functions of photons.

 

[Antiphon]

Maxwell's equation describe classical electromagnetic fields only, not wave functions of photons.

It would give correct results to interpret the square of the electromagnetic field as being prportional to the probability of finding a photon there. That makes Maxwell's eqations work as an effective wavefunction for describing the motion of individual photons.

 

[sheaf]

There is some discussion on using E+iB as a single photon wave function http://www.uoregon.edu/~oco/Group_Pages/Raymer/Tutorials/TTRL5_V1.pdf"