Can Low E photons combine into High E photons by themselves

[Albertgauss]

This post is not related to my E=mc^2 post but is a follow-up on the thread: photon collision by misnoma. The following questions were not addressed in that post but I wanted to ask anyway since that thread is now locked. This is better a high energy question anyway.

A) Is it possible for two photons to merge into a single photon of higher frequency all by themselves without help from at atom, nuclei, vacuum, particle of mass m?

B) Can a high energy photon ever be split into two lower energy photons?

Specifically: Is this reaction possible with only the interaction of the photons: hf1 + hf2 = hfT where the resulting photon has the combined energy of the two previous photons that combined to form it? Would the reverse reaction occur

I looked up the following articles mentioned on this website from the previous thread:

http://www.hep.ucl.ac.uk/opal/gammag...-tutorial.html

http://2physics.blogspot.com/2006/03...cattering.html

The former link is confusing and seems to involve particles of mass. The second link requires a vacuum. I also looked up Delbrück scattering, but you need an atomic nuclei to be involved. Compton also needs an atom. Quantum transitions involves energy levels of electrons.

If the probability for such an event is non-zero in any higher order correction, does anyone know where I can find that information?

If the answer to my questions are "No", that photons can't merge into photons or separate into lower energy photons without help, would I be right in saying that I would therefore absolutely need an atom, nuclei, particle, or vacuum in order for photons to merge or separate into other photons?

 

[kurros]

The answer is indeed "no", and I struggled for a while with exactly why that was, since it appears not to violate conservation of energy like in the massive case, so long as the ingoing/outgoing photons are all exactly co-linear. There is a fairly long thread about it here https://www.physicsforums.com/showthread.php?t=512811.

Turns out to not be very straightforward. In any case, it is not observed experimentally.

And yes, in isolation photons cannot do these things, but all bets are off when other particles are involved.

 

[someGorilla]

No. Just notice that total momentum is not conserved in your scenario.
But you can have TWO particles created, even two photons - see photon-photon scattering.

 

[Bill_K]

a) It violates energy-momentum conservation unless the photons are collinear, and b) It violates conservation of charge parity, since a photon is odd under charge conjugation, C = -1. As someGorilla says, in principle you can have photon-photon scattering where four photons are involved.

 

[someGorilla]

But now I'm wondering whether two "coincident" photons on the same path could produce one with double frequency. Sounds strange but is there anything to prevent it? My knowledge of QM is about zero.
Actually if we had a beam of photons and some of them combined to double-frequency photons we should be able to measure a half-life, which is paradoxical. So the answer must be no.
But comments are welcome!

 

[someGorilla]

Good link kurros!

here https://www.physicsforums.com/showthread.php?t=512811

 

[mfb]

But now I'm wondering whether two "coincident" photons on the same path could produce one with double frequency. Sounds strange but is there anything to prevent it? My knowledge of QM is about zero.

No, it would violate charge partity, as mentioned by Bill_K.
3 photons... might be possible, if you get perfect alignment. But that would require some correlated production, I think. And even then, I doubt that it actually happens. The cosmic microwave background should give some upper limits on "photon splitting", which is the time-reversed process.

 

[someGorilla]

3 photons... might be possible, if you get perfect alignment.

Still I think the impossibility to define a half life rules it out.

 

[Haelfix]

The two photon case is ruled out by conservation of energy momentum and angular momentum.

The three photon and n photon case is ruled out by computation of the amplitude, where it can be seen that it vanishes due to the kinematics. See the paper and discussion in the previous thread.. Especially fzeros posts.

The paper generalizes the discussion to all cases, eg photon, scalar and graviton splitting.

 

[Vanadium 50]

Three photons (actually, any odd number) is not allowed by Furry's Theorem. Four photons (actually, any even number) is not allowed by charge conjugation, as Bill K said. If it can't be even and it can't be odd, we're done here.

 

[kurros]

Aren't those essentially the same thing? i.e. I think furry's theorem forbids diagrams with odd external photon lines, i.e. *even* incoming lines if there is one outgoing. But yeah the amplitudes vanish due to the kinematics nonetheless.

 

[Haelfix]

Essentially yes (and there are other ways to see that the n odd case vanishes). Furry's theorem however doesn't seem to generalize as its only applicable to QED proper and is thus less powerful than the Ward identity analysis done in that paper (where you can see scalar and spin 2 splitting is also forbidden).

Whats actually rather interesting about Furry's theorem imo, is that you don't really need to use the gauge structure of QED in order to show the amplitude vanishes. It essentially follows from Lorentz invariance and the structure of Feynman diagrams.