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Q&A Why is it forbidden for two photons to turn into one?

Olin and Derek have covered the biggest part of this: the combination of energy and momentum conservation rules out the two-into-one combination of photons that are not co-linear. That might leave...

posted 6mo ago by dmckee‭

Answer
#1: Initial revision by user avatar dmckee‭ · 2024-05-16T02:23:51Z (6 months ago)
[Olin](https://physics.codidact.com/posts/288242/288245#answer-288245) and [Derek](https://physics.codidact.com/posts/288242/288244#answer-288244) have covered the biggest part of this: _the combination of energy and momentum conservation rules out the two-into-one combination of photons that are not co-linear_.

That might leave you optimistic about having a special case, but there is one more rule to respect: _conservation of angular momentum_.

Photons have angular momentum with magnitude $\hbar$ that is directed either parallel or anti-parallel to the linear momentum. As a result a system of two photons moving in the same direction have a total angular momentum along the direction of travel of $\pm 2\hbar$ or $0$ none of which are values that a single photons can take on. This rules out two-into-one combination of co-linear photons.

I suppose that leaves an even fainter glimmer of hope for three-into-one and higher (initially odd) combinations, but I have no idea what that would look like at tree level.

The other place to look for an escape hatch is that this discussion assumes free-space: in a medium new tricks become possible (and, indeed, frequency doubling media is a thing you can buy commercial off the shelf for some wavelengths).