[particle physices] pair production not possible in absence of matter?

[nonequilibrium]

Homework Statement

"Prove that pair production is not possible in the absence of matter."

Homework Equations

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The Attempt at a Solution

First of all, I'll assume a photon is considered matter, cause two photons can create a pair.
Second: I thought pairs pop into and out of existence all the time, in the absence of matter (vacuum fluctuations). So I'll also assume they mean non-virtual pairs.

Okay: imagine a virtual pair popping into existence. If there isn't anything with energy/that can give off energy nearby (matter), nothing can pay for the virtual energy, thus the pair must annihilate.

That's my attempt... Maybe I'm missing the point? (it certainly feels like that)

Thank you.

 

[vela]

Yeah, you're missing the point. The question is asking you to explain why a single real photon of sufficient energy can't spontaneously decay (by itself) into, say, an electron-positron pair.

 

[nonequilibrium]

Huh? Okay I get that that is not possible (momentum and energy conservation), but can you please tell me how you got that that was the question? Why can we exclude two photons coming together to form a pair?

 

[vela]

I've heard it before, even phrased exactly like that. It's a pretty common homework question in particle physics courses.

You can't exclude the possibility of two photons interacting to produce a pair, but I'd guess that pair production more typically occurs when a single photon is in the vicinity of matter.

 

[nonequilibrium]

Oh... okay then, thanks a lot :)