1

I know that in free space, photon cannot decay into an electron and a positron since momentum is frame dependent for massive particles while invariant for a photon.

Given this, how is spontaneous pair creation and annihilation possible? Can someone shed some light on it? Or is it that it is actually impossible, and that I had a wrong comprehension?

Thomas Fritsch
  • 39,317
Nugi
  • 541
  • This is impossible. Such a process never happens. – knzhou Oct 21 '19 at 22:31
  • 1
    Most references that explain the why it can't happen in free space make at least a passing mention of the loophole that explains why it pair-production processes are observed. Is the problem that you haven't seen such an explnation or that you don't understand why it solves the issue? – dmckee --- ex-moderator kitten Oct 21 '19 at 22:36

1 Answers1

3

Pair creation

You are right: In free space a photon cannot decay into an electron-positron pair (because it would violate energy/momentum conservation).

However, near an atomic nucleus a photon can decay into an electron-positron pair. In this process the atomic nucleus receives some recoil.

See also Wikipedia: Pair production.

The process can be visualized by a Feynman diagram like below.
Feynman diagram of pair production
image from Wikipedia: Pair production

Pair annihilation

You are also right, that an electron-positron pair in free space cannot decay into a photon (again because it would violate energy/momentum conservation).

However, an electron-positron pair can decay into two photons. The two gamma ray photons depart in roughly opposite directions.

See also Wikipedia: Electron–positron annihilation.

The process can be visualized by the Feynman diagram below.
Feynman diagram of pair annihilation
image from Feynman diagram for annihilation

Thomas Fritsch
  • 39,317
  • 1
    Isn't it also possible, although rare, for photons to "collide" and generate a pair; i.e., your pair annihilation diagram run backward? – TimWescott Oct 21 '19 at 23:19
  • @TimWescott Might be possible, but I don't know enough QED to be sure. – Thomas Fritsch Oct 21 '19 at 23:26
  • That said there is nothing wrong with a pair combining into an on-shell photon in the precense of a spectator (the time reversal of your upper process), it just has a very small cross-section. – dmckee --- ex-moderator kitten Oct 21 '19 at 23:39
  • Also in the upper diagram, the virtual photon interacting with the electron line, could be a virtual graviton , explaining where the energy comes from, to make the vertex real in the Hawking radiation. – anna v Oct 22 '19 at 04:16