How did they come into existence from a photon? Is it really understood how the process works? Is there even a process or is it just something fundamental?
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It is understood how the process works. In a nutshell, the energy of a photon is converted to the mass of an electron and positron as is given by Einstein's $E = mc^2$. This is spelled out as follows:
$γ → e^− + e^+$
There are two musts for this:
- The photon must have a higher energy than the sum of the rest mass energies of a positron and electron for this to happen ($2 * 0.511 MeV = 1.022 MeV$).
- The photon must be near a nucleus in order to satisfy conservation of energy and momentum.
The basic properties, energy transfer, and cross section can be specifically calculated. So, yes, I'd say the mathematics and process are fairly well defined.
More information can be found here.
Hope this helps!
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