Lies in education [was Re: The "loop and a half"]

[Steve D'Aprano]

On Thu, 5 Oct 2017 03:54 pm, Stefan Ram wrote:

> Steve D'Aprano <steve+python at pearwood.info> writes:
>>In actual annihilation events, there is (as far as I know)
>>generally a single real photon produced
> 
>       »There are only a very limited set of possibilities for
>       the final state. The most probable is the creation of
>       two or more gamma ray photons«
> 
> en.wikipedia.org/wiki/Electron%E2%80%93positron_annihilation.
> 
>   "two or more"

Ah, that makes sense: as you say:


>   (Conservation of momentum requires that two particles whose
>   center of gravity is at rest cannot annihilate to a single
>   photon with a non-zero momentum.)

Of course it can't. In hindsight it is obvious.

But that demonstrates exactly the sort of thing I'm talking about. I'm not an
expert at quantum mechanics. I've seen (or at least, I remember seeing)
diagrams of matter/antimatter annihilation with the two particles coming
together and a single photon coming out: a simplified and strictly wrong view
of the physics.

e+
  \
   \ /-\   /-\
   /    \-/   \-/
  /
e-


It turns out that's half the Feynman diagram for Bhabha scattering, not
annihilation. I cannot say for sure whether I have ever been explicitly
taught (in a book, say) that there is one photon, but I'm sure I've seen
equations like:

e+ + e-  ->  γ


Writing the equation as:

e+ + e-  ->  2γ

would be equally wrong, since there may not be two photons -- that's just the
most likely case.

So thank you, today I learned something.




-- 
Steve
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.