Electron Positron annihilation Feynman Diagram

I am having some trouble understanding this fenyman diagram, it seems to indicate that the electron produces the positron, as the arrow of the positron is pointing from the electron.

Additionally the arrow is in directed downwards, implying that the particle is going backwards in time? Is this diagram wrong, or does the arrow mean something else, or does the positron go back in time?!?

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Ahrrgggg! Goofy cosmology convention for time and space! Real physicists know that time increases to the right, damnit! –  dmckee Nov 27 '11 at 19:37
don't listen to dmckee. Everyone knows that time is the queen of the dimensions and deserves the vertical slot (and the plus sign in the signature) ! –  twistor59 Nov 27 '11 at 19:43
Oh by the way, related question –  twistor59 Nov 27 '11 at 19:44
Fair enough, I have no idea about the conventions, I jet found this on Wikipedia and google, and got confused :) –  Jonathan. Nov 27 '11 at 19:45
@Jonathan: I tend to just look to see if the arrow on the line is pointing in the opposite direction to time flow, if yes, I assume it's a positron. –  twistor59 Nov 27 '11 at 20:53
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3 Answers

The first thing to notice, as pointed out in the comments, is that time increases going up. So if you are more familiar with viewing Feynman diagrams where time increases to the right, this problem is easily solved: just rotate the diagram by 90 degrees when you are interpreting it.

If the problem is that you're not all that familiar with matter lines in Feynman diagrams in general, here's the rule:

• If the arrow points in the direction of increasing time, it's a matter particle (in this case, an electron).
• If the arrow points in the direction of decreasing time, it's an antimatter particle (in this case, a positron).

That's it. The arrow on the line doesn't indicate the direction in which anything is actually moving.* It's simply a convention to show whether the particle is matter or antimatter.

This rule is convenient because, if the diagram is correctly drawn, you can trace along a lepton (or quark) line from one endpoint to another, always going with the arrows.

Note that sometimes you'll encounter an arrow which points in the spatial direction, perpendicular to the time axis, such as the horizontal line segment in the middle of this diagram. Don't take that segment too literally. It doesn't mean that the electron actually moves in a spacelike direction. It's just "code" for whatever (leading order) processes actually do occur in which the electron and positron annihilate with each other while emitting two photons in the process.

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*Actually, it does indicate the orientation of the current of the corresponding field, but for purposes of interpreting the diagram, I'd suggest you just consider that a technical detail of the QFT calculations and not worry about it.

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the arrow indicates the direction in which the proper-time for the particle is increasing, and it is perfectly correct to say that the positron is moving back in time. It doesn't lead to causality violations because causality is entropic and computational and only matters for doing stuff, and for this purpose, you can use a Hamiltonian formalism and not a proper-time particle formalism. –  Ron Maimon Nov 28 '11 at 2:47
Thanks David, if I were to turn the diagram sideways, would the arrow of the positron then need to be reversed? Also wouldn't that show one of the photons going back in time. –  Jonathan. Nov 28 '11 at 8:10
No. If you turn the diagram sideways, time would be increasing to the right, not up. That's why I said you should turn it sideways if you are used to seeing Feynman diagrams where time increases to the right. –  David Z Nov 28 '11 at 8:14
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The positron is the electron going back in time. This is what the arrow means. But you have to remember that in physics, cause and effect are not by the direction of the arrows, but by the direction of entropy increase, which is up in the diagram regardless of which way the particles go relative to their own proper time.

The idea that positrons are electrons going back in time is due to Ernest Stueckelberg, but it was misattributed to Feynman, who got it indirectly from Stueckelberg through Wheeler. The idea is correct, and it solves the problem of creating a relativistic particle formalism. But it requires that the particle trajectories are not causal, they either produce an S-matrix, or correlation functions. The notion of causality is only for a higher level description.

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If the positron were going back in time, it wouldn't be a positron :-P –  David Z Nov 28 '11 at 3:05
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It is more than curious that to preserve O(3,1) symmetry in the Maxwell equations both charge conjugation and time reversal must both occur. In that sense the Feynman diagram is not a mere visual aid, but accurately reflects the physics. Under normal conditions that implies that the positron is going backwards in time, BUT we must always remember that spacetime cannot be subjected to anthropomorphic visualisation in which man's universal time plays the chief role. There are 4 dimensions, but what is time and what is space are human conventions; Nature is ambivalent over what we call timelike and spacelike intervals (See Misner, Thorne, Wheeler, p. 409, Gravitation). Coordinates are the work of man, not Nature.

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