An electron and a positron can annihilate, producing a pair of photons. Or two photons can annihilate, producing an electron and a positron. Or...
Well, in fact the symmetry works for any rotation, not just 180 degrees. An electron and a photon can "annihilate", producing an electron* and a photon going the other way. This is also known as "A photon bouncing off a mirror".
*: The careful reader will note there's no positron in this one. That's because positrons are what happen when an electron hits a photon so hard it bounces backwards in time -- that is, it's an electron going backwards in time. For one definition of 'time', at least.
To make the mirror version work, the photon needs to have lower energy than would be involved with matter annihilation. Otherwise your gamma-ray photon will tear through the mirror instead of bouncing back, probably making a nice hole. This doesn't mean the rotation doesn't work, it's just that what I was describing wasn't really a "mirror" as commonly considered. But also, because momentum (or, more usefully, rapidity) is defined in terms of the angle the particle makes with time, rotations other than 180 degrees don't conserve momentum. So it's not a gamma-ray photon anymore.**
**: Photons, obviously, have a fixed 'angle with relation to time'. You can take that as referring to the angle their waves make with time, instead.
An electron and a positron can annihilate, producing a pair of photons. Or two photons can annihilate, producing an electron and a positron. Or...
Well, in fact the symmetry works for any rotation, not just 180 degrees. An electron and a photon can "annihilate", producing an electron* and a photon going the other way. This is also known as "A photon bouncing off a mirror".
*: The careful reader will note there's no positron in this one. That's because positrons are what happen when an electron hits a photon so hard it bounces backwards in time -- that is, it's an electron going backwards in time. For one definition of 'time', at least.
To make the mirror version work, the photon needs to have lower energy than would be involved with matter annihilation. Otherwise your gamma-ray photon will tear through the mirror instead of bouncing back, probably making a nice hole. This doesn't mean the rotation doesn't work, it's just that what I was describing wasn't really a "mirror" as commonly considered. But also, because momentum (or, more usefully, rapidity) is defined in terms of the angle the particle makes with time, rotations other than 180 degrees don't conserve momentum. So it's not a gamma-ray photon anymore.**
**: Photons, obviously, have a fixed 'angle with relation to time'. You can take that as referring to the angle their waves make with time, instead.