charge conjugation (C)
/ see (the letter C) /
Imagine a magic button that swaps every particle for its antiparticle: every electron becomes a positron, every proton an antiproton, every quark an antiquark, while leaving everything else — positions, motions, spins — untouched. That swap is called charge conjugation, written with the letter C. It flips the sign of electric charge and of every other particle-versus-antiparticle label, turning a world made of matter into one made of antimatter.
C is a symmetry if the laws of physics behave exactly the same in the swapped world as in ours. For electromagnetism and the strong force, this is true to very high precision: an experiment built entirely of antimatter would obey the same rules of electricity and nuclear binding as the matter version. You can think of C as asking, 'if I rebuilt this whole process out of antiparticles, would it unfold the same way?' For most of physics the honest answer is yes.
But the weak force flagrantly breaks C symmetry, and this is one of the genuine surprises of twentieth-century physics. The weak force treats matter and antimatter differently — for instance, the neutrinos it produces always spin one way, while their antineutrino mirror-images spin the other way, so simply swapping particle for antiparticle does not give a process the weak force will allow. C is therefore not an exact law of nature. Physicists usually pair it with parity (the mirror flip) into the combined CP, which the weak force respects much more closely, though even CP is slightly violated — a clue that may be connected to why the universe contains matter at all.
A photon is its own antiparticle, so under charge conjugation it stays a photon — it is a C eigenstate; physicists say its eigenvalue is C = -1, meaning the photon's state picks up a minus sign under C (a C = +1 state would be the truly unchanged one). This single fact forbids a neutral pion, which has C = +1, from decaying into three photons more strongly than into two — C-symmetry of electromagnetism is built right into the prediction.
C-symmetry of electromagnetism dictates which photon decays are allowed.
C is not an exact symmetry of nature: the weak force violates it strongly. Only the combination CPT is believed to be exact, so do not assume swapping matter for antimatter always leaves physics unchanged.