# Why is electric charge conserved?

We have long been taught that electric charges are neither created nor destroyed. But somehow it is okay to destroy two oppositely charged particles at once ! Why is that so?

Let's just take a look at electron-positron annihilation; Two equally oppositely charged particle are bombarded into each other, both are instantly destroyed (lose their existence) and gamma ray photons emerge. It is certainly convenient to say that at $t$ second the net charge in system was 0 and at $t+1$ second it is also zero. But certainly it also raises the question what if you observe only a positron or an electron, in observed system certainly charge will not be conserved however overall it maybe.

It jumps out and say that you cannot destroy individual charges, but if you get 2 equally and oppositely charged particles we can destroy both ! (kind of Romeo-Juliet) Then why is the fundamental postulate of conservation of charge that /charge can neither be created nor destroyed"? Since, clearly it can be destroyed, just in pairs (also created in pairs)

• Possible duplicates: physics.stackexchange.com/q/2721/2451 and links therein. – Qmechanic Feb 9 '14 at 23:03
• what if you observe only a positron or an electron, in observed system certainly charge will not be conserved electric charge is locally conserved too. – jinawee Feb 9 '14 at 23:12
• @jinawee : please expand on your comment, I seem to be getting entangled in the wordings of it. Are you saying that locally charge is not conserved ? Please elaborate and explain your comment. – Rijul Gupta Feb 10 '14 at 0:18
• I'm just saying that charge is locally conserved. – jinawee Feb 10 '14 at 10:23

We have long been taught that electric charges are neither created nor destroyed.

No, we have not been taught that. We've been taught that electric charge, i.e., the net electric charge, is conserved.

Imagine that, within some volume there is some net electric charge Q. Assuming there is no current through the boundary of the volume, we are taught that the net electric charge within the volume will always be Q. This comes from the continuity equation

$$\frac{\partial \rho}{\partial t} + \nabla \cdot \vec J = 0$$

which express the conservation of electric charge.

Now, the fact that Q does not change with time does not imply that pairs of oppositely charged particles cannot be created or destroyed.

For example, assume $Q = 0$. This means that the number of positively charged particles must equal the number of negatively charge particles at all times. But this does not mean that the number of charged particles within the volume must be constant.

• Might be worth mentioning to the OP to imagine electron-positron pair production by energetic enough "light". – WetSavannaAnimal Feb 10 '14 at 4:20
• @Alfred Centauri: Is it not the other way around: experimentally, net charge is conserved, and the continuity equation applies, rather than the continuity equation implying charge conservation? – ZeroTheHero Jan 21 '17 at 16:31

When opposite charges annihilate, all conservation laws must be obeyed. 1 + -1 = 0, before and after for charge. If it is an electron squeezing into a proton to make a neutron, an electron neutrino is emitted and all conservation laws are obeyed. Following are symmetries and their associated conserved quantities via Noether's theorems. The universe does not cheat (except for discrete symmetries. Noether can leak through a loophole).

Invariance                  Conserved Quantity
Proper orthochronous Lorentz symmetries
translation in time (homogeneity)   energy
translation in space(homogeneity)   linear momentum
rotation in space   (isotropy)      angular momentum
Discrete symmetry
P, coordinates' inversion   spatial parity
C, charge conjugation       charge parity
T, time reversal            time parity
CPT                         product of parities (100% conserved)
Internal symmetries (independent of spacetime coordinates)
U(1) gauge transformation   electric charge
U(1) gauge transformation   lepton generation number
U(1) gauge transformation   hypercharge
U(1)Y gauge transformation  weak hypercharge
U(2) [or U(1)xSU(2)]        electroweak force
SU(2) gauge transformation  isospin
SU(2)L gauge transformation weak isospin
PxSU(2)                     G-parity
SU(3) "winding number"      baryon number
SU(3) gauge transformation  quark color
SU(3) (approximate)         quark flavor
S((U2)xU(3))
[or U(1)xSU(2)xSU(3)]       Standard Model