Law of Conservation of Electric Charge
Charge conservation states that in an isolated system, the total electric charge remains constant over time.
Electric charge is a fundamental physical quantity, conserved in every process known to particle physics.
In simple terms, the algebraic sum of all charges before and after an interaction is always the same.
The charge may be redistributed, but it can never be created or destroyed.
Worked example
In beta decay, a neutron transforms into a proton, an electron, and an electron antineutrino.
$n \rightarrow p^+ + e^- + \bar{\nu}_e$
The total charge is 0 both before (the neutron) and after the decay.
We can confirm this by recalling the charges of the particles involved:
- proton = +1
- electron = -1
- antineutrino = 0
If we replace each particle with its charge, the equation balances: $ 0 = 1-1+0 $.
$$n^{(0)} \rightarrow p^{(+1)} + e^{(-1)} + \bar{\nu}_e^{(0)} $$
Thus, electric charge is conserved in the transformation.
Charge conservation in fundamental interactions
Three fundamental interactions involve charged particles:
- Electromagnetic interaction
In QED (quantum electrodynamics), charged particles (such as electrons and quarks) interact by exchanging virtual photons. At every vertex of the interaction, charge is exactly conserved.Example. An electron emits a photon: $$e^- \rightarrow e^- + \gamma$$ The electron’s charge is -1 both before and after, while the photon is neutral. Once again, the charge balance is preserved.
- Strong interaction
In QCD (quantum chromodynamics), quarks exchange gluons to keep nucleons bound inside atoms. Gluons carry color charge but are electrically neutral, so they play no role in electric charge conservation. This ensures that in every QCD process, electric charge remains unchanged.Example. Inside a proton, consider an up quark (charge +2/3) and a down quark (charge -1/3). The up quark (u) emits a gluon (g), changing its color (say, from red to blue). $$
u_{red}^{(+2/3)} \rightarrow u_{blue}^{(+2/3)} + g_{red\bar{blue}} $$ The gluon is then absorbed by the down quark (d), which changes color (e.g., from blue to red). $$ d_{blue}^{(-1/3)} + g_{red\bar{blue}} \rightarrow d_{red}^{(-1/3)} $$ The total electric charge remains exactly the same: $$ (+2/3) + (-1/3) = (+2/3) + (-1/3) $$ The gluon exchange reshuffles color, but never electric charge. This is why QCD strictly obeys charge conservation in every interaction. - Weak interaction
This is the only interaction that can change the type of particle: a quark or lepton may transform into another. Even so, charge is always conserved, with W± bosons carrying or absorbing the required amount.Example. In beta decay, a down quark becomes an up quark. $$d \rightarrow u + W^-$$ The emitted W boson quickly decays into an electron $ e^- $ and an electron antineutrino $ \bar{\nu}_e $. $$W^- \rightarrow e^- + \bar{\nu}_e$$ Checking charges: the down quark has -1/3, the up quark +2/3, and the $W^-$ boson -1. $$ - \frac{1}{3} + \frac{2}{3} - 1 = -\frac{1}{3} $$ The sum is the same as at the start, so charge is conserved.
Example 2. Consider neutrino-induced scattering. An electron neutrino $\nu_e$ interacts with a neutron $n$, turning it into a proton $p$ and an electron $e^-$. $$\nu_e + n \rightarrow p + e^-$$ The initial total charge is zero (both neutrino and neutron are neutral). The final total charge is also zero: the proton has +1, the electron -1. $$\nu_e^{(0)} + n^{(0)} \rightarrow p^{(+1)} + e^{(-1)} $$ Once again, the accounting of charge works perfectly.
In short, in every known physical interaction, electric charge is conserved.
Even in the weak interaction - where particles can change identity - the balance is maintained thanks to the W± bosons.
No experimental violation of charge conservation has ever been observed. It remains one of the bedrock principles of modern physics.
Theoretical origin of charge conservation
The conservation of electric charge arises directly from a fundamental mathematical symmetry of nature.
Specifically, it follows from the local U(1) gauge symmetry of quantum electrodynamics (QED).
What are gauge symmetries? In theoretical physics, gauge symmetries are transformations that leave the laws of physics unchanged. For electromagnetism, the relevant symmetry is U(1), which corresponds to a phase shift of a particle’s wavefunction. Such a transformation leaves the electromagnetic interaction intact.
According to Noether’s theorem, every continuous symmetry corresponds to a conserved quantity. For U(1), that conserved quantity is electric charge.
Thus, as long as electromagnetic theory respects U(1) symmetry, charge can neither be created nor destroyed.
The photon, which mediates the force, is neutral and does not upset the charge balance. Even in broader frameworks such as the electroweak theory, U(1) symmetry persists, ensuring charge conservation.
Charge conservation is therefore not only an experimental fact but also a built-in consequence of the mathematical structure of fundamental physics.
And so on.
