Charge conservation

In physics, charge conservation is a fundamental principle of an experimental nature. It states that the total electric charge in an isolated system never changes. This principle acts as a universal accounting system for electricity. The net quantity of charge is the amount of positive charge minus the negative charge. In our universe, this net quantity is always conserved. This means that while charges move, the total balance remains constant. Most evidence suggests the net charge of the entire universe is zero. This implies there are equal quantities of positive and negative charges everywhere.

To understand how this works, we look at the continuity equation. This equation describes the relationship between charge in a region and its flow. If you look at a specific volume of space, the charge can change in only one way. The change in charge is equal to the amount flowing into the volume minus the amount flowing out. This process involves charge density, which is the amount of charge in a space. It also involves current density, which is the flow of that charge. If the system reaches a steady state, the amount of charge flowing in equals the amount flowing out. In this state, the total charge inside the volume remains unchanged.

It is important to note that individual charges can be created or destroyed. Subatomic particles, such as electrons and protons, carry these electric charges. In elementary particle reactions, these charged particles can appear or disappear. However, the law of conservation still holds during these reactions. If a reaction creates charged particles, it must create equal numbers of positive and negative particles. This ensures the net amount of charge stays exactly the same. Similarly, when particles are destroyed, they must be destroyed in pairs that balance the charge. This keeps the total balance of the universe perfectly steady.

Humanity has been studying this principle for many years. The idea of charge conservation was first proposed by the British scientist William Watson in 1746. Just one year later, in 1747, the American scientist and statesman Benjamin Franklin also proposed it. While these early ideas were important, they were not yet proven. The first convincing proof of the law was provided by Michael Faraday in 1843. Since then, all empirical observations have supported this rule without exception. Scientists continue to use these foundations to study the smallest parts of our world.

Scientists use incredibly precise measurements to test if charge conservation ever fails. One major test involves comparing the charge of a proton to an electron. The magnitude of these charges must be almost identical. They differ by no more than a factor of 10⁻²¹. If the charges were even slightly different, ordinary matter would be highly charged. Because like charges repel, all matter would push itself apart. Another test involves watching for an electron to decay into a neutrino and a single photon. This specific decay has a mean lifetime greater than 6.6 × 10²⁸ years. Such a massive number shows how rarely, if ever, the rule is broken.

In advanced physics, charge conservation is linked to a concept called gauge invariance. This is explained through a mathematical idea known as Noether's theorem. This theorem asserts that every conservation law is linked to a specific symmetry in nature. Charge conservation is associated with the global gauge invariance of the electromagnetic field. This means the physics of the field does not change if you shift the electrostatic potential. In quantum mechanics, this is related to the phase of a particle's wavefunction. Because changes in the overall phase are unobservable, the charge remains conserved. This deep connection provides a strong theoretical reason for why the law exists.

This principle also connects to other major areas of science and mathematics. In electromagnetic field theory, scientists use vector calculus to express the law. They use the divergence of the current density to show how charge moves through points. The law can also be derived as a consequence of Maxwell's equations. These equations are the foundation of how we understand electricity and magnetism. Furthermore, gauge invariance requires that the photon, a particle of light, must be massless. The fact that experimental evidence shows the photon has zero mass supports the idea that charge is conserved. This makes charge conservation a central pillar of our understanding of the physical universe.