probability amplitude

When you roll dice, you can simply add up chances: the probability of either of two outcomes is the sum of their separate probabilities. The quantum world plays a stranger game. To each possible way something can happen, it assigns not a probability directly but a more subtle quantity called a probability amplitude — and amplitudes do not just add like ordinary chances. They can reinforce each other or cancel out, like overlapping waves.

An amplitude is a number with both a size and a phase, much like a wave that has a height and a point in its cycle. The recipe for predicting what nature does has two steps. First, add the amplitudes for all the indistinguishable ways an event could occur. Second, square the size of that total to get the actual probability. The order matters enormously: adding first and squaring second lets the phases interfere. Two paths whose amplitudes are out of step subtract, so an outcome that each path alone would allow can become impossible when both are open. This is the mathematical heart of the double-slit pattern, where dark bands appear precisely where two amplitudes cancel.

Probability amplitude is the central currency of particle physics calculations. Every Feynman diagram is a recipe for one contribution to an amplitude; physicists add the amplitudes for all the ways a collision or decay can happen, then square the sum to predict how often it occurs (the cross-section or decay rate). Interference between these amplitudes is not an exotic curiosity but a routine, measurable effect that shapes scattering rates and underlies precision tests of the Standard Model. The key takeaway: in quantum physics you add amplitudes, then square; you never just add probabilities.