An electron passes through two parallel slits in a barrier and lands on a detector screen behind it. When both slits are open, the electron lands in a striped interference pattern — as if it went through both slits simultaneously. When you place a detector at one slit to watch which one the electron uses, the interference pattern disappears. The act of observing the electron changes where it lands. This is quantum mechanics, and the mathematics behind it is a fundamentally different kind of probability.
Classical Probability vs. Quantum Probability
In classical probability, things have definite states. A coin is either heads or tails — we might not know which, but it is one. Quantum particles are different. Before measurement, an electron genuinely has no definite position, spin, or energy. It exists in a superposition — a combination of multiple possible states simultaneously. The mathematics that describes this isn't the ordinary probability you know. It uses something called probability amplitudes.
The crucial difference: classical probability adds probabilities. Quantum mechanics adds amplitudes — which can be negative or complex numbers. When you square amplitudes to get probabilities, the cross terms can cancel (destructive interference) or reinforce (constructive interference). This is why quantum probability produces interference patterns that ordinary probability never could.
The Two-Slit Experiment Explained
An electron heading toward two slits has two possible paths: through slit 1, or through slit 2. In quantum mechanics, its amplitude is the sum of the amplitude for path 1 and the amplitude for path 2. These two amplitudes can interfere — adding where the paths are in sync, canceling where they're out of sync. The result at the detector screen: bright stripes (constructive interference) alternating with dark stripes (destructive cancellation). The interference pattern comes directly from adding amplitudes before squaring.
When you place a detector at one slit to watch which path the electron takes, the measurement forces the electron to "choose" — it can no longer be in superposition. Now only one amplitude contributes, and there's nothing to interfere with. The pattern disappears, replaced by two simple bright spots behind each slit. Observing the path destroys the superposition.
Schrödinger's Equation
The quantum state evolves over time according to Schrödinger's equation — the quantum equivalent of Newton's laws of motion. It describes how the superposition of possibilities changes moment to moment, wave-like, until a measurement collapses it to a definite value. Between measurements, the quantum state spreads and interferes like a wave. At measurement, it suddenly becomes a particle at a specific location. This wave-particle duality is not a paradox — it's what the mathematics predicts, and experiments confirm it with extraordinary precision.
Other Applications
Quantum probability underlies modern technology more than most people realize. MRI machines work because hydrogen nuclei in your body exist in quantum spin superpositions that can be manipulated and measured to map tissue density. Lasers work because quantum superposition allows atoms to emit light coherently. Quantum computers — currently in early development — exploit superposition to process multiple possible answers simultaneously, potentially solving certain problems exponentially faster than classical computers. Every transistor in your phone operates on quantum tunneling, another consequence of quantum probability.
Conclusion
Quantum probability differs from ordinary probability in one essential way: it uses amplitudes — numbers that can cancel — rather than probabilities, which can only add. This produces interference: possibilities can reinforce or cancel each other. The two-slit experiment is the starkest demonstration — electrons interfere with themselves when unobserved, but land in ordinary spots when watched. The mathematics is precise and experimentally perfect. The physical interpretation — that particles genuinely have no definite state before measurement — remains the strangest verified fact in science.