superpositioner

Superpositioner, or the principle of superposition, is a foundational idea in physics that states a system can be in a combination, or superposition, of multiple states at once. In classical physics, this applies most clearly to waves: the displacement of a vibrating string or the electromagnetic field can be described as the sum of individual wave solutions, and the resulting wave is the sum of those components. In quantum mechanics, the principle is extended to states of a quantum system, such as the energy levels or spin orientations, where a state is a linear combination of basis states.

A general quantum state is written as |ψ> = ∑i ci |i>, with complex coefficients ci called probability amplitudes. The probability of measuring outcome i is |ci|^2 (Born rule). The relative phases of the amplitudes determine interference patterns, so the superposition can produce effects not explainable by a statistical mixture.

Measurement collapses the state to one of the basis states with probabilities |ci|^2; subsequent evolution depends on the new state. The difference between a pure superposition and a statistical mixture is crucial: a superposition preserves coherence and can interfere, whereas a mixture arises from ignorance about the state and lacks coherence.

In practice, interactions with the environment quickly destroy coherence, yielding classical probabilities in macroscopic objects.

Notable examples include the double-slit experiment, quantum interference, and qubits in quantum computing, which rely on coherent superpositions of computational basis states. In optics, multiple light waves passing through a medium interfere according to superposition.

Despite its success, superposition is not easily observed in large systems due to decoherence and practical measurement constraints.