superposition principle

superposition principle [‚sü·pər·pə′zish·ən ′prin·sə·pəl]

(electricity)

principle of superposition

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Superposition principle

The principle, obeyed by many equations describing physical phenomena, that a linear combination of the solutions of the equation is also a solution.

An effect is proportional to a cause in a variety of phenomena encountered at the level of fundamental physical laws as well as in practical applications. When this is true, equations which describe such a phenomenon are known as linear, and their solutions obey the superposition principle. Thus, when f, g, h, · · ·, solve the linear equation, then s, where α, β, γ, · · ·, are coefficients) also satisfies the same equation.

For example, an electric field is proportional to the charge that generates it. Consequently, an electric force caused by a collection of charges is given by a superposition—a vector sum—of the forces caused by the individual charges. The same is true for the magnetic field and its cause—electric currents. Each of these facts is connected with the linearity of Maxwell's equations, which describe electricity and magnetism. See Electric field, Maxwell's equations

The superposition principle is important both because it simplifies finding solutions to complicated linear problems (they can be decomposed into sums of solutions of simpler problems) and because many of the fundamental laws of physics are linear. Quantum mechanics is an especially important example of a fundamental theory in which the superposition principle is valid and of profound significance. This property has proved most useful in studying implications of quantum theory, but it is also a source of the key conundrum associated with its interpretation.

Its effects are best illustrated in the double-slit superposition experiment, in which the wave function representing a quantum object such as a photon or electron can propagate toward a detector plate through two openings (slits). As a consequence of the superposition principle, the wave will be a sum of two wave functions, each radiating from its respective slit. These two waves interfere with each other, creating a pattern of peaks and troughs, as would the waves propagating on the surface of water in an analogous experimental setting. However, while this pattern can be easily understood for the normal (for example, water or sound) waves resulting from the collective motion of vast numbers of atoms, it is harder to understand its origin in quantum mechanics, where the wave describes an individual quantum, which can be detected, as a single particle, in just one spot along the detector (for example, photographic) plate. The interference pattern will eventually emerge as a result of many such individual quanta, each of which apparently exhibits both wave (interference-pattern) and particle (one-by-one detection) characteristics. This ambivalent nature of quantum phenomena is known as the wave-particle duality. See Interference of waves, Quantum mechanics