Editing Wave–particle duality (section)

== Classical waves and particles ==
Before proceeding further, it is critical to introduce some definitions of waves and particles both in a classical sense and in quantum mechanics.  Waves and particles are two very different models for physical systems, each with an exceptionally large range of application. Classical waves obey the [[wave equation]]; they have continuous values at many points in space that vary with time; their spatial extent can vary with time due to [[diffraction]], and they display [[wave interference]]. Physical systems exhibiting wave behavior and described by the mathematics of wave equations include [[water waves]], [[seismic waves]], [[sound waves]], [[radio waves]], and more.

Classical particles obey [[classical mechanics]]; they have some [[center of mass]] and extent; they follow [[trajectories]] characterized by [[Position (geometry)|positions]] and [[velocities]] that vary over time; in the absence of [[forces]] their trajectories are straight lines. [[Stars]], [[planets]], [[spacecraft]], [[tennis balls]], [[bullets]], [[sand grain]]s: particle models work across a huge scale. Unlike waves, particles do not exhibit interference.

{{multiple image
| header            = Classical waves interfere. Particles follow trajectories.
| align             = center
| perrow            = 2
| total_width       = 500
| image_style       = border:none;
| image1            = Rippletanksource1plus2superpositionBnW.png
| alt1              = Wave interference in water due to two sources marked as red points on the left
| caption1          = [[Wave interference]] in water due to two sources marked as red points on the left.
| image2            = Inclinedthrow.gif|thumb|400px
| caption2          = Classical [[trajectories]] for a mass thrown at an angle of 70°, at different speeds.
| image3            = BachEtAl Interference.png
| caption3          = Line trace for a two-slit electron interference pattern. Compare to a slice through the image of the water wave pattern above.
| image4            = PositronDiscovery.png
| alt4              = Curved arc shows a cloud chamber trajectory of a positron.
| caption4          = Curved arc shows a [[cloud chamber]] trajectory of a [[positron]] acting like a particle.
| footer            = '''Both interference and trajectories are observed in quantum systems'''
}}
Some experiments on quantum systems show wave-like interference and diffraction; some experiments show particle-like collisions.

Quantum systems obey wave equations that predict particle probability distributions. These particles are associated with discrete values called [[quantum|quanta]] for properties such as [[Spin (physics)|spin]], [[electric charge]] and [[magnetic moment]]. These particles arrive one at time, randomly, but build up a pattern. The probability that experiments will measure particles at a point in space is the square of a complex-number valued wave. Experiments can be designed to exhibit diffraction and interference of the [[probability amplitude]].<ref name=Messiah/> Thus statistically large numbers of the random particle appearances can display wave-like properties. Similar equations govern collective excitations called [[quasiparticle]]s.