ABSTRACT
According to classical physics (i.e., physics prior to the 20th century), particles and waves are
distinct classes of physical entities that possess markedly different properties. For instance, particles
are discrete, which means that they cannot be arbitrarily divided. In other words, it makes sense to
talk about one electron, or two electrons, but not about a third of an electron. Waves, on the other
hand, are continuous, which means that they can be arbitrarily divided. In other words, given a wave
whose amplitude has a certain value, it makes sense to talk about a similar wave whose amplitude
is one third, or any other fraction whatsoever, of this value. Particles are also highly localized in
space. For example, atomic nuclei have very small radii of order 10−15 m, whereas electrons act like point particles (i.e., they have no discernible spatial extent). Waves, on the other hand, are non-
localized in space. In fact, a wave is defined as a disturbance that is periodic in space, with some
finite periodicity length (i.e., wavelength). Hence, it is fairly meaningless to talk about a disturbance
being a wave unless it extends over a region of space that is at least a few wavelengths in size.
