# Waveparticle duality

In physics, wave-particle duality holds that light and matter can exhibit properties of both waves and of particles. It is a central concept of quantum mechanics.

In the usual formulations of classical mechanics a given object is either a particle or a wave. For example, an electron is a particle (because they are observed to behave in particle-like ways), and light is a wave (because it behaves in wave-like ways, such as interference: see below). This categorisation was applied even to objects below the scale of direct observation, essentially by analogy with macroscopic phenomena.

However, problems emerge with the viewpoint in that electrons too can be made to interfere and thus appear wave-like. Light (especially in the photoelectric effect, as analysed in 1905 by Albert Einstein) can possess particle-like properties. Quantum mechanics emphasises the primacy of measurement and not attributing to objects properties that cannot be measured. Hence the concept of wave-particle duality arose. It is not necessary, or useful, to say that an electron is a particle - or a wave - just that in certain circumstances it behaves like a wave, and in others like a particle.

## Duality of light

It can be shown that light has a wave nature, due to wave characteristics such as frequency and wavelength, which relate to the color of light. It can also be shown that light has a particle nature, since an individual light particle (photon) can be detected experimentally. Thus, light exhibits wave-particle duality.

## Theories of light

The earliest comprehensive theory of light was advanced by Christiaan Huygens, who proposed a wave theory of light, and in particular demonstrated how waves might interfere to form a wave-front, propagating in a straight line. However, the theory had difficulties in other matters, and was soon overshadowed by Isaac Newton's corpuscular theory of light. That is, Newton proposed that light consisted of small particles, with which he could easily explain the phenomenon of reflection. With considerably more difficulty, he could also explain refraction through a lens, and the splitting of sunlight into a rainbow by a prism.

Because of Newton's immense intellectual stature, his theory went essentially unchallenged for over a century, with Huygens' theories all but forgotten. With the discovery of diffraction in the 19th century, the wave theory was revived, and so by the advent of the 20th century, a scientific debate over waves vs. particles had already been thriving for a very long time.

## Fresnel, Maxwell, and Young

In the early 1800s, the double-slit experiments by Young and Fresnel provided evidence for Huygens' theories: these experiments showed that when light is sent through a grid, a characteristic interference pattern is observed, very similar to the pattern resulting from the interference of water waves; the wavelength of light can be computed from such patterns. Maxwell, during the late-1800s, explained light as the propagation of electromagnetic waves with the Maxwell equations. These equations were verified by experiment, and Huygens' view became widely accepted.

## Einstein and photons

In 1905, Einstein reconciled Huygens' view with that of Newton; he explained the photoelectric effect (an effect in which light did not seem to act as a wave) by postulating the existence of photons, quanta of energy with particulate qualities. Einstein postulated that light's frequency, ν, is related to the energy, E, of its photons:

$\displaystyle E = h \nu \,$

where h is Planck's constant (6.626 x 10-34 J seconds).

## De Broglie

In 1924, de Broglie claimed that all matter has a wave-like nature; he related wavelength, λ (lambda), and momentum, p:

$\displaystyle \lambda = \frac{h}{p}$

This is a generalization of Einstein's equation above since the momentum of a photon is given by p = E / c where c is the speed of light in vacuum, and λ = c / ν.

De Broglie's formula was confirmed three years later for electrons (which have a rest-mass) by two independent experiments. At the University of Aberdeen George Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted interference patterns. At Bell Labs Clinton Joseph Davisson and Lester Halbert Germer guided their beam through a crystalline grid. Thomson and Davisson shared the Nobel Prize for Physics in 1937 for their work.

Similar experiments have since been conducted with neutrons and protons. Authors of similar recent experiments with atoms and molecules claim that these larger particles also act like waves. The most famous experiments are those of Estermann and Otto Stern in 1929, and the diffraction of fullerene C60 by researchers from the University of Vienna Template:Fn in 1999; in the later case, the wavelength of de Broglie is 2.5 pm whereas the diameter of the molecule is about 1 nm, i.e. about 400 times larger.

This is still a controversial subject because these experimenters have assumed arguments of wave-particle duality and have assumed the validity of deBroglie's equation in their argument.

The Planck constant h is extremely small and that explains why we don't perceive a wave-like quality of everyday objects: their wavelengths are exceedingly small. The fact that matter can have very short wavelengths is exploited in electron microscopy.

In quantum mechanics, the wave-particle duality is explained as follows: every system and particle is described by state functions which encode the probability distributions of all measurable variables. The position of the particle is one such variable. Before an observation is made the position of the particle is described in terms of probability waves which can interfere with each other.

In quantum electrodynamics, Richard Feynman shows the wave-particle duality of photons and electrons is an illusion. In his view, photons and electrons obey rules that share some qualities of both particles and waves. They are neither particle nor wave, but some generalized object with no direct macroscopic analog.

## The 'double-slit' experiment

An intriguingly simple and well reported experiment, the double-slit experiment, summarizes the duality. An electron gun is pointed at a screen with two slits and the positions of detection of the electrons recorded by a detector behind the screen. An interference pattern just like the one produced by diffraction of a light or water will be observed on the screen.

This pattern will even appear if the electron source is slowed down so that only one electron's worth of charge per second comes through. In the classical sense, every electron is a point particle and must either travel through the first or through the second slit. The same interference pattern should appear if the experiment lasts twice as long, but closing one slit for the first half, then closing the other slit for the second half of the experiment. However, it is found that the same pattern does not emerge. Furthermore, if detectors are placed around the slits in order to determine which path a particular electron takes, this very measurement destroys the interference pattern. This result shows that something much more profound is taking place.

The interference pattern can be explained as a result of the charge wave being diffracted by both slits and interfering with itself. In quantum mechanics, the state function is a complex-valued function of space and time. The square of the magnitude of this function describes the probability of finding the electron at a given location at a given time. Interference is due to the fact that the square of the magnitude of the sum of two complex numbers may be different from the sum of the squares of their magnitudes.

The experiment also illustrates an interesting feature of quantum mechanics. Until an observation is made the position of a particle is described in terms of probability waves, but after the particle is observed, it is described as a fixed value. How to conceptualize the process of measurement is one of the great unresolved questions of quantum mechanics. The standard interpretation is the Copenhagen interpretation which leads to interesting thought experiments such as Schrödinger's cat. Owing to this confusion, some theorists (including Stephen Hawking and Murray Gell-Mann) believe that the many-worlds interpretation is true. However, there is currently some doubt over the validity of both the Copenhagen interpretation and the many-worlds interpretation, due to the controversial Shahriar Afshar's experiment [1], a variation of the two-pin-hole "which way" experiment.

Notes

Template:Fnb Wave-particle duality of C60, M. Arndt , O. Nairz, J. Voss-Andreae, C. Keller, G. van der Zouw, A. Zeilinger, Nature 401, 680-682, 14 October 1999