Wave Particle Duality in LightIn the 1600s, Christiaan Huygens and Isaac Newton proposed competing theories for light's behavior. Huygens proposed a wave theory of light while Newton's was a "corpuscular" (particle) theory of light. Huygens' theory had some issues in matching observation. Newton's prestige helped lend support to his theory, so for over a century his theory was dominant.
In the early nineteenth century, complications arose for the corpuscular theory of light. Diffraction had been observed, for one thing, which it had trouble adequately explaining. Thomas Young's double slit experiment resulted in obvious wave behavior and seemed to firmly support the wave theory of light over Newton's particle theory.
A wave generally has to propagate through a medium of some kind. The medium proposed by Huygens had been luminiferous aether (or in more common modern terminology, ether). When James Clerk Maxwell quantified a set of equations (called Maxwell's laws or Maxwell's equations) to explain electromagnetic radiation (including visible light) as the propagation of waves, he assumed just such an ether as the medium of propagation, and his predictions were consistent with experimental results.
The problem with the wave theory was that no such ether had ever been found. Not only that, but astronomical observations in stellar aberration by James Bradley in 1720 had indicated that ether would have to be stationary relative to a moving Earth. Throughout the 1800s, attempts were made to detect the ether or its movement directly, culminating in the famous Michelson-Morley experiment. They all failed to actually detect the ether, resulting in a huge debate as the twentieth century began. Was light a wave or a particle?
In 1905, Albert Einstein published his paper to explain the photoelectric effect, which proposed that light traveled as discrete bundles of energy. The energy contained within a photon was related to the frequency of the light. This theory came to be known as the photon theory of light (although the word photon wasn't coined until years later).
With photons, the ether was no longer essential as a means of propagation, although it still left the odd paradox of why wave behavior was observed. Even more peculiar were the quantum variations of the double slit experiment and the Compton effect which seemed to confirm the particle interpretation.
As experiments were performed and evidence accumulated, the implications quickly became clear and alarming:
Light functions as both a particle and a wave, depending on how the experiment is conducted and when observations are made.
Wave Particle Duality in MatterThe question of whether such duality also showed up in matter was tackled by the bold de Broglie hypothesis, which extended Einstein's work to relate the observed wavelength of matter to its momentum. Experiments confirmed the hypothesis in 1927, resulting in a 1929 Nobel Prize for de Broglie.
Just like light, it seemed that matter exhibited both wave and particle properties under the right circumstances. Obviously, massive objects exhibit very small wavelengths, so small in fact that it's rather pointless to think of them in a wave fashion. But for small objects, the wavelength can be observable and significant, as attested to by the double slit experiment with electrons.
Significance of Wave Particle DualityThe major significance of the wave particle duality is that all behavior of light and matter can be explained through the use of a differential equation which represents a wave function, generally in the form of the Schrodinger equation. This ability to describe reality in the form of waves is at the heart of quantum mechanics.
The most common interpretation is that the wave function represents the probability of finding a given particle at a given point. These probability equations can diffract, interfere, and exhibit other wave-like properties, resulting in a final probabilistic wave function that exhibits these properties as well. Particles end up distributed according to the probability laws, and therefore exhibit the wave properties. In other words, the probability of a particle being in any location is a wave, but the actual physical appearance of that particle isn't.
While the mathematics, though complicated, makes accurate predictions, the physical meaning of these equations are much harder to grasp. The attempt to explain what the wave particle duality "actually means" is a key point of debate in quantum physics. Many interpretations exist to try to explain this, but they are all bound by the same set of wave equations ... and, ultimately, must explain the same experimental observations.