The evolution in our understanding of the physical nature of light forms one of the most fascinating accounts in the history of science. Since the dawn of modern science in the sixteenth and seventeenth centuries, light has been pictured either as particles or waves incompatible models each of which enjoyed a period of prominence among the scientific community. In the twentieth century it became clear that somehow light was both wave and particle, yet it was precisely neither. For some time this perplexing state of affairs, referred to as wave particle duality, motivated the greatest scientific minds of our age to find a resolution to apparently contradictory models of light. The solution was achieved through the creation of quantum electrodynamics, one of the most successful theoretical structures in the annals of physics.
Christian Huygens, a Dutch scientist contemporary with Newton, championed the view that light is a wave motion, spreading out from a light source in all directions and propagating through an all-pervasive elastic medium called the ether. Adopting a wave theory, Huygens was able to derive the laws of reflection and refraction and to explain double refraction in calcite as well.
Within two years of the centenary of the publication of Newton's Optics, the Englishman Thomas Young performed a decisive experiment that seemed to demand a wave interpretation. It was the double-slit experiment, in which an opaque screen with two small, closely spaced openings was illuminated by monochromatic light from a small source. The "shadows" observed formed a complex interference pattern like those produced with water waves.
Victories for the wave theory continued up to the twentieth century. In the mood of scientific confidence that characterized the latter part of the nineteenth century, there was little doubt that light, like most other classical areas of physics, was well understood. In 1821 Augustin Fresnel published results of his experiments and analysis, which required that light be a transverse wave. On this basis, double refraction in calcite could be understood as a phenomenon involving polarized light. It had been assumed that light waves in an ether were necessarily longitudinal, like sound waves in a fluid. For each of the two components of polarized light, Fresnel developed the Fresnel equations, which give the amplitude of light reflected and transmitted at a plane interface separating two optical media.
Working in the field of electricity and magnetism, James Clerk Maxwell synthesized known principles in his set of four Maxwell's equations. The equations yielded a prediction for the speed of an electromagnetic wave in the ether that turned out to be the measured speed of light, suggesting its electromagnetic character. From then on, light was viewed as a particular region of the electromagnetic spectrum of radiation.
The experiment of Albert Michelson and Edward Morley, which attempted to detect optically the earth's motion through the ether, and the special theory of relativity of Albert Einstein, were of monumental importance. Together they led inevitably to the conclusion that the assumption of an ether was superfluous. The problems associated with transverse vibrations of a wave in a fluid vanished.
If the nineteenth century served to place the wave theory of light on
a firm foundation, this foundation was to crumble as the century came to
an end. Difficulties in the wave theory seemed to show up in situations
that involved the interaction of light with matter. In 1900, Max Planck
announced at a meeting of the German Physical Society that he was able
to derive the correct blackbody radiation spectrum only by making the curious
assumption that atoms emitted light in discrete energy chunks rather than
in a continuous manner. Thus quanta and quantum mechanics
were born. According to Planck, the energy E of a quantum of electromagnetic
radiation is proportional to the frequency of the radiation, 
,
(1.1)
where the constant of proportionality, Planck's constant, has the
value of h = 6.63 x 10-34 J-s. Five
years later, Albert Einstein offered an explanation of the photoelectric
effect, the emission of electrons from a metal surface when irradiated
with light. Central to his explanation was the conception of light as a
stream of photons whose energy is related to frequency by Planck's equation.
Then in 1913, the Danish physicist Niels Bohr once more incorporated the
quantum of radiation in his explanation of the emission and absorption
processes of the hydrogen atom, providing a physical basis for understanding
the hydrogen spectrum. In 1922, the photon model of light was used by Arthur
Compton, who explained the scattering of x-rays from electrons as particle-like
collisions between photons and electrons in which both energy and momentum
are conserved.
All these examples of the photon, or particle, model of light indicated
that light could be treated as a particular kind of matter, possessing
both energy and momentum. It was Luis de Broglie who finally connected
the two views, and in so doing revolutionized our understanding of matter
itself. In 1924 he published his speculations that (subatomic) particles
are endowed with wave properties. He suggested that a particle with
momentum p has an associated wavelength of
.
(1.2)
Experimental confirmation of de Broglie's hypothesis appeared during the
years 1927-1928, when Clinton Davisson and Lester Germer in the United
States and Sir George Thomson in England performed experiments that could
only be interpreted as the diffraction of a beam of electrons.
Thus, the wave-particle duality came full circle. Light behaved like waves in its propagation and in the phenomenon of interference and diffraction; it could, however, also behave as particles in its interaction with matter, as in the photoelectric effect. On the other hand, electrons usually behaved like particles, as observed in the point-like scintillations of a phosphor exposed to a beam of electrons; in other situations they were found to behave like waves, as in the diffraction produced by an electron microscope.
Photons and electrons that behaved both as particles and as waves seemed at first an impossible contradiction, since particles and waves are very different entities. Gradually it became clear, to a large extent through the reflections of Niels Bohr and especially in his principle of complementarity, that photons and electrons were neither waves nor particles, but something more complex than either.
In attempting to explain physical phenomena, it is natural to appeal to well-known physical models like waves and particles. As it turns out, however, the full intelligibility of a photon or an electron is not exhausted by either model. In certain situations, wave-like attributes may predominate; in other situations, particle-like attributes stand out. We can appeal to no simpler physical model that is adequate to handle all cases.
Quantum mechanics deals with all particles more or less localized in
space, and so describes both light and matter. Combined with special relativity,
the momentum p, wavelength 
,
and speed v for both material particles and photons are given by
the same equations:
,
(1.3)
,
(1.4)
and
.
(1.5)
In these equations, m is the rest mass and E is the total
energy, the sum of rest mass energy and kinetic energy. We can also view
the work as supplying the kinetic energy. The relativistic mass is given
by 
, where
.
Notice that, since the photon is massless, equations (1.3) - (1.5) simplify
and show us that v = c, while for matter with a
non-zero rest mass, they are constrained to always satisfy v <
c.
Last updated: June 12, 1997
Comments to: D-Suson@tamuk.edu