As the dawn of a new century approached, physics was intoxicated with what the ancient Greeks wisely called hubris -- false, insolent, destructive pride.  Indeed, as a young man eager to pursue physics, Max Planck was advised by the head of the physics department at Munich "The important discoveries [in physics] have been made.  It is hardly worth entering physics anymore (Kotz and Treichel, 320)."  Fortunately, this advise he did not heed.  Classical physics -- that is, Newtonian mechanics and Maxwell's theory of electromagnetism -- seemingly accounted for all observed natural phenomena.  It was a deterministic universe.  The planets, eternally whirling with their inscrutable precision; the ebbing and flowing of the sea's tides; the oscillations of a pendulum; the way bodies exchange energy and momentum; waves of light propagating through space -- do they all not obey a deterministic model?  Some claimed that given the initial conditions of the universe, all of its future behavior could calculated.

      Alas, as so often occurs in science, a crisis arose that was fatal in nature to classical physics: it failed to account for certain important phenomena.  This was the ultraviolet catastrophe, and standing at the center of it was the man who had been discouraged from pursuing physics because all but the minor details had been worked out, Max Planck.

     An ideal object that absorbs all radiation incident upon it is known as a blackbody.  A reasonable approximation may be made by employing a cavity that has a very small aperture.  Only a negligible amount of radiation entering the cavity escapes.  The characteristic energy radiation of a blackbody -- ergo, the name -- is not visible, but rather in the infrared region of the electromagnetic spectrum.  In classical physics, the spectral distribution function is given by the Raleigh-Jeans law,

where l is the wavelength, T is the temperature, and k is the Boltzmann constant.  The agreement between the predicted values and observed was excellent for large wavelengths.  However, as l approaches zero, it is predicted it would radiate an infinite amount of energy of extremely small wavelengths, the ultraviolet region.

     Tacit in this model is that radiation, such as visible light, propagates through space and exchanges energy as a wave.  That is, it is continuous, non-localized, spread out.  Newton had argued that it is transmitted in discrete particles called corpuscles.  However, later experiments with interference and diffraction seemed to indicate it was a wave.

     Planck's approach was to alter the model.  For the the sake of developing an accurate model, and only for the sake of accurate model, assume that energy emitted or absorbed by a blackbody came in discrete units, or quanta, like particles.  He even determined the relationship by which the energy is quantized:
 

The energy is given by some integer, n, multiplied by Planck's constant, h, and the frequency,  f, of the radiation.  However, he insisted this was not the way nature actually behaved, merely a model.  Indeed, some years later when Einstein used this principle to explain the photoelectric effect, Planck questioned the veracity of the argument.  Eventually, as did the whole of the scientific community, he came around and realized the implications.

     Though he did not initially appreciate it, he had open the door for a new paradigm that would assert itself with such vigor that virtually no field of science would be left untouched by it: quantum physics.   In particular, he had stumbled into the thorny briar of wave-particle duality.  Light seems to propagate like a wave and exchange energy like a particle.  Einstein commented on the counterintuitive nature of this dichotomy saying
 

     One such neophyte was a french prince and graduate student in physics, Louis-Victor DeBroglie.  Suppose the concept of the light quanta of Planck and Einstein is broadened.  What if it is not merely light that exhibits both wave and particle properties?  What if an electron or a proton or a atom or a baseball or a planet exhibits them?  And what does this tell us of the nature of matter?  DeBroglie's answer was that, indeed, wave-particle duality is not limited to just light.  All objects, microscopic and macroscopic, display it.  He postulated that the wavelength of these so-called matter waves is given by
 

where h is, once again, Planck's constant, p is momentum, m is mass, and v is velocity.

     This postulate was quickly confirmed using x-ray crystallography to examine the behavior of electrons.  As may be seen in the adjacent illustration, electrons exhibit a diffraction pattern that is characteristic of waves.  That is, as they propagate, they interfere with one another, yet it is known that they are indeed discrete units or particles.  Interference may only occur if they also possess wave properties.  Therefore, matter -- not only light -- propogates as waves and exchanges energy as particles.  The troubling dichotomy of waves and particle of light quanta cannot be escaped.  It is replete throughout nature: in packets of light quanta, photons; in subatomic particles such as electrons and protons; in the flight of a baseball; in the orbit of a planet.  However, the wavelength for macroscopic objects, such as baseballs and planets,  is so small as to be virtually undetectable.