The Quantum Theory
The theory of electromagnetism embodied in Maxwell's equations also conflicted with the understanding of thermodynamics -- the behavior of systems in thermal equilibrium. In particular, a hot object (a so-called `black-body') emits electromagnetic radiation with a certain well-defined spectrum (intensity as a function of the frequency of the radiation). The problem with this is that if one adds up the energy carried off by radiation at all the different frequencies, the formulas imply that the total is infinite, which is an absurd result.
Just before the turn of the century, Max Planck realized that if the energy was emitted in discrete packets (or `quanta'), rather than in a continous distribution, the total energy would be finite. He postulated that radiation of frequency n comes in quanta of energy E = hn, where h is a fundamental constant of nature, known as Planck's constant. The individual quanta of light are called ``photons''. This was the beginning of the idea of wave-particle duality and the quantum theory.
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