Breakdown of Classical Physics

The necessity for a departure from classical physics is demonstrated by the following phenomena:

1. Anomalous Atomic and Molecular Stability. According to classical physics, an electron orbiting an atomic nucleus undergoes acceleration and should, therefore, lose energy via the continuous emission of electromagnetic radiation, causing it to gradually spiral in towards the nucleus. Experimentally, this is not observed to happen.

2. Anomalously Low Atomic and Molecular Specific Heats. According to the equipartition theorem of classical physics, each degree of freedom of an atomic or molecular system should contribute $R/2$ to its molar specific heat capacity, where $R$ is the molar ideal gas constant. In fact, only the translational, and some rotational, degrees of freedom seem to contribute. The vibrational degrees of freedom appear to make no contribution at all (except at high temperatures). Incidentally, this fundamental problem with classical physics was known and appreciated by the middle of the nineteenth century. Stories that physicists at the start of the twentieth century thought that classical physics explained everything, and that there was nothing left to discover, are largely apocryphal (see Feynman, Volume I, Chapter 40).

3. Ultraviolet Catastrophe. According to classical physics, the equilibrium energy density of an electromagnetic field contained within a vacuum cavity whose walls are held at a fixed temperature is infinite, due to a divergence of energy carried by short wavelength modes. This divergence is called the ultraviolet catastrophe. Experimentally, there is no such divergence, and the total energy density is finite.

4. Wave-Particle Duality. Classical physics treats waves and particles as completely distinct phenomena. However, various experiments (e.g., the interference of light, the photoelectric effect, electron diffraction) demonstrate that waves sometimes act as if they were streams of particles, and streams of particles sometimes act as if they were waves. This behavior is completely inexplicable within the framework of classical physics.