Breakdown of Classical Physics

The necessity for a departure from classical physics at the microscopic (i.e., atomic, molecular, and particle) level is amply demonstrated by the following well-known phenomena:

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 [49], causing it to gradually spiral in towards the nucleus. (See Exercise 1.) Experimentally, this is not observed to happen.

Anomalously Low Atomic and Molecular Specific Heats:

According to the equipartition theorem of classical statistical thermodynamics, each degree of freedom of an atom or molecule should contribute $R/2$ to the molar specific heat capacity of a macroscopic system made up of a great many such atoms or molecules, where $R$ is the molar ideal gas constant [91]. 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 very high temperatures) [91]. Incidentally, this fundamental problem with classical physics was known and appreciated by the middle of the nineteenth century. Stories that physicists at the commencement of the twentieth century thought that classical physics explained everything, and that there was nothing left to discover, are largely apocryphal [46].

Ultraviolet Catastrophe:

According to classical statistical thermodynamics, 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 [35]. Experimentally, there is no such divergence, and the total energy density is finite [91].

Wave-Particle Duality:

Classical physics treats waves and microscopic particles as completely distinct phenomena. However, various experiments (e.g., the photoelectric effect [37,74], Compton scattering [22], and electron diffraction [25,111]) demonstrate that waves sometimes act as if they were streams of particles, and streams of particles sometimes act as if they were waves [26]. This behavior is completely inexplicable within the framework of classical physics.