The Origin of Quantum Mechanics: the Black Body Radiator and the Quantization of the Electromagnetic Field

 

In order to solve the black body radiation problem, German theoretical physicist Max Planck obtained an empirical relationship in 1900, which is illustrated in the picture below. "How does the strength of the electromagnetic radiation emitted by a black body depend on the frequency of the radiation (i.e., the colour of the light) and the temperature of the body?" asked Kirchhoff in 1859.

 

A black body is a hypothetical physical body that can absorb all incident light (all frequencies or colours of the electromagnetic spectrum that we call light) independent of frequency or angle of incidence. It also has the property of being an optimum perfect thermal radiation or heat emitter because of this feature.

 

The black body radiation spectra, or the energy density of the radiation emitted by a black body at various wavelengths

When nearing ultraviolet frequencies, classical theory predicts that such an item will emit an unlimited and continuous intensity of light (smaller wavelengths in the figure above). This means that as the intensity of the emitted light increases, the item begins to release the extra energy as light of increasing intensity and frequency (or shorter wavelengths), eventually reaching infinite intensity at the ultraviolet frequency. If there is no such ideal body, how can we tell if this traditional theoretical prediction is correct?

 

Kirchhoff realised in 1859 that we can build a nearly perfect absorber; a small hole in the side of a large box would be an excellent absorber because any radiation passing through it bounces around inside, getting absorbed by the walls (and thus heating the walls) with each bounce and having little chance of ever getting out again. An oven that is growing increasingly hot with a tiny hole in the side through which, presumably, the radiation is escaping is an equally good representation of a perfect emitter, and this is what scientists used as a guide to simulate a perfect black body radiator. Kirchhoff challenged theorists to calculate the energy or frequency curve for this "cavity radiation," as he named it, and experimentalists to observe it.

 

 

Kirchhoff's challenge in 1859, in fact, was the catalyst for quantum theory forty years later! University of Virginia's Michael Fowler.

 

By the 1890s, experimental techniques had advanced enough that the energy distribution emitted from this hollow or black body radiator could be measured pretty precisely. In 1895, at the University of Berlin, Wien and Lummer cut a small hole in the side of an otherwise perfectly covered oven and began measuring the radiation that emerged. Experiments revealed that radiance does not reach infinity; rather, it reaches a maximum and then decreases (as shown by the white curves above), resulting in a black body spectral distribution of the emitted wavelengths that could not be explained by classical wave theory, earning it the moniker "ultraviolet catastrophe." These exquisitely precise experimental results were the catalyst for a revolution: Planck's theory of energy quantization was inspired by its "non classical" behaviour. When Planck was working on enhancing the lifetime of lightbulbs, he ran upon the problem of the ultraviolet catastrophe.

 

Max Planck performed the first successful theoretical analysis of Wein and Lummer's experimental data in 1900. He focused on modelling the oscillating charges that must exist in the oven walls that radiate heat inwards, driven by the radiation field, and discovered that he could account for the observed curve only if he required these oscillators to lose or gain energy in chunks or steps, called quanta, of size hf, for an oscillator of frequency f, rather than radiating energy continuously at any frequency, as the classical theory would demand. In other words, the energy could only have values that were multiples of an elementary unit of energy hf (where f is the frequency and h is a constant that will be explained later), in contrast to the traditional assumption of a smooth curve for which the emitted energy could have any continuous value. The birth of quantum mechanics was characterised by the quantization of hf in integers, which established one of its fundamental constants, the Planck's constant h = 6.621034 J*s (Joules * seconds). We can see that h is a very small number (34 zeros after the decimal point), and that the Planck units, which are based on it, are also quite small. This helps to explain why it has remained for so long outside the scope of experimental observations at the scale of our daily lives. Planck proposed a solution to the black body radiation problem with this concept, and he was awarded the Nobel Prize in 1918 for his finding.

 

Like fire in a chimney, hotter the wood is burning, brighter the light it emits, and shorter its wavelength (or higher its frequency). Higher frequency means higher energy, and this increase in energy is not continuous as predicted by classical theory, but occurs in steps of hf.

 

Einstein discovered in 1905, five years after Plank published his solution to the Black Body radiation problem, that the equation E = hf could explain the photoelectric effect (the emission of electrons from a metal when shining light on it), and thus determined the smallest amount of energy exchanged by an oscillator at frequency f, given by E = hf, to be the quantum of the electromagnetic field, coined photon, and thus giving the radiation field a corpuscular or corpuscular or corp In 1921, Einstein was awarded the Nobel Prize for this discovery.

 

On the other hand, Louis de Broglie came up with the notion of applying the Einstein-Planck connection E = hf to a particle with mass and energy equal to Einstein's E = mc2. He got a "natural frequency" of f = mc2/h by combining Einstein's E = mc2 and Planck's E = hf, which gives particles a wavelike property. In his relationship, the wave-particle duality is partially justified.

 

When this equation is applied to the electron, the natural frequency is defined as fe = mec2/h (where me is the electron mass), and this was understood as a true oscillatory motion of the electron at the time.

Reference: Peer Reviewed