Max Planck and the blackbody

Quantums of light

During the 1800s, all the sciences seemed to take giant steps. In particular, Mechanics, Thermodynamics and Electromagnetism seemed, together with Chemistry, able to correctly interpret all worldly phenomena. The electric light best represented the victory of light over darkness: in 1880, Thomas Edison patented the incandescent carbon filament lamp and then in 1890 the tungsten filament was patented. The newborn electronics industry dedicated to the production of lightbulbs had a problem however: there was no way to absolutely measure the luminous power of the bulbs, a fundamental aspect of the product. There needed to be a reference source of light to be able to calibrate the measuring instruments.

In theory, an absolute reference source existed: the Black Body, an ideal object that absorbs all luminous radiation and reflects none. Remember that the color of an object depends on the wavelength of reflected light radiation: if it reflects red light it’s colored red, green if it reflects green; if it reflects nothing then it’s color is black. But the fact that the blackbody doesn’t reflect light of any color doesn’t mean that it doesn’t itself emit light. Not reflecting, the blackbody thus absorbs all the incident energy and re-radiates it continuously along the whole radiant light spectrum.

In 1864, two years after the introduction of the blackbody concept, James Clerk Maxwell formulated the equations that describe electromagnetism as an undulatory phenomenon: with Maxwell we learn that the color of light, an electromagnetic wave, depends on its wavelength. It had been experimentally observed that the intensity of the radiation emitted by a blackbody as a function of its wavelength has a characteristic bell curve and its peak emission is determined by the temperature of the body itself. The description that Maxwell’s equations offered of the phenomenon of blackbody emission powerfully contradicted, however, experimental observations; his equations predicted that the quantity of energy contained in the blackbody was not finite and that it would grow in an uncontrolled manner as the frequencies rose. This evidence violated the principle of energy conservation. So a new interpretation of nature on an atomic scale was needed to resolve this problem.

Almost 40 years would pass before discovering a standard source. During this time, the lightbulb producers widely financed research on this theme in universities and research centers. In 1900, Max Planck theorized that energy exchange in emission phenomena and electromagnetic radiation absorption occurred separately, proportional to the oscillatory frequency of the radiation and not continuously as classical electromagnetic theory sustained. In this hypothesis, calculating the blackbody emissions spectrum, experimental results were correctly replicated, as long as a constant value of proportionality between energy and frequency in accord with the experiments was chosen. This constant was called Planck’s Constant. In this way it became possible to calculate the total intensity of emitted radiation, fundamental for using the blackbody as a standard source, exactly what the lightbulb industry had been asking for.

Albert Einstein and the light quanta

Light: waves and particles

A few years later, Albert Einstein correctly interpreted a very peculiar observed phenomenon that would reinforce Planck’s quantistic hypothesis: the photoelectric effect.  This effect is characterized by the emission of electrons from the surface of a metal when it’s hit by electromagnetic radiation of a certain frequency. More precisely, it was observed that electron emission happens only if the frequency of the luminous radiation is greater than a certain limit, a limit which varies from substance to substance. If the frequency is under that limit, as the power of the incident radiation increases, no electrons are extracted; if the frequency is above the limit electrons are extracted even at very low power. Augmented power corresponds to an augmented number of extracted electrons as well.

Einstein intuited that electron extraction from the metal could be explained if electromagnetic radiation were made up of packets of light of an energy proportional to the frequency as had been assumed in fact by Planck. Einstein’s quantistic hypothesis wasn’t accepted for years by a large part of the scientific community who believed that the existence of photons was an unacceptable theory. This conviction was based on the observation of the phenomena of interference of light that can only be explained if electromagnetic radiation acts like waves. Interference is, in fact, due to the juxtaposition of two or more waves in a point in space. The intensity of the resulting wave can vary from a minimum to a maximum of the sum of the intensities. However, if we have particles such as photons, how can interference be explained? It would take another 20 years to solve this paradox.