cavity, but small enough not to interfere with the equilibrium within.
Such a hot EM emitting device is a Black Body Emitter. It emits Black Body Radiation [15]. A Black Body is a theoretical device, which absorbs all EM radiation perfectly, so it would be perceived as an utterly black object. It had already become possible, at the end of the 19th century, to compare the light output of different light sources very accurately with these Black Emitter devices. Edison's light bulbs came out as slightly more efficient than those of his competitor Siemens.
Physicists prefer understandably mathematical theories with which the behavior of physical systems can be predicted as precisely as possible. Firstly, this is a confirmation of the correctness of the theory, secondly, it reduces the number of constants that physics requires for its models, and thirdly, a pen and paper exercise usually costs considerably less than a real physical experiment.
Max Planck [16] (1858-1947), who had become professor at the Friedrichs-Wilhems Universität in Berlin, had been commissioned by Siemens to do research on maximizing the light intensity from lightbulbs while minimizing energy. At the Physikalische-Technische Reichsanstalt he worked hard to find a theoretical solution for what was known as the UV catastrophe. Theoretical physics calculations - using the Maxwell equations for EM radiation - on the emission spectrum of a black emitter resulted in a 'catastrophic' prediction. The prediction of the theory was, that a black emitter, heated to 5000 oK - this is 5000 degrees above absolute zero - would emit almost all its energy as UV radiation. Just lighting a candle would be disastrous.
Figure 3.12: Black Body emission spectrum compared with UV-catastrophe.
Source: Wikimedia Commons.
Fortunately, reality was different. That was, of course, a challenge for physics. Another theoretical physics approach of Black Body radiation predicted the emission in the UV area somewhat better but got out of hand in the area of infrared radiation. Both classical theoretical approaches misfired spectacularly. Figure 3.12 illustrates the intensity distribution of EM radiation at different temperatures of a "Black Emitter", an emission spectrum. The far-right curve, - going through the roof at a wavelength around 1.3 micrometer (μm) - is the theoretical calculated behavior for a temperature of 5000 oK. This predicts a continuously increasing radiation intensity at decreasing wavelengths, the UV catastrophe.
The other three curves represent the actual measured intensity distribution for absolute temperatures of 3000, 4000 and 5000 oK. At a temperature 5000 oK of a Black Emitter the maximum of the emitted radiation is located exactly in the middle of the visible light spectrum, between 0.4 and 0.7 μm. That is also - and certainly not by coincidence - the temperature of the photosphere, the radiant outer shell of our sun. Our eyes are optimized for our own local star. The blue curve shows you that the intensity of Black Body emission at 5000 oK drops quickly for the shorter wavelengths of UV radiation, beyond 0.2 μm it stops entirely.
A desperate act
Physicists had tried to calculate the theoretical Black Body emission applying classical physics in a similar way as Ludwig Boltzmann [17] had successfully done for gases. They combined Boltzmann's statistic methods with Maxwell's laws. To achieve this, they imagined vibrating electrical charges in the inner walls of the Black Body emitter. Based on the Maxwell equations, those vibrating charges should emit and absorb EM radiation in all possible frequencies from infrared to very deep ultraviolet. But according to classical physics theory, an unimaginably huge amount of ultraviolet radiation would be emitted by a white-hot glowing Black Body. The disturbing fact that the classical physics prediction totally derailed in the UV domain - see the rightmost curve in figure 3.12 -challenged physicists like Max Planck to find a better theory.
Planck had, by heuristic trial and error, already found a formula that fitted the measured emission spectra for different temperatures. This success was already very useful, of course, but what he was really searching for was a theory derived from the foundations of physics. He undertook a heroic attempt to derive his heuristic formula from the bottom-up. To that end, he tried - with great reluctance and just as a last resort - to insert in his theory the idea of discrete energy packages of EM radiation that would be emitted and absorbed by the vibrating electrical charges in the walls of the Black Body emitter. He assigned to those discrete energy packages a precise amount of energy proportional to their frequency and named them: quanta. Eureka! His last resort attempt delivered the correct emission prediction and dealt completely with the UV catastrophe. In 1900 Planck published the first quantum theory, 'Zur Theorie der Wärmestrahlung', in the Annalen der Physik [18].
Planck confessed later that his idea was born out of an act of desperation. In his desperate attempts, seeking a way out, he assumed that the energy exchange of such an EM quantum - which Albert Einstein later supposed to be a real energy particle - was proportional to the frequency f. Which gives us the formula that every physics student now knows by heart, Planck's Law: E = h.f.
The utterly small value of h - Planck's constant: 6,626 × 10−34 Joule seconds - is now engraved on his headstone. With this last-resort daring assumption he was able to derive his equations for the emission of a Black Body emitter completely from basic principles and arrived thus at the perfect prediction for the spectrum of the standard light source. Goal achieved, you would think. But the kinder reactions from his colleague physicists were that it was a nice trick at best, but that his quanta could not have anything to do with physical reality. Such peer responses on a groundbreaking idea are not uncommon in the history of science. In 1918 Planck justly received the Nobel Prize in Physics, 18 years after his publication and only after Einstein had explained the photoelectric effect with Planck's quanta.
Despite this success, Planck, and the later quantum physicists also, were not able to explain how an electromagnetic wave first expands spherically according to Maxwell, its intensity diminishing inversely proportional to the square of the distance to the source, and then changes suddenly into the very local and precise amount of energy transfer represented by the Planck quantum. The question is also, whatever is meant by the frequency of a quantum. This is precisely the problem that the remaining sections of this book will focus on.
Planck himself was at first not really satisfied with his quantum hunch because it clearly could not be reconciled - actually still not - with the wave theories of Huygens, Young and Maxwell, a generally accepted theory at that time. He searched a long time extensively for a "classical" solution, but it evaded him. In the end he radically changed his views on physics, according to his later statements about the relationship between quantum physics and consciousness.
Until then, energy transfer had been considered a continuous phenomenon such as water flowing from a tap. You can fill a container with a thin jet of water slowly, or you can turn the flow up when you are in a hurry. A small, strong jet yields just as much water as a broader but weaker jet. EM radiation behaves entirely different. Consider for example the effect of UV light on your skin. You will never acquire a bronzed skin by sitting patiently in front of a strong infrared source, such as a central heating radiator.
The success of Planck's formula was the beginning of the end of the absolute deterministic view of the world of classical physics. For the infamous demon of Laplace,
