A History Wall
of Quantum Physics

The spectral lines of hydrogen had been observed since the late 1870s, but it took an analogy from architecture to grasp their regularity (later explained by quantum theory). The grammar school teacher Johann Jakob Balmer realised that the perspective foreshortening of a row of columns or a flight of stairs seen from a certain angle could be applied to the spectral series of hydrogen. This led to what is now known as the Balmer formula.

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The Rydberg formula gives the wavelengths of spectral series lines of many chemical elements. The formula was primarily presented as a generalization of the Balmer series for hydrogen. It was first empirically stated in 1888 by the Johannes Rydberg, then theoretically derived by Niels Bohr in 1913.

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The so-called black body was actually a hole in the wall of a platinum box, divided by diaphragms, the inside of which was blackened with iron oxide. Otto Lummer and Ferdinand Kurlbaum at the Physikalisch-Technische Reichsanstalt in Berlin had perfected this cavity radiation source, which became an important component in the ever-improving measurements of the frequency distribution of light and heat radiation that led to the discovery of Planck's law.

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The 19th century was full of speculation about a connection between light and electromagnetic fields. Pieter Zeeman had been interested in the influence of magnetic fields on spectral lines since the early 1890s, but it was not until 1896 that he overcame all the experimental and instrumental difficulties and observed the splitting of the extremely narrow blue-green cadmium line at 4678 Å into a triplet. He employed a concave Rowland reflection grating and a high magnetic field from a Rühmkorff magnet.

The splitting was predicted by a classical theory of Hendrik Antoon Lorentz, as was the direction of polarisation of the components. However, the splitting of the lines seemed much too large to support the view that the light was emitted by an oscillating 'ion'. While the oscillating object was soon identified with the recently discovered electron, the prediction of Lorentz's theory was only in qualitative agreement with observation. Most investigations showed different splittings into doublets, quadruplets and so on (the anomalous Zeeman effect), a phenomenon that was not understood until 1925, when the half-integer spin was introduced into quantum physics.

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It was the urgent need for improved photometric standards in the light bulb industry -- at a time when the business of illuminating streets and buildings with electric light was flourishing -- that led the Berlin Imperial Institute of Technology to turn to the investigation of the laws of radiation. Here, technological advances such as a new bolometer designed by Otto Lummer and Ferdinand Kurlbaum (using the resistance of four extremely thin platinum foils in a Wheatstone bridge as heat detectors in a bolometric device capable of measuring temperature differences down to \$\$10^{-7}\$\$ °C), as well as electrically heated blackbody and infrared spectroscopy, became necessary foundations on which industry, but also physical theory, would build.

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The radiation equation that provided a perfect fit with the newest experimental values had been written down by Max Planck already in October 1900 using formal constants \$\$c\$\$ and \$\$C\$\$. However, only in December 1900 he would introduce what is now called Planck's constant \$\$h\$\$, the universal constant that characterized the energy component and guaranteed that energy and frequency were proportional (\$\$E=h\nu\$\$). At the same time \$\$k\$\$, Boltzmann's constant, ensured that the entropy of a state was proportional to its probability (\$\$S=k \log W\$\$).

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In 1902, Philipp Lenard observed that the energy of individual electrons emitted by a charged metal plate when exposed to light is independent of the intensity of the light. He thus disproved the applicability of Maxwell's wave theory of light. His results were qualitative rather than quantitative because the experimental challenges of avoiding oxidation of the metal plate and of vacuum technology were considerable.

These experimental results were the starting point for Albert Einstein, who interpreted the photoelectric effect with a corpuscular model, leading to the concept of the light quantum.

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The phenomenon of radioactivity had been observed since 1896, but it was not until 1902 that the exponential decay law was identified in experiments by Ernest Rutherford and Frederick Soddy who found \$\$I_t/I_0 = e^{-\lambda t}\$\$.

In 1928, when Ronald Gurney and Edward Condon were finally able to explain decay in terms of quantum mechanics, they described the evolution of the understanding as follows After 1902 "... it soon became clear that the time of disintegration of an atom was independent of the previous history of the atom and depended solely on chance. ... It has hitherto been necessary to postulate some special arbitrary ‘instability ’ of the nucleus; but in the following note it is pointed out that disintegration is a natural consequence of the laws of quantum mechanics without any special hypothesis."

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The atom is as empty as the cosmos, with tiny particles like electrons and 'dynamides' instead of stars and planets. This was the conclusion reached by Philip Lenard in 1903 after extensive experiments with cathode rays, which penetrated apparently solid matter almost unaffected.

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To explain the photoelectric effect and various other experiments, the idea of quantifying the energy (and later the momentum) of light was tentatively proposed by Albert Einstein in 1905. He called this assumption of "light quanta" a heuristic point of view to emphasise how tentative this bold assumption was, since it discretised light into energy packets, whereas in Maxwell's highly successful electromagnetic theory light and other forms of electromagnetic waves were considered to be spatially and energetically strictly continuous.

In later experiments by James Franck and Gustav Hertz, by Robert Millikan or Arthur Compton, this assumption also turned out to work, although it was by no means clear how to conceptualise it. The search for suitable mental models of light quanta (or photons, as they were called from 1926) occupied Einstein and many other physicists for the rest of their lives.

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While there are many examples of mathematical structures and tools being established much earlier than their application in physics, it is surprising to see the extent to which David Hilbert's theory of integral equations prepared the mathematical foundations of quantum mechanics, even coining the relevant concepts of 'eigenvalues' and 'spectrum', which would then correspond to sharp energy values and atomic spectra.

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