Tracing Quantum Origins—Quantization

Historical science article: This text was restored from the complete same-title public-account manuscript with minimal factual corrections. The institution and research experience in the author biography are historical information from the time of the original manuscript.

Tracing Quantum Origins—Quantization

Lin Jun'an (林俊安)

Institute for Quantum Computing, University of Waterloo

Quantum, quantum mechanics, blackbody radiation, the photoelectric effect

Quantum: a word that may feel both familiar and unfamiliar. Perhaps you have heard news of world-leading research achievements by Chinese scientists in quantum communication and quantum computing. Perhaps you have also come across dazzling advertisements for “quantum water,” “quantum insoles,” and similar products. Have you ever wondered which of these quantum-related concepts belong to modern science, and which are simply misleading the public? Are seemingly intimidating scientific concepts such as quantum physics, quantum information, and quantum communication really so difficult to understand?

If these questions interest you, but you feel held back by a lack of background knowledge, read on! In this series, we will guide you through the “quantum fog” and help you understand, step by step, the scientific concepts behind quantum technologies.

What exactly is a quantum?

When discussing quantum technologies, the first concept we need to introduce is, naturally, the quantum itself. Today, we will explore what a quantum is and look back at the early story of the birth of quantum mechanics.

Let us begin with a definition. Quantum, whose plural is quanta, is a noun derived from the Latin quantus, meaning “how much.” In modern physics, it describes discrete units of certain physical quantities. For light of a particular frequency, the energy of a single light quantum is determined by that frequency; there is no single minimum energy unit that applies to every frequency. In the term “quantum mechanics,” quantum acts as a noun modifier (note 1), referring to a particular kind of theory of mechanics. After translation into Chinese, however, the expression can easily be interpreted too literally, as though quantum were an adjective. It is therefore not hard to understand why so many products on the market have “quantum” attached to their names!

The theory of blackbody radiation

In 1900, Max Planck, one of the founders of quantum mechanics, introduced discrete units of energy while studying blackbody radiation. In 1905, Albert Einstein took this idea further in his light-quantum hypothesis, applying it to light and proposing that light energy could be exchanged in discrete light quanta. The quantum thus became a key concept for describing the discreteness of certain physical quantities. These studies concerned two major theories connected with the origins of quantum mechanics: the theory of blackbody radiation and the theory of light quantization.

On April 27, 1900, the British physicist Lord Kelvin said in a lecture, “The dynamical theory asserts that heat and light are modes of motion. But now the beauty and clarity of this theory are obscured by two clouds, leaving it dimmed…” [2]. One of these “two clouds” concerned the equipartition theorem and cannot simply be equated with the blackbody-radiation problem. Blackbody radiation was another important problem confronting physics during the same period. A blackbody is a hypothetical physical model: it completely absorbs the electromagnetic radiation it receives from its surroundings, without reflection or transmission. After absorbing electromagnetic waves, its energy increases, and its temperature rises. As its temperature rises, it also emits electromagnetic waves into its cooler surroundings. When the power it absorbs equals the power it emits, we can say that the blackbody has reached thermal equilibrium with its surroundings and has a definite temperature. In experiments, one can measure the power of the electromagnetic radiation emitted by a blackbody at different wavelengths. The relationship between this power and wavelength is called the blackbody radiation spectrum at thermal equilibrium.

The prediction of Wien's formula

Before Planck, the German physicist Wilhelm Wien had proposed Wien's radiation formula in 1896, predicting the spectrum of blackbody radiation. The formula agreed very well with experimental results at short wavelengths, but deviated from the experimental data at longer wavelengths, as shown by the Wien curve in Figure 2. This discrepancy was one of the problems troubling physicists at the time. Could Wien's formula be modified to agree with the experimental data at the long-wavelength end?

Planck's modification

Planck took on this problem (note 2). During his derivation, he found that if the energy of the oscillators in the blackbody model was distributed in discrete energy units, rather than treated as a quantity that could be divided continuously into arbitrary amounts, the resulting formula could predict the radiation spectrum very accurately across wavelengths [4], as shown by the Planck curve in Figure 2. The energy unit is proportional to the oscillator's frequency. The proportionality coefficient is what we now call Planck's constant.

Of course, the idea that energy values came in minimum units was deeply counterintuitive at the time, and Planck himself took a very cautious view of the formula. To him, introducing a minimum unit of energy was merely a small mathematical device for making the theoretical prediction agree with experimental data. For that reason, Planck did not explore in depth the physical meaning that the assumption might imply. Moreover, because his explanation of energy quantization was unclear in the paper in which he first introduced Planck's constant, the theory failed to attract much attention from mainstream physics at the time. Even during the decade or more after he proposed the first version of the theory in 1900, Planck himself continued searching for other “harmless” assumptions that could replace the energy-quantization hypothesis, in an effort to preserve the traditional idea that energy was continuous. Planck's conservative disposition made the spread of this emerging theory even more difficult.

Einstein's light-quantum hypothesis

In 1905, Einstein, who was then working at the Swiss Patent Office, published a paper explaining the photoelectric effect, bringing a turning point in the initially slow development of quantum mechanics. The photoelectric effect, discovered in 1887 by the German physicist Heinrich Hertz, is the phenomenon in which electrons, called photoelectrons, can be detected leaving the surfaces of certain metals when light shines on them. According to the wave theory of light that was prevalent at the time, light of sufficient intensity should allow a metal to absorb enough energy for electrons to overcome the binding at its surface and be emitted. In the single-photon photoelectric-effect experiments normally discussed, however, researchers found that, for each particular metal, photoelectron emission could be detected only when the incident light's frequency exceeded a threshold. When the frequency was below that threshold, increasing the intensity did not produce photoelectrons through the absorption of a single photon, as shown in Figure 3.

Einstein drew on Planck's assumption and went a step further by proposing the light-quantum hypothesis. He assumed that light energy was not continuous, but consisted of individual units, called light quanta, with the energy of each unit proportional to the light's frequency. He also conjectured that the proportionality coefficient was the same Planck constant that Planck had used in solving the blackbody-radiation problem. Because a beam of light consists of individual light quanta, now called photons, light with a frequency above a metal's threshold gives each photon enough energy for an electron that absorbs it to overcome the metal's work function and leave the surface. Conversely, in the single-photon photoelectric effect, if the frequency is below the threshold, increasing the light intensity still does not provide any individual photon with enough energy to release an electron.

As a theory ahead of its time, the light-quantum hypothesis unsurprisingly met skepticism and opposition from mainstream physics. The objections were also quite substantial: by then, people knew that light exhibited diffraction and interference, phenomena that strongly demonstrated its wave nature. James Maxwell's elegant electromagnetic theory had classified light as electromagnetic radiation and accurately predicted its various phenomena, with the photoelectric effect, of course, being an exception. To most people, Einstein's theory merely revived the corpuscular theory of light that Newton had supported but that had come to be regarded as obsolete. Gradually, however, people found that Einstein's theory could explain a series of experimental phenomena very well, including the photoelectric effect. Einstein consequently received the 1921 Nobel Prize in Physics (note 3). In 1924, Louis de Broglie went further, proposing that material particles such as electrons also had wave properties. He extended the idea of wave–particle duality to matter; it was not only at that point that light's wave nature was explained.

By this point, you probably have a deeper understanding of the word quantum. It describes the way certain physical quantities occur or are exchanged in discrete units; for light, the energy of such a unit changes with frequency. Looking back at the early history of the quantization hypothesis, one cannot help reflecting that great theories ahead of their time are often accompanied by criticism and setbacks from many directions. Human understanding of such theories also proceeds through a difficult journey from simple to deeper interpretations, and even a theory's creator may not be exempt. Much of the knowledge that has long been common sense today and appears in textbooks left even the leading scholars puzzled when it first emerged. It is precisely through the rigorous scholarship of generation after generation of researchers that human knowledge can continue moving toward a fuller understanding of nature. This vividly and accurately illustrates the scientific spirit: the sole criterion for testing the accuracy of a theory is how well it agrees with experimental data, rather than whether it was proposed by a famous person, accords with “common sense,” or is quickly accepted by the majority. For those of us standing on the shoulders of giants today, this is an especially important lesson.

1 English frequently uses nouns as modifiers.

2 It is worth pointing out that, contrary to the descriptions in many popular-science accounts, Planck did not study blackbody radiation in order to solve the so-called ultraviolet catastrophe. That name refers to the complete divergence from experimental results at short wavelengths of another blackbody-radiation law, the Rayleigh–Jeans formula. James Jeans proposed the formula in 1905 after correcting a numerical error in the formula of John Strutt, 3rd Baron Rayleigh. This was later than Planck's quantization hypothesis. The term ultraviolet catastrophe itself was coined by Paul Ehrenfest in 1911.

3 Although many people know Einstein as the founder of relativity, he did not receive the Nobel Prize for relativity, which was not yet a universally accepted theory at the time.

About the author (historical information from the manuscript)

Lin Jun'an (林俊安)

Hello, everyone! I am Lin Jun'an from the PhDSciNet team.

Institution: At the time of the original manuscript, I was pursuing a PhD in quantum information at the University of Waterloo.

Research interests: Error detection and analysis in quantum computing systems. I am also interested in quantum thermodynamics and the foundations of quantum mechanics.

Thoughts on science communication: I hope this platform can help everyone become more familiar with scientific concepts and develop a scientific, rational way of thinking in everyday life. I also hope to meet more friends who share these interests.

References in the original manuscript

[1] Do you guys just put the word quantum in front of everything?   https://movquotes.com/5730/

[2] Jones, A. Z.  Kelvin's"Clouds" Speech.   https://www.thoughtco.com/kelvins-clouds-speech-2699230

[3] Blackbody radiation formulas http://www.51dzw.com/embed/embed_115415.html

[4] Boya, L.J. The Thermal Radiation Formula of Planck (1900). Rev. Academia de Ciencias,Zaragoza. 58 (2003) 91-114.

[5] Photoelectric_effect, Wikipedia

Revised on 2026-10-10: Corrected Wien's nationality and the 1896 date of his radiation formula, the relationship between Kelvin's “clouds” and the blackbody problem, the description of Planck's oscillator-energy quantization, and the history of de Broglie's extension of wave properties to matter. Clarified that light-quantum energy depends on frequency, and limited the photoelectric-effect discussion to the single-photon case.

Supplementary references

• Wien's original 1896 paper: Ueber die Energievertheilung im Emissionsspectrum eines schwarzen Körpers
• NobelPrize.org: Wilhelm Wien's Nobel Lecture
• European Space Agency: Max Planck and energy quanta
• NobelPrize.org: Louis de Broglie and matter waves
• NobelPrize.org: The dual nature of light as reflected in the Nobel archives
• Research paper: Kelvin's clouds