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

Image: Ekaterina Kulaeva/Shutterstock 

^{By Dr. Inés Urdaneta / Physicist at Resonance Science Foundation}

In a past article entitled “The origin of quantum mechanics I: The Electromagnetic field as a wave” we had introduced the most relevant features of light as an electromagnetic field propagating in a 3D trajectory through space. Among the notions addressed we had explained the spectrum -or colors- of light, the components of the electromagnetic fields and their continuous, wavelike nature. In this second article we explain why the wavelike nature of light was not enough to explain certain behaviors of the interaction between light and matter; the understanding of such phenomena required introducing a “corpuscular” description of light that marked the origin of quantum theory, changing the paradigm with respect to classical physics.     

 The Black body Radiator and the quantization of the electromagnetic field 

Quantum mechanics was born in an empirical relationship that German theoretical physicist Max Planck obtained in 1900 to solve the black body radiation problem, depicted in the figure below. The problem was first stated by Kirchhoff in 1859: "how does the intensity of the electromagnetic radiation emitted by a black body depend on the frequency of the radiation (i.e., the color of the light) and the temperature of the body?" 

A black body is an idealized physical body that can absorb all incident light (all frequencies or colors of the electromagnetic spectrum we call light) that shines upon it, regardless of its frequency or angle of incidence. This feature also grants it the property of being an ideal perfect thermal radiation or heat emitter.

_{Figure: The black body radiation spectra, or the energy density of the radiation emitted by a black body at various wavelengths. A black body is an idealized physical body that absorbs all incident electromagnetic radiation upon it, regardless of frequency or angle of incidence. As a result, it is also a perfect thermal radiation emitter. The emitted spectrum depends on the absolute temperature of the body and displays a spectra of frequencies that, when plotted, shows a broad peak that sequentially increases, shifting from red (longer wavelengths, lower frequency) to blue (shorter wavelengths, higher frequency) as the temperature increases. It should be noted that a black hole is a perfect black body, as is the sun. This fact is important in the context of Unified Physics Theory.} 

Classical theory predicts that such an object will emit an infinite and continuous intensity of light when approaching ultraviolet frequencies (smaller wavelengths in the figure above). This means that when the object is radiated with increasing intensity, it would start emitting this excess energy as emission of light at increasing intensity and frequencies (or shorter wavelengths), going to infinite intensity at the ultraviolet frequency. How can we tell if this classical theoretical prediction is correct, if there is no such perfect body? 

Kirchhoff realized in 1859 that we can construct a nearly perfect absorber; a small hole in the side of a large box would be an excellent absorber since any radiation going through the hole bounces around inside, getting absorbed by the walls (hence, heating the walls) with each bounce and having little chance of ever getting out again. The inverse also holds true; an oven which is becoming increasingly heated with a tiny hole in the side out of which, presumably, the radiation is escaping is an equally good representation of a perfect emitter, and that is what scientists used as a guide in order to mimic a perfect black body radiator. Kirchhoff challenged theorists to figure out, and experimentalists to measure, the energy or frequency curve for this “cavity radiation,” as he called it. 

In fact, it was Kirchhoff’s challenge in 1859 that led directly to quantum theory forty years later! Michael Fowler, University of Virginia.

By the 1890’s, experimental techniques had improved enough to make fairly precise measurements of the energy distribution emitted from this cavity or black body radiator. In 1895, Wien and Lummer at the University of Berlin, punched a small hole in the side of an otherwise completely closed oven and began to measure the radiation coming out. Experiments showed that radiance does not go to infinity; instead, it reaches a certain maximum and then decreases (as shown above by the white curves), obtaining a black body spectral distribution of the emitted wavelengths that could not be explained by classical wave theory, earning it the name the ultraviolet catastrophe as a result. These beautifully precise experimental results were the key to a revolution: it was their “non classical” behavior that led Planck to the idea of energy quantization. Planck initially encountered the problem of the ultraviolet catastrophe while working on improving the lifetime of lightbulbs. 

The first successful theoretical analysis of the experimental data from Wein and Lummer was made by Max Planck in 1900. He concentrated on modeling the oscillating charges that must exist in the oven walls which radiate heat inwards, driven by the radiation field, and he found that he could account for the observed curve only if he required these oscillators not to radiate energy continuously at any frequency, as the classical theory would demand, and instead, they could lose or gain energy in chunks or steps, called quanta, of size hf, for an oscillator of frequency f. In other words, the energy could only have values which are multiples of an elementary unit of energy hf (where f is the frequency and h is a constant to be explained hereafter), which opposed the classical assumption of a smooth curve for which emitted energy can have any continuous value. This quantization in integers of hf marked the birth of quantum mechanics and introduced one of its fundamental constants, the Planck’s constant h = 6.62×10⁻³⁴ J*s (Joules * seconds). We see that h is a very small value (34 zeros after the decimal point) and since the Planck units are based on this constant, they are very small, as well. This partly explains why it has remained beyond the limits of experimental observations at the scale of our daily life for so long. With this hypothesis, Planck proposed a solution to the black body radiation problem, and he was granted the Nobel prize in 1918 for this discovery.  

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. 

Five years after Plank published his solution for the Black Body radiation problem, Einstein found in 1905 that the equation E = hf could explain the photoelectric effect (the emission of electrons from a metal, when shining light on the metal), and thus determined this 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 thereby giving the radiation field a corpuscular or particle nature. Einstein was awarded a Nobel prize in 1921 for this discovery. 

Louis de Broglie, on the other hand, had the idea of applying Einstein-Planck relationship E = hf to a particle with mass having an energy given by Einstein’s E = mc². By combining Einstein’s E = mc² and Planck´s E = hf, he obtained a “natural frequency” of f = mc²/h that assigns particles a wavelike nature. The wave-particle duality is partially justified in his relation. 

When applied to the electron, this equation defines the natural frequency for the electron as f_e = m_ec²/h (where m_e is the electron mass), and this was interpreted at that time as a real oscillatory motion of the electron. 

_{Louis de Broglie} 

_{RSF in perspective}

It is worth noting that the most accurate value for the Planck constant was announced in 2019. Measuring the Planck constant to a suitably high precision of ten parts per billion required decades of work by international teams across continents, which allowed this constant to be fixed at exactly 6.626070150 × 10⁻³⁴ kg⋅m²/s.

This allowed a more accurate redefinition of the units of mass, such that since 2019 all the MKS units (Meter for distance, Kilogram for mass, and Seconds for time) of measure are now completely described in terms of vacuum and quantum regime properties, which are fundamental agents (our RSF article from Nov. 2018 entitled From the Planck constant to the Kilogram gives a detailed description of the history of the redefinition of the SI units). The units of mass, time, and distance have unified around the Planck constant!

Having all units defined relative to the Planck constant, the limitation in accuracy is posed by the gravitational constant G upon which all Planck units depend. G is the constant with the lowest accuracy at 10^-5 digits, while other constants have accuracy at 10^-9 and even 10^-12 digits. Therefore, the accuracy of G is a limiting factor. 

Now that the Planck constant has been fixed to a more accurate value and now that the units of mass depend on it, the increase in the accuracy of G depends only on achieving the solution to quantum gravity, and this is where the generalized holographic model reaches its climax. We already have the complete solution to quantum gravity expressed in terms of our surface-to-volume ratio 𝝓, and it is beautiful!

Haramein's coming paper, entitled Scale invariant Unification of Forces, Fields, and Particles in a Quantum Vacuum Plasma, will demonstrate the unification of all the units, constants, forces, and increase the accuracy of the Planck Units by calculating the gravitational constant G up to 10^-12 digits of accuracy! 

Note to the reader: This article is part of section 7.1, Module 7 “New Advances in Unified Physics” of our Unified Science course, which is online, for free.  

References

[1] N. Haramein, Phys. Rev. Res. Int. 3, 270 (2013)

[2] N. Haramein, e-print https://doi.org/10.31219/osf.io/4uhwp (2013)

[3] A. Antognini, F. Nez, K. Schuhmann, F. D. Amaro, F. Biraben, J. M. R. Cardoso, D. S. Covita, A. Dax, S. Dhawan, M. Diepold, L. M. P. Fernandes, A. Giesen, A. L. Gouvea, T. Graf, T. W. Hänsch, P. Indelicato, L. Julien, C-Y. Kao, P. Knowles, F. Kottmann, E-O. Le Bigot, Y-.W Liu, J. A. M. Lopes, L. Ludhova, C. M. B. Monteiro, F. Mulhauser, T. Nebel, P. Rabinowitz, J. M. F. dos Santos, L. A. Schaller, C. Schwob, D. Taqqu, J. F. C. A. Veloso, J. Vogelsang, and R. Pohl, Science 339, 417 (2013)

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