Saturday, February 2, 2008

Planck’s constant and black bodies

Physicists help explain the basics

In the early twentieth century, the deeper nature of matter was thought to be whole and continuous- much like water in a swimming pool. Even the merging of electromagnetism and thermodynamics, two of the eras greatest accomplishments in physics, supported this vision- or so it was assumed.

A looming complication though was that this wonderful fusion of electromagnetism and thermodynamics could not account for the phenomena observed in cavity radiation- better known as black body radiation. If you take an opened lidded box- even if the interior is painted white- and close the lid, the radiation (i.e.; light photons) bouncing around its interior will eventually be absorbed thereby causing the box to become “black”. You might ask- So what?

This phenomenon was the source of considerable consternation at the time and had to do with a common feature of matter that did not jibe a prediction derived from these theories. Jim Al-Khalili notes “All bodies emit radiation, and over the whole frequency range of the spectrum. The distribution over frequency depends on the body’s temperature. If a solid is hot enough it will glow visibly, but as it cools its glow will diminish as the longer wavelength radiation- beyond the visible- dominates. This does not mean that it ceases to emit visible light, but simply that the intensity of light will be too weak for us to see. Of course all matter also absorbs and reflects radiation falling on it. Which wavelengths are absorbed and reflected defines the colour of everything we see.”

In the latter 19th and early 20th centuries, it was assumed that emitted radiation from objects did so in a continuous and smooth way. According to what was known, you could turn the knob up or down and vary the frequency ad infinitum both ways.

Black bodies are efficient absorbers and distributors of radiation. According to Al-Khalili “Black bodies are so called because they are perfect absorbers of radiation and do not reflect any light or heat. Of course, a black body must somehow dispose of all the energy it absorbs- otherwise its temperature would become infinite!”

Physicists observed this similar phenomenon with any “cavity”, but could not account for it in their calculations- it was an empirical observation that didn’t fit in any existing formula. Kenneth Ford notes “scientists had learned a remarkable fact about this radiation: its properties depend only on the temperature of the walls, not on the material of which they are composed. Yet despite this marvelous simplification, all efforts to account for the way in which the intensity is distributed over different frequencies failed.

This was one of those moments- a crossroads- in history where the merging of previously very successful theories created a stumbling block. The solution to this one problem opened the flood gates that would eventually give rise to quantum mechanics and all of its predictive glory.

Explaining the obvious observation that black bodies somehow distributed these radiations without, for example, spiraling towards an infinite series of escalating temperatures became an urgent matter at the time. Physicists such as Wilhelm Wien and Lord Rayleigh came up with formulas that came close- but not close enough to agree with the observed data.

In the end, it was through the enormous effort of Max Planck- basing himself on Weins formulas- that finally led him in October of 1900 to create a mathematical formula that agreed with the observed black body distribution of energies. This was the key that opened the door of the world of quantum mechanics. Planck realized that the behavior of black body radiant energy distribution could be accounted for if the vibrating charges emitted radiation not continuously (as previously assumed) but in lumps- which he called “quanta.”

According to Ford “Planck had to postulate that the minimum energy quantum a vibrating charge can emit is directly proportional to the frequency of vibration.” Hence was born Planck’s formula:


Where E is the quantum energy, f is the frequency, and h is the “constant of proportionality”- Planck’s constant. It is this little constant –by coherently connecting energy to frequency- that caused a revolution.

This led, perhaps to Planck’s dismay, ultimately to the realization that matter and energy at these levels seemed to behave in a granular and lumpy way- “not continuously like water from a fire hose but instead in lumps like baseballs from a pitching machine.” Over the next quarter century luminary physicists such as Max Born, Neihl Bohr, and Erwin Schrodinger gave form to a more general theory of the sub-atomic world and gave rise to the framework of today’s quantum mechanics.

As one delves into the incredibly small depths of Planck level reality, the fluidness of the “classic” macroscopic world gives way to lumpiness and the familiar gives way to strangeness. It is a world of bizarre interactions, of “wave” probabilities, corpuscle behaviors, and (as far as we know) truly fundamental particles.

This elemental world -possibly the very core of matter as we know it- lies within all of us. Yet, despite the many claims of fantastic powers feeding off of a “quantum consciousness” or assertions that mind over matter can cure all ills; this realm -in that way- is beyond our reach.

On the other hand, we can use real quantum knowledge to explore incredible horizons and perhaps invent unimaginable technologies based on its properties. It is important to remember that without the incredible work of Planck and others we would never have known this realm even existed.

As Ford aptly notes “Plancks constant remains the fundamental constant of quantum theory, with ramifications that go far beyond its original role in relating radiated energy to radiated frequency…it is the constant that sets the scale of the subatomic world and that distinguishes the subatomic world from the “classical” world of everyday experience.”


Ford, K. The quantum world. Harvard university press.Cambridge, Mass. 2005

Al-Khalili. Quantum.Weidenfeld &nicolson, London, UK. 2004

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