Saturday, April 20, 2013

History of Science -- Part Nine: Max Planck

As the nineteenth century ended, the search for Nature’s basic laws seemed close to its goal. There was a sense of a task accomplished. Physics presented an orderly scene that fit the proper Victorian mood of the day.

Objects both on Earth and in the Heavens behaved in accord with Newton’s laws. So, presumably, did atoms. The nature of atoms was unclear. But to most scientists the rest of the job of describing the universe seemed a filling in of the details of the giant machine as the British scientist James Jeans pointed out.

What we now call Classical Physics explains the world quite well; it’s just the details it can’t handle. Ironically, Quantum Physics handles the details perfectly; it’s just the world it can’t explain. (More later on that point.)

Quantum physics does not replace classical physics the way the sun-centered solar system replaced the earlier view with the Earth as the cosmic center. Rather, quantum physics encompasses classical physics as a special case. Classical physics is usually an extremely good approximation for behavior of objects that are larger than atoms. But, you dig deeply enough into any natural phenomenon — physical, chemical, biological, or cosmological — you hit quantum mechanics.

Quantum theory has been subject to challenging tests for almost 100 years. No prediction by the theory has ever been shown to be wrong. It is the most battle-tested theory in all of science. Nevertheless, if you take the implications of the theory seriously, it is downright mind boggling. Niels Bohr, a founder of quantum theory, claimed that unless you’re shocked by quantum mechanics, you have not understood it.

On Friday, April 27, 1900, the British physicist Lord Kelvin gave a speech entitled "Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light," which began:

The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds.

Kelvin went on to explain that the "clouds" were two unexplained phenomena, which he portrayed as the final couple of holes that needed to be filled in before having a complete understanding of the thermodynamic and energy properties of the universe, explained in classical terms of the motion of particles.

Note that, even though Lord Kelvin identified these two issues of physics, he strongly believed the main role of physics in that day was to just measure known quantities to a great degree of precision, out to many decimal places of accuracy. He must have assumed the two holes would easily be filled in using the basic physics known at that time.

The "clouds" to which Kelvin was referring were:

  1. The inability to detect the luminous ether, specifically the failure of the Michelson-Morley experiment.
  2. The black body radiation effect known as the ultraviolet catastrophe.

The last chapter of this history described how Einstein’s theory of Relativity addressed the first cloud in a most unexpected way.

The second “cloud,” the so-called “ultraviolet catastrophe” started a chain of discoveries and propositions that revolutionized physics in a way at least equal to Einstein’s theories. In the final week of the nineteenth century, Max Plank suggested something outrageous — that the most fundamental laws of physics were violated. This was the first hint of the quantum revolution, that the worldview we now call “classical” had to be abandoned.

Max Planck, son of a distinguished professor of law, was careful, proper, and reserved. His clothes were dark and his shirts stiffly starched. Raised in the strict Prussian tradition, Planck respected authority, both in society and in science. Not only should people rigorously obey the laws, so should physical matter. Not your typical revolutionary.

In 1875, when young Max Planck announced his interest in physics, the chairman of his physics department suggested he study something more exciting. Physics, he said, was just about complete: “All the important discovers have already been made.” (Notice that this opinion of the completion of science was very prevalent in the late 1800s.)

Undeterred, Planck completed his studies in physics and plugged away for years as a Privatdozent, an apprentice professor, receiving only the small fees paid by students attending his lectures.

Planck chose to work in the most properly lawful area of physics, thermodynamics, the study of heat and its interaction with other forms of energy. His solid but unspectacular work eventually won him a professorship. His father’s influence is said to have helped.

A nagging unexplained phenomenon in thermodynamics was thermal radiation: the spectrum, the colors, of the light given off by hot bodies. (Problem #2 of Kelvin’s two “clouds.”) Planck set about to solve it.

What’s the problem? That a hot poker should glow seems obvious. Although at the turn of the century the nature of atoms, even the existence of atoms, was unclear, electrons had just been discovered. Presumably these little charged particles jiggled in a hot body and therefore emitted electromagnetic radiation. This light seemed important to understand a fundamental aspect of Nature because it was the same no matter what material it came from.

The radiation one observed seemed reasonable. As a piece of iron gets hotter, its electrons should shake harder and, presumably, at a higher rate, meaning at a higher frequency. Therefore, the hotter the metal, the brighter and higher the frequency of the glow. As it gets hotter, its color goes from the invisible infrared, to a visible red, to orange, and eventually the metal becomes white hot as the emitted light covers the entire visible frequency range.

Since our eyes can’t see frequencies above the violet, superhot objects, which emit mostly in the ultraviolet, appear bluish. Materials on Earth vaporized before they get hot enough to glow blue, but we can look at hot blue stars. Even cool objects “glow,” though weakly and at low frequencies. Bring you palm close to your cheek and feel the warmth from the infrared light your hand emits. The sky shines down on us with invisible microwave radiation left over from the flash of the Big Bang.

In this figure that I’ve sketched the actual intensity of radiation from the Earth’s Sun and its 6,000° C surface at different frequencies, which are labeled as colors. (Colors are different frequencies of light.) An object hotter than our Sun emits more light at all frequencies, and its maximum intensity is at a higher frequency. But the intensity always drops at very high frequencies.

The dashed line is the problem — it is the intensity calculated with the laws of physics accepted in 1900. It worked well in the infrared. But at higher frequencies, classical physics not only gave a wrong answer, it gave a ridiculous answer. It predicted a forever increasing light intensity at frequencies beyond the ultraviolet.

Were this true, every object would instantaneously lose its heat by radiating a burst of energy at frequencies beyond ultraviolet. This embarrassing deduction was derided as the “ultraviolet catastrophe.” But no one could say where the seemingly sound reasoning of Classical Physics went wrong.

Max Planck struggled for years to derive a theory that fit the experimental data. In frustration, he decided to work the problem backward. He would first try to guess a formula that agreed with the data and then, with that as a hint, try to develop the proper theory. In a single evening, studying the data others had given him, he found a fairly simple formula that worked perfectly.

(What a wonderful example of one way we do science.)

If Planck put in the temperature of the body, his formula gave the correct radiation intensity at every frequency. His formula needed a “fudge factor” to make it fit the data, a number he called “.” We now call it “Planck’s constant” and recognize it as a fundamental constant of Nature, like the speed of light.

With his formula as a hint, Planck sought to explain thermal radiation in terms of the fundamental principles of physics. In the most straightforward models, an electron, though bound to its parent atom, would start vibrating if it were bumped by a jiggling neighboring atom in a hot metal. This little charged particle would then gradually lose its energy by emitting light. The following sketch is a plot of such an energy loss. In a similar fashion, a pendulum bob on a string, or a child on a swing, given a shove, would continuously lose energy to air resistance and friction.

However, every description of the electron radiating energy according to the physics of the day shown in this graph led to the same crazy prediction, the ultraviolet catastrophe. After a long struggle, Planck ventured an assumption that absolutely violated the universally accepted principles of classical physics. At first, he didn’t take it seriously, He later called it an “act of desperation.”

Max Planck assumed an electron could radiate energy only in chunks, in “quanta” (the plural of quantum). Moreover, each quantum would have an energy equal to the number ℎ in his formula times the frequency of vibration of the electron.

Behaving this way, an electron would vibrate for a while at constant energy. That is, this electric charge would vibrate without losing energy to radiation. Then, randomly, and without cause, without an impressed force, it would suddenly lose a quantum of energy, radiating it as a pulse of light. (Electrons would also gain their energy from the hot atoms by such “quantum jumps.”)

In the following sketch I plot an example of such energy loss in sudden steps. The dashed line repeats the classically predicted, gradual energy loss.

Planck was allowing the electrons to violate both the laws of electromagnetism and Newton’s universal equation of motion. Only by this wild assumption could he get the formula he had guessed, the formula that correctly describe thermal radiation.

If this quantum-jumping behavior is indeed a law of Nature, it should apply to everything. Why, then, do we see the things around us behaving smoothly? Why don’t we see children on swings suddenly change their swinging motion in quantum jumps? It’s a question of numbers, and ℎ is an extremely small number.

Not only is ℎ small (ℎ = 6.626 times 10-34 joule-seconds), but since the frequency of a child moving back and forth on a swing is much lower than the frequency at which an electron vibrates, the quantum steps of energy (ℎ times frequency) are vastly smaller for the child. And, of course, the total energy of a swinging child is vastly larger than that of an electron. Therefore, the number of quanta involved in the child’s motion is vastly, vastly greater than the number involved in the motion of the electron. A quantum jump, the change in energy by a single quantum, is thus far too small to be seen for the child on a swing.

But back in Planck’s day the reaction to the solution he proposed for the thermal radiation problem was not very good, even though his formula fit the experimental data well. But his explanation seemed more confounding than the problem it presumed to solve. Planck’s theory seemed silly. No one laughed, at least no in public — Herr Professor Planck was too important a man for that. His quantum-jumping suggestion was simply ignored.

Physicist were not about to challenge the fundamental laws of mechanics and electromagnetism. Even if the classical laws gave a ridiculous prediction for the light emitted by glowing bodies, these basic principles seemed to work everyplace else. And they made sense. Planck’s colleagues felt a reasonable solution would eventually be found. Planck himself agreed and promised to seek one. The quantum revolution arrived with an apology, and almost unnoticed.

In later years, Planck even came to fear the negative social consequences of quantum mechanics. Freeing the fundamental constituents of matter from the rules of proper behavior might seem to free people from responsibility and duty. The reluctant revolutionary would have liked to cancel the revolution he sparked.

But Nature is not to be ignored and experimental results are the deciding factor, not social comfort. Now enters a familiar character from a previous episode. Tune in next time to learn the rest of the story.

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