Sunday, April 21, 2013

History of Science -- Part Ten: Particles vs. Waves

Recall that Newton had a troubling time classifying light during his research. He thought it had some wave properties, but he finally decided light was a particle that he called a “corpuscule.” He postulated that, since light followed his laws of motion in both reflection and refraction, it had to be a stream of particles. Others thought it was a wave, but Newton's reputation won out his view, at least in England. Finally Thomas Young proved conclusively that light was a wave with his double slit experiment. And then Maxwell showed that light was a complex electromagnetic wave that was a combination of an electric field and a magnetic field. That was the state of the science at the turn of the twentieth century.

But God is more subtle than even all these great minds had concluded. It took another scientist to finally discover the surprising truth. Another troubling result that is part of Quantum Mechanics. Planck had already calculated that these tiny, atom-sized particles that made up all matter followed rules unlike any we had experienced in our “macro” world. Now more mystery and confusion will be added to QM.

His parents worried about mental retardation when this young boy was slow in starting to talk. Later, though he became an avid and independent student of things that interested him, his distaste for the rote instruction of the Gymnasium (High School) led to his not doing well. Asked to suggest a profession that he might follow, the headmaster confidently predicted, “I doesn’t matter, he’ll never make a success of anything.”

His parents left Germany for Italy after the family electrochemical business failed. The new business in Italy fared little better and soon the young man was on his own. He took the entrance exam to the Zurich Polytechnical Institute but did not pass. He was finally admitted the next year. On graduation, he was unsuccessful in trying for a position as Privatdozent. He had the same luck in applying for a teaching job at the Gymnasium. For a while he supported himself as a tutor for students having tough with high school. Eventually, through a friend’s influence, he got a job in the Swiss patent office.

His duties as Technical Expert, Third Class, were to write summaries of patent applications for his superiors to use in deciding whether an idea warranted a patent. He enjoyed the work, which did not take his full time. Keeping an eye on the door in case a supervisor came in, he worked on his own projects.

Initially, he continued on the subject of his doctoral thesis, the statistics of atoms bouncing around in a liquid. This work soon became the best evidence for the atomic nature of matter, something still debated at that time. He concluded that the apparent random movement of tiny dust motes suspended in water was caused by the microscopic jostling of individual atoms. This is called Brownian Motion. He was the first to understand the cause.

Then he was struck by a mathematical similarity between the equation for the motion of atoms and Planck’s radiation law. He wondered: Might light be not only mathematically like atoms, but also physically like atoms?

If so, might light, like matter, come in compact lumps? Perhaps the pulses of light energy emitted in one of Planck’s quantum jumps did not expand in all directions as Planck assumed. Could the energy instead be confined to a small region? Might there be atoms of light as well as atoms of matter?

He speculated that light is a stream of compact lumps, “photons” (a term that came later). Each photon would have an energy equal to Planck’s quantum (Planck’s constant times its frequency). Photons would be created when electrons emit light. Photons would disappear when light is absorbed.

Seeking evidence that his speculation might be right, he looked for something that would display a granular aspect to light. It was not hard to find. The “photoelectric effect” had been known for almost twenty years. Light shining on a metal could cause electrons to pop out.

The situation was messy. Unlike thermal radiation, where a universal rule held for all materials, the photoelectric effect for each substance was different. Moreover, the data was inaccurate and not particularly reproducible.

But never mind the poor data. Spread out light waves shouldn’t kick electrons out of a metal at all. Electrons are too tightly bound. While electrons are free to move about within a metal, they can’t readily escape it. We can “boil” electrons out of a metal, but it takes a very high temperature. We can pull electrons out of a metal, but it takes a very large electric field. Nevertheless, dim light, corresponding to an extremely weak electric field, still ejects electrons. The dimmer the light, the fewer the electrons. But no matter how dim the light, some electrons are always ejected.

The photoelectric effect was just what the twenty-five year old scientist needed. Planck’s radiation law implied that light came in packets, quanta, whose energy was larger for higher frequency light. If the quanta were actually compact lumps, all the energy of each photon could be concentrated on a single electron. A single electron absorbing a whole photon would gain a whole quantum of energy.

Light, especially high-frequency light with its high-energy photons, could then give electrons enough energy to jump out of the metal. The higher the energy of the photon, the higher the energy of the ejected electron. For light below a certain frequency, its photons would have insufficient energy to remove an electron from the metal, and no electrons would be ejected.

In 1905, the young scientist wrote, “According to the presently proposed assumption the energy in a beam of light emanating from a point source is not distributed continuously over larger and larger volumes of space, but consists of a finite number of energy quanta, localized at points of space which move without subdividing and which are absorbed and emitted only as units.”

This scientist believed what Max Planck did not. He believed in the quantum theory which all the others had ignored.

Assuming that light comes as a stream of photons and that a single electron absorbs all the energy of a photon, he used the conservation of energy of the ejected electrons. If you plot the energy-frequency of ejected electrons it shows that photons with energy less than the binding energy of the metal does not kick any electrons out. That explains the photoelectric effect being different for different metals. He hypothesized it was tied to the electron binding energy.

A striking aspect of his photon hypothesis is that the slope of the straight line in his graph is exactly Planck’s constant, "ℎ." Until this time, Planck’s constant was just a number needed to fit Planck’s formula to the observed thermal radiation. It appeared nowhere else in physics. Before this young scientist’s photon hypothesis, there was no reason to think the ejection of electrons by light had anything at all to do with the radiation emitted by hot bodies. This slope of the graph was the first indication that the quantum was universal.

Ten years after this work on the photoelectric effect, the American physicist Robert Millikan found that his formula in every case predicted “exactly the observed results.” Through careful experiment the quality of the photoelectric effect data was finally improved. Nevertheless, Millikan called the photon hypothesis leading to that formula “wholly untenable” and called the young scientist's suggestion that light came as compact particles “reckless.”

Millikan was not alone. The physics community received the photon postulate “with disbelief and skepticism bordering on derision.” Nevertheless, eight years after proposing the photon, the young scientist had gained a considerable reputation as a theoretical physicist for many other achievements and was nominated for membership in the Prussian Academy of Science. Planck, in his letter supporting that nomination, felt he had to defend the young scientist. “[T]hat he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta, cannot really be held too much against him …” Remember, even Planck didn’t believe in quanta, although he had first thought of it.

Ultimately, in 1922, this scientist was awarded the Nobel Prize for his analysis of the photoelectric effect, yet the citation avoided explicit mention of the then seventeen-year-old idea, but still unaccepted photon. A biographer later wrote, “From 1905 to 1923, he was a man apart in being the only one, or almost the only one, to take the light-quantum theory seriously.”

Though the reaction of the physics community to photons was, in a word, rejection, they were not just being pig-headed. Light was proven to be a spread-out wave. Light displayed interference. A stream of discrete particles could not do that.

Recall my description in a previous chapter of the History of Science of Young’s experiment with the double slit. Light coming through a single narrow slit illuminates a screen more or less uniformly, displaying the spreading nature of waves. Once a second slit is added a pattern of dark bands appears whose spacing depends on the spacing of the two slits. At those dark places, wave crests from one slit arrive together with wave troughs from the second slit. Waves from one slit thus cancel waves from the other. Interference demonstrates that light is a wave. There was no other possible conclusion.

Nevertheless, the now Nobel Prize winning physicist held that the photoelectric effect showed light to be a stream of photons — tiny compact bullets. But how could tiny bullets produce the interference patterns seen with light?

One might suppose that the tiny bullets might bounce off each other and stack up non-uniformly making the bands that were assumed to be an interference pattern, but that loophole was quickly closed by careful experiments that sent one photon at a time through the slits. This had to be repeated hundreds of times, but the ultimate effect was the build up of an interference pattern.

A great mystery: Choosing to demonstrate interference, something explicable only in terms of waves, you could prove light to be a widely spread-out wave. However, by choosing a photoelectric demonstration, where a single electron absorbed a whole light quantum, you could prove light to be a stream of tiny compact objects. There seems to be an inconsistency. It appeared that light was playing with the experimenters and would act like a wave if tested as a wave and act like particles if tested as particles. But it has to be one or the other. Right?

Though the paradoxical nature of light disturbed the young scientist, he clung to his photon hypothesis. He declared that a mystery existed in Nature and that we must confront it. He did not pretend to resolve the problem.

And we do not pretend to resolve it now. The mystery is still with us a hundred years later. The implications of our being able to choose to prove either of two contradictory things extend beyond physics. It’s the quantum enigma. We now accept this dual nature of light, even though we still don’t understand it. Remember, we use experimental results to demonstrate the truth of theories. In this case, the various experiments seem to contradict each other, and we’re left with no choice but to accept the dual nature. Light manifests itself both as a wave and as a particle. This dual nature of light is disturbing, but — as the magician said — you ain't seen nothin' yet.

In 1906, the young scientist I’ve been talking about had discovered photons, firmly established the atomic nature of matter in his work on Brownian Motion, and formulated the theory of Relativity. Yes, the young man’s name was Albert Einstein. In that year he was promoted by the Swiss patent office to Technical Expert, Second Class.

No comments:

Post a Comment