Hitting the Books: How Planck’s ‘chain of tiny beads’ helps explain why lightbulbs work

The laws of thermodynamics help to govern in virtually every aspect of the known universe — from the biological functions of single cells to the formation of black holes at our galactic core. And without the Herculean efforts of scientists, theorists, engineers and tinkerers over the course of nearly two centuries, humanity would not be enjoying even nearly the level of technological advancement we do today. Modern conveniences like refrigerators, light bulbs, central air, and jet engines have only come about because of our relatively new understanding of these fundamental forces of physics. In his new book, Einstein’s Fridge, author, documentary filmmaker, and science communicator Paul Sen, explores the works and quirks of these pioneering researchers — from Lord Kelvin and James Joule to Emmy Noether, Alan Turing, and Stephen Hawking — as they sought to better understand the thermal underpinnings of the universe.

“Excerpted from Einstein’s Fridge: How the Difference Between Hot and Cold Explains the Universe by Paul Sen. Copyright © 2021 by Furnace Limited with permission by Scribner, a division of Simon & Schuster, Inc.”

In 1900, Max Planck, a critic of Boltzmann’s science for nearly two decades, published papers that hinted at a change of heart. Even more unexpectedly he seemed to be saying that Boltzmann’s statistical methods might have relevance far beyond thermodynamics.

This reluctant conversion was forced upon Planck by the advent of a new technology—the electric light bulb. In these electric current flows through a filament, warming it and making it glow. This focused scientific minds on investigating the precise relationship between heat and light.

There are three ways—conduction, convection, and radiation—that heat can flow out of an object. All can be observed in most kitchens.

Conduction is how electric hot plates transfer heat. The whole heated surface of the plate is in contact with the underside of a pan, and the heat flows from one to the other. Kinetic theory explains this as follows: As the hot plate’s temperature rises, its constituent molecules vibrate at faster and faster rates. Because they’re touching the molecules of the saucepan, they shake them. Soon all the saucepan molecules are vibrating more vigorously than before, which manifests as the saucepan’s temperature rising.

Heat flow through convection occurs in ovens. The heating elements within the oven’s wall cause the air molecules nearby to zip about more quickly. These then collide with molecules deeper in the oven, increasing their speed, and soon the entire oven’s temperature rises.

The third kind of heat transfer, by radiation, is the one linked to light. Turn on a grill, and as the element’s temperature rises, it glows red. In addition to the actual red light, it’s also giving off infrared light, which is what feels hot. When this strikes an object, say the sausages in the grill pan, it causes their constituent molecules to vibrate, raising their temperature.

Scientists’ understanding of radiating heat had improved in the 1860s thanks to James Clerk Maxwell, who published a set of mathematical equations describing “electromagnetism.”

For a sense of Maxwell’s reasoning, imagine holding one end of a very long rope. It’s stretched fairly tight and the other end is, say, a mile away. Jerk the end you’re holding up and down. You see a kink travel away from you down the rope. Now move the end of the rope up and down continuously. A continuous undulating wave travels down the rope.

To see why, imagine the rope as a chain of tiny beads. Each is connected to the next by a short stretch of elastic. When you move the first bead in the chain, it pulls the one adjacent to it. That then pulls the one beyond it and so on. The up and down movement of the first bead is thus passed sequentially down all the beads, which looks a wave moving down the rope.

How fast does the wave travel down the rope? It depends on how heavy the beads are and on the tension in the connecting elastic. Making the beads heavier will slow it down because it takes more effort to move them. Increasing the tension will speed it up. Each bead can pull harder on the next if the elastic between them is tauter. Intuitively, if you shake the end of a heavy, slack rope, the wiggles travel down it slowly. In contrast, waves will race down a taut, light guitar string at over one thousand kilometers an hour.

In Maxwell’s imagination, empty space is filled with taut “strings” of this kind. They emanate from many of the particles that make up all the “stuff” in the world around us. Take, for example, the tiny negatively charged electron, a constituent part of all atoms. Imagine just one electron motionless in empty space. Tight strings stretch out from in all directions through even the vacuum. Known as “electric field lines,” they’re invisible and incorporeal but if you put another charged particle, like a positively charged proton, in a field line, it feels pulled towards the electron just as a bead in the chain feels pulled.

Now imagine the electron starts oscillating up and down. Just as the wave traveled down the rope, waves travel away from the electron down the electric field lines emanating from it.

So how fast do these electric field waves move? In one of the great insights of science, Maxwell identified how to estimate this. Take one field line stretching out from the electron. Imagine along its length, there are tiny compass needles. As the wave moves up and down along the field line, the compass needles swivel back and forth, towards it and then away from it. Readers may know an electric current flowing down a wire can have a similar effect, creating what’s known as a magnetic field around it. Maxwell was saying that as waves move down electric field lines, they generate waves in an accompanying magnetic field. He pictured these waves at right angles to each other. For example, say the electric field wave oscillates up and down as it moves past you from left to right. Then the accompanying magnetic field wave will oscillate towards you and away from you. And, importantly, creating this magnetic wave takes effort just as moving the weighted beads in the rope took effort.

Maxwell’s reasoning was intuitive, a hunch. But it had an enormous benefit. Remember with the wiggling chain, we could predict the speed at which a wave will travel along it by weighing one of its beads and by measuring the tension in the interconnecting elastic bands. Similarly, Maxwell could easily obtain measurements for their equivalents in field lines. The tension could be obtained by measuring how strongly two charged objects attract each other. The equivalent of the weight of a bead came from measuring the strength of the magnetic field created as a known current flowed down a wire.

Using these measurements, Maxwell estimated that these “electromagnetic” waves travel at about 300,000 kilometers per second. Lo and behold, that was remarkably close to measured estimates of the speed of light—too close to be a coincidence. It seemed highly unlikely that light “just happens” to move at the same speed as an electromagnetic wave; it seemed far more likely that light actually is an electromagnetic wave.

The point is any oscillating electric charge will emit an electromagnetic wave. Daylight thus exists because electrons in the sun are constantly being vibrated. They send waves down the field lines emanating from them. When these reach our eyes, they shake charged particles in our retinas. (This is otherwise known as “seeing.”)

Maxwell showed that the color of light is determined by the rate or the frequency at which the electromagnetic waves oscillate. The faster it does so, the bluer the light. Red light, the lowest-frequency visible light, is an electromagnetic wave oscillating 450 trillion times a second. Green light oscillates at a higher frequency, at around 550 trillion times a second, and blue light at around 650 trillion times a second.

Not only did Maxwell’s theory describe visible colors, but it also predicted the existence of invisible electromagnetic waves. Sure enough, these were found from the 1870s onward. Radio waves, for instance, have frequencies that range from fewer than a hundred oscillations per second to up to around three million. The term “microwave” covers a range from there up to three hundred billion. Infrared sits between microwaves and visible light. When frequencies are greater than that of blue light, they are ultraviolet rays. Then comes X-rays, and oscillating up and down over a hundred billion billion times per second are gamma rays. The entire range, from radio waves to gamma rays, is called the electromagnetic spectrum.

Maxwell’s discovery meant physicists knew in principle how the filament in a light bulb was made to glow. An electric current makes the filament hot. This in turn causes its constituent electrons to oscillate and emit electromagnetic waves. In fact, all objects emit some electromagnetic waves. Atoms are in constant motion, which means so are their electrons. For instance, at a healthy temperature of around 97°C, human bodies emit detectable infrared waves. Snakes, such as vipers, pythons, and boas, have evolved organs to detect such radiation to help them hunt and find cool places to rest.

The puzzle in the late nineteenth century was—what is the precise relationship between the temperature of an object and the frequencies of electromagnetic waves it produces?