Hitting the Books: How Planck’s ‘Chain of Tiny Beads’ Helps Explain Why Light Bulbs Work


The laws of thermodynamics help govern virtually every aspect of the known universe – from the biological functions of individual cells to the formation of black holes in our galactic nucleus. And without the Herculean efforts of scientists, theorists, engineers and tinkerers over nearly two centuries, humanity would not even enjoy the level of technological advancement we see today. Modern conveniences like refrigerators, light bulbs, central air, and jet engines only came about thanks to our relatively new understanding of these fundamental forces in physics. In his new book, Einstein’s refrigerator, author, documentary maker 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 thermal foundations universe.

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


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

This reluctant conversion was forced on Planck by the advent of a new technology – the light bulb. In these electric currents flow through a filament, warming it and making it glow. This focused scientific minds on studying the precise relationship between heat and light.

Heat can flow from an object in three ways – by conduction, convection, and radiation. Everything can be observed in most kitchens.

Conduction is how electric hot plates transfer heat. The entire heated surface of the griddle is in contact with the underside of a pan and heat circulates from one to the other. Kinetic theory explains this as follows: As the temperature of the hotplate increases, its constituent molecules vibrate at increasingly rapid rates. Because they touch the molecules in the pan, they shake them. Soon all the molecules in the pan vibrate more vigorously than before, which manifests itself as the temperature of the pan increases.

A flow of heat by convection occurs in the ovens. Heating elements inside the oven wall cause nearby air molecules to move faster. These then collide with molecules deeper in the furnace, increasing their speed, and soon the temperature of the entire furnace increases.

The third type of heat transfer, by radiation, is that related to light. Fire up a grill and as the element temperature rises, it turns red. In addition to the actual red light, it also emits infrared light, which is what gets hot. When it hits an object, for example sausages in the drip pan, it vibrates their constituent molecules, raising their temperature.

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

To get a feel for Maxwell’s reasoning, imagine holding one end of a very long rope. It’s pretty tight and the other end is, say, a mile away. Jerk the end you are holding up and down. You see an elbow moving away from you on the rope. Now move the end of the rope up and down continuously. A continuous undulating wave descends the rope.

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

How fast does the wave descend the rope? It depends on the weight of the beads and the tension of the connecting elastic. Making the beads heavier will slow it down as it takes more effort to move them. Increasing the voltage will speed it up. Each bead can pull harder on the next if the elastic between them is tighter. Intuitively, if you shake the end of a heavy, relaxed rope, the ripples slowly descend it. On the other hand, the waves will hurtle down a light guitar string stretched at more than a thousand kilometers per hour.

In Maxwell’s imagination, empty space is filled with stretched “ropes” like this. They emanate from many particles that make up all “things” in the world around us. Take, for example, the tiny negatively charged electron, a building block of all atoms. Imagine a single electron standing still in empty space. Tight ropes extend in all directions, even in a vacuum. Known as “electric field lines,” they are invisible and incorporeal, but if you place another charged particle, such as a positively charged proton, in a field line, it feels attracted to the electron just like an electron. bead of the chain feels pulled.

Now imagine that the electron starts to oscillate up and down. Just as the wave has traveled the cord, the waves move away from the electron through the electric field lines emanating from it.

So how fast are these electric field waves moving? In one of the great overviews of science, Maxwell identified how to estimate this. Take a field line extending from the electron. Imagine along its length there are tiny compass needles. As the wave rises and falls along the field line, the compass needles rotate back and forth, towards it and then away from it. Readers may know that an electric current flowing through a wire can have a similar effect, creating what is called a magnetic field around it. Maxwell said that when waves travel along electric field lines, they generate waves in an accompanying magnetic field. He represented these waves perpendicular to each other. For example, let’s say the electric field wave oscillates up and down as it passes in front of you from left to right. Then the accompanying magnetic field wave oscillates towards you and moves away from you. And, more importantly, creating this magnetic wave takes effort, just as moving the weighted balls through the rope takes effort.

Maxwell’s reasoning was intuitive, a hunch. But it had a huge advantage. Remember that with the choppy chain, we could predict how fast a wave will travel along it by weighing one of its beads and measuring the tension in the interconnected elastic bands. Likewise, Maxwell could easily obtain measurements for their field line equivalents. Tension could be obtained by measuring the force with which two charged objects attract each other. The equivalent of the weight of a pearl came from measuring the strength of the magnetic field created when a known current flows through a wire.

Using these measurements, Maxwell estimated that these “electromagnetic” waves travel at around 300,000 kilometers per second. Lo and behold, it was remarkably close to measured estimates of the speed of light – too close to be a coincidence. It seemed highly unlikely that light would “manage” to travel at the same speed as an electromagnetic wave; it seemed much more likely that the light was in fact an electromagnetic wave.

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

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

Not only did Maxwell’s theory describe visible colors, but it also predicts the existence of invisible electromagnetic waves. Sure enough, these were found from the 1870s. Radio waves, for example, have frequencies ranging from less than a hundred oscillations per second 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 the frequencies are higher than that of blue light, they are ultraviolet rays. Next are x-rays, and gamma rays oscillate up and down over a hundred billion billion times per second. The entire range, from radio waves to gamma rays, is called the electromagnetic spectrum.

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

The enigma of the late 19th century was: What is the precise relationship between the temperature of an object and the frequencies of the electromagnetic waves it produces?



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