Faraday pictured the physical link between the electrical current in a wire and the compass needle as a ‘field’, one that could be visualised as the pattern formed when iron filings are scattered on a piece of paper above a magnet.
Einstein wrote about how he imagined Maxwell must have felt in an essay entitled ‘The Fundaments of Theoretical Physics’: ‘Imagine his feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarised waves and with the speed of light! To few men in the world has such an experience been vouchsafed. At that thrilling moment he surely never guessed that the riddling nature of light, apparently so completely solved, would continue to baffle succeeding generations. Meantime, it took physicists some decades to grasp the full significance of Maxwell’s discovery, so bold was the leap that his genius forced upon the conceptions of his fellow workers.’
These words afford an insight not only into the magnitude of Maxwell’s discovery, but also into the mind of a true explorer of nature. It is amongst the most wonderful feelings available to a human being to understand something about the physical world for the first time. Few experience the privilege of genuine discovery, but the overwhelming excitement of understanding is available to all and is what drives a child to become a scientist.
Jodrell Bank radio telescope. It can send messages to Venus and catch the echo in four minutes. It will record radio signals of disturbances in space which happened 1000 million light years ago.
Light as an Electromagnetic Wave
Light is a wave, according to Maxwell, and it therefore has a wavelength. The wavelength is defined as the distance between two wave-crests, see illustration. Visible light waves are a tiny fraction of the electromagnetic waves travelling through the Universe. They span wavelengths from around 400 nanometres (400 thousand millionths of a metre) in the blue to 700 nanometres in the red. Beyond the red, the electromagnetic spectrum extends to wavelengths too long for our eyes to detect. They are still light – still the sloshing back and forth of electric and magnetic fields driving through the void – it’s just that our eyes didn’t evolve to see them. Instead we feel them in the residual heat of a fire or the ground at the end of a hot summer’s day. Beyond the infra-red, we arrive at microwaves, with wavelengths unsurprisingly about the size of a microwave oven. The spectrum then seamlessly slides into the radio region, with wavelengths the size of mountains. For most of our history we have been blind to these more unfamiliar forms of light, but until recently everyone had a detector capable of intercepting them and turning them into sound. When tuning an old-fashioned radio, you’re simply tuning an electronic circuit so that it is sensitive to a particular wavelength of light, broadcast from a transmitter. Music can be encoded in the wave by varying the amplitude of the waves (am radio, standing for amplitude modulation) or the wavelength itself (fm radio, standing for frequency modulation). Today you may be more likely to get your music over the internet, but if you’re using wifi, electromagnetic waves are delivering the data, with wavelengths of the order of 10 centimetres.
The electromagnetic spectrum.
Just as there is plenty of visible light in the Universe that isn’t manmade, so there are also naturally occurring microwaves and radio waves. And, just as for visible light from the most distant galaxies, the microwave and radio light carries information about these distant places across the Universe and into artificial eyes. The sky is ablaze at a wavelength of 21 centimetres, which is the wavelength of light emitted by hydrogen atoms when their solitary electron flips its spin from parallel with the proton to anti-parallel. Telescopes such as the 76-metre Lovell at the University of Manchester’s Jodrell Bank Observatory scan the skies at or around these wavelengths.
Light as an electromagnetic wave. The wavelength is the distance between two crests.
At shorter wavelengths, beyond the visible, there is ultraviolet light. The Sun glows brightly in the UV, which we cannot see but we feel its effect on our skin as sunburn. At shorter wavelengths there are X-rays, which can penetrate skin just as visible light penetrates glass, but are absorbed by bone, making them useful for medical imaging. Finally, at ultra-short wavelengths, are gamma rays, produced by high-energy astrophysical events such as supernova explosions and in nuclear radioactive decay processes. Gamma ray bursts are some of the highest-energy phenomena in the known Universe; bright flashes of electromagnetic radiation thought to be caused by the deaths of super-massive stars or collisions between binary neutron stars. The brightest gamma ray bursts release energy equivalent to converting a hundred planet Earths into pure radiation.
It is amongst the most wonderful feelings available to a human being to understand something about the physical world for the first time.
It is interesting, and perhaps revealing of Einstein’s character, that he didn’t mention that Maxwell’s insight turned out to be extremely useful. Heinrich Hertz confirmed the existence of Maxwell’s electromagnetic waves in a series of experiments conducted between 1886 and 1889, in which he inadvertently invented the radio transmitter. I say inadvertently, because when asked by one of his students the perennial question of which scientists often tire, ‘What use is all this?’ Hertz replied, ‘It’s of no use whatsoever. This is just an experiment that proves Maestro Maxwell was right. We just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there.’
On reading Hertz’s 1888 journal article, a young Italian named Guglielmo Marconi noticed that Hertz’s work could be used for signalling, and by 1901 (arguably), and certainly by 1902, he had transmitted messages using radio waves across the Atlantic, just over a decade after Hertz’s assertion that his research was of little practical use. Marconi received the Nobel Prize for his pioneering work on radio transmission in 1909. This is often the way in fundamental physics research; anyone who works at CERN, or NASA, or the European Space Agency, or the European Southern Observatory, or in any field that doesn’t produce clearly identifiable widgets, will have been asked to justify the expenditure on curiosity-driven acquisition of knowledge at some stage in their careers. Pointing to the fact that the questioner would probably be dead if a Scottish biologist named Alexander Fleming hadn’t isolated penicillin in 1928 because he was curious, rarely does the trick. As Fleming later said, ‘When I woke up just after dawn on 28 September 1928, I certainly didn’t plan to revolutionise all medicine by discovering the world’s first antibiotic, or bacteria killer, but I suppose that was exactly what I did.’ How anyone can fail to recognise that understanding the natural world, in which we live and of which we are a part, is unlikely to be useless. Perhaps Fleming could have specified in his will that those who cannot grasp this should be denied the use of his serendipitous discovery? A Darwinian solution to stupidity, admittedly, but evolution by natural selection is also a fact of life. Reason red in tooth and claw.
Einstein also points the way towards the rich insights yet to come as a result of Maxwell’s discovery; ‘he surely never guessed that the riddling nature of light, apparently so completely solved, would continue to baffle succeeding generations.’ As we have already seen in Chapter Two, Einstein felt so strongly about the value of Maxwell’s discovery because the universal speed of light was the clue that led him to replace Newton’s laws of motion with the Einstein’s Theory of Special Relativity. On its own, this is a most beautiful demonstration of the interconnected character of fundamental physics. Studying electrical currents in wires ultimately mandates a reformulation of our understanding of space and time. But there’s much more! F. Scott Fitzgerald said that inserting an exclamation mark is like laughing at your own joke, but I will now attempt to justify its use.
Why do hot things shine?
Part 2: Max Planck and the quantum revolution
We now understand in broad outline that matter emits light because it is made up of moving electrically charged particles. In the language of fields, when electrical charges jiggle they create
a changing magnetic field, which creates a changing electrical field, which creates a changing magnetic field, and so on, and the resulting moving disturbance is light. Maxwell’s equations describe this process mathematically.
This should immediately suggest a link between the temperature of something and the light it emits. The temperature of something is a measure of how fast its constituents are ‘jiggling around’; the higher the temperature, the more jiggling, and therefore the ‘more light’. We’ve been deliberately vague here, but the details matter. The correct answer, discovered by the German physicist Max Planck in 1900, saw the introduction of the fundamental physical constant that lies at the heart of quantum theory – Planck’s Constant.
Here’s why we are allowed an exclamation mark, Fitzgerald be damned. In order to answer the question of how hot things emit light, we’ve already been led to the door of Einstein’s Theory of Special Relativity via Maxwell’s equations. We now find that we stand at another door and the other great pillar of twenty-first-century physics, quantum theory, lies beyond. Yet again, we face the interconnectedness of physics. Without an understanding of quantum theory, we wouldn’t understand the structure of atoms, possess accurate theories describing the action of three of the four fundamental forces of nature, or be able to read the stories of distant planets from their reflected light alone. At a more prosaic level, there would be no transistors, and therefore no electronics, and the modern world would be a very different place. Imagine a valve-powered iPhone; it would have a shit battery life.
Planck’s foundational insight came to him on the evening of 7 October 1900. We know this because he spent the afternoon at his house in Berlin with a colleague, Heinrich Rubens, discussing theoretical models for the emission of light from hot objects. The experimental results, which were well known and of high precision, are shown schematically in the illustration, left.
The wavelengths of light radiated by a hot object depend on its temperature. Hotter objects radiate more light at shorter wavelengths.
The problem with the theoretical models of the day was that they all overestimated the amount of short-wavelength light emitted at a given temperature. Use of the term ‘overestimated’ might be to understate the problem; the preferred pre-Planckian model, known as the Rayleigh-Jeans law, predicted that an infinite amount of energy should be radiated away at shorter wavelengths by a hot object. This is obviously not right. The problem lay with the use of one of the foundational theorems of classical physics known as the equipartition theorem. If a lump of matter is considered as a series of little oscillating electric charges that radiate light, in accord with Maxwell’s equations, then the equipartition theorem states that all oscillations available to the electrical charges will happen, and they will all share the available energy equally. Faster vibrations correspond to shorter wavelengths of light, and according to classical theory there are more fast vibrations available to the charged particles than slow vibrations. If there is no reason why faster oscillations can’t happen, they should dominate and more light should be radiated away at the short-wavelength ultraviolet end of the spectrum, simply because there are more vibrations available. This was known as the Ultraviolet catastrophe, because it is not how hot things behave. Indeed, as can be seen in the illustration on here, cooler objects don’t emit much UV light at all.
When Rubens left the house after a long lunch, Planck was no nearer to a solution, but by the evening he’d sent his friend a formula, scribbled on the back of a postcard. Planck described it as an act of desperation, having tried everything else he could think of. In his scientific biography of Albert Einstein, Abraham Pais writes that Planck’s reasoning was ‘mad, but his madness has that divine quality that only the greatest transitional figures can bring to science’.
Planck’s Constant, devised by German physicist Max Planck (1858–1947) lies at the heart of quantum theory.
For reasons unknown, not even fully to himself, Planck decided that light can only be emitted in packets, or quanta, whose energy is related to their wavelength through the formula E = h c / λ, where c is the speed of light, λ is the wavelength of the light and h is a completely new constant of nature which is now known as Planck’s Constant. With that assumption he was able to derive the correct description for the spectrum of light emitted by an object of a given temperature. To see how this works, notice that Planck’s formula says that shorter wavelengths of light carry more energy, and since there is only a limited amount of energy available, shorter wavelengths will be harder and harder to radiate. The extreme scenario would be for a wavelength that would require more energy than is present in the object: Planck’s assumption provides a natural cut-off at the short-wavelength end of the spectrum, and solves the Ultraviolet catastrophe.
Until Einstein, everyone assumed that Planck’s insight related to the structure of matter itself, and not to Maxwell’s electromagnetic field.
Planck thought this was a neat mathematical trick, and didn’t appreciate its fundamental physical significance for many years. The reason we quote from a biography of Einstein is that it fell to Einstein, yet again, to take Planck’s prediction seriously as a fundamental discovery about nature. In 1905 he proposed that light is not only emitted and absorbed in little packets, but is actually composed of little packets, called photons. This is not a trivial distinction. Until Einstein, everyone assumed that Planck’s insight related to the structure of matter itself, and not to Maxwell’s electromagnetic field, which must surely be able to oscillate freely in accord with his beautiful equations. Einstein suggested something much more radical – that the electromagnetic field itself is made up of little particles of light. Just as he replaced Newton’s laws with Special Relativity, Einstein proposed that Maxwell’s equations are an approximation to something deeper. As late as 1913, Planck was having none of it. In a proposal written in support of Einstein’s admission to the Prussian Academy in that year, Planck wrote: ‘In sum, one can say that there is hardly one among the great problems in which modern physics is so rich to which Einstein has not made a remarkable contribution. That he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta, cannot be held too much against him, for it is not possible to introduce really new ideas even in the most exact sciences without sometimes taking a risk.’
Einstein’s instincts, as usual, turned out to be correct. There is a deeper theory than Maxwell’s called quantum electrodynamics, which was formulated by Richard Feynman and others during the 1940s and 50s. It was for this theory that Feynman, Julian Schwinger and Sin-Itiro Tomonaga shared the 1965 Nobel Prize in Physics. Einstein himself received the 1921 Nobel Prize for his explanation of something called the photoelectric effect, which was motivated by Planck’s insight. Light shining on a metallic surface causes electrons to be released from that surface, but if the light is all above a certain wavelength, no electrons will be released no matter how bright the light. The explanation is that photons of light of too long a wavelength have too little energy to release the electrons, and it doesn’t matter whether a million or a billion or a trillion photons hit the metal, no electrons will be emitted because they will never encounter a photon with enough energy to release them. Einstein’s explanation is regarded, along with Planck’s explanation for the observed spectrum of light emitted by hot objects, as the birth of quantum theory.
We now have everything we need to understand how glowing objects emit light, and why cooler objects emit redder light. Temperature is a measure of how fast things move around, which is a measure of how much energy is available. Electrically charged particles emit light when they are accelerated, in accord with Maxwell’s equations. Thinking in this way doesn’t explain the colour of the light emitted by hot objects. For that, we need quantum theory. Light can be treated as a stream of particles, whose energy is inversely proportional to the wavelength of the light in accord with Einstein’s extension of Planck’s hypothesis. Richard Feynman introduced a b
eautiful way of picturing the process known as a Feynman diagram (see here).
A Feynman diagram of an electron emitting a photon, which is absorbed by another electron.
Electrons can emit and absorb photons. The photon will carry away energy and momentum from the electron and deliver it to another one. In this case, we can image one electron being inside a lump of glowing lava. If it’s got a lot of energy, it is more likely to emit a photon of high energy, which can be radiated out and absorbed by another electron, which could be inside your retina. This is how you see the world. Since high-energy photons have shorter wavelengths, hotter objects will have a higher probability of emitting short-wavelength photons, simply because the charged particles inside them have more energy on average with which to emit them. Hot things are more likely to emit short-wavelength blue photons, which is why hot things glow blue and cooler things glow red.
The solar spectrum. Super-imposed is the calculation from Planck’s formula showing the spectrum from a ‘blackbody’ at a temperature of 6000 degrees Celsius.
We can now round everything off and answer our initial question about why the Sun shines. It shines because its outer layers are jiggling around, heated by the nuclear fusion reactions in its core. The temperature at the surface is approximately 5500 degrees Celsius, and this is a measure of how much energy is available for the charged particles in its surface to emit photons. The solar spectrum is shown in the illustration, left. Because the surface is 5500 degrees Celsius, the peak power is radiated in the visible part of the spectrum. All visible wavelengths are present, which is why the Sun appears ‘white hot’ in the sky. The surface is hot enough to radiate into the ultraviolet, down to wavelengths of around 250 nm, and there is a long tail of emission into the infrared. Planck’s theoretical curve, for a perfect emitter (known as a black body) of temperature 5500 degrees Celsius, is also shown.
Forces of Nature Page 21
