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CHAPTER 1

Setting Sail

Having obtained a small but seaworthy vessel, with a makeshift crew of professional physicists and curious amateurs, we set sail. The hold contains provisions, a mix of scientific equipment, and a guitar. We have some theories to test, and we need data. We hope, like Darwin on the voyage of the Beagle, to find that we will be improved by a journey to distant countries.

We enter the mysterious seascape of the invisibly small from the west. On our map, the western fringes are objects at a human scale. As we sail eastward we will shrink further, gazing from the bow of our boat into the heart of matter, mapping the otherwise invisible.

Most things are made of smaller things. Our boat is made of wood, metal, fiberglass. It doesn't take much effort to see that these materials are themselves made of smaller stuff: splinters of wood, glass fibers, plastic. The glass fiber strands, the thickness of cotton thread, are made of silica. Each one of these strands is made of silicon atoms bound to oxygen atoms, with two atoms of oxygen for each of silicon — silicon dioxide. A silicon atom is a billion times smaller than the thickness of the thread. If each silicon atom were the size of one of the peas in the ship's galley, the fibers would have a diameter close to that of the Earth.

Each atom consists of a nucleus surrounded by fourteen electrons, each with a negative electric charge. The nucleus has a positive electric charge of fourteen times that of the electron, which is why fourteen electrons are attracted to it. That is a familiar kind of configuration. The solar system has eight planets (and some rocks and rejects) in orbit around the central Sun. It is tempting to picture the silicon atom as a tiny solar system with fourteen little electron-planets orbiting the nucleus. But as we will discover, electrons are not little planets; they are in reality something quite new and different.

As our boat sails east and we shrink to ever-smaller size, the world around us changes. Most of the predictable laws governing the lands we travel turn out to be obeyed only on average, and electrons and the other objects we encounter are radically different from the features we are familiar with in the west.

For reasons connected with this, in ways that should become clearer during this voyage, the ability to see smaller and smaller pieces of matter requires particle beams — microscopes, effectively — of higher and higher energy. This means that the frontier of the very small also becomes the frontier of high energy. The important point of high energy in particle physics is the concentration of the energy into a small space, or equivalently into a small number of particles. Because of this, a map of high energies and short distances also informs us about the physics of the very early universe: the hot, dense moments just after the Big Bang. In those first few moments, the energy in any given volume of space was so high that the smallest constituents of matter were laid bare.

To understand all of that, we first need to find out what inhabits this strange new world. What might we find inside an atom? For now, all we know is that the things we find will be very small, and that we need a lot of energy to access them. But where are we going? What strange seas are we sailing, and what laws, if any, apply? The place to start our first expedition is in the first relatively safe harbor we spot in the distance — Port Electron, on the strange shores of an unknown island.

The Ocean Wave ...

From our harbor of Port Electron, we want to chart a course toward the coast we see faintly on the horizon. The local pilot we have engaged is impatient to steer us out of the harbor, through the calm of the bay, and around the patches of choppy water we can see by the harbor's entrance. But our navigator and captain are cautious. Conscious of the challenges ahead, they want to understand what causes the choppiness and how to steer the boat safely themselves. The pilot shrugs and starts talking about particles.

Particle-like behavior is something we are quite familiar with. If you shoot a gun, the bullet will travel onward in a straight line until some force acts to change its direction or slow it down. Sand will trickle through your fingers and form neat piles. These particle-like things will not travel in anything other than a straight line unless they ricochet off something or some other force acts on them to bend their path. They will also stay the same shape as they travel. To properly describe a particle and predict its behavior, we need to know its size, speed, and mass. We think of the molecules in a gas as particles, bouncing off each other, and with that picture we can understand temperature, pressure, and quite an array of interesting and useful behaviors, including convection currents that transfer heat energy around the cabin. Particles also provide a way of transferring information. The letters the crew sent home before we set off on our journey are particles, too, in a sense — discrete packets of stuff traveling in a well-defined path from sender to recipient.

Waves provide a very different way of transferring information and energy. The ship's radio (emergency use only) sends signals back to base, and the ship's microwave heats up the captain's soup. Most of what we know about the world around us comes from waves — generally light waves and sound waves in everyday life, but also radio, X-rays, and more esoteric forms once we bring scientific instruments into play. The physics of waves is in many ways more interesting and more complex than the physics of particles, and gives rise to a richer mix of effects, including the choppy and calm patches the captain saw as we arrived.

To properly describe a wave, we must know its wavelength, frequency, and amplitude. Traveling waves have peaks and troughs that move as they go. But what is actually traveling? The pilot draws our attention to a seagull sitting on the water of the bay as ripples in the otherwise calm sea pass by and lap at the shoreline. The gull bobs up and down as the waves pass but does not otherwise move. Though waves are traveling across the bay to the shore, the seagull, and indeed the water through which the waves are transmitted, only move up and down; they do not travel along the surface. It is only the "up-and-down" motion, the displacement, that is somehow traveling across the bay.

The height of the "up" or the depth of the "down" compared to the surface of the undisturbed bay is what is called the "amplitude" of the wave. Any wave has an amplitude of some kind — the displacement that it causes from the average. An amplifier in a sound system is so called because it increases the amplitude of a wave — it amplifies it, and the sound gets louder.

As the ripples continue — perhaps a dolphin is having a good time nearby, splashing around — then the gull will keep on bobbing up and down. The number of times it bobs in a given period of time is known as the frequency of the wave — the number of peaks or troughs passing a given point in a certain time interval. Usually it is measured in hertz (Hz), a slightly odd unit that should really be called "per second." If the wave in the bay has a frequency of 2 Hz, the gull will bob up and down twice every second.

The wavelength, on the other hand, is simply the distance between two neighboring peaks in the series of ripples. And since the displacement has to travel a distance of one wavelength each time the gull bobs, the speed with which the wave travels across the pond is quite easily calculated by multiplying the frequency by the wavelength.

So if we know the amplitude, the wavelength, and the frequency of a wave, we also know its speed, and that specifies all of its most important properties. How is the behavior of waves any more interesting than the way particles behave?

Well, consider this. Two dolphins are splashing around in different places in the bay, making waves with the same amplitude, frequency, and wavelength as each other, but traveling in different directions. Things might be looking a bit turbulent for the gull. But perhaps not.

If the peaks of two waves arrive at the seagull at the same time, then indeed the bird is in for a bumpy ride. The amplitudes of the waves will add up, and the gull will bob twice as high and dip twice as low. But, depending on how far away each dolphin is from the gull, it might be the case that the peak of one wave arrives just as the trough of the wave from the other dolphin turns up. In this case, the trough will cancel out the peak; or, thinking of it in terms of the water under the seagull, the force from one wave is telling it to move up, while an equal and opposite force from the other wave is telling it to move down. It won't move. The gull can relax. The waves will carry on past it, but it will be left in peace.

Such quiet spots are seen when all kinds of waves meet each other. Radio waves and microwaves, such as those that carry Wi-Fi signals, exhibit them, too. These effects, when waves come together, are known collectively as "interference." When two waves arrive with the peaks of one hitting the troughs of another, they are said to be "out of phase." And obviously, when the peaks come together, they are "in phase." Phase is another important property of waves, but it can only really be defined when you have two waves. Phase differences — such as whether two waves are in or out of phase — have a real physical effect. In our example, the gull bobs up and down, or does not, depending upon the relative phase of the two waves. But phase has to be defined relative to something. If there is only one wave, we might decide to define the phase relative to some arbitrary time — say, the moment we first saw the dolphin — but regardless, if there is only a single dolphin making a single set of waves, the gull will bob up and down, whatever the phase of the wave might be. It is only when we have multiple waves with phase differences between them that we see really different behavior. This rather simple fact has surprisingly far-reaching consequences.

This interference behavior is very different from the more familiar behavior of particles. While bullets fired at a seagull from different directions may collide, there is no way that firing more shots could reduce the number of bullets. But making more waves might indeed make its part of the bay calmer.

Waves do other interesting, non-particle-like things. The bay contains a harbor, connected by a narrow channel. All the dolphin-and-seagull action is happening in the bay, and some of the waves impinge on the narrow channel leading to the harbor. What happens?

If waves behaved like particles, then any that were directed accurately enough at the channel would pass through and travel in a straight line across the harbor, leaving most of the surface of the harbor undisturbed. But this is not what happens. The waves hit the channel, and the channel acts as the source of waves in the harbor — as though a dolphin had actually gotten in there. (This works most effectively if the width of the channel is comparable to the wavelength of the waves, as in that case it looks like a single source of waves, rather than a row of sources.) Waves will spread out from the channel concentrically, across the dolphin-free harbor. This spreading out is called diffraction; it allows waves to go around corners without any bending force being applied. It's another key property that features in the quantum-particle-wave world of the Standard Model.

One important practical consequence of this kind of wave behavior is that there is a limit to the smallest structures they can be used to study. Roughly speaking, effects such as diffraction and interference mean that a wave cannot give us good information about objects that are smaller than the wavelength of the wave. Smaller than that, and things become too blurred and confused. In the case of the harbor channel above, wavelengths much shorter than the width of the channel lead to a tight beam pointing back to the position of the channel. Wavelengths the same size as the channel spread out and fill the harbor; longer wavelengths won't even pass through the gap.

Any setup that can support a wave has an equation behind it — a wave equation, of course — that describes how the wave will work. The surface of the bay we are sailing on is one such system. Another example is the air. A small region of dense, high-pressure air will spread out, compressing neighboring regions, which in turn compress their neighbors, and so on. A high-pressure pulse propagating through the air like this is a sound wave, created when air is compressed somehow, say by a vibrating drum, or your larynx. Electric and magnetic fields form another system, which is how light, radio, and other electromagnetic waves travel. The important point here is that the general behaviors of these systems are similar in some very important ways — including the fact that diffraction and interference occur — because the underlying wave equations are very similar.

Because they will be such a vital navigational aid in our coming voyages, it might be worth taking a moment to examine why equations are so important in physics. We won't need to go into the detailed mathematics, and I won't be writing out any equations explicitly, but there will be several moments when an equation of some kind is so vital to navigating the physical world that we will need to discuss it. An equation in mathematics relates different concepts to each other in an abstract, but completely definite way. When used in physics, the concepts on each side of the equation are physical objects, and an equation relating them gives new insight into how those objects behave, and especially how changing one of them affects the others.

In the current case, a wave equation describes changes in some physical quantity — the height of the water, the pressure of the air, the strength of the electric field. It relates how they change as time passes to how they change with position. Specifically, the wave equation for our bay tells us that if the height of the surface is different at different points in the bay, this implies that the surface will also change with time. Imagine a wriggle from the tail of one of our dolphins that raises a region of water to be higher than its surroundings. This is an unstable situation. The small hill of water created by the dolphin will be pulled down by gravity, and this will spread ripples across the surface as a traveling wave. The wave equation is simply the mathematical description of how this happens. It tells us how differences in the height of the water at different places lead to changes in the height at different times. It can be used to predict how waves will travel and interact — water waves, sound waves, radio waves, or quantum waves.

Our boat heads out of the harbor in a straight, particle-like line, the crew cheered by our pilot's instruction and buoyed by the waves. We now know, and hopefully understand, two distinct behaviors — particle-like and wave-like. They differ from each other profoundly, and it is very hard to see how the two could ever be mixed together. But we are sailing uncharted and dangerous seas, and we should expect surprises. And, to the frustration of some of the more impatient crew members, our pilot is not done yet.

... Or Particle?

Before we travel on, we need to really understand the medium we are moving in. If we don't do this, the pilot assures us, we will understand little of what we see, and in particular the interior of Atom Land, the target of our next voyage, will be an impenetrable jungle. The coastline already appears closer, though we have barely left port.

What the pilot has to tell us is so weird that he knows we may not believe him, so he urges the captain to drop anchor and assemble the crew belowdecks for a demonstration. After a few moments' preparation, in the pitch-black hold of our ship, the pilot fires a beam of laser light at a screen with two small slits in it. On the other side of the screen is a detector to monitor the light that makes it through the slits.

The first thing to note is that light behaves like a wave. If the slits are narrow enough, the slits themselves start acting as sources of waves. That is, the light diffracts as it passes through the slits, just like the water waves in the narrow channel in the harbor. This indicates that the light has a wavelength that is similar in size to the width of each slit, just as the water waves that diffracted the most had wavelengths similar to the width of the harbor entrance.

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Excerpted from "Atom Land"
by .
Copyright © 2018 Jon Butterworth.
Excerpted by permission of The Experiment Publishing.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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