The Hoover Dam was built to control the timing of water flow, but the principle it demonstrates goes far beyond water use. When it comes to harvesting energy, all we are ever really doing is providing a few obstacles to energy that was already on its way from somewhere to somewhere else. The physical world will always move toward equilibrium, but sometimes we can control where the nearest equilibrium is and how quickly something in the world can get there. By controlling that flow, we also control the timing of energy release. Then we make sure that as the energy flows through our artificial obstacles on its way toward equilibrium, it does something useful for us. We don’t create energy and we don’t destroy it. We just move the goalposts and divert it.
Like many civilizations before ours, we face the problem of limited resources. Fossil fuels are made up of plants that built themselves using energy from the Sun, diverting that energy from its alternative outlet: gentle warmth, which is the equivalent of the bottom of the river when it comes to usefulness. Fossil fuels are the energy equivalent of dams, a form that stores energy in a temporary equilibrium. When we come along, dig them up, and provide the right kick, we’re choosing the timing of energy release by providing a route to another accessible equilibrium, via a flame and chemical decomposition to carbon dioxide and water. The problem we have is that there are only so many “upstream” resources in the form of fossil fuels, and in a few human lifetimes we have released energy that took millions of years to accumulate. The fossil fuel reservoirs are being emptied, and they will not be refilled for millions of years more. Renewable energy, like the hydroelectricity from the Hoover Dam and many others like it, diverts the waterfall of solar energy that is flowing through our world now. The game facing our civilization remains the same: How do we stop and start the energy flow efficiently, so that we can do what we want without changing our world too much?
Next time you turn on something that is battery-powered, you’re choosing the time of energy release from the battery by opening an electrical gate, and guiding the energy through the circuits of the device to help you do something useful. After that, it’ll end up as heat, which it would have done anyway. This is what the switches in our world are, all of them. They’re the gatekeepers controlling the timing of a flow, and the flow is only ever going one way: toward equilibrium. If we let the flow whoosh through all at once we get one result; if we slow it down, letting it trickle through at times that suit us, we get an entirely different result. Time matters here because it’s only ever going in one direction: By choosing when the flow toward equilibrium happens, and the speed of that flow, we give ourselves enormous control over the world. But it’s not always the case that things reach equilibrium and then stop. If they’re going really fast as they approach the balance point, they may well just keep going and fly right through. This opens the door to a whole new set of phenomena, including some problems.
Mid-afternoon tea break is an essential part of my working day. But I noticed recently that even acquiring a mug of tea forces me to slow down, and it’s not just about the time taken to boil the kettle. My office at University College London is at one end of a long corridor, and the tearoom is at the other end. The journey back to my office, accompanied by a full mug of tea, happens at the slowest pace of my entire day (my normal walking speed at work is somewhere between “brisk” and “race pace”). It’s not that there’s too much tea in the mug; the problem is the sloshing. Every step makes it worse. Any sensible person would accept that slowing down is a reasonable solution. But any physicist would do some experiments first, just to see whether that’s the only solution. You never know what you might find. And I wasn’t going to give in to the obvious without a fight.
If you put water in a mug, sit the mug on a flat surface, and give it a bit of a push, the water will start to slosh from side to side. What’s happening is that as you shove it, the mug moves but the water initially gets left behind, so it piles up against the side of the mug you’ve pushed. Then you have a mug that has higher water on one side than the other, so gravity pulls the higher water down, and the water on the other side is pushed upward. For an instant the surface is flat again, but the water has no reason to stop moving. It just carries on going up the other side. Gravity is tugging on it as it goes, but it takes a while to stop the water completely. By the time it’s stopped, the water level is higher on the second side than the first, and then the cycle starts all over again. If the mug is sitting on a flat surface, the sloshing from one side to the other will gradually die away, and equilibrium will be reached. But if you’re walking, things are different.
The cycle is where the problem lies. If you try the shoving test with mugs of a few different sizes, you’ll see that the sloshing happens in the same way for them all, but it happens more quickly in a narrow mug and more slowly in a wider mug. A mostly full mug always sloshes the same number of times each second, however big the initial push was. But that number depends on the mug, and the thing that matters most is the mug radius.
There’s a conflict between the downward force of gravity, which is pulling everything back to equilibrium, and the momentum of the fluid, which is greatest just as it passes through the equilibrium position. In a bigger mug, there’s more fluid and it has farther to go, so the cycle takes longer to turn around. The special frequency that each mug has is known as its natural frequency, the rate it will slosh at if pushed and then left to get back to equilibrium by itself.
I spent a while playing with the mugs in my office. I have one tiny one with a picture of Newton on it that is only 1? inches across. Water in this one sloshes about five times each second. The biggest one is about 4 inches across, and it sloshes about three times each second. This large mug is old and cheap and ugly and I’ve never really liked it, but I still have it because sometimes you just need a lot of tea.