Time keeping was elevated to a completely new level of accuracy with the invention of pendulum clocks. Galileo was the first scientist to investigate the physics of a swinging pendulum. The key property of the pendulum, which makes it useful as a timekeeping device, is that the period of the swing – the familiar tick-tock of the clock – depends only on the length of the pendulum and Earth’s gravitational pull. Perhaps counterintuitively, the period doesn’t depend on how high you lift the pendulum to start the swing, as long as it’s not too high. Physics students have the formula for the time period of a pendulum permanently etched in their minds. It is:
where T is the period, L is the length and g is the acceleration due to gravity – in other words, a measure of the strength of Earth’s gravitational field, which is almost the same wherever you are on Earth; approximately 9.81 metres (300 feet) per second squared. This means that all you need to do to make a clock that ticks accurately is get the length of the pendulum right. Most grandfather clocks have a pendulum that swings with a period of two seconds, which a little simple mathematics will tell you requires a pendulum approximately one metre long. The Dutch astronomer Christiaan Huygens invented the first pendulum clock in 1656, and it remained the most accurate way of telling the time until the 1930s.
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Christiaan Huygens invented the first pendulum clock in 1656, and it remained the most accurate way of telling the time until the 1930s.
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Galileo first investigated the physics of a swinging pendulum and how it could be used effectively for keeping time.
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Today we rely on atomic clocks to measure time with extraordinary accuracy. Atomic clocks use the frequency of light emitted when electrons jump around in atoms (usually caesium) as the ‘pendulum’. This is highly accurate because the structure of atoms is unchanging, and therefore the light emitted from them always has the same frequency. This light can be used, with some clever engineering, to keep an oscillator ticking at a precise rate, allowing atomic clocks to tell the time with an accuracy of one-thousand-millionth of a second per day. The second itself has been defined since 1967 using the theory behind atomic clocks; one second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. In English, this means a second is the time it takes for 9,192,631,770 peaks in a wave of light, emitted when an electron makes a specific jump in an atom of caesium, to fly past you.
Atomic clocks allow us to measure incredibly small periods of time. Until now, the shortest period we have been able to measure is 12 attoseconds, or 12 quadrillionths of a second. This is how long it takes light to travel past 36 hydrogen atoms lined up together. That’s not far at all
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For all the accuracy and precision we have achieved in keeping time, we have never managed to do anything more than observe it. From the very earliest solar calendars to the electrons jumping around in caesium atoms, one thing about the nature of time is clear: we can measure its passing, but we cannot control it. It moves inexorably forward; it cannot be stopped. This tells us something profound about our universe.
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The Perito Moreno glacier in Patagonia, Southern Argentina, is a stark but beautiful place where the passage of time moves progressively forward but so slowly that it almost goes unnoticed.
THE ARROW OF TIME
Few places on our planet are as spectacular as the Perito Moreno glacier in Patagonia, southern Argentina. This dense blue wall of frozen water in the Los Glaciares National Park is part of a system of hundreds of glaciers that sweep down the continent from the southern Patagonian ice fields. Together they form the third-largest icecap on our planet. The Perito Moreno glacier alone covers an area of 250 square kilometres (96 square miles) and in places it is 170 metres (560 feet) deep. The ice ends where solid meets liquid at Lake Argentino; a great wall of ice towers over the surface of the lake, and the few who make it to this bleak but utterly beautiful place have the chance to sail along its edge across one of the most dramatic expanses of water in the world.
At first sight the glacier appears static and unmoving; standing on the lake shore, this seems like a place where the passage of time goes as unnoticed as the laws of physics will allow. Yet there is a reason why boats don’t venture too close to the edge of the ice cliff. As we approached I didn’t only see the passage of time; I felt it. Tthis glacier is in constant motion; relentlessly carving its way down from the Andes as it has done for tens of thousands of years. At the glacier’s edge, the wall of ice is 70 metres (230 feet) high, and the whole face of the glacier is sliding into the lake at around 50 centimetres (20 inches) per day. That means that well over a quarter of a billion tonnes of ice cascades into the lake every year. You don’t often see it, but you can hear it; every now and then there is a tremendous cracking sound, followed by a deep rumbling. The surface of the lake comes alive as a turbulent wave powers beneath your boat. The pace of change in this place is anything but glacial. It is so vast and complex that you perceive it to be alive; an unpredictable, overwhelmingly powerful organism clawing the land in vain as it inevitably slides into the waters.
This is all part of a highly ordered sequence. As time passes, snow falls, ice forms, the glacier gradually inches down the valley, and when the ice meets the water, pieces break off and fall into the lake creating waves. In many ways this ordering of events into a sequence is the simplest way to think about time. The fact that sequences of events always happen in order is a fundamental part of our experience of the world. We expect to see ice fall from the glacier, splash into the water and create waves. If it happened in any other way we’d immediately know there was something wrong. Yet there is a legitimate question here about what we mean by events happening ‘in order’. However long we might stand on the edge of this beautiful lake we would never expect to see this dramatic sequence of events happen in reverse, even though there is nothing in the laws of nature that prevents this happening. There is no physical reason why all the water molecules moving around in the lake shouldn’t gather together on the surface, reduce their collective temperature such that they bind together to form ice, jump out of the water and glue themselves onto the surface of the glacier. We do, however, have a scientific explanation for why such a dramatic reversal never happens; we call it the ‘arrow of time’.
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We expect to see ice fall from the glacier, splash into the water and create waves. If it happened in any other way we’d immediately know there was something wrong.
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This phrase was first used by the British physicist Sir Arthur Eddington in the early twentieth century to describe this deceptively simple and yet profound quality of our universe: it always seems to run in a particular direction. Eddington was instrumental in bringing Einstein’s theory of relativity to the English-speaking world during the First World War, and also one of the first scientists to directly confirm the findings of relativity when he led an expedition to observe the total solar eclipse on 29 May 1919. In 1928 he published The Nature of the Physical World, in which he introduced two great ideas that have endured in popular scientific culture to this day. The first was the image of the infinite monkey theorem, which states that given an infinite amount of time, anything consistent with the laws of physics will happen: ‘If an army of monkeys were strumming on typewriters, they might write all the books in the British Museum’. This is related in a deep way to the arrow of time, which Eddington described as follows:
A great wall of ice towers over the surface of Lake Argentino, where this vast, seemingly immovable glacier is slowly and relentlessly sliding down into the icy waters below.
‘Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the
past. That is the only distinction known to physics. This follows at once if our fundamental contention is admitted that the introduction of randomness is the only thing that cannot be undone. I shall use the phase “time’s arrow” to express this one-way property of time which has no analogue in space.’
Eddington’s arrow vividly and economically expresses a key property of time; it only goes in one direction. But what does he mean by randomness? It seems obvious that the Universe is constantly evolving, but what drives this evolution? How should we quantify how random something is? Why is the past different from the future? Why is there an arrow of time? Time is something we all understand, and yet a plausible scientific reason as to why time marches inexorably forward wasn’t offered until the late nineteenth century, coming about as the solution to a practical problem on Earth
THE ORDER OF DISORDER
In 1712 the English inventor Sir Thomas Newcomen created the first commercially successful steam engine, paving the way for the Industrial Revolution. This accolade is more usually awarded to the Scottish inventor James Watt. In 1763 Watt was asked to repair a Newcomen engine by the University of Glasgow, and in doing so he developed a new steam engine which, it is appropriate to say without hyperbole, transformed the landscape of modern life. Watt’s steam engine was more efficient and more flexible than its predecessor; it used far less coal than the Newcomen for a given power output, and was therefore much cheaper to run. More importantly still, Watt’s engine could do more than pump water out of the wet mines, it could also generate the rotary motion that was needed to power the machines on the factory floor. No longer did a factory have to be situated by a river to turn its equipment; with the help of Watt’s engine a factory could be sited anywhere, catalysing the emergence of the modern industrial landscape. Steam-powered machines changed the course of history, and yet despite their importance, the nineteenth-century engineers who followed Watt struggled to improve them. There seemed to be fundamental principles that restricted their efficiency, but with profit margins to maximise, even a small increase in their effectiveness would be highly valuable. So understanding how hot the fire should be or what substance should be boiled in the engine were problems that were not only interesting from a scientific perspective but were also critical for businesses. It was out of these questions of engineering design that the science of thermodynamics arose, and with it the concepts of heat, temperature and energy entered the scientific vocabulary in a precise way for the first time.
In a series of simple experiments, Joule demonstrated that mechanical work could be converted into heat. Using a paddle wheel turned by falling weights, he stirred water in an insulated barrel and observed how the temperature of the water rose by the amount that depended on how far the weights fell.
One of the scientists working on these problems was the German mathematician Rudolf Clausius. Clausius was interested in heat, which until the first half of the nineteenth century was thought to be a fluid that flowed from hot things to cold things. Clausius and others realised that this description was not able to explain the cycle of a steam engine. The foundation for Clausius’s theoretical advances was laid by one of his contemporaries, the English physicist and brewer James Joule, who was working to improve the efficiency of the steam engines in his brewery. What finer motivation for the advance of fundamental physics? The quest for cheaper beer motivated him to investigate the relationship between the work his steam engines could do, and heat. In doing so he managed to reduce the costs of beer production and lay one of the cornerstones of the science of thermodynamics.
Using a series of beautifully simple experiments, Joule was able to demonstrate that mechanical work could be converted into heat. One such experiment used a falling weight to spin a paddle within an insulated barrel of water. Joule knew how much work was done by the falling weight and so could measure the temperature rise of the water. He conducted similar experiments on compressed gases and flowing water, and each time he found that it took the same amount of work to raise the temperature of a fixed amount of water by one degree Fahrenheit. Inscribed on his tombstone in Brooklands cemetery near Manchester is the number 772.55 – his measurement of the amount of work done in foot-pounds force that is required to raise the temperature of one pound of water by one degree Fahrenheit.
The reason that Joule’s work was important is that it demonstrated that heat is not a thing that can be created or destroyed. It doesn’t literally flow between things or move around, it is in fact a measure of something else. Even today, this is perhaps not obvious because we still speak of the flow of heat from hot to cold things. Heat, we now understand, is simply a form of energy. Just as a ball resting on a table has energy which can be released by dropping it (known as gravitational potential energy), so a hot thing has energy that can be released, at least in part, by putting it next to a cold thing. To heat something up, you simply have to transfer energy to it by doing work on it, as Joule found by using a falling weight, and it doesn’t matter how that work is done. It can be a falling weight, a shining light or an electric current, but as long as you do the same amount of work, the temperature increase will be the same. This was all quantified, as a result of Joule’s work, into the First Law of Thermodynamics, which is a statement of the fact that energy cannot be created or destroyed; it can only be changed from one form into another. Rudolf Clausius made the first explicit statement of the law, and laid down the foundations of the science of thermodynamics, in his landmark 1850 publication ‘On the mechanical theory of heat’.
Newcomen’s engine, created in 1712, was the first commercially successful steam engine and laid the foundations for the work of other inventors, such as James Watt, which would power forward the industrial revolution in Britain. the Newcomen atmospheric engine was used to pump water out of coal mines, using a pivoted arm (top) to transfer power between the piston and the rod. the piston was driven down by the pressure of a partial vacuum in the cylinder, which drew the rod upwards. as steam in the cylinder condensed, the piston was forced up, and the rod down.
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The first law can be written down mathematically as
which in words says that the increase in the internal energy of something (ΔU) is equal to the heat flow into it (Q) minus the work performed by it (W). If you performed work on it, the W would have a plus sign, and if you took heat out of it, the Q would have a minus sign.
Fifteen years after writing down the first law of thermodynamics, and far more importantly for our understanding of the arrow of time, Clausius introduced a new concept known as entropy, which lies at the heart of the Second Law of Thermodynamics. Clausius’s statement of the second law does not at first sight sound as if it has profound implications for the future of our universe. He simply stated that ‘No process is possible whose sole result is the transfer of heat from a body of lower temperature to a body of higher temperature’. This simple proposition occupies such a profound position in modern science that Arthur Eddington said of the second law:
‘If someone points out to you that your pet theory of the Universe is in disagreement with Maxwell’s equations, then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.’
The concept of entropy enters when the second law is written down in quantitative form. The change in entropy of a system, such as a tank of water, is simply the amount of heat added to it at a fixed temperature. In symbols,
where ΔS is the change in the entropy as a result of adding a small amount of heat, ΔQ, at a fixed temperature T. It may still be unclear what this has to do with the Universe, but here is the profound point discovered by Clausius. In any physical process at all, you find that entropy either stays the sam
e or increases. It never decreases. Here is the thermodynamic arrow of time. Clausius had discovered a physical quantity that can be measured and quantified which only ever increases in practice, and never decreases even in theory, no matter how cleverly you design your experiment or piece of machinery. This is extremely useful information if you are designing a steam engine, because it puts a fundamental limit on the efficiency. It also prevents the construction of the so-called ‘perpetual motion machines’ so beloved of crackpot inventors to this day. You could say that the second law tells you that you can’t get something for nothing, but the second law is more profound than this, because it introduces a difference between the past and the future. In the future, entropy will be higher than it is in the present because it always increases. In the past, entropy was lower than it is now because it always increases.
Clausius introduced the concept of entropy because he found it useful, but what exactly is entropy, and what is the deep reason that it always increases? And what was the meaning of Eddington’s cryptic quote about randomness and the arrow of time? He seemed to be equating entropy with the amount of randomness in the world, and indeed he was. Understanding this will make it clear why the Second Law of Thermodynamics mandates that our entire universe must, one day, die
ENTROPY IN ACTION
In 1908 in the small town of Kolmanskop in southern Namibia, a railway worker by the name of Zacharias Lewala found a single diamond lying in the sand. He showed the precious stone to his manager – railway inspector August Stauch – who immediately realised its significance and set in motion a train of events that turned this desolate place into one of the most valuable diamond mines in the world. The colonial German government closed the entire area to outsiders; only German entrepreneurs were allowed to make their fortunes here. For 40 years, Kolmanskop was home to a thriving community as over a thousand people gathered, seeking to become millionaires by picking diamonds out of the desert. As the money rolled in, the residents built a town in the finest German tradition; grand houses stood beside a casino, a ballroom and the first X-ray station in the Southern Hemisphere. They led a champagne lifestyle in the desert, and created a little piece of opulent German architecture in the sand. Eventually, though, as with all cash cows, the diamonds could no longer be found and the town gradually lost its sparkle until it was abandoned in 1954. For half a century it has fallen into disrepair as the buildings are slowly reclaimed by the sands.
Wonders of the Universe Page 20
