Wonders of the Universe
Page 4
This is profound in itself, but there is an extra, more profound conclusion. Maxwell’s equations also predict exactly how fast these waves must fly away from the electric charges that create them. The speed of the waves is the ratio of the strengths of the electric and magnetic fields – quantities that had been measured by Faraday, Ampère and others and were well known to Maxwell. When Maxwell did the sums, he must have fallen off his chair. He found that his equations predicted that the waves in the electric and magnetic fields travelled at the speed of light! In other words, Maxwell had discovered that light is nothing more than oscillating electric and magnetic fields, sloshing back and forth and propelling each other through space as they do so. How beautiful that the work of Faraday, Ampère and others with coils of wire and pieces of magnets could lead to such a profound conclusion through the use of a bit of mathematics and a sprinkling of Scottish genius! In modern language, we would say that light is an electromagnetic wave.
In order to have his epiphany, Maxwell needed to know exactly what the speed of light was. Remarkably, the fact that light travels very fast, but not infinitely so, had already been known for almost two hundred years. As we will discover now, it had first been measured by Ole Romer in 1676
CHASING THE SPEED OF LIGHT
Open your eyes and the world floods in; light seems to jump from object to retina, forming a picture of the world instantaneously. Light seems to travel infinitely fast, so it is no surprise that Aristotle and many other philosophers and scientists believed light travelled ‘without movement’. However, as the Greek philosophers gave more thought to the nature of light, a debate about its speed of travel ensued that continued for thousands of years.
In one corner sat eminent names such as Euclid, Kepler and Descartes, who all sided with Aristotle in believing that light travelled infinitely fast. In the other, Empedocles and Galileo, separated by almost two millennia, felt that light must travel at a finite, if extremely high, velocity. Empedocles’s reasoning was elegant, pre-dating Aristotle by a century. He considered light travelling across the vast distance from the Sun to Earth, and noted that everything that travels must move from one point to another. In other words, the light must be somewhere in the space between the Sun and the Earth after it leaves the Sun and before it reaches the Earth. This means it must travel with a finite velocity. Aristotle dismissed this argument by invoking his idea that light is simply a presence, not something that moves between things. Without experimental evidence, it is impossible to decide between these positions simply by thinking about it!
Galileo set out to measure the speed of light using two lamps. He held one and sent an assistant a large distance away with another. When they were in position, Galileo opened a shutter on his lamp, letting the light out. When his assistant saw the flash, he opened his shutter, and Galileo attempted to note down the time delay between the opening of his shutter and his observation of the flash from his assistant’s lamp. His conclusion was that light must travel extremely rapidly, because he was unable to determine its speed. Galileo was, however, able to put a ‘limit’ on the speed of light, noting that it must be at least ten times faster than the speed of sound. He was able to do this because if it had been slower, he should have been able to measure a time delay. So, the inability to measure the speed of light was not deemed a ‘no result’, but in fact revealed that light travels faster than his experiment could quantify.
The question, how fast is the speed of light, has plagued scientists for thousands of years. Part of the answer came from observing how light travels between points: from the Sun to Earth.
The first experimental determination that the speed of light was not infinite was made by the seventeenth-century Danish astronomer, Ole Romer. In 1676, Romer was attempting to solve one of the great scientific and engineering challenges of the age; telling the time at sea. Finding an accurate clock was essential to enable sailors to navigate safely across the oceans, but mechanical clocks based on pendulums or springs were not good at being bounced around on the ocean waves and soon drifted out of sync. In order to pinpoint your position on Earth you need the latitude and longitude. Latitude is easy; in the Northern Hemisphere, the angle of the North Star (Polaris) above the horizon is your latitude. In the Southern Hemisphere, things are more complicated because there is no star directly over the South Pole, but it is still possible with a little astronomical know-how and trigonometry to determine your latitude with sufficient accuracy for safe navigation.
Longitude is far more difficult because you can’t just determine it by looking at the stars; you have to know which time zone you are in. Greenwich in London is defined as zero degrees longitude; as you travel west from Greenwich across the Atlantic, your time zone shifts so that in New York it’s earlier in the day than in London. Conversely, as you travel east from Greenwich your time zone shifts so that in Moscow or Tokyo it’s later in the day than in London.
Your precise time zone at any point on Earth’s surface is defined by the point at which the Sun crosses an imaginary arc across the sky between the north and south points on your horizon, passing through the celestial pole (the point marked by the North Star in the Northern Hemisphere). Astronomers call this arc the Meridian. The point at which the Sun crosses the Meridian is also the point at which it reaches its highest position in the sky on any given day as it journeys from sunrise in the east to sunset in the west. We call this time noon, or midday. Earth rotates once on its axis every twenty-four hours – fifteen degrees every hour. This means two points on Earth’s surface that are separated by fifteen degrees of longitude will measure noon exactly one hour apart. So to determine your longitude, set a clock to read 12 o’clock when the Sun reaches the highest point in the sky at Greenwich. If it reads 2pm when the Sun reaches its highest point in the sky where you are, you are thirty degrees to the west of Greenwich. Easy, except that you need a very accurate clock that keeps time for weeks or months on end
These spectacular star trails are produced in the sky as a result of diurnal motion. This is the motion created as Earth spins on its axis at fifteen degrees per hour, rotating once over twenty-four hours.
© Scott Smith/Corbis
THE SEARCH FOR A COSMIC CLOCK
In the early seventeenth century, King Philip III of Spain offered a prize to anyone who could devise a method for precisely calculating longitude when out of sight of land. The technological challenge of building sufficiently accurate clocks was too great, so scientists began to look for high-precision natural clocks, and it seemed sensible to look to the heavens. Galileo, having discovered the moons of Jupiter, was convinced he could use the orbits of these moons as a clock, as they regularly passed in and out of the shadow of the giant planet. The principle is beautifully simple; Jupiter has four bright moons that can be seen relatively easily from Earth, and the innermost moon, Io, goes around the planet every 1.769 days, precisely. One might say that Io’s orbit is as regular as clockwork, therefore by watching for its daily disappearance and re-emergence from behind Jupiter’s disc you have a very accurate and unchanging natural clock. Thus by using the Jovian system as a cosmic clock, Galileo devised an accurate system for keeping time. Observing the eclipses of these tiny pinpoints of light around three-quarters of a billion kilometres (half a billion miles) from Earth from a rolling ship was impractical, however, so although the logic was sound, Galileo failed to win the King’s prize. Despite this, it was clear this technique could be used to measure longitude accurately on land, where stable conditions and high-quality telescopes were available. Thus observing and cataloguing the eclipses of Jupiter’s moons, particularly Io, became a valuable astronomical endeavour.
By the mid-seventeenth century, Giovanni Cassini was leading the study of Jupiter’s moons. He pioneered the use of Io’s eclipses for the measurement of longitude and published tables detailing on what dates the eclipses should be visible from many locations on Earth, together with high-precision predictions of the times. In the process of
further refining his longitude tables, he sent one of his astronomers, Jean Picard, to the Uraniborg Observatory near Copenhagen, where Picard employed the help of a young Danish astronomer, Ole Romer. Over some months in 1671, Romer and Picard observed over one hundred of Io’s eclipses, noting the times and intervals between each. He was quickly invited to work as Cassini’s assistant at the Royal Observatory, where Romer made a crucial discovery. Combining the data from Uraniborg with Cassini’s Paris observations, Romer noticed that the celestial precision of the Jovian clock wasn’t as accurate as everyone had thought. Over the course of several months, the prediction for when Io would emerge from behind Jupiter drifted. At some times of the year there was a significant discrepancy of over twenty-two minutes between the predicted and the actual observed timings of the eclipses. This appeared to ruin the use of Io as a clock and end the idea of using it to calculate longitude. However, Romer came up with an ingenious and correct explanation of what was happening.
These sketches (published in Istoria e Dimonstrazione in 1613) show the changing position of the moons of Jupiter over 12 days. Jupiter is represented by the large circle, with the four moons as dots on either side.
Ole Romer’s recorded observations show his detailed research into the movement of Io.
Jupiter appears spotty in this false-colour picture from the Hubble Space Telescope’s near-infrared camera. The three black spots are the shadows of the moons Ganymede (top left), Io (left) and Callisto. The white spot above centre is Io, while the blue spot (upper right) is Ganymede. Callisto is out of the image to the right.
NASA
Romer noticed that the observed time of the eclipses drifted later relative to the predicted time as the distance between Jupiter and Earth increased as the planets orbited the Sun, then drifted back again when the distance between Jupiter and Earth began to decrease. Romer’s genius was to realise that this pattern implied there was nothing wrong with the clockwork of Jupiter and Io, because the error depended on the distance between Earth and Jupiter and had nothing to do with Io itself. His explanation, which is correct, was simple. Imagine that light takes time to travel from Jupiter to Earth; as the distance between the two planets increases, so the light from Jupiter will take longer to travel between them. This means that Io will emerge from Jupiter’s shadow later than predicted, simply because it takes longer for the light to reach you. Conversely, as the distance between Jupiter and Earth decreases, it takes the light less time to reach you and so you see Io emerge sooner than predicted. Factor in the time it takes light to travel between Jupiter and Earth and the theory works. Romer did this by trial and error, and was able to correctly account for the shifting times of the observed eclipses. The number that Romer actually calculated was the light travel time across the diameter of Earth’s orbit around the Sun, which he found to be approximately twenty minutes. For some reason, perhaps because he felt the diameter of Earth’s orbit was not known with sufficient precision, he never turned this number into the speed of light in any Earth-based units of measurement. He simply stated that it takes light twenty-two minutes to cross the diameter of Earth’s orbit. The first published number for the speed of light was that obtained by the Dutch astronomer Christiaan Huygens, who had corresponded with Romer. In his ‘Treatise sur la lumière’ (1678), Huygens quotes a speed in strange units as 110 million toises per second. Since a toise is two metres (seven feet), this gives a speed of 220,000,000 metres per second, which is not far off the modern value of 299,792,458 metres (983,571,503 feet) per second. The error was primarily in the determination of the diameter of Earth’s orbit around the Sun.
ROMER’S THEORY: predicting the emergence of io from behind jupiter, as seen from earth, is affected by the varying distance between earth and jupiter.
No consensus about the speed of light was reached until after Romer’s death in 1710, but his correct interpretation of the wobbles in the Jovian clock still stands as a seminal achievement in the history of science. His measurement of the speed of light was the first determination of the value of what scientists call a constant of nature. These numbers, such as Newton’s gravitational constant and Planck’s constant, have remained fixed since the Big Bang, and are central to the properties of our universe. They are crucial in physics, and we would live (or not live, because we wouldn’t exist) in a universe that was unrecognisable if their values were altered by even a tiny amount
SPEED LIMITS
Everything in our universe has a speed limit, and for much of the twentieth century humans seemed obsessed with breaking one of them. In the 1940s and 1950s the sound barrier took on an almost mythical status as engineers worldwide tried to build aircraft that could exceed the 1236 kilometres per hour (768 miles per hour) at which sound travels in air at twenty degrees Celsius. But what is the meaning of this speed limit? What is the underlying physics, and how does it affect our engineering attempts to break it?
Sound in a gas such as air is a moving disturbance of the air molecules. Imagine dropping a saucepan lid onto the floor. As it lands, it rapidly compresses the air beneath it, pushing the molecules closer together. This increases the density of the air beneath the lid, which corresponds to an increase in air pressure. In a gas, molecules will fly around to try to equalise the pressure, which is why winds develop between high and low pressure areas in our atmosphere. With a falling lid, some of the molecules in the high-pressure area beneath it will rush out to the surrounding lower-pressure areas; these increase in pressure, causing molecules to rush into the neighbouring areas, and so on. So the disturbance in the air caused by the falling lid moves outwards as a wave of pressure. The air itself doesn’t flow away from the lid (this would leave an area of lower pressure around it that would have to be equalised), it is only the pulse of pressure that moves through the air.
Once we reached 12,800 metres, the pilot put the Hawker Hunter into the roll and we dived down through the clouds, upside down. Almost immediately, we broke through the sound barrier.
The speed of this pressure wave is set by the properties of the air. The speed of sound in air depends on the air’s temperature, which is a measure of how fast the molecules in the air are moving on average, the mass of the air molecules (air is primarily a mixture of nitrogen and oxygen) and the details of how the air responds when it is compressed (known as the ‘adiabatic index’). To a reasonable approximation, the speed of the sound wave depends mainly on the average speed of the air molecules at a particular temperature.
The speed of sound is therefore not a speed limit at all; it is simply the speed at which a wave of pressure moves through the air, and there is no reason why an object shouldn’t exceed this. This was known long before aircraft were invented, but it did not satisfy those who wanted to propel a human faster than sound. Many attempts were made during World War II to produce a supersonic aircraft, but the sound barrier was not breached until 14 October 1947, when Chuck Yeager became the first human to pilot a supersonic flight. Flying in the Bell–XS1, Yeager was dropped out of the bomb bay of a modified B29 bomber, through the sound barrier and into the history books.
* * *
The speed of sound is not a speed limit at all; it is simply the speed at which a wave of pressure moves through the air, and there is no reason why an object shouldn’t exceed this.
* * *
Today, aircraft routinely break the sound barrier, but the routine element hides the fascinating aerodynamic and engineering challenges that had to be overcome so that humans could travel faster than sound. Test pilot Dave Southwood demonstrated these to me in the making of the programme in a beautiful aircraft that was not designed to break the sound barrier in level flight – the Hawker Hunter.
Designed in the 1950s, the Hawker Hunter is a legendary British jet fighter of the post-war era. Designed to fly at Mach 0.94, this aircraft cannot fly supersonic in level flight, but in the right hands it can exceed the 1,200 kilometres (745 miles) per hour to take me through the sound barrier. We climbed to 12
,800 metres (42,000 feet), flipped the Hunter into an inverted dive, then plunged full-throttle towards the Bristol Channel. In just seconds the jet smashed through the sound barrier and the air flow surrounding the jet changed, which is heard on the ground as an explosion, or a sonic boom.
Once we reached 12,800 metres, the pilot put the Hawker Hunter into the roll and we dived down through the clouds, upside down. Almost immediately, we broke through the sound barrier.
So the sound barrier is not a barrier at all; it is a speed limit only for sound itself, determined by the physics of the movement of air molecules. Is the light barrier the same? It would seem from our description of light as an electromagnetic wave that is so. Why shouldn’t a sufficiently powerful aircraft or spacecraft be able to fly faster than a wave in electric and magnetic fields? The answer is that the ‘light barrier’ is of a totally different character and cannot be smashed through, even in principle. The reason for this is that light speed plays a much deeper role in the Universe than just being the speed at which light travels. A true understanding of the role of this speed, 299,792,458 metres (983,571,503 feet) per second, was achieved in 1905 by Albert Einstein in his special theory of relativity. Einstein, inspired by Maxwell’s work, wrote down a theory in which space and time are merged into a single entity known as ‘spacetime’. Einstein suggested we should not see our world as having only three directions – north/south, east/west and up/down, as he added a fourth direction – past/future. Hence spacetime is referred to as four-dimensional, with time being the fourth dimension.