Читать книгу Big Bang - Simon Singh, Simon Singh - Страница 15

[Einstein’s theory of relativity] is probably the greatest synthetic achievement of the human intellect up to the present time.

BERTRAND RUSSELL

It is as if a wall which separated us from the Truth has collapsed. Wider expanses and greater depths are now exposed to the searching eye of knowledge, regions of which we had not even a presentiment. It has brought us much nearer to grasping that plan that underlies all physical happening.

HERMANN WEYL

But the years of anxious searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving, and the final emergence into light – only those who have experienced it can appreciate it.

ALBERT EINSTEIN

It is impossible to travel faster than the speed of light, and certainly not desirable, as one’s hat keeps blowing off.

WOODY ALLEN

During the course of the early twentieth century, cosmologists would develop and test a whole variety of models of the universe. These candidate models emerged as physicists gained a clearer understanding of the universe and the scientific laws that underpin it. What were the substances that made up the universe and how did they behave? What caused the force of gravity and how did gravity govern the interactions between the stars and planets? And the universe was made up of space and evolved in time, so what exactly did physicists mean by space and time? Crucially, answering all these fundamental questions would be possible only after physicists had addressed one seemingly simple and innocent question: what is the speed of light?

When we see a flash of lightning, it is because the lightning is emitting light, which might have to travel several kilometres towards us before reaching our eyes. Ancient philosophers wondered how the speed of light affected the act of seeing. If light travels at a finite speed, then it would take some time to reach us, so by the time we see the lightning it may no longer actually exist. Alternatively, if light travels infinitely fast then the light would reach our eyes instantaneously, and we would see the lightning strike as it is happening. Deciding which scenario was correct seemed to be beyond the wit of the ancients.

The same question could be asked about sound, but this time the answer was more obvious. Thunder and lightning are generated simultaneously, but we hear the thunder after we see the lightning. For the ancient philosophers, it was reasonable to assume that sound has a finite speed and certainly travels much slower than light. They thus established a theory of light and sound based on the following incomplete chain of reasoning:

1. A lightning strike creates light and sound.

2. Light travels either very fast or infinitely fast towards us.

3. We see lightning very soon after the event, or instantaneously.

4. Sound travels at a slower speed (roughly 1,000 km/h).

5. Therefore we hear the thunder some time later, depending on the distance to the lightning strike.

But still the fundamental question relating to the speed of light – whether it was finite or infinite – continued to exercise the world’s greatest minds for centuries. In the fourth century BC, Aristotle argued that light travelled with infinite speed, so the event and the observation of the event would be simultaneous. In the eleventh century AD, the Islamic scientists Ibn Sina and al-Haytham both took the opposite view, believing that the speed of light, though exceedingly high, was finite, so any event could be observed only some time after it had happened.

There was clearly a difference of opinion, but either way the debate remained merely philosophical until 1638, when Galileo proposed a method for measuring the speed of light. Two observers with lamps and shutters would stand some distance apart. The first observer would flash a signal to the second, who would then immediately flash a signal back. The first observer could then estimate the speed of light by measuring the time between sending and receiving signals. Unfortunately Galileo was already blind and under house arrest when he came up with this idea, so he was never able to conduct his experiment.

In 1667, twenty-five years after Galileo’s death, Florence’s illustrious Accademia del Cimento decided to put Galileo’s idea to the test. Initially, two observers stood relatively close together. One flashed a lantern at the other, and the other would see the signal and flash back. The first man estimated the time between sending the original flash and seeing the response flash, and the result was an interval of a fraction of a second. This, however, could be attributed to their reaction times. The experiment was repeated over and over again, with the two men moving farther apart, measuring the time of the return flash over increasing distances. Had the return time increased with distance, it would have indicated a relatively low and finite speed of light, but in fact the return time remained constant. This implied that the speed of light was either infinite, or so fast that the time taken by the light to travel between the two observers was insignificant compared with their reaction times. The experimenters could draw only the limited conclusion that the speed of light was somewhere between 10,000 km/h and infinity. Had it been any slower, they would have detected a steadily increasing delay as the men moved apart.

Whether the speed of light was finite or infinite remained an open question until a Danish astronomer named Ole Römer addressed the issue a few years later. As a young man, he had worked at Tycho Brahe’s former observatory at Uraniborg, measuring the observatory’s exact location so that Tycho’s observations could be correlated with others made elsewhere in Europe. In 1672, having earned a reputation as an excellent surveyor of the heavens, he was offered a post at the prestigious Academy of Sciences in Paris, which had been set up so that scientists could pursue independent research, free from having to pander to the whims of kings, queens or popes. It was in Paris that fellow Academician Giovanni Domenico Cassini encouraged Römer to study a strange anomaly associated with Jupiter’s moons, in particular Io. Each moon should orbit Jupiter in a perfectly regular manner, just as our Moon orbits the Earth regularly, so astronomers were shocked to discover that Io’s timings were slightly irregular. Sometimes Io appeared from behind Jupiter ahead of schedule by a few minutes, while at other times it was a few minutes late. A moon should not behave in this way, and everybody was baffled by Io’s lackadaisical attitude.

In order to investigate the mystery, Römer studied in minute detail a table of Io’s positions and timings that had been logged by Cassini. Nothing made sense, until it gradually dawned on Römer that he could explain everything if light had a finite speed, as shown in Figure 19. Sometimes the Earth and Jupiter were on the same side of the Sun, whereas at other times they were on opposite sides of the Sun and farther apart. When the Earth and Jupiter were farthest apart, then the light from Io had to travel 300,000,000 km farther before reaching the Earth compared with when the two planets were closest together. If light had a finite speed, then it would take longer for the light to cover this extra distance and it would seem as if Io was running behind schedule. In short, Römer argued that Io was perfectly regular, and its apparent irregularity was an illusion caused by the different times required for the light from Io to cover different distances to the Earth.

To help understand what is going on, imagine that you are near a cannon that is fired exactly on the hour. You hear the cannon, start your stopwatch and then start driving away in a straight line at l00 km/h, so that you are 100 km away by the time the cannon is fired again. You stop the car and hear a very faint cannon blast. Given that sound travels at roughly 1,000 km/h, you will perceive that it was 66 minutes, not 60 minutes, between the first and second cannon blasts. The 66 minutes consists of 60 minutes for the actual interval between firings and 6 minutes for the time taken for the sound of the second blast to cover the 100 km and reach you. The cannon is perfectly regular in its firings, but you will experience a delay of 6 minutes because of the finite speed of sound and your new position.

Figure 19 Ole Römer measured the speed of light by studying the movements of Jupiter’s moon Io. These diagrams represent a slight variation on his actual method. In diagram (a), Io is about to disappear behind Jupiter; in diagram (b) Io has completed half a revolution so that it is in front of Jupiter. Meanwhile, Jupiter has hardly moved and the Earth has moved significantly, because the Earth orbits the Sun twelve times more quickly than Jupiter. An astronomer on the Earth measures the time that has elapsed between (a) and (b), namely the time taken for Io to complete half a revolution.

In diagram (c), Io has completed another half-revolution back to where it started, while the Earth has moved on to a position that is farther from Jupiter. The astronomer measures the time between (b) and (c), which should be the same as the time between (a) and (b), but in fact it turns out to be significantly longer. The reason for the extra time is that it takes the light from Io a little longer to cover the extra distance to the Earth in diagram (c), because the Earth is now farther away from Jupiter. The time delay and the distance between Earth and Jupiter can be used to estimate the speed of light. (The distances moved by the Earth in these diagrams are exaggerated, because Io orbits Jupiter in less than two days. Also, Jupiter’s position would change and complicate matters.)

Having spent three years analysing the observed timings of Io and the relative positions of the Earth and Jupiter, Römer was able to estimate the speed of light to be 190,000 km/s. In fact, the true value is almost 300,000 km/s, but the important point was that Römer had shown that light had a finite speed and derived a value that was not wildly inaccurate. The age-old debate had been resolved at last.

However, Cassini was distraught when Römer announced his result, because he received no acknowledgement from Römer, even though the calculation was based largely on his observational data. Cassini became a harsh critic of Römer and a vocal spokesman for the majority who still favoured the theory that the speed of light was infinite. Römer did not relent, and used his finite light speed to predict that an eclipse of Io on 9 November 1676 would occur 10 minutes later than predicted by his opponents. In a classic case of ‘I told you so’, Io’s eclipse was indeed several minutes behind schedule. Römer was proved right, and he published another paper confirming his measurement of the speed of light.

This eclipse prediction should have settled the argument once and for all. Yet, as we have already seen in the case of the Sun-centred versus Earth-centred debate, factors beyond pure logic and reason sometimes influence the scientific consensus. Cassini was senior to Römer and also outlived him, so by political clout and simply by being alive he was able to sway opinion against Römer’s argument that light had a finite speed. A few decades later, however, Cassini and his colleagues gave way to a new generation of scientists who would take an unbiased look at Römer’s conclusion, test it for themselves and accept it.

Once scientists had established that the speed of light was finite, they set about trying to solve yet another mystery concerning its propagation: what was the medium responsible for carrying light? Scientists knew that sound could travel in a variety of media –talkative humans send sound waves through the medium of gaseous air, whales sing to each other through the medium of liquid water, and we can hear the chattering of our teeth through the medium of the solid bones between teeth and ears. Light can also travel through gases, liquids and solids, such as air, water and glass, but there was a fundamental difference between light and sound, as demonstrated by Otto von Guericke, the Burgomeister of Magdeburg, Germany, who conducted a whole series of famous experiments in 1657.

Von Guericke had invented the first vacuum pump and was keen to explore the strange properties of the vacuum. In one experiment he placed two large brass hemispheres face to face and evacuated the air from inside them so that they behaved like two exceedingly powerful suction cups. Then, in a marvellous display of scientific showmanship, he demonstrated that it was impossible for two teams of eight horses to pull the hemispheres apart.

Although this equine tug-of-war showed the power of the vacuum, it said nothing about the nature of light. This question was addressed in a somewhat daintier experiment, which required von Guericke to evacuate a glass jar containing a ringing bell. As the air was sucked out of the jar, the audience could no longer hear the ringing, but they could still see the clapper hitting the bell. It was clear, therefore, that sound could not travel through a vacuum. At the same time, the experiment showed that light could travel through a vacuum because the bell did not vanish and the jar did not darken. Bizarrely, if light could travel through a vacuum, then something could travel through nothing.

Confronted with this apparent paradox, scientists began to wonder if a vacuum was really empty. The jar had been evacuated of air, but perhaps there was something remaining inside, something that provided the medium for conveying light. By the nineteenth century, physicists had proposed that the entire universe was permeated by a substance they termed the luminiferous ether, which somehow acted as a medium for carrying light. This hypothetical substance had to possess some remarkable properties, as pointed out by the great Victorian scientist Lord Kelvin:

Now what is the luminiferous ether? It is matter prodigiously less dense than air – millions and millions and millions of times less dense than air. We can form some sort of idea of its limitations. We believe it is a real thing, with great rigidity in comparison with its density: it may be made to vibrate 400 million million times per second; and yet be of such density as not to produce the slightest resistance to any body going through it.

In other words, the ether was incredibly strong, yet strangely insubstantial. It was also transparent, frictionless and chemically inert. It was all around us, yet it was clearly hard to identify because nobody had ever seen it, grabbed it or bumped into it. Nevertheless, Albert Michelson, America’s first Nobel Laureate in physics, believed that he could prove its existence.

Michelson’s Jewish parents had fled persecution in Prussia in 1854, when he was just two years old. He grew up and studied in San Francisco before going on to join the US Naval Academy, where he graduated a lowly twenty-fifth in seamanship, but top in optics. This prompted the Academy’s superintendent to remark: ‘If in the future you’d give less attention to those scientific things and more to your naval gunnery, there might come a time when you would know enough to be of some service to your country.’ Michelson sensibly moved into full-time optics research, and in 1878, aged just twenty-five, he determined the speed of light to be 299,910 ± 50 km/s, which was twenty times more accurate than any previous estimation.

Then, in 1880, Michelson devised the experiment that he hoped would prove the existence of the light-bearing ether. His equipment split a single light beam into two separate perpendicular beams. One beam travelled in the same direction as the Earth’s movement through space, while the other beam moved in a direction at a right angle to the first beam. Both beams travelled an equal distance, were reflected off mirrors, and then returned to combine into a single beam. Upon combining they underwent a process known as interference, which allowed Michelson to compare the two beams and identify any discrepancy in travel times.

Michelson knew that the Earth travels at roughly 100,000 km/h around the Sun, which presumably meant that it also passed through the ether at this speed. Since the ether was supposed to be a steady medium that permeated the universe, the Earth’s passage through the universe would create a sort of ether wind. This would be similar to the sort of pseudo-wind you would feel if you were speeding along in an open-top car on a still day – there is no actual wind, but there seems to be one due to your own motion. Therefore, if light is carried in and by the ether, its speed should be affected by the ether wind. More specifically, in Michelson’s experiment one light beam would be travelling into and against the ether wind and should thus have its speed significantly affected, while the other beam would be travelling across the ether wind and its speed should be less affected. If the travel times for the two beams were different, then Michelson would be able to use this discrepancy as strong evidence in favour of the ether’s existence.

This experiment to detect the ether wind was complicated, so Michelson explained the underlying premise in terms of a puzzle:

Suppose we have a river of width 100 feet, and two swimmers who both swim at the same speed, say 5 feet per second. The river flows at a steady rate of 3 feet per second. The swimmers race in the following way: they both start at the same point on one bank. One swims directly across the river to the closest point on the opposite bank, then turns around and swims back. The other stays on one side of the river, swimming downstream a distance (measured along the bank) exactly equal to the width of the river, then swims back to the start. Who wins? [See Figure 20 for the solution.]

Figure 20 Albert Michelson used this swimming puzzle to explain his ether experiment. The two swimmers play the same role as the two beams of light heading in perpendicular directions, then both returning to the same starting point. One swims first with and then against the current, while the other swims across the current – just as one light beam travels with and against the ether wind, and the other across it. The puzzle is to work out the winner of a race over a distance of 200 feet between two swimmers who both can swim at 5 feet per second in still water. Swimmer A goes downstream 100 feet and back upstream 100 feet, whereas swimmer B goes across the river and back, also covering two legs of 100 feet. The river has a 3 ft/s current.

The time of swimmer A, going downstream and then upstream, is easy to analyse. With the current, the swimmer has an overall speed of 8 ft/s (5 + 3 ft/s), so the 100 feet takes just 12.5 seconds. Coming back against the current means that he is swimming at only 2 ft/s (5 - 3 ft/s), so swimming this 100 feet takes him 50 seconds. Therefore his total time is 62.5 seconds to swim 200 feet.

Swimmer B, going across the river, has to swim at an angle in order to compensate for the current. Pythagoras’ theorem tells us that if he swims at 5 ft/s at the correct angle, he will have an upstream component of 3 ft/s, which cancels the effect of the current, and a cross-stream component of 4 ft/s. Therefore he swims the first width of 100 feet in just 25 seconds, and then takes another 25 seconds to return, giving a total time of 50 seconds to swim 200 feet. Although both swimmers would swim at the same speed in still water, the swimmer crossing the current wins the race against the swimmer who goes with and against the current. Hence, Michelson suspected that a light beam travelling across the ether wind would have a shorter travel time than a beam travelling with and then against the ether wind. He designed an experiment to see if this was really the case.

Michelson invested in the best possible light sources and mirrors for his experiment and took every conceivable precaution in assembling the apparatus. Everything was carefully aligned, levelled and polished. To increase the sensitivity of his equipment and minimise errors, he even floated the main assembly in a vast bath of mercury, thereby isolating it from external influences such as the tremors caused by distant footsteps. The whole point of this experiment was to prove the existence of the ether, and Michelson had done everything possible to maximise the chance of its detection – which is why he was so astonished by his complete and utter failure to detect any difference in the arrival times of the two perpendicular beams of light. There was no sign of the ether whatsoever. It was a shocking result.

Desperate to find out what had gone wrong, Michelson recruited the chemist Edward Morley. Together they rebuilt the apparatus, improving each piece of equipment to make the experiment even more sensitive, and then they carried out the measurements over and over again. Eventually, in 1887, after seven years of repeating their experiment, they published their definitive results. There was still no sign of the ether. Therefore they were forced to conclude that the ether did not exist.

Bearing in mind its ridiculous set of properties – it was supposed to be the least dense yet the most rigid substance in the universe – it should have come as no surprise that the ether was a fiction. Nevertheless, scientists discarded it with great reluctance because it had been the only conceivable way to explain how light was transmitted. Even Michelson had problems coming to terms with his own conclusion. He once nostalgically referred to the ‘beloved old ether, which is now abandoned, though I personally still cling a little to it’.

The crisis of the non-existent ether was magnified because it was supposed to have been responsible for carrying both the electric and magnetic fields as well as light. The dire situation was nicely summarised by the science writer Banesh Hoffmann:

First we had the luminiferous ether,

Then we had the electromagnetic ether,

And now we haven’t e(i)ther.

So, by the end of the nineteenth century Michelson had proved that the ether did not exist. Ironically, he had built his career on a whole series of successful experiments relating to optics, but his greatest triumph was the result of a failed experiment. His goal all along had been to prove the existence of the ether, not its absence. Physicists now had to accept that light could somehow travel through a vacuum – through space devoid of any medium.

Michelson’s achievement had required expensive, specialist experimental apparatus and years of dedicated effort. At roughly the same time, a lone teenager, unaware of Michelson’s experimental breakthrough, had also concluded that the ether did not exist, but on the basis of theoretical arguments alone. His name was Albert Einstein.