The Book of Nothing Read online

  Michelson spent two years moving between some of the leading European universities, learning about the new developments in physics and, inevitably, listening to some of the foremost theoretical physicists expound their theories of the ether – the great puzzle of the day. It became a source of continuing fascination for Michelson. Did this strangely elusive medium exist or not? Was there a way of measuring it?

  James Clerk Maxwell had suggested30 that by checking whether the speed of light was the same in different directions we would learn something about the motion of the ether stream through which the light had to propagate; for

  “If it were possible to determine the velocity of light by observing the time it takes to travel between one station and another on the earth’s surface, we might by comparing the observed velocity in opposite directions determine the velocity of the ether with respect to these terrestrial stations.”

  But Maxwell doubted whether it would be possible to conduct this experiment and discover the answer. Michelson ignored these pessimistic predictions. He saw that there was a straightforward way to realise Maxwell’s inspired suggestion. Suppose that the ether is not moving, so it specifies some state of absolute rest. Then we must be moving through it, as the Earth spins on its axis and orbits the Sun. A suitable detector might be able to measure the wind of ether that our movement through it would create, just like a cyclist feels the wind on his face as he rides through still air. If the ether was moving, then we should feel different effects when we move upstream and downstream within it.

  Michelson began to develop his ideas by drawing up simple analogies. Moving through the ether should be like swimming in a river. The flow of the river is the flow of ether past us caused by the Earth’s motion through the stationary sea of ether. Now imagine a swimmer who makes two return trips in the river. The first is across the river at right angles to the flow; the second is downstream and then back upstream. In both cases he ends up at the same point at which he began; the two round-trip paths are shown in Figure 4.4. If the same total distance is swum in each case then it is always quicker to swim the cross-river circuit than the down-and-upstream circuit. To see this, let’s do a simple example. Suppose the river flows at a speed of 0.4 metres per second and the swimmer can swim at a speed of 0.5 metres per second in still water. Each leg to be swum will be 90 metres in length.

  Figure 4.4 A swimmer makes two round trips of equal distance: one across the river and back, the other upstream and downstream.

  The swim downstream followed by the return upstream has the swimmer moving at 0.5 + 0.4 = 0.9 metres per second relative to the bank on the downward trip. The time to swim 90 metres is therefore 90 ÷ 0.9 = 100 seconds. Returning upstream his speed relative to the bank is only 0.5 − 0.4 = 0.1 metres per second and he takes 90 ÷ 0.1 = 900 seconds to make it back to the start. The total round-trip time is therefore 900 + 100 = 1000 seconds.

  Now consider the cross-river route. He will find it just as hard to swim each way as he is always swimming at right angles to the current. His speed perpendicular to the flow of the river is given by an application of Pythagoras’ theorem for triangles, applied to the velocities. The actual speed he can swim across the river will be equal to the square root of 0.52 − 0.42 = 0.09, which is 0.3 metres per second (see Figure 4.5). Thus he can swim 90 metres in 90 ÷ 0.3 = 300 seconds. The total time he takes to swim 90 metres across the river and 90 metres back is therefore 600 seconds. This is different from the round-trip time up and downstream because of the speed of flow of the river. Only if the speed of flow of the river is zero will the two round-trip times be the same.

  Figure 4.5 The speed that the swimmer can achieve across the river is given by Pythagoras’ theorem applied to the triangle of velocities.

  Michelson concluded that the same should happen if light was ‘swimming’ through the ether. Two light rays emitted in perpendicular directions and reflected back to their starting point should take different times to complete their round trips over the same distance because, like the swimmer in the river, they would experience different total amounts of drag from the flowing ether. Most important of all, if there was no ether then the two round-trip travel times by the different light rays should be exactly the same.

  Michelson conceived of a beautiful experiment to test the ether hypothesis. He sent two beams of light simultaneously in directions at right angles to each other and then reflected them back along the directions they had come. The ether hypothesis could then be tested by checking if they both returned to the starting point at the same moment. The experimental set-up is shown in Figure 4.6. Very high precision was possible by exploiting the wavelike character of light. If the light waves arrived back at the same point slightly out of phase with the source waves then there would a slight darkening caused by the overlap of peaks of one light wave with troughs of the other and a brightening where peaks overlap peaks and troughs overlap troughs. The phenomenon, known as interference, creates an alternating sequence of dark and light bands.31 In Michelson’s experiment, seeing no interference pattern of alternating fringes would mean that there could be no effect of the ether slowing the light in one direction but not in a direction perpendicular to it.32

  Although the concept of the experiment was simple, the execution was a considerable challenge. The speed of light is 186,000 miles per second whilst the speed of the Earth in its annual orbit around the Sun is only about 18 miles per second. Extraordinary care and accuracy was required if the experimental measurements were going to be accurate and not disrupted by measurement errors and other fluctuations in the experimental set-up. To get some idea of the challenge, if the ether did exist then the tiny difference that should be detected in the light-travel time for rays moving in the two directions would be just one-half of the square of the ratio of the speed of the Earth to the speed of light – less than one part in one hundred million! In order to convince scientists that there was no etherinduced time difference, the accuracy of the measurement had to be better than that.

  Figure 4.6 A simplified sketch of Michelson’s experiment. A light beam is divided by a partially reflecting glass plate at G into two beams at right angles. One moves along the path of length L, the other along the path of length K. Each is reflected back by mirrors at M and N and the two light beams are recombined at G and observed. If the times required by the two light beams to travel their two paths are different they will be out of phase when they recombine at G and interference bands will be created.

  Fortunately for Michelson, the famous telephone engineer Alexander Graham Bell put up the money to fund the experiment and the interferometer was built in Berlin in 1881. Michelson made his first attempt at the experiment at the University of Berlin, in the laboratory of the famous German physicist Hermann von Helmholtz. He immediately encountered problems. He had to make sure that his array of mirrors was kept at constant temperature by surrounding the entire experiment with melting ice at zero degrees Centigrade, then he had to deal with the vibrations created by the Berlin traffic thundering past outside. The traffic noise ultimately proved unbeatable in Berlin, so he dismantled his apparatus and moved it to the Astrophysical Observatory nearby in Potsdam. Faced now with only the modest vibrations caused by pedestrians, and with his apparatus firmly mounted on the rigid base of the telescope, Michelson finally succeeded in creating the quiet conditions needed to carry out the measurement to the accuracy he needed. The experiment was repeated many times with the apparatus in different orientations, and also at different times of the year, so that the Earth’s motion relative to the Sun would be different. The result was entirely unexpected. With an accuracy that was easily able to detect the Earth’s motion through the ether, it was found that there was no interference pattern. The Earth was not ploughing its way through a ubiquitous ether at all. Michelson’s momentous paper reported his results in August 1881 and concluded that ‘The hypothesis of a stationary ether is erroneous’.33

  The responses to Michelson’s discovery f
ell into two camps. Some concluded that the ether must be non-stationary and dragged around by the Earth as it orbits the Sun so that there is no relative motion between the ether and Earth; others simply concluded that the ether didn’t exist after all. Michelson remained agnostic about the theoretical interpretation of his result.

  Michelson returned to a new position at the Case Institute of Technology in Cleveland.34 There he gained a new collaborator, an American chemistry professor fifteen years his senior, called Edward Morley. Morley was deeply religious. His original training had been in theology and he only turned to chemistry, a self-taught hobby, when he was unable to enter the ministry. Michelson, by contrast, was a religious agnostic. But what they had in common was great skill and ingenuity with scientific instruments and experimental design. Together they repeated Michelson’s experiment to discover if the speed of light was the same in different directions of space. When they finished analysing their results in June 1887 there again were no interference fringes. Light was travelling at the same speed in different directions irrespective of the speed of its source through space. There was no stationary ether.35 This was an incredible conclusion. It meant that if you fired a light beam from a moving source it would be found to have the same speed relative to the ground that it would have if the source were stationary. Light moved like nothing else that had ever been seen.

  THE AMAZING SHRINKING MAN

  “A mathematician may say anything he pleases, but a physicist must be at least partially sane.”

  Josiah Willard Gibbs

  How could the ether still exist in the face of the null result of Michelson and Morley? An answer was suggested first in 1889 by George FitzGerald at Trinity College Dublin and then developed independently a little later by the Dutch physicist Hendrik Lorentz at Leiden. They suggested that the length of an object will be seen to diminish if it moves at increasing speeds.36 If we take two rulers and hold one still on the Earth but let the other fly past at high speed parallel to it then, as the moving ruler passes by, it will be seen to be shorter than the stationary one. This sounded crazy, even to physicists, but FitzGerald and Lorentz derived their claim from the properties of Maxwell’s theory of light and electromagnetism. FitzGerald even tried to explain the basis of the contraction by arguing that the inter-molecular forces holding solid bodies together are probably electromagnetic in origin and so were likely to be affected if they moved through the ether. He thought that an increase in their attractiveness could be responsible for drawing molecules closer together and reducing the length of any chain they formed.

  The amount of the FitzGerald-Lorentz shrinkage was predicted to be very small. Lengths of moving objects would contract by a factor equal to √(1–v2/c2), where v is their speed and c is the speed of light. For a speed of 500 km per hour, we are looking at a contraction that is not much bigger than one hundred billionth of one per cent.

  FitzGerald had noticed that if this √(1–v2/c2) correction factor was applied to the analysis of Michelson’s apparatus fixed on the Earth’s surface as it moved around the Sun, it could explain why Michelson measured no effect from the ether. The arm of the interferometer contracts by a factor √(1–v2/c2) in the direction of its motion through the ether at a speed v. At an orbital speed of 29 kilometres per second this results in a contraction of only one part in 200,000,000 in the direction of the Earth’s orbital motion. The length of the arm perpendicular to the ether’s motion is unaffected. This small contraction effect exactly counterbalances the time delay expected from the presence of a stationary ether. If the FitzGerald-Lorentz contraction occurred then it allowed the existence of a stationary ether to be reconciled with the null result of the Michelson-Morley experiment. Space need not be empty after all.

  The ideas of FitzGerald and Lorentz37 were regarded as extremely speculative by most physicists of their day, and not taken very seriously as a defence of the ether. They were considered to be purely mathematical excursions devoid of real physical motivation. Attitudes began to change in 1901 when a young German physicist, Walter Kaufmann, studied the fast-moving electrons, called beta particles, emitted by radioactive elements, and showed that the measured masses of these electrons were also dependent on their speeds, just as Lorentz had predicted. Their masses increased with increasing speed, v, to a value equal to their mass when at rest divided by the FitzGerald-Lorentz factor √(1–v2/c2).

  The most awkward feature of these attempts to evade casting out the ether was the need to distinguish between a system that was moving and one that was not in some absolute sense. It is all very well to enter a value for v which corresponds to the Earth’s orbital velocity around the Sun in the FitzGerald contraction formula, but what if the Sun and its local group of stars are themselves in motion? What velocity do we use for v and with respect to what do we measure it?

  EINSTEIN AND THE END OF THE OLD ETHER

  “Navy: Please divert your course 15 degrees to the North to avoid a collision.

  Civilian: Recommend you divert your course 15 degrees to South to avoid a collision.

  Navy: This is the Captain of a US Navy ship. I say again, divert your course.

  Civilian: No, I say again, divert your course.

  Navy: This is the aircraft carrier Enterprise. We are a large warship of the US Navy. Divert your course now!!

  Civilian: This is a lighthouse. Your call.”

  Canadian naval radio conversation38

  The nineteenth century ended with a confusing collection of loose ends dangling from Michelson and Morley’s crucial experiment: the absence of the expected ether effect, the need to know the absolute value of velocity, the possibility that motion affects length and mass, and the significance of the speed of light. Albert Einstein made his first appearance on the scientific stage in 1905, at twenty-six years of age, by solving all of these problems at once in an announcement39 of what has become known as the ‘special theory of relativity’. The English translation of his famous paper has the innocuous-sounding title ‘On the Electrodynamics of Moving Bodies’.

  Einstein abandoned the idea that there was any such thing as absolute motion, absolute space or absolute time. All motion was relative and two postulates, that the laws of motion and those of electromagnetism must be found to be the same by all experimenters moving at constant velocities relative to one another, and that the velocity of light in empty space must be measured to be the same by all observers regardless of their motion, sufficed to explain everything. This enabled him to deduce as a simple consequence the precise laws for length, mass and time change proposed by FitzGerald and Lorentz. This theory reduced to Newton’s classical theory of motion when the motions occurred at velocities far less than that of light but behaved in quite different ways as velocities approached that of light in empty space. Newton’s theory was seen to be a limiting case of Einstein’s.

  This feature of a successful new theory of physics is worth dwelling on as it is overlooked by many commentators. Recently, there have been many newspaper polls to pick the most influential thinkers of the millennium. Newton has topped some polls, but finished behind Shakespeare, Einstein and Darwin in others. On one occasion, Newton’s lower position was justified on the grounds that some of his laws of motion had been shown to be ‘wrong’ by the work of Einstein. Indeed, the outsider might be tempted to think that the whole progression of our knowledge about the workings of Nature is replacing wrong theories by new ones which we think are right for a while but which will eventually be found to be wrong as well. Thus, the only sure thing about the currently favoured theory is that it will prove to be as wrong as its predecessors.

  This caricature misses the key feature. When an important change takes place in science, in which a new theory takes the stage, the incoming theory is generally an extension of the old theory which has the property of becoming more and more like the old theory in some limiting situation. In effect, it reveals that the old theory was an approximation (usually a very good one) to the new one that ho
lds under a particular range of conditions. Thus, Einstein’s special theory of relativity becomes Newton’s theory of motion when speeds are far less than that of light, Einstein’s general theory of relativity becomes Newton’s theory of gravity when gravitational fields are weak and bodies move at speeds less than that of light. In recent years we have even begun to map out what the successor to Einstein’s theory may look like. It appears that Einstein’s theory of general relativity is a limiting, low-energy case of a far deeper and wider theory, which has been dubbed M theory.40

  In some respects this pattern of ‘limiting’ correspondence is to be expected. The old theory has been useful because it has explained a significant body of experimental evidence. This evidence must continue to be well explained by the new theory. So, wherever physics goes in the next millennium, if there are still high-school students learning it in a thousand years’ time, they will still be learning Newton’s laws of motion. Their application to everyday problems of low-speed motion will never cease. Although they are not the whole truth, they are a wonderful approximation at low speeds41 to a part of the whole truth. They are not ‘wrong’ unless you try to apply them to motions close to the speed of light.