by Marcus Chown
25 Actually, if the speed of light is independent of the speed of its source, it follows from the principle of relativity that its speed is also independent of the speed of an observer.
26 The American physicist John Wheeler said: ‘Time is what stops everything happening at once.’
27 If the train is travelling at a velocity, v, it is a matter of simple geometry to work out that a clock on the train runs slower than one not on the train by a factor of 1/√(1 – u2/c2). It is also possible to deduce that a ruler on the train shrinks by a factor of 1/√(1 – u2/c2). The quantity 1/√(1 – u2/c2) is known as the Lorentz factor and is usually represented by the Greek symbol γ
28 What does it mean to say that something happens at a particular time — say, someone strikes a match at 11 o’clock? It means, Einstein realised, that two events – the hands reaching the arrangement we refer to as 11 o’clock and the striking of the match – are simultaneous. But consider someone striking the match at the centre of a train carriage which is travelling from left to right. Someone at the far-left end of the carriage will see the match ignite earlier than someone at the far-right because, in the time the light is travelling to them, the train will have moved forward, shortening the distance the light needs to travel. Since being able to agree on events being simultaneous is, according to Einstein, the very foundation of telling the time, not being able to do so means there can be no such thing as universal time everyone agrees on.
29 Max Fliickiger, Albert Einstein in Bern, Verlag Paul Haupt, Bern, 1972, p. 158.
30 Quoted in Charles Misner, Kip Thorne and John Wheeler, Gravitation, W. H. Freeman, New York, 1973, p. 937.
31 ‘No time like the present’: Marcus Chown, The Never-Ending Days of Being Dead, Faber & Faber, London, 2007.
32 Strictly speaking, momentum and energy.
33 Albert Einstein, ‘Does the inertia of a body depend on its energy content?’, Annalen der Physik, vol. 18,1905, pp. 639—41. Received 27 September 1905.
34 The speed of light is uncatchable only for a body with mass. A massless particle – and a particle of light, or ‘photon’, is massless – can travel at the speed of light.
35 Einstein was not the one to coin the term ‘relativity’. In fact, he did not like it. It was the great German physicist Max Planck, who at a meeting in Stuttgart on 19 September 1906, first spoke of ‘relative theory’. This was gradually morphed by others into ‘relativity theory’. It was not until 1911 that Einstein reluctantly used the term in the title of a paper, and even then in inverted commas. After a few more years, he accepted the inevitable and dropped the quotation marks.
36 Asked by William Gladstone, British Chancellor of the Exchequer, ‘What is the practical use of electricity?’ Faraday replied: ‘Why, sir, there is every probability that you will soon be able to tax it.’
37 In general a ‘field’ is a physical quantity that has a value for each point in space and time. It could be something simple like a temperature, which merely has a magnitude, or it could be something more like a magnetic field, which has not only a magnitude but a direction in 3D space.
38 Conrad Habicht was a friend of Einstein’s from his Zurich student days. The pair, together with Maurice Solovine, rather grandiosely called themselves the ‘Olympia Academy’. They met in cafés and talked of the ideas they had absorbed from their readings of science, philosophy and literature.
Chapter 6
1 Quoted in Engelbert Schucking and Eugene Surowitz, Einstein’s Apple: Homogeneous Einstein Fields, World Scientific, Singapore, 2015, p. 2.
2 Michio Kaku, ‘A theory of everything?’ (http://p-i-a.com/Magazine/ Issue6/MichioKaku.htm).
3 The Collected Papers of Albert Einstein, Volume 5: The Swiss Years, Correspondence, 1902-1914, translated by Anna Beck (Princeton University Press, Princeton, 1995, p. 46). In the seven years from 1902 to 1909, Einstein assessed an estimated 2,000 patent applications, but his review of the AEG application is the only one that survives. Swiss bureaucracy ensured the destruction of all other examples of Einstein’s expert opinions, despite his being a stellar figure in the world of physics after 1905.
4 ‘I was falling. Falling through time and space and stars and sky and everything in between. I fell for days and weeks and what felt like lifetimes across lifetimes. I fell until I forgot I was falling’ – Jess Rothenberg, The Catastrophic History of You and Me, Penguin, London, 2012.
5 Fortunately, all lifts in operation are safety lifts. If the cable breaks, the lift jams in the shaft. Not very pleasant but rarely deadly for its occupants.
6 Ideally, this experiment should be done on an ice rink where friction with the ground does not complicate things!
7 1g = 9.8 metres per second per second. It is the acceleration that gravity causes at the Earth’s surface. In other words, every second, a falling apple – or anything else – increases its speed by 9.8 metres per second.
8 For an acceleration as small as 1g, the effect would actually be so tiny as to be unnoticeable except with precision instruments.
9 You might think that this explanation of the slowing down of time in strong gravity is a trick because it uses a clock with a beam of light which travels horizontally between mirrors and not vertically between mirrors. But the reason for using a clock with a horizontal beam is so as to be able to define a tick at a constant height – that is, where gravity is constant.
10 James Chin-Wen Chou et al., ‘Optical clocks and relativity’, Science, vol. 329, 24 September 2010, p. 1,630.
11 David Berman, ‘String theory: From Newton to Einstein and beyond’ (https://plus.maths.org/content/string-theory-newton-einstein-and-beyond).
12 The ants-on-the-trampoline analogy of how gravity works is not perfect. A major flaw is that it implicitly uses gravity to explain gravity! After all, it is gravity that pulls the bowling ball downwards and creates the depression in the trampoline. Of course, the trampoline could be floating in space in zero-gravity and the bowling ball could be electrically charged and pulled from one side of the trampoline by the electric force of another electrically charged body. But that would make the analogy complicated and confusing. Best to stick with the imperfect analogy and try to ignore the imperfection!
13 Kaku, ‘A Theory of Everything?’
14 You may wonder why our natural motion is to head for the bottom of the valley of space-time centred on the Earth but that the Earth’s natural motion is to circle the valley of space-time centred on the Sun. The reason is that the Earth is flying through space with an appreciable velocity and so cannot fall into the Sun, whereas we are not flying relative to the Earth.
15 Isaac Newton, The Principia, edited by Florian (1687), p. 643.
16 The first gravitational wave detector – a 2-metre-long, 1.4-tonne aluminium cylinder designed to ring like a bell when hit by a spacetime ripple – was built by Joe Weber of the University of Maryland. His spurious claim, in the 1970s, that he had detected gravitational waves destroyed his scientific reputation but kick-started the whole field.
17 Dennis Overbye, ‘Gravitational Waves Detected, Confirming Einstein’s Theory’, New York Times, 11 February 2016 (http://www.nytimes. com/2016/02/12/science/ligo-gravitational-waves-black-holes-einstein. html).
18 Janna Levin, Black Hole Blues, The Bodley Head, London, 2016.
19 Davide Castelvecchi, ‘The black-holë collision that reshaped physics’, Nature, 23 March 2016 (http://www.nature.com/polopoly_fs/l.19612!/#x00A0;menu/main/topColumns/topLeftColumn/pdf/531428a.pdf).
20 This is a personal recollection of mine. As a physics graduate student at the California Institute of Technology – co-constructor of LIGO along with the Massachusetts Institute of Technology – I remember attending a talk given by Drever at Caltech, probably in 1984.
21 Albert Einstein, Autobiographische Skizze. In Carl Seelig (ed.), Bright Times – Dark Times, Europa Verlag, Zurich, 1956, p. 11.
22 Alex Bellos, Here’s Looking at Euclid!, Free Press, New York, 2010.<
br />
23 Einstein to Heinrich Zangger, 6 December 1917, Collected Papers of Albert Einstein, vol. 8, doc. 403, p. 411 (http://einsteinpapers.press. princeton.edu/).
24 Despite his key role in developing poison gases during the First World War, Fritz Haber won the 1919 Nobel Prize for Chemistry for the invention of the Haber-Bosch process for synthesising the ammonia used in fertilisers from hydrogen and atmospheric nitrogen.
25 Quoted in Lee Smolin, Three Roads to Quantum Gravity, Basic Books, London, 2000, p. 137.
26 Because energy curves space-time (that is, creates gravity) and curved space-time contains energy, it follows that energy creates curvature, which creates more curvature, which creates yet more curvature, and so on. Consequently, the general theory of relativity reduces to Newton’s theory of gravity when the energy contained in the curvature of spacetime is small, so that the only significant term is the gravity created by mass-energy. And, of course, when all bodies are moving much slower than the speed of light.
27 Einstein letter to Conrad Habicht, Bern, 24 December 1907.
28 Abraham Pais, Subtle is the Lord, Oxford University Press, Oxford, 1983, p. 20.
29 Ibid., p. 257.
30 Einstein letter to Paul Ehrenfest, Berlin, 16 January 1916.
31 Simon Newcomb, The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy: Supplement to the American Ephemeris and Nautical Almanax for 1897, Government Printing Office, Washington DC, 1895, p. 184.
32 In 1902, Simon Newcomb famously declared: ‘Flight by machines heavier than air is unpractical and insignificant, if not utterly impossible.’ The following year Orville Wright proved him wrong.
33 Dennis Overbye, ‘A Century Ago, Einstein’s Theory of Relativity Changed Everything’, Neiv York Times, 24 November 2015.
34 The ‘stress energy tensor’ is just a bag that holds a lot of information about what is present in space-time at some point: its energy density, its momentum densities, pressures, stresses and so on (http://pitt. edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity/index. html).
35 Although Einstein was German-born and German-based, he was strictly speaking no longer a German citizen, having renounced his citizenship at the age of twenty-one in 1896.
36 A particle of light, known as a ‘photon’, has no intrinsic, or ‘rest’, mass (if it did, it could never travel at the speed of light). Its effective mass is entirely due to its energy or, more precisely, its ‘energy-momentum’.
37 1 arc second is 1/60th of an arc minute, which is 1/60th of a degree. 1 arc second is consequently 1/3,600th of a degree.
38 Thomas Levenson, The Hunt for Vulcan, Head of Zeus, London, 2015, p. 161.
39 Ilse Rosenthal-Schneider, Reality and Scientific Truth, Wayne State University Press, Detroit, 1981, p. 74.
40 Charles Chaplin, My Autobiography, Penguin, London, 2003.
41 Simone Bertault, Piaf, Harper & Row, New York, 1972.
42 Pais, Subtle is the Lord, pp. 311–12.
Chapter 7
1 Gregory Benford, ‘Leaping the Abyss’, Reason Magazine, April 2002 (http://reason.com/archives/2002/04/01/leaping-the-abyss).
2 John Wheeler and Kenneth Ford, Geons, Black Holes & Quantum Foam, W. W. Norton, New York, 2000. *
3 Karl Schwarzschild’s solution was for a ‘non-spinning’ black hole. But all astronomical bodies are spinning. Nevertheless, it was not until 1963 – almost half a century after Einstein published his general theory of relativity — that the distortion of space-time by a realistic, ‘spinning’, black hole was deduced by the New Zealand physicist Roy Kerr.
4 Although John Wheeler is often credited with coining the term ‘black hole’, actually he merely popularised it. ‘In the fall of 1967, [I was invited] to a conference . . . on pulsars,’ he wrote. ‘In my talk, I argued that we should consider the possibility that the center of a pulsar is a gravitationally completely collapsed object. I remarked that one couldn’t keep saying “gravitationally completely collapsed object” over and over. One needed a shorter descriptive phrase. “How about black hole?” asked someone in the audience. I had been searching for the right term for months, mulling it over in bed, in the bathtub, in my car, whenever I had quiet moments. Suddenly this name seemed exactly right. When I gave a more formal Sigma Xi-Phi Beta Kappa lecture . . . on December 29, 1967,1 used the term, and then included it in the written version of the lecture published in the spring of 1968.’ Wheeler and Ford, Geons, Black Holes & Quantum Foam, p. 296.
5 Irrespective of the appearance of a star that shrank down to form a black hole, the resultant black hole is identical and characterised by just three things – its mass, how fast it is spinning and its electrical charge. Since big things tend to have an equal quantity of negative and positive charge, making them chargeless, in practice a black hole is characterised by only its mass and spin rate. The American physicist John Wheeler summarised this state of affairs as: ‘A black hole has no hair.’ In other words, there is nothing that can be learnt from observing the exterior of a black hole about the events that led to its birth.
6 Initially, Schwarzschild believed that the singularity was at the horizon of the black hole. But it turned out this was just an artefact of the coordinate system he used. The true singularity is at the heart of the hole.
7 See Chapter 8.
8 The Heisenberg Uncertainty Principle also makes atoms possible for, as Richard Feynman observed: ‘Atoms are completely impossible from the classical point of view.’ An electron in an atom orbits an ‘atomic nucleus’ like a planet around the Sun. According to the theory of electromagnetism, it should act like a tiny radio transmitter, radiating away its orbital energy as electromagnetic waves and spiralling into the nucleus in less than a hundred-millionth of a second. It is prevented from doing so because the quantum wave of an electron cannot be squeezed into an arbitrarily small volume. Or, from the particle point of view, an electron squeezed close to the nucleus is like a bee in an ever-shrinking box, getting angrier and battering itself ever more violently against the walls of its prison.
9 Marcus Chown, We Need to Talk About Kelvin, Faber & Faber, London, 2010.
10 The Pauli Exclusion Principle makes possible the variety of atoms -nature’s fundamental Lego bricks – and so is ultimately behind the complexity of the world. According to the theory of electromagnetism, all electrons in an atom, having radiated away their orbital energy, should crowd into the lowest-energy orbit, as close to the nucleus as possible. If this happened not only would the atoms of all ninety-two naturally occurring elements have the same size but they would all behave in the same way. This is because the behaviour of the atoms of an element is determined by the way in which the electrons are arranged. The Pauli Exclusion Principle dictates that they occupy ‘shells’ around the nucleus, with the exact number of electrons in the outer shell determining the way in which the atom links up with other atoms to form chemical compounds.
11 Electrons have intrinsic ‘spin’, something with no analogue in the everyday world. They are not actually spinning but behave as if they do. Imagine, however, that they are spinning. They are spinning at the lowest rate that nature permits, and there are two possible ways they can spin: clockwise or anticlockwise (‘up’ and ‘down’, in the physics jargon). This means that two electrons are not in the same state if they have opposite spins. The Pauli Exclusion Principle therefore permits two electrons in the same location – not one – to have the same velocity.
12 Why is it the electrons that hold up the star against gravity and not the atomic nuclei? The answer is that the nuclei are big and sluggish and so supply a lot less outward force than the fast-moving electrons. But why are there free electrons about anyway? Normally, in a cold gas -and remember, the star no longer has any internal fires – all the free electrons are tucked up in bed around their nuclei. The answer is they are so close together that the orbits of electrons are bigger than the separation of the nuclei. In the jargon, they are ‘
pressure ionised’.
13 Although there have now been three Nobel Prizes for Physics awarded for work on pulsars, none has gone to their discoverer, Jocelyn Bell.
14 Terry Pratchett, Small Gods, Corgi, London, 2013.
15 Dan Simmons, The Fall of Hyperion, Gollancz, London, 2005.
16 The term ‘big bang’ was coined by the British astrophysicist Fred Hoyle during a BBC radio broadcast in 1949. Ironically, Hoyle, one of the creators of the alternative ‘Steady State’ theory in 1948, never believed in the big bang.
17 Cepheid variables have the property, discovered by Henrietta Leavitt in 1908, that the greater their pulse period the greater their intrinsic luminosity. This means it is always possible to deduce from a Cepheid’s period its true luminosity. Knowing how bright it appears from Earth, astronomers can then ask: how far away would it have to be to appear as faint as it does?
18 ‘Space is big. Really big. You just won’t believe how vastly, hugely, mind-bogglingly big it is.’ Douglas Adams, The Hitchhiker’s Guide to the Galaxy, Chapter 8.
19 In exactly the same way that the frequency, or ‘pitch’, of a police siren gets higher as it approaches and lower as it recedes, the frequency of light emitted by atoms in a star becomes higher or lower depending on whether the star is approaching or receding from the Earth. By measuring the magnitude of this ‘Doppler shift’ in frequency for common atoms of elements such as hydrogen, astronomers can determine the velocity of a star’s movement towards us and away from us.