The Ascent of Gravity

by Marcus Chown

  20 The reason that the building of elements requires a high temperature is that the nuclei of atoms are positively charged. Like charges repel, so two nuclei have a ferocious resistance to being pushed together. But, if they are slammed together at high enough speed, this repulsion can be overcome and they can approach close enough to be grabbed by the ‘nuclear force’ and stick together. High speed is synonymous with high temperature, temperature being nothing more than microscopic motion.

  21 Arthur Eddington, who had invented the theory of stellar interiors, believed that, as stars rotate, currents of gas circulating in their interiors thoroughly mix their gas. This means that as a star turns its hydrogen fuel into helium ash, the by-product of which is sunlight, the hydrogen is spread throughout the star, becoming ever more dilute until the star’s fires dim and go out. Eddington was wrong. There is no such mixing. Instead, helium ash falls to the centre of the star, where it is compressed and heated. When hydrogen in the core is exhausted, helium may burn to carbon, which in turn falls to the centre of the star and is compressed and heated. The upshot is that stars, far from being uniformly mixed and going out with a whimper, become ‘chemically differentiated’, their interiors supporting ever more extreme temperatures and densities for millions or billions of years. Exactly the kind of furnace needed to build up elements.

  22 The main reason the big bang fireball could not forge all the elements is that it expanded and cooled too quickly. The conditions necessary for element building existed from about a minute after the moment of creation until the Universe was about 10 minutes old. Nevertheless, there was time to forge the lightest elements like lithium and beryllium. In particular, the fireball of the big bang could convert 10 per cent of the hydrogen nuclei into helium nuclei. This is exactly the proportion astronomers observe in the Universe today and is taken as strong evidence for the big bang. Pretty much all the heavier elements — from the iron in your blood and the calcium in your bones to the oxygen you take in with every breath – have been forged in stars since the big bang.

  23 A black body absorbs all the heat that falls on it. The heat is distributed between all the atoms by countless collisions in which fast-moving atoms transfer energy to slower-moving atoms. The result is that the black body emits heat that depends in no way on the kind of atoms the body is made of. Instead, ‘black body radiation’ has a universal spectrum which depends only on one number; the body’s temperature.

  24 Marcus Chown, Afterglow of Creation, Faber & Faber, London, 2010.

  25 L. S. Schulman, ‘Source of the observed thermodynamic arrow’, Journal of Physics: Conference Series, vol. 174, 2008, p. 12,022.

  26 Einstein himself never believed in black holes. In fact, in October 1939 he published a paper in which he claimed (incorrectly) that, for a black hole to form from a collection of stars, they would have to orbit each other faster than the speed of light, which is forbidden by the special theory of relativity. See Albert Einstein, ‘On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses’, Annals of Mathematics, Second Series, vol. 40, No. 4, 1939, p. 922 (http:// www.jstor.org/stable/1968902).

  27 See Marcus Chown, Quantum Theory Cannot Hurt You, Faber & Faber, London, 2014.

  28 Strictly speaking, quantum theory is not a theory of small things but a theory of ‘isolated’ things – that is, things not influenced by their surroundings. In practice, though, this makes quantum theory a theory of small things because it is easy to isolate an atom from its surroundings but hard to isolate, for instance, a human being like you. Molecules of air and particles of light are continually bouncing off you.

  29 Albert Einstein,‘Naherungsweise Integration der Feldgleichungen der Gravitation’ [Approximate integration of the field equations of gravitation], Sitzungsber der Preussische Akademien der Wissenschaften, 22 June 1916, p. 688. (Also in The Collected Papers of Albert Einstein, vol. 6, The Berlin Years: Writings, 1914–1917, Princeton University Press, 1997, p. 201.)

  Chapter 8

  1 William Bragg, ‘Electrons and Ether Waves (The Robert Boyle Lecture 1921)’, Scientific Monthly, vol. 14, 1922, p. 158.

  2 Said by Niels Bohr to Wolfgang Pauli after his presentation of Heisenberg’s and Pauli’s nonlinear field theory of elementary particles, Columbia University (1958), as reported in Freeman Dyson, ‘Innovation in Physics’, Scientific American, vol. 199, No. 3, September 1958, p. 74.

  3 ‘Gamma rays’ are even more energetic than X-rays. They were discovered by the French chemist and physicist Paul Villard in 1900 and named by New Zealand physicist Ernest Rutherford in 1903. Gamma rays come from inside the atomic nucleus, which is the seat of enormous energies.

  4 When light is shone on certain metals, electrons are ejected from their surface. Increasing the amount, or ‘intensity’, of the light liberates more electrons. But, if the light has less than a threshold energy, no electrons are emitted, no matter how intense the light. As Einstein realised, this ‘photoelectric effect’ is explained if light consists of photons, and only photons of sufficient energy can kick out electrons from the metal.

  5 In fact, once the existence of atoms was confirmed, and they were shown to be so small that 10 million would span the full stop at the end of this sentence, there was the paradox that the wavelength of visible light is about 10,000 times bigger than an atom. There seems no way an atom can absorb or spit out light of that size — unless light, like an atom, is a small and localised thing – a photon.

  6 According to the standard picture of cosmology, known as ‘inflation’, the Universe started out so ultra-tiny that it contained hardly any information. Today, by contrast, it contains a truly vast amount – just imagine how much is needed to describe the type and location of every atom in the Universe. The puzzle of where all the information came from is explained by quantum theory since randomness is synonymous with information. Every random quantum event since the big bang, such as the decay of a radioactive atom, has injected information/ complexity into the Universe. When Einstein said, ‘God does not play dice with the Universe’, he could not have been more wrong. If God had not played dice, there would be no Universe — certainly no Universe with anything interesting going on in it. See the chapter ‘Random Reality’ in Marcus Chown, The Never-Ending Days of Being Dead, Faber & Faber, London, 2007.

  7 See Chapter 7.

  8 Werner Heisenberg, Physics and Philosophy, Penguin Classics, London, 2000.

  9 Interference is a defining feature of waves. If two waves overlap, where the peaks of the two waves coincide, they boost each other, or ‘constructively interfere’, and where the peaks of one wave coincide with the troughs of the other wave, they cancel each other out, or ‘destructively interfere’. It is precisely this effect which was demonstrated for light by Thomas Young in 1801. (See Chapter 5.)

  10 Strictly speaking, the probability of finding a particle at any location is the square of the amplitude wave at a particular location. The probability is always a number between 0 and 1, with 0 corresponding to 0 per cent probability and 1 corresponding to 100 per cent probability.

  11 Most physicists believe that quantum systems are isolated systems and that they stop behaving in a quantum manner because of a process called ‘decoherence’. The key thing to understand is that we never actually see quantum behaviour directly. When a photon is detected by the human eye, for instance, the photon leaves an impression on hundreds of atoms. It is this impression that the brain observes (so, in a sense, we only ever observe ourselves!). And it is because it is very hard to keep hundreds of atoms in a superposition – the waves stop overlapping, or decohere – that quantumness is lost. The flip side of this is that, if it were possible to keep all those atoms in a superposition, quantumness could in principle manifest itself at any size. Currently, physicists are trying to do that. In a ‘quantum computer’, they want to exploit the ability of quantum systems to do many things at once, to do many calculations at once. Roger Penrose, however, believes that quantumness c
annot manifest itself at any size and there is a threshold mass beyond which there is a transition from quantum to classical physics. The question of who is right may have to be resolved by experiment. See Marcus Chown, Quantum Theory Cannot Hurt You, Faber & Faber, London, 2006.

  12 In fact, the problem of reconciling the quantum world, where things exist as a haze of probabilities, and the everyday world, where things exist with certainty, is fundamental and mysterious. There are at least thirteen ‘interpretations’ of quantum theory that attempt to do this, all of which predict the same outcome for every known experiment. Perhaps the most mind-blowing is the one proposed by Hugh Everett III in 1957. According to the ‘Many Worlds’ interpretation, the separate waves in a superposition actually describe separate arms of reality. So, in the case of the oxygen atom in superposition of two waves, one describing it on the left-hand side of a room and the other on the right-hand side, the oxygen atom really is in two places at once, one in one parallel reality and the other in a separate parallel reality.

  13 This is a remarkable discovery of the French mathematician Joseph Fourier (1767-1830), who found that, by superposing sine waves of different wavelengths and different ‘phases’ (that is, different locations of their peaks relative to each other), it was possible to create a wave of any shape whatsoever – even a square, top-hat-shaped one. One way of putting this is that, just as atoms are the basic building blocks of all matter, sine waves are the basic buildng blocks of all waves.

  14 See Chapter 8.

  15 Heisenberg himself came up with another explanation of the Uncertainty Principle, claiming that the wave nature of anything used to ‘see’ an object made it impossible to know exactly where it was. This is what countless university physics students are taught. But Heisenberg was incorrect. The Uncertainty Principle has nothing to do with measurement. The uncertainty is intrinsic to the submicroscopic world. See Geoff Brumfiel, ‘Quantum uncertainty not all in the measurement: A common interpretation of Heisenberg’s uncertainty principle is proven false’, Nature, 11 September 2012.

  16 Consider a wave packet made of light that passes by. Because there is an uncertainty in its location (dx), it follows that there is an uncertainty in the exact time it passes (dt) equal to dx/c, where c is the speed of light. And because there is an uncertainty in momentum (dp), it follows that there is an uncertainty in its energy (dE) equal to dp×c. Since dp×dx > h/2π, it follows that dE×dt > h/2π. In this case, the wave is (conveniently) travelling at the speed of light. But the result can also be shown to be true for a more general wave packet representing a quantum particle – though a demonstration would be more complicated.

  17 The quantum vacuum is an unavoidable consequence of two things, the first of which is the existence of fields of force. As pointed out, physicists view fundamental reality as a vast sea of such fields. In their picture, known as ‘quantum field theory’, the fundamental particles are mere localised humps, or knots, in the underlying fields. The best understood of all the fields, and the one with the greatest bearing on the everyday world because it glues together the atoms in our bodies — not to mention all other normal matter – is the electromagnetic field. The electromagnetic field can undulate in an infinite number of different ways, each oscillation ‘mode’ corresponding to a wave with a different wavelength. Think of the waves at sea, which can range all the way from huge, rolling waves down to tiny ripples. Naively, the vacuum of empty space would be expected to contain no electromagnetic waves whatsoever. And this would be true but for the small matter of the Heisenberg Uncertainty Principle. According to the principle, every conceivable oscillation of the electromagnetic field must contain at least a minimum amount of energy. This seemingly innocuous rule has dramatic and profound implications for the vacuum because it means that each of the infinite number of possible oscillation modes of the electromagnetic field must be jittering with the minimum energy dictated by the uncertainty principle. In other words, the existence of each mode is not simply a possibility, it is a certainty. Far from being empty, the ‘quantum vacuum’ has an extraordinary energy density – far greater than even inside an atomic nucleus. The reason we do not notice it is the same reason we do not notice the air: because it is the same everywhere.

  18 Vlasios Vasileiou et a1., ‘A Planck-scale limit on space-time fuzziness and stochastic Lorentz invariance violation’, Nature Physics, vol. 11, 2015, p. 344 (http://www.nature.com/nphys/journal/vll/n4/full/ nphys3270.html); Eric Perlman et a1., ‘New constraints on quantum gravity from X-ray and gamma-ray observations’, Astrophysical Journal, vol. 805, No. 1, 20 May 2015, p. 10 (http://arxiv.org/ pdf/1411.7262v5.pdf).

  19 Natalie Wolchover, ‘Visions of Future Physics’, Quanta Magazine, 22 September 2015 (https://www.quantamagazine.org/20150922-nima-arkani-hamed-collider-physics/).

  20 Max Planck, ‘Über irreversible Strahlungsvorgänge’, Annalen der Physik, vol. 4(1), 1900, p. 122.

  21 Tony Rothman and Stephen Boughn, ‘Can gravitons be detected?’, 2008 (http://arxiv.org/pdf/gr-qc/0601043.pdf).

  22 An electronvolt (eV) is the energy gained by an electron after being accelerated by 1 volt. A gigaelectronvolt (GeV) is an energy 1 billion times bigger.

  23 Tushna Commissariat, ‘BICEP2 gravitational wave result bites the dust thanks to new Planck data’, Physics World, 22 September 2014 (http:// physicsworld.com/cws/article/news/2014/sep/22/bicep2-gravitational-wave-result-bites-the-dust-thanks-to-new-planck-data).

  Chapter 9

  1 Preussische Akademien der Wissenschaften, Sitzungsberichte, Berlin, 1916, p. 688.

  2 Douglas Adams, The Restaurant at the End of the Universe, Pan Books, 1980.

  3 ‘Why is quantum gravity so hard? And why did Stalin execute the man who pioneered the subject?’, Scientific American guest blog, 14 July 2011 (http://blogs.scientificamerican.com/guest-blog/why-is-quantum-gravity-so-hard-and-why-did-stalin-execute-the-man-who-pioneered-the-subject/.

  4 Matvei Bronstein, ‘Vsemirnoe tyagotenie i elektrichestvo (novaya teoriya Eynshteyna)’ [‘Universal gravity and electricity (new Einstein theory)’], Chelovek i priroda, vol. 8, 1929, p. 20.

  5 A particle with spin 2 looks the same if you rotate it through half a turn. Think of a double-headed arrow. A particle with spin 1 looks the same after if you rotate it through 1 turn. Think simply of a normal arrow. But a particle with spin ½ looks the same only after it has been rotated through two turns! Say you were not the same person if you turned round once but only if you turned round twice. Well, that is the way it is for electrons, the most common example of a particle with spin ½ If quantum spin is something new under the sun, spin ½ is something doubly new under the sun.

  6 See ‘No more than two peas in a pod at a time’, Marcus Chown, We Need to Talk About Kelvin, Faber & Faber, London, 2009.

  7 Special relativity and quantum theory also impose a tight constraint on how particles interact via a force-carrier. You might imagine that a particle can interact simultaneously with five or twelve or any number of force-carriers. But, actually, it can interact with only one. The space-time diagram commonly used to depict such an event is known as a Feynman diagram. And, on a Feynman diagram, the restriction is equivalent to only three particles meeting at a space-time point, or ‘vertex’. For instance, an electron comes into a vertex, a photon meets it and is absorbed, and an electron (redirected, or ‘scattered’) flies outwards. But special relativity and quantum theory simplify things only in the normal, low-energy/long-range world. In the high-energy/ short-range world of quantum gravity there is sufficient energy for the more complex interactions.

  8 Steven Weinberg, The Quantum Theory of Fields, Cambridge University Press, Cambridge, 2005.

  9 See Chapter 8.

  10 The best candidate for the dark matter is the lowest-mass supersymmetric particle. The ‘neutralino’ is in fact a superposition of three particles – a photino, a Higgsino and a Z-ino.

  11 One of the biggest unsolved mysteries is why we live in a matterdominated U
niverse. The best guess of physicists is that, in the big bang, some lop-sidedness in the laws of physics either favoured the creation of matter or preferentially destroyed antimatter.

  12 Gottfried Leibniz, Discours de métaphysique, 1686.

  13 The Polish-born Nobel prize-winner actually said, ‘Who ordered that?’ on the discovery of the muon, a heavy version of the electron, in 1936.

  14 A rival, but more conservative, approach to finding a deeper theory than Einstein’s theory of gravity is called ‘loop quantum gravity’: see Lee Smolin, Three Roads to Quantum Gravity, Basic Books, London, 2002. The theory describes gravity at the quantum scale but makes no attempt to unify it with the other forces. Also, no one has yet been able to show that it leads to the general theory of relativity on the large scale.

  15 Actually, quarks are confined in two distinct configurations. A triplet of quarks makes a ‘baryon’, the most common of which are the proton and neutron; whereas a quark—antiquark pair makes a ‘meson’. Quarks are actually confined within baryons and mesons only at low energies. At ultra-high energies such as those that existed in the first moments of the big bang, they can break free of their prisons to form an amorphous ‘quark-gluon’ plasma.

  16 Since gravity leaks out in all directions, at a distance r from a mass, its effect is spread out over the surface of a sphere of area 4πr2 and so diluted by UAnr2. This is the origin of gravity’s inverse-square-law force.

  17 This is exactly what happens to a magnetic field inside a ‘superconductor’, a material cooled to a temperature at which its electrical resistance vanishes. Within the material, the magnetic field is confined to narrow channels known as ‘flux tubes’.

  18 Gabriele Veneziano, ‘Construction of a crossing-symmetric, Regge-behaved amplitude for linearly rising trajectories’, Nuovo Cimento A, vol. 57, 1968, p. 190. Veneziano’s theory was called the ‘dual resonance model’ and only later became known as string theory.