1. THE COSMOS AND THE MICROWORLD
1 Images depicting the full range of scales in our universe, from largest to smallest, were originally presented by Dutchman Kees Bieke in Cosmic View: the Universe in Forty Jumps (John Day, 1957) but were developed further, and achieved widest currency, in a film and book entitled Powers of Ten by the office of Charles and Ray Eames, together with Philip and Phyllis Morrison. (W. H. Freeman, 1985)
2. OUR COSMIC HABITAT I: PLANETS, STARS AND LIFE
1 An alternative technique being developed is to repeatedly measure the star’s position accurately enough to trace its orbital ‘wobble’. (Whereas the Doppler technique measures motions along the line of sight, this method detects transverse motions in the plane of the sky.)
3. THE LARGE NUMBER N: GRAVITY IN THE COSMOS
1 This is the mechanical work that must be done to remove an atom from a sphere. It can be thought of as the ‘inverse square’ force, scaling as (mass)/(radius)2, multiplied by the distance through which the force acts, which is proportional to (radius). It is also known as the ‘binding energy’. It scales as (mass)/(radius), and therefore as (mass)2/3 because, for constant densities, (radius) scales as (mass)1/3.
2 The End of Time (Weidenfeld & Nicolson, 1999).
3 This uncertainty about extreme conditions near the singularity doesn’t erode our confidence in the existence of black holes or in our understanding of their external properties. No more does the mystery of quarks reduce our confidence in the standard physics of atoms, which depends on the behaviour of electrons in orbits on much larger scales.
4. STARS, THE PERIODIC TABLE, AND ε
1 Livio et al. (Nature, 340, 281 1989) have computed just how sensitive the carbon production is to changes in the nuclear physics.
5. OUR COSMIC HABITAT II: BEYOND OUR GALAXY
1 According to Einstein’s theory, the gravitational attraction depends not on density alone but on [(density)+3(pressure)/c2]. Leaving out the second term makes a factor of two difference when the pressure of radiation is important. However, we shall see in Chapter 7 that even in empty space there may be some energy. If so, it will have a pressure that is negative (i.e. like a ‘tension’). The second term then cancels out the first, and causes a major qualitative change: the expansion actually accelerates rather than slows down. This counterintuitive result is important in the early inflationary universe, and also at present if the energy of empty space (lambda – see Chapter 7) is dominant.
2 There is no mixing between the Sun’s centre and its outer layers, so there would be still more helium in the core, because of the spent fuel from the fusion that has kept it shining over its 4.5 billion year history.
6. THE FINE-TUNED EXPANSION: DARK MATTER AND Ω
1 The precise value of the critical density, and indeed some of the other densities quoted here, depend on the actual scale of the universe – something that is only known with 10–20 per cent precision because of the problems of determining the so-called ‘Hubble constant’. These issues merit a whole book to themselves. However, I should mention, for the benefit of specialists, that the numbers quoted here correspond to a Hubble constant (in the usual units) of sixty-five kilometres per second per megaparsec.
2 A much more interesting question is whether the inverse-square law breaks down on very small scales, or – which is more or less the same thing – whether some extra ‘fifth force’ comes into play on scales below a few metres. Speculations connected with superstring theories (see Chapter 10) suggest that the extra spatial dimensions may conceivably manifest themselves in this way. Here again, experimental evidence is meagre, and less exact than we would wish, because gravity is so feeble between laboratory-sized objects.
3 Less deuterium when the density is higher at first sight seems a perverse result, but it’s actually quite natural. The higher the density, the more often the nuclei would hit each other, and the more quickly nuclear reactions would convert hydrogen (one proton) into helium (two protons and two neutrons). Deuterium (one proton and one neutron) is an intermediate product. Not much would survive if the density were high, because the reactions would have gone so quickly that nearly all the deuterium would have been processed into helium; on the other hand, if the density were lower, we would expect more ‘fossil’ deuterium left over from the first three minutes of our universe’s existence. The dependence is quite sensitive, so any reasonably accurate measurement of the deuterium fraction tells us the average density of atoms in the universe.
4 The evidence actually tells us the differences between the squares of the masses of two different species of neutrinos. An earlier version of Kamiokande recorded eleven events due to high-energy neutrinos from the nearby 1987 supernova, mentioned in Chapter 4; an American experiment (in a salt mine in Ohio) recorded eight more. These numbers pleased astrophysicists because they fitted well with what supernova theories predicted.
5 The next step in our theoretical understanding of sub-nuclear physics may involve a concept called ‘supersymmetry’, which aims to relate the nuclear force to the other forces within atoms (and thereby give us a better understanding of our cosmic number ε). Integral to this concept are some new kinds of electrically neutral particles that would have been made in the Big Bang, and whose masses might be calculable.
7. THE NUMBER λ: IS COSMIC EXPANSION SLOWING OR SPEEDING?
1 The successive ‘wavecrests’ in the light from any atom or molecule are due to its vibrations, which are essentially a microscopic clock. The wavecrests arrive slower when the source is receding and the wavelengths are stretched.
2 From Nature’s Imagination, edited by J. Cornwell (Oxford University Press, 1998).
8. PRIMORDIAL ‘RIPPLES’: THE NUMBER Q
1 At first sight, this may seem contrary to the statement that Q is the same on all scales. However, Q is actually measured by the overdensity multiplied by the square of the lengthscale. According to Newton’s laws of gravity, the gravitational binding energy at the surface of a sphere depends on mass/radius. However, for spheres of different mass but the same density, mass depends on (radius)3, and so the binding energy varies as (radius)2. So the density fluctuations have smaller amplitude on larger scales.
2 One might wonder why the substructure within galaxies has been erased, whereas individual galaxies survive within a cluster of galaxies (which doesn’t become a single ‘supergalaxy’). This is because, in the later stages of the hierarchical clustering, the gas is too hot and diffuse to be able to condense into stars. The star formation process is ‘quenched’ on scales bigger than galaxies.
9. OUR COSMIC HABITAT III: WHAT LIES BEYOND OUR HORIZON?
1 In particular, the intensity measured by COBE at millimetre wavelengths might have been weaker than the predicted extrapolation from what had already been reliably determined at centimetre wavelengths. Many processes could have added extra millimetre-wave radiation – for instance, emission from dust, or from stars at very high redshifts – and so we would not have been fazed if it had been more intense than a black body at these wavelengths. But it would be hard to interpret a millimetre-wave temperature that was lower than that at centimetre wavelengths.
2 The Inflationary Universe is published by Jonathan Cape, 1997.
10. THREE DIMENSIONS (AND MORE)
1 Time’s Arrow is published by Jonathan Cape, 1991.
11. COINCIDENCE, PROVIDENCE – OR MULTIVERSE?
1 From Quarks, Chaos and Christianity, by John Polkinghorne (SPCK Triangle Press, 1994).
2 From Dialogues Concerning the Two Chief Systems of the World, translated by S. Drake (Berkeley, 1953).
3 William of Ockham advanced the view which (translated from Latin) means ‘Don’t multiply entities more than is absolutely necessary’.
4 As the cosmologist John Barrow has quipped: if this statement is true, it certainly isn’t original.