The Book of Nothing
Page 34
23. J. Schwinger, ‘Casimir light: field pressure’, Proc. Nat. Acad. Sci. USA, 91, pp. 6473–5 (1994); C. Eberlein, ‘Sonoluminescence as quantum vacuum radiation’, Phys. Rev. Lett., 76, pp. 3842–5 (1996).
24. K.A. Milton and Y.J. Ng, ‘Observability of the bulk Casimir effect: can the dynamical Casimir effect be relevant to sonoluminescence?’, Phys. Rev. E, 57, pp. 5504–10 (1998); V.V. Nesterenko and I.G. Pirozhenko, ‘Is the Casimir effect relevant to sonoluminescence?’, Sov. Physics JETP Lett., 67, pp. 420–4 (1998).
25. J. Masefield, Salt-water Ballads, ‘Sea Fever’ (1902).
26. P.C. Causeé, L’Album du Marin, Charpentier, Nantes (1836).
27. S.L. Boersma, ‘A maritime analogy of the Casimir effect’, American J. Physics, 64, p. 539 (1996). The author says that his attention was drawn to this problem in Causeé’s book by Hazelhoff Roelfzema of the Amsterdam Shipping Museum.
28. The force of attraction calculated by Boersma is equal to F = 2π2mηhA2/(QT2) where m is the mass of each ship (the two ships are assumed to be of equal mass), A is the angle in radians of their rolling in the swell, h is the metacentric height of the ship, T is the period of the oscillations of the ships, Q the quality factor of the oscillation, and η is the efficiency of the energy losses through friction. Substituting m = 700 tons, h = 1.5 metres, A = 8 degrees (= 0.14 radians), T = 8 seconds, Q = 2.5, η = 0.8 we find F = 2000 Newtons.
29. In J. Weintraub, Peel Me a Grape (1975), p. 47.
30. W. Lamb and R.C. Retherford, Phys. Rev., 72, p. 241 (1947). The theoretical interpretation was supplied by T.A. Welton, Phys. Rev., 74, p. 1157 (1948).
31. P. Kerr, The Second Angel, Orion, London (1998), p. 316.
32. To see what else is needed to understand the world, see J.D. Barrow, Theories of Everything, Vintage, London (1988).
33. Because the quantum wavelength of a particle is inversely proportional to its mass.
34. F. Close and C. Sutton, The Particle Connection, Oxford University Press (1987).
35. Despite its intrinsic weakness gravity wins out over electromagnetism in controlling the behaviour of matter in large aggregates because electric charges come in two varieties, positive and negative, and it is hard to assemble a large amount of matter that has a non-zero charge. Gravity acts on mass, and mass, by contrast, comes only in a positive variety and so its effect is cumulative when large aggregates of material are assembled.
36. Lao-tzu, Tao Te Ching, chap. 11.
37. This number, first defined by Arnold Sommerfeld in 1911, is called the fine structure constant and is given by 2πe2/hc. For further details of these developments see Chapter 4 of J.D. Barrow and F.J. Tipler, The Anthropic Cosmological Principle, Oxford University Press (1986).
38. C. Pickover, Computers and the Imagination, St Martin’s Press, NY (1991), p. 270.
39. The positron is the antiparticle of the electron. It has the same mass but opposite sign of its electric charge. When an electron encounters a positron they will annihilate to produce two photons of light. The electric charges cancel out to zero.
40. The term ‘black hole’ was invented by the American physicist John A. Wheeler in 1968 in an article entitled ‘Our Universe: the known and the unknown’, American Scholar, 37, p. 248 (1968), reprinted in American Scientist, 56 p. 1 (1968). Eleven years earlier he had coined the term ‘wormhole’.
41. The radius of a black hole, R, is proportional to its mass, M, therefore its density, proportional to M/R3, varies as 1/M2. Hence, the more massive the black hole, the lower its density.
42. The ‘killer’ feature of a black hole is the strong variation in gravitational pull that it exerts over an object of a finite (the ‘tidal force’). For a point particle of zero size no such variation exists and it would feel nothing as it fell freely under gravity into a black hole, big or small. Objects of finite size get stretched out because the part of them closest to the hole gets pulled in more strongly than the part furthest away. The density of the black hole (see the previous footnote) is a good measure of the strength of this tidal force. It becomes more significant for small black holes. Black holes smaller than about one hundred million times the mass of our Sun are able to tear stars apart when they fall through the horizon. Bigger black holes allow whole stars to fall through the horizon without breaking them up.
43. J.P. Luminet, Black Holes, Cambridge University Press (1992).
44. M. Begelman and M.J. Rees, Gravity’s Fatal Attraction, W.H. Freeman, San Francisco (1996).
45. S.W. Hawking, ‘The Quantum Mechanics of Black Holes’, Scientific American, January (1977).
46. The black hole does not gain mass as a result of capturing one of the pair of particles. The black hole loses mass as a result of this process after one takes into account the change in the potential energy of the particle-antiparticle pair. The pairs will preferentially appear at a separation that gives them zero total energy.
47. The temperature of the black hole is inversely proportional to its mass. The time required to radiate away all of its mass is proportional to the cube of its mass.
48. In Einstein’s theory of gravitation the local effects of gravity should be indistinguishable from those experienced by undergoing accelerated motion at a suitable rate. Thus, for very short intervals of time, we should not be able to distinguish being in a small lift that is freely falling under gravity from one that is being accelerated downwards. If we apply this to the situation of black holes in the vacuum, we should not be able to distinguish the situation that exists in the gravitational field of the black hole very close to the event horizon from that experienced by an observer moving with an acceleration equal to the acceleration due to gravity at the horizon. In fact, as first shown by Bill Unruh and Paul Davies, this is exactly what is predicted. If an observer is accelerated through the quantum vacuum at a uniform rate, A, then that observer should detect thermal radiation with a temperature given by T = hA/4πck, where c is the speed of light, k is Boltzmann’s constant and h is Planck’s constant.
chapter eight
How Many Vacuums Are There?
1. Quoted in the Observer newspaper, 4 July 1999.
2. Contrary to the situation that exists in many other subjects, research journals are now largely superfluous in subjects like physics and astronomy. All research articles are ‘published’ electronically and are revised in the light of the comments, requests for credit, or corrections, that come in by email to the authors.
3. Note that Newton’s famous laws of motion did not satisfy this dictum of Einstein’s. The first law, which was that ‘all bodies acted upon by no forces remain at rest or move at constant speed’, is not one that would be found true by all observers. Newton specified that it would be seen only by observers who were not accelerating or rotating with respect to absolute space. These are known as ‘inertial observers’. For example, if an astronaut in a rotating spaceship were to look out of the window he would see a neighbouring satellite accelerating past his window even if it were acted upon by no forces. The astronaut in his rotating spaceship is not an inertial observer.
4. Quoted in Observer, 12 December 1999, p. 30.
5. J.D. Barrow, Theories of Everything, Vintage, London (1991); B. Greene, The Elegant Universe, Vintage, London (2000).
6. A. Linde, ‘The Self-Reproducing Inflationary Universe’, Scientific American, no. 5, vol. 32 (1994).
7. A. Guth, The Inflationary Universe, Vintage, London (1998).
8. Fractal surfaces do not. They can have structure on all scales of magnification.
9. W. Allen, Getting Even, Random House, NY (1971), p. 33.
10. This hierarchy of clustering of clusters does not carry on indefinitely. The clustering of galaxy clusters into so-called ‘superclusters’ seems to be the end of the line.
11. A term coined by the sociologist Robert Merton to describe the way in which people who are awarded honours and prizes then seem to be awarded even more honours and prizes. It is taken from Christ’s w
ords in the Gospel of St Matthew chap. 13 v. 12: ‘For whosoever hath, to him shall be given, and he shall have more abundance: but whosoever hath not, from him shall be taken away even that he hath.’
12. When it was about ten million years old.
13. P. de Bernadis et al, ‘A flat universe from high-resolution maps of the cosmic microwave background radiation’, Nature, 404, pp. 955–9 (2000). See also www.physics.ucsb.edu/~boomerang/for further pictures and information about the experiment and the significance of its results.
14. The Independent, quoted in third Leader article in Review section, p. 3, 13 November 1999.
15. Based on data presented by the Boomerang Collaboration on their website www.physics.ucsb.edu/~boomerang/.
16. J.D. Barrow, ‘Dimensionality’, Proc. Roy. Soc. A., 310, p. 337 (1983); J.D. Barrow & F.J. Tipler, The Anthropic Cosmological Principle, Oxford University Press (1986), chap. 6; M. Tegmark, ‘Is “the theory of everything” merely the ultimate ensemble theory?’, Annals of Physics (NY), 270, pp. 1–51 (1998).
17. There was once some interest in science-fiction stories about biochemists based upon silicon chemistry. These do not look promising (as explained in Barrow and Tipler, op. cit.), but, ironically, it is silicon physics that looks the most likely route to a form of artificial life brought into being by means of the catalytic help of (human) carbon-based life.
18. During inflation the pressure contributed by the scalar matter field responsible is negative and so a change in energy of the expanding material actually provides energy for work.
19. A few years ago Sidney Coleman proposed a partial solution of this sort. He suggested that if the topology of the Universe was sufficiently complicated, with many holes, handles and tubes (‘wormholes’), then the presence of any lambda term would tend to create an opposing stress that cancelled out the lambda term to very high precision. The most probable value of lambda that would be measured when the Universe expanded and became very large would be zero with great accuracy. Unfortunately, the appealing idea did not survive further scrutiny and there are no similar general arguments which have so far provided us with an understanding of lambda’s tiny value.
20. I Corinthians chap. 15 v. 51–2.
21. The later editions of inflation, like chaotic inflation, could make do with a single vacuum.
22. P. Hut and M.J. Rees, ‘How stable is our vacuum?’, Nature, 302 (1983), pp. 508–9; M.S. Turner and F. Wilczek, ‘Is our vacuum metastable?’, Nature 298 (1982), pp. 633–4. For a wider review of possible ‘sudden’ ends to the world see J. Leslie, The End of the World.
23. Recently, there seems to have been some public worry in the United States that a planned sequence of high-energy particle collisions at a national laboratory might induce just such a catastrophe.
24. N. Eldridge and S.J. Gould, ‘Punctuated equilibria: an alternative to phyletic gradualism’, in T.J.M. Schoof (ed.), Models in Paleobiology, W.H. Freeman, San Francisco (1972), pp. 82–115.
25. From P. Bak, How Nature Works, Oxford University Press (1997), p. 39.
26. A.S.J. Tessimond, Cats, p. 20 (1934).
27. T. Kibble, ‘Topology of Cosmic Domains and Strings’, Journal of Physics A, 9, pp. 1387–97 (1972).
28. These should not be confused with superstrings or superstring theories. Superstring theories may permit the existence of cosmic strings but not necessarily.
29. From P. Bak, op. cit.
30. This gravitational lensing phenomenon, predicted by Einstein, is now commonly observed but is believed to be created by objects other than cosmic strings in the cases where it is seen. In our own galaxy and nearby in the Large Magellanic Cloud (a neighbouring very small galaxy) it is created by non-luminous objects that have masses similar to those of stars.
chapter nine
The Beginning and the End of the Vacuum
1. M. Proust, Le Côté de Guermantes (1921), transl. as Guermantes’ Way, by C.K. Scott-Moncrieff (1925), vol. 2, p. 147.
2. G.K. Chesterton, The Napoleon of Notting Hill, first published in 1902, Penguin, London (1946), p. 9.
3. E.O. James, Creation and Cosmology, E.J. Brill, Leiden (1969); C. Long, Alpha: the Myths of Creation, G. Braziller, New York (1963); C. Blacker and M. Loewe (eds), Ancient Cosmologies, Allen & Unwin, London (1975); M. Leach, The Beginning: Creation Myths around the World, Funk and Wagnalls, New York (1956).
4. M. Eliade, The Myth of the Eternal Return, Pantheon, New York (1954); see also J.D. Barrow & F.J. Tipler, The Anthropic Cosmological Principle, Oxford University Press (1986).
5. T. Joseph, ‘Unified Field Theory’, New York Times, 6 April 1978.
6. An interesting collection of articles is to be found in R. Russell, N. Murphy & C. Isham, Quantum Cosmology and the Laws of Nature, 2nd edn, University of Notre Dame Press, Notre Dame (1996).
7. A. Ehrhardt, ‘Creatio ex Nihilo’, Studia Theologica (Lund), 4, p. 24 (1951), and The Beginning: A Study in the Greek Philosophical Approach to the Concept of Creation from Anaximander to St. John, including a memoir by J. Heywood Thomas, Manchester University Press (1968); D. O’Connor and F. Oakley (eds), Creation: the impact of an idea, Scribners, New York (1969).
8. With St Augustine, this idea was made more sophisticated by including the idea that time must have come into being along with the world, thus avoiding questions about what existed ‘before’ the world was.
9. S. Jaki, Science and Creation, Scottish Academic Press, Edinburgh (1974), and The Road of Science and the Ways to God, University of Chicago Press (1978).
10. G.F. Moore, Judaism in the First Centuries of the Christian Era I, Cambridge, Mass. (1966), p. 381.
11. Wisdom chap. 11 v. 17.
12. 7 v.28.
13. G. May, Creatio ex Nihilo, transl. A.S. Worrall, T & T Clark, Edinburgh (1994), p. 8.
14. H.A. Wolfson, ‘Negative Attributes in the Church fathers and the Gnostic Basilides’, Harvard Theol. Review, 50, pp. 145-56 (1957), J. Whittaker, ‘Basilides and the Ineffability of God’, Harvard Theol. Review, 62, pp. 367–71 (1969).
15. A beautiful expression of this is found in the Tripartite Tractate of Valentius in the Jung Codex, cited by May, op.cit., p. 75, translation by H.W. Attridge and E. Pagels: ‘No one else has been with him from the beginning; nor is there a place in which he is, or from which he has come forth, or into which he will go; nor is there a primordial form, which he uses as a model as he works; nor is there any difficulty which accompanies him in what he does; nor is there any material which is at his disposal, from which he creates what he creates; nor any substance within him from which he begets what he begets; nor a co-worker with him, working with him on the things at which he works. To say anything of this sort is ignorant.’
16. Four centuries later the argument will still be used by John Philoponus to counter the same suggestions. He defines the creativity of the artist as an activity which rearranges existing elements in a new way and the creativity of the natural world as the bringing of living beings out of non-living matter. Divine creation is superior to both because it can create the material out of nothing.
17. Nevertheless, other aspects of his view of the world were different to those that would be adopted by the central Christian tradition. Basilides appears to have been a Deist in believing that God played no further role in the unfolding of the Universe after laying down the starting conditions. God’s creative activity was limited to a single act.
18. F.M. Cornford, Microcosmographia Academica, Cambridge University Press (1908), p. 28.
19. See N. Rescher, The Riddle of Existence, University Press of America, Lanham (1984), p. 2.
20. J.D. Barrow, Impossibility, Oxford University Press (1998).
21. N. Malcolm, Ludwig Wittgenstein: A Memoir, Oxford University Press (1958), p. 20.
22. M. Heidegger, Introduction to Metaphysics, Yale University Press, New Haven (1959); L. Wittgenstein, Tractatus Logico-Philosophicus, London (1922), section 6.44.
23. H. Bergson, Creati
ve Evolution, trans. A. Mitchell, Modern Library, NY (1941), p. 299. This type of set-theoretic basis for conjuring something out of nothing is also hinted at in the discussion to be found in the final chapter of Gravitation by C. Misner, K. Thorne & J.A. Wheeler, W.H. Freeman, San Francisco (1972); and in P. Atkins, The Creation, W.H. Freeman, San Francisco (1981).
24. For example, the three interior angles of a triangle sum to 180 degrees in a Euclidean geometry but not in a non-Euclidean geometry.
25. A. Hodges, The Enigma of Intelligence, Unwin, London (1985), p. 154.
26. J.D. Barrow, Impossibility, Oxford University Press (1998).
27. R. Penrose, The Emperor’s New Mind, Oxford University Press (1989).
28. The feature that there exist statements of arithmetic whose truth or falsity cannot be established using the rules and axioms of arithmetic; see J.D. Barrow, Impossibility, Oxford University Press (1998), for a fuller discussion.
29. N. Rescher, The Riddle of Existence, University Press of America, Lanham (1984), p. 3.
30. T. Joseph, ‘Unified Field Theory’, New York Times, 6 April 1978.
31. Einstein thought that infinities and singularities were unacceptable in physical theories. His assistant at Princeton, Peter Bergmann, writes: ‘It seems that Einstein always was of the opinion that singularities in classical field theory are intolerable. They are intolerable from the point of view of classical field theory because a singular region represents a breakdown of the postulated laws of nature. I think that one can turn this argument around and say that a theory that involves singularities and involves them unavoidably, moreover, carries within itself the seeds of its own destruction.’ Contribution in H. Woolf, Some Strangeness in the Proportion, Addison Wesley, MA (1980), p. 156.
32. For a recent overview of the mathematical ideas see the first chapter of S.W. Hawking & R. Penrose, The Nature of Space and Time, Princeton University Press (1996). For a descriptive account see J.D. Barrow & J. Silk, The Left Hand of Creation (2nd edn.), Penguin, London, and Oxford University Press, New York (1993).