تمهيد وشكر وتقدير
(1)Bernard Carr and Martin Rees, “The Anthropic Principle and the Structure of the Physical World,” Nature, vol. 278 (1979), p. 605.
(2)John Barrow and Frank Tipler, The Anthropic Cosmological Principle (New York: Oxford University Press, 1986).
(3)Martin Gardner, “WAP, SAP, PAP, & FAP,” New York Review of Books, May 8, 1986.
(4)Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (New York: Little, Brown, 2005), p. 138.
(5)Bernard Carr (ed.), Universe or Multiverse? (Cambridge, UK: Cambridge University Press, 2007).
(6)Paul Davies, The Mind of God (New York: Simon & Schuster, 1992).
الفصل الأول: الأسئلة الكبرى
(1)I shall restrict my discussion to life as we know it. The possibility of exotic forms of life based on other chemical elements, or other physical processes entirely, is certainly fascinating but completely speculative. If life is common, we have no reason to suppose that our form of life is atypical. Readers interested in a less conservative approach will find an up-to-date discussion in Peter Ward, Life as We Do Not Know It (New York: Viking, 2005).
(2)Fred Hoyle, “The Universe: Past and Present Reflections,” Annual Review of Astronomy and Astrophysics, vol. 20 (1982), p. 16.
(3)See, for example, David Park, The Grand Contraption: The World as Myth, Number, and Chance (Princeton, NJ: Princeton University Press, 2005).
(4)The term was popularized by the physicist Heinz Pagels in The Cosmic Code (New York: Simon & Schuster, 1982).
(5)See, for example, Edward Craig, The Mind of God and the Works of Man (New York: Oxford University Press, 1987).
(6)See, for example, John W. Carroll, Laws of Nature (New York: Cambridge University Press, 1994); and Alan Padgett, “The Roots of the Western Concept of ‘Laws of Nature’: From the Greeks to Newton,” Perspectives on Science and Christian Faith, vol. 55, no. 3 (December 2003), p. 212.
(7)Lucretius, De rerum natura, edited by M. F. Smith (Indianapolis: Hackett Publishing, 2001), p. 138.
(8)Marcus Manilius, Astronomica, translated by G. P. Goold (Cambridge, MA: Harvard University Press, 1977), p. 121.
(9)Augustine, The Literal Meaning of Genesis, vol. 2, translated by J. H. Taylor (New York: Paulist Press, 1983), p. 92.
(10)Stillman Drake, Discoveries and Opinions of Galileo (New York: Doubleday-Anchor, 1957), p. 70.
(11)James Jeans, The Mysterious Universe (Cambridge, UK: Cambridge University Press, 1930), p. 140.
(12)Unbeknownst to me, Lindsay’s naive question was being asked at about the same time by one of the world’s leading theoretical physicists, Eugene Wigner: see his “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Communications in Pure and Applied Mathematics, vol. 13, no. 1 (1960), p. 1.
(13)A minority school of thought says that this is all baloney, that the laws of physics are just human inventions constructed for convenience, and that there are no “real” laws at all. I am going to ignore this dissenting position because I think it is totally wrong and does not merit serious discussion.
(14)Nancy Cartwright, How the Laws of Physics Lie (New York: Oxford University Press, 1983).
(15)David Mowaljarli and Jutta Malnic, Yorro Yorro (Rochester, VT: Inner Traditions, 1993), chapter 23.
(16)Richard Feynman, “The Meaning of It All,” 1963 John Danz Lecture, published under the same title by Addison Wesley (Reading, MA: 1998), p. 14.
(17)Steven Weinberg, The First Three Minutes (New York: Basic Books, 1977), p. 149.
الفصل الثاني: تفسير الكون
(1)K is the symbol for the unit of temperature called the Kelvin. A temperature interval of one degree Kelvin is the same as an interval of one degree Celsius, but the Kelvin scale starts from absolute zero, or about −273°C.
(2)Roughly speaking, this is the final state into which a closed system settles, following which no large-scale changes occur. For a simple gas, it is a state of uniform pressure and density.
(3)An ionized gas, also called a plasma, is one in which the atoms are dissociated into electrons and nuclei, as is caused by extreme heat. I shall describe the primordial gas in more detail in Chapter 3.
(4)The subsequent scattering of the CMB from early clumps of gas produced subtle effects in the polarization of the radiation, effects that have also been detected by WMAP.
(5)Reproduced by kind permission of the correspondent.
(6)Sometimes cosmologists refer to “the last scattering surface,” the spherical shell of matter surrounding Earth from which the radiation emanates at the moment of transition from opaque to transparent. This transition is technically termed the decoupling of matter and radiation.
(7)For a careful exposition of this point, see Tamara Davis and Charles Lineweaver, “Misconceptions About the Big Bang,” Scientific American (March 2005), p. 36.
(8)This issue is complicated by the theory of inflation, which I shall describe in Chapter 3.
(9)Analogously, when a ship disappears over the terrestrial horizon, we do not infer that the Earth ends there.
(10)This admirable term was suggested by Alan Guth, and I have decided to adopt it here.
(11)Time is not a dimension of space, but a dimension of spacetime.
(12)This won’t apply if theories about “branes” turn out to be correct—see Hiding Dimensions of Space.
(13)To sound a note of caution, some cosmologists are concerned that the largest features mapped by WMAP (technically, the lowest multipoles) display some oddities not predicted by the conventional big bang model of the universe. It is too soon to know whether this is due to problems with the equipment and/or data analysis or if it points to something significant and unexpected about the structure of the universe.
(14)The limited accuracy of these observations cannot establish that the universe is exactly flat. What they tell us is that if the universe is shaped like Einstein’s hypersphere, then the radius of the hypersphere is exceedingly large, so that within the volume of space probed by our instruments we cannot discern any curvature. Similar remarks apply to any negative curvature.
(15)Even if space is flat, it need not necessarily be infinite. That is because Einstein’s theory says nothing about the topology of space. One possible topology involves identifying points. Think of a sheet of paper on which a particle enters from the left, traverses the paper, and exits from the right. Now imagine rolling up the paper and gluing the left and right edges together. The particle that previously exited from the right would now reappear from the left. Some cosmologists have suggested that space might be like this and resemble a hall of mirrors. If we inhabited such a universe, it might look to us at first sight as if “the hall of mirrors” extended to infinity, but on closer inspection we would discover that a finite volume of space repeats itself, infinitely often. It is possible that the universe consists of three-dimensional cells, repeated periodically, and that light which we take to be from far away is in fact wrapping around one or more times, creating the illusion of distance. More complicated shapes, such as the three-dimensional analogue of the surface of a segmented soccer ball, have also been suggested.
(16)I am being a little cavalier with my terminology. The word matter here includes both dark matter and dark energy, topics I shall discuss in Chapter 6.
(17)Flatland: A Romance of Many Dimensions by E. A. Abbott is now available in an edition annotated by Ian Stewart (New York: Perseus Publishing, 2001).
(18)See, for example, Lisa Randall, Warped Passages (New York: Harper-Collins, 2005).
(19)Gerald Whitrow, “Why Space Has Three Dimensions,” British Journal for the Philosophy of Science, vol. 6, no. 21 (1955), p. 1.
الفصل الثالث: كيف بدأ الكون؟
(1)The helium that is used to fill balloons comes not from the big bang, but from the product of radioactive decay in the Earth’s interior.
(2)This “happy medium” is related to the fact that space is flat.
(3)Inflation was originally invented by Guth to solve a different problem—the absence of entities known as magnetic monopoles. Alan Guth’s own account can be read in his book The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (New York: Perseus Publishing, 1998).
(4)The word scalar means that the field can be described simply by specifying a single number (the strength of the field) at each point in space. By contrast, an electric field has both a magnitude and a direction at each point; it is a so-called vector field. Gravitation is more complicated still—a tensor field—requiring even more numbers at each point to fully describe it.
(5)Don’t confuse the mechanical force exerted by the pressure, which is huge and outward (though contained by Earth), with the gravitational force that this pressure generates, which is tiny and inward.
(6)Pressure and energy are normally measured in different units. To discuss the correspondence between these quantities you must divide the pressure by c2, which then gives it the same units as energy density. This large divisor explains why energy gravitates so much more strongly than pressure.
(7)Mechanically, the scalar field sucks—fiercely; gravitationally it repels—gently. You might be wondering why, if this scalar field sucks so much, it doesn’t pull itself into a smaller and smaller region. That is because it is spread uniformly through space, so there is no privileged place for it to converge: it is being sucked every way at once, and there is no net force to pull it to any particular place.
(8)There is, however, a further issue about the creation of matter, related to the question of antimatter. I shall defer this complication until the next chapter.
(9)Good popular accounts have been written by some of the originators. In addition to Guth’s book, see, for example, Andrei Linde, Inflation and Quantum Cosmology (San Diego, CA: Academic Press, 1990).
(10)The Born-Einstein Letters, translated by Irene Born (London: Macmillan, 1971), p. 91.
(11)Particle creation by the expansion of the universe is a purely gravitational (and normally very weak) process. It should not be confused with particle production from the decay of the inflaton field, or from heat energy (such as occurred at the end of inflation).
(12)“Ex nihilo, nihil fit.” De rerum natura in Lucretius, On the Nature of the Universe, translated by R. E. Latham (New York: Penguin, 1951).
(13)In Chapter 10, I shall consider the extremely speculative idea of backward-in-time causation, where the big bang could be said to have been caused by later events retroactively.
(14)City of God, Book xi.6, in Basic Writings of St. Augustine, edited by W. T. Oates (New York: Random House, 1948).
(15)It is sometimes conjectured that in the cyclic model the state of the universe is somehow reset at the bounce (technically, the entropy is reduced). However, this step is rather contrived. It either has to be imposed by hand or tied to a more complicated—and speculative—model of the sort I explain in Chapter 10.
(16)For the mathematically inclined, the Planck length is given by (Gh/2 π c3) 1/2.
(17)You may wonder why quantum effects of electromagnetism set in at atomic dimensions, whereas quantum effects of gravitation are predicted to be important only on much smaller scales of size. The reason stems in part from the huge disparity in strength between the two forces, a topic I shall discuss in the next chapter.
(18)This is known technically as the “no-boundary” proposal.
(19)Hawking’s own account can be found in his book A Brief History of Time (New York: Bantam, 1988).
(20)John Leslie, Universes (New York: Routledge, 1989), p. 95.
(21)This is a curious inversion of the usual situation in quantum mechanics. In the inflating universe, the most conspicuous consequences of quantum mechanics are on the largest scale of size.
(22)In this respect, eternal inflation is reminiscent of the old steady-state theory of cosmology, championed by Hoyle, in which the universe has no beginning or end, but new matter is continually created as the universe expands so as to maintain an unchanging average density. Where eternal inflation differs is that entire universes are created rather than particles of matter.
(23)Andre Linde, “Inflation and Quantum Cosmology,” in 300 Years of Gravitation, edited by S. W. Hawking & W. Israel (New York: Cambridge University Press, 1987), p. 618.
(24)Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (New York: Little, Brown, 2005), chapter 11.
(25)This is something of a simplification. When using the theory of relativity, we have to remember that distances, like times, are not absolute but relative, so we must always specify the circumstances of the observer when discussing a distance. Paradoxically, if the observer is located inside one of the bubbles (as we are within our pocket universe), it is possible for the size of the bubble to be infinite relative to that observer, even though, viewed from outside the bubble, it is finite.
(26)David Hume, Dialogues Concerning Natural Religion, edited by Martin Bell (New York: Penguin, 1990), part V, p. 77.
الفصل الرابع: مِمَّ يتألف الكون؟ وكيف تترابط أجزاؤه؟
(1)Even uranium plays a role in life on Earth. Its slow radioactive decay over billions of years keeps the interior of our planet hot, driving the convection currents that move the continental crust around, an essential process for recycling carbon and other substances used to maintain our ecosystem.
(2)Positrons are today familiar from their role in medical imaging in the form of positron emission tomography (PET) scans.
(3)These decay schemes also involve neutrinos.
(4)When heavy particles decay into lighter ones, the excess mass-energy appears in the form of kinetic energy: the decay products are created moving at high speed.
(5)Why stop there? Perhaps quarks (and maybe leptons too) are made out of yet smaller particles, which are in turn made of even smaller particles, and so on. Such ideas have been tried. But most physicists think that quarks and leptons are the bottom level, in terms of composite particle combinations. They may not be the last word, however, as I shall discuss at the end of this chapter.
(6)The masses of the neutrinos are still being worked out. They all seem close to zero.
(7)The stability of neutrinos is more complicated. They don’t decay as such: instead, they keep rotating their identities between different neutrino flavors.
(8)The word recoil is a bit misleading here, because if the charges were of opposite sign, the deflection would be inward rather than outward. As a result of Heisenberg’s uncertainty principle, the momentum transfer can be negative in quantum processes, causing an inward jerk rather than an outward deflection. However, the general picture in terms of virtual photon exchange is the same.
(9)Mathematically speaking, one integrates over a weighted set of possibilities.
(10)This procedure is known as perturbation theory.
(11)This statement refers to the photon’s rest mass (see Box 1).
الفصل الخامس: إغراء التوحيد الكامل
(1)How might a process that takes on average much longer than the age of the universe show up in an experiment? The answer lies with the statistical nature of quantum mechanics. There is a certain probability that, from among a huge number of protons (many tons of material), one or two protons will decay in, say, a month. The experimenters looked for such occasional isolated decay events, but saw nothing.
(2)It is important to understand that the particles emanating from high-energy collisions are not just the constituents of the impacting bodies: many of them are created ab initio from the energy of impact. For example, physicists routinely create electron-positron pairs, or proton-antiproton pairs.
(3)The link between the spins of particles and the collective properties of assemblages of them as governed by the Pauli exclusion principle is not obvious, and has to do with certain abstract symmetries involved in the quantum concept of spin.
(4)This law has the same general form as gravitation, as shown in Figure 1-1.
(5)The technical term given to this difficulty is non-renormalizability.
(6)It does have something to say about the ultrahot, very early universe, though, and it is not impossible that some stringy relic may be found by cosmologists. But so far there is no sign of any.
(7)The problem of multiplicity is greatly exacerbated by the existence in the theory of so-called fluxes, analogous to lines of electric or magnetic force, which can thread through the compactified spaces in a colossal number of different ways.
(8)Amazingly, the idea of “an extensible model of an electron” as a membrane was introduced into theoretical physics as long ago as the 1960s, by Paul Dirac. In the 1980s the class of extended objects was generalized from strings and membranes to any number of higher dimensions that is less than the dimensionality of the space in which they moved. This wider class became known as p-branes. The early history of branes is reviewed by Michael Duff in “Benchmarks on the Brane” (hep-th/0407175v3; February 23, 2005).
(9)Polchinski called these membranes D-branes, as distinct from p-branes, and like p-branes they can be generalized to three, four, and so on, dimensions.
(10)Michio Kaku, “Unifying the Universe,” New Scientist, April 16, 2005.
الفصل السادس: قوى الكون المظلمة
(1)Light elements is the term used to mean the lowest-mass elements. They include deuterium—which, confusingly, is also known as “heavy hydrogen.”
(2)The word massive here means “high mass”: it does not mean large in physical size. WIMPs would be pointlike particles but individually weighing more than the heaviest atoms.
(3)An excellent account of dark matter in its different forms is given by Joel Primack and Nancy Abrams, The View from the Center of the Universe (New York: Riverhead, 2006).
(4)Stephen Baxter, Time (New York: HarperCollins, 1999).
(5)P.C.W. Davies, “Cosmological Event Horizons, Entropy and Quantum Particles,” Annales de l’Institut Henri Poincaré, vol. 49, no. 3 (1988), p. 297.
(6)Robert R. Caldwell, Marc Kamionkowski, and Nevin N. Weinberg, “Phantom Energy: Dark Energy With w < −1 Causes a Cosmic Doomsday,” Physical Review Letters, vol. 91 (2003), 071301–1.
(7)Freeman Dyson, “Time Without End: Physics and Biology in an Open Universe,” Reviews of Modern Physics, vol. 51, no. 3 (1979), p. 447.
(8)It is possible that a supercivilization could engineer a new “baby” universe as an escape route: see Chapter 8.
الفصل السابع: كون ملائم للحياة
(1)Nicolaus Copernicus, De revolutionibus orbium coelestium (“On the Revolutions of the Heavenly Spheres”) (Amherst: Prometheus Books, 1995), p. 8. Originally published in Nuremberg, 1543.
(2)The anthropic principle has a large literature. A comprehensive treatment with many references is given by John Barrow and Frank Tipler, The Anthropic Cosmological Principle (New York: Oxford University Press, 1986).
(3)Brandon Carter, “Large Number Coincidences and the Anthropic Principle in Cosmology,” in Confrontation of Cosmological Theories with Observational Data, IAU Symposium 63, edited by M. Longair (Dordrecht, Netherlands: Reidel, 1974), p. 291.
(4)See, for example, Paul Davies, The Fifth Miracle (New York: Simon & Schuster, 1998). Actually, it is rather more favorable for the transfer to occur the other way—that is, for life to start on Mars and come to Earth inside ejected rocks. Either way, one would still be dealing with a single genesis event.
(5)Some science fiction writers, and a few scientists, have speculated about life based on very different chemical or physical processes, and it’s true that scientists have no clear idea of what might or might not be possible. Even harder to assess are the possibilities for life based on radically different laws of physics. I shall adopt the conservative position that, in the absence of evidence to the contrary, life is restricted to something close to what we know.
(6)I shall discuss only a handful of examples. Readers wanting a more complete treatment should refer to Barrow and Tipler, The Anthropic Cosmological Principle.
(7)As a result, neutrinos are emitted. The neutrino flux from the sun has been measured with very sensitive equipment. Neutrinos have extremely low (rest) mass. If that were not the case, protons would lack the necessary mass-energy to turn into neutrons inside stars, thus preventing the sun from shining steadily and sustaining life.
(8)For full details, see Richard Dawkins, The Ancestor’s Tale (New York: Houghton Mifflin, 2005).
(9)Lithium and beryllium get manufactured as by-products of other reactions.
(10)H. Oberhummer, A. Csótó, and H. Schlattl, “Stellar Production Rates of Carbon and Its Abundance in the Universe,” Science, vol. 289 (2000), p. 88.
(11)The word ylem is an obsolete Middle English word meaning the primordial substance from which matter formed. Gamow used the term to mean a mixture of protons and neutrons.
(12)Tritium is an isotope of hydrogen with nuclei containing two neutrons and one proton, so it is even heavier than deuterium.
(13)By this, Gamow means a nucleus with either two protons and three neutrons or three protons and two neutrons. As I have mentioned, neither configuration is stable.
(14)George Gamow, My World Line: An Informal Biography (New York: Viking, 1970), p. 127. Reprinted courtesy of the Gamow Family Estate.
(15)More familiar is the decay of a neutron into a proton, with an attendant release of an antineutrino. The reverse process I am discussing here, with a proton turning into a neutron, can happen in an imploding star because the intense gravitational field that is created supplies the necessary energy.
(16)There are other, less efficient, ways for stars to divest themselves of carbon, so it is not clear how critical the neutrino interaction strength is to the fine-tuning argument for this element.
(17)Neutron decay is a statistical process subject to quantum fluctuations. Half-life is defined as the average time it takes for exactly half of a population of neutrons to decay.
(18)Max Tegmark, Anthony Aguirre, Martin Rees, and Frank Wilcek, “Dimensionless Constants, Cosmology and Other Dark Matters,” Physical Review I, vol. 77 (2206), p. 23505.
(19)That is, why is the model so wrong—I don’t think we made a mistake in our sums!
(20)Inflation requires dark energy to be non-zero for a very brief time just after the big bang, but physicists still assumed that in the post-inflation phase the dark energy would drop to precisely zero.
(21)Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (New York: Little, Brown, 2005), p. 78.
(22)As far as I know, Sidney Coleman of Harvard University, who helped to pioneer the subject of symmetry-breaking in the early universe, was the first person to use the phrase “the big fix” to describe the dramatic suppression of dark energy.
(23)Steven Weinberg, “Anthropic Bound on the Cosmological Constant,” Physical Review Letters, vol. 59 (1987), p. 2607.
(24)The formation of galaxies depends delicately on the magnitudes of both the dark energy and the primordial density fluctuations. In my discussion I am assuming that the latter is held fixed while the former is allowed to vary. If both quantities are allowed to vary together, the analysis is more complicated. See, for example, Tegmark et al., “Dimensionless Constants, Cosmology and Other Dark Matters.”
الفصل الثامن: هل تحل نظرية الكون المتعدد لغز جولديلوكس؟
(1)That solitary individual was I. L. Rozenthal, who succeeded in publishing a credible review paper (Soviet Physics Uspekhi, vol. 23 , p. 296). This was no mean feat in a regime that strongly discouraged any discussion that departed from the strict Marxist philosophy of dialectical materialism.
(2)The various constants I have mentioned assume numerical values that depend on the system of units used to express them. For example, the speed of light is either (roughly) 300,000 km per second or 186,000 miles per second. Constants may be combined to form dimensionless ratios, which are pure numbers, independent of units. For example, the square of the charge on the electron divided by Planck’s constant and the speed of light is a pure number with a value close to 0.001617. When considering whether the laws of physics contain free parameters that might vary from place to place, it makes sense only to discuss variations of such dimensionless ratios.
(3)Neutrinos fall outside this scheme. Experiments show that they do have a tiny mass, but its explanation lies beyond the Standard Model.
(4)The Higgs particle is a boson because it has spin 0.
(5)James Watson, The Double Helix (New York: Touchstone, 2001).
(6)This example can be likened to the rule of the road. In some countries people drive on the right; in others they drive on the left. Which one is chosen is just a matter of historical accident. It doesn’t make any difference so long as everybody uses the same rule.
(7)If you did the experiment very precisely, the selection of the direction could be traced back to chaotic molecular jiggles.
(8)This example comes from Sidney Coleman.
(9)By “low-temperature” and “low-energy” I mean low compared with the temperature and energy of symmetry-breaking. As we shall see, that may involve GUT or even Planck values. Given these elevated scales, what physicists normally refer to as “high-energy physics” is still very low-energy indeed. So the low-energy world includes the world of subatomic accelerators such as the LHC, as well as everyday experience.
(10)The alert reader may notice that this is about the time when inflation is supposed to have happened—which is no coincidence. It was by considering the application of GUTs to the very early universe that Alan Guth got the idea of the inflationary universe scenario in the first place, and in fact a plausible candidate for the inflaton field is one of the GUT Higgs fields.
(11)Actually, I’m making this up. Nobody knows because the theory is too complicated. But there are lots of options.
(12)Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design (New York: Little, Brown, 2005), p. 21.
(13)The existence of a landscape is based on a consideration of the five “corners” of M theory representing the five original string theories, which can be studied using an approximation method called perturbation theory. Some theorists believe that the landscape is an artifact of this approximation and predict that if the full underlying M theory could be properly formulated and solved exactly, it would yield a single, unique description—just one world. I shall have more to say about the alternative view in Chapter 9.
(14)The idea that eternal inflation might provide a natural mechanism to generate large cosmic domains (pocket universes) with very different low-energy physics, and with obvious anthropic consequences, dates from the early 1980s. See A. D. Linde, “The New Inflationary Universe Scenario,” in The Very Early Universe, edited by G. W. Gibbons, S. W. Hawking, and S. Siklos (New York: Cambridge University Press, 1983), p. 205. For an up-to-date account of this “landscape exploration” process, see Chapter 11 of Susskind’s book The Cosmic Landscape.
(15)The theories I have described here are by no means the only ideas for a multiverse. A list of various multiverse theories has been compiled by Nick Bostrom in Anthropic Bias: Observations and Selection Effects (New York: Routledge, 2002); see also John Leslie, Universes (New York: Routledge, 1989).
(16)An excellent in-depth discussion and critique of these issues can be found in Neil Manson (ed.), God and Design (New York: Routledge, 2003).
(17)The Edge annual question, 2006. See www.edge.org.
(18)This type of reasoning is fully convincing only if one can assign precise statistical weights to different universes, but we don’t know how to do that yet. Another assumption is that there is no obvious minimum value of the dark energy below which life would be impossible, unless one considers negative values. A substantial amount of negative dark energy would be life-threatening for a different reason: it would add to the gravitational attraction of the universe and cause rapid collapse to a big crunch.
(19)More details of this work can be found in John Barrow, The Constants of Nature (New York: Random House, 2003).
(20)Max Tegmark, “Parallel Universes,” Scientific American (May 2003), p. 31.
(21)There is also a hidden assumption that the systems being considered have a finite, albeit very large, number of possible states. This is the case for discrete variables, as arise from the application of quantum mechanics, but there is no logical reason why some physical variables should not be continuous. If that were so, there would be infinitely many “shades of gray,” and the question of truly identical copies would be more subtle.
(22)Nick Bostrom, “The Simulation Argument: Why the Probability That You Are Living in a Matrix Is Quite High,” Times Higher Education Supplement, May 16, 2003. For a more scholarly analysis see Bostrom’s “Are You Living in a Computer Simulation?” Philosophical Quarterly, vol. 53, no. 211 (2003), p. 243.
(23)The assumption that all physical processes can in principle be simulated by a universal computer rests on an unproven but widely believed conjecture called the Church-Turing thesis named after Alan Turing and the American logician Alonzo Church). See, for example, David Deutsch, The Fabric of Reality (New York: Viking, 1997), p. 134.
(24)Cited in J. R. Newman, The World of Mathematics (New York: Simon & Schuster, 1956).
(25)A collection of essays on this topic can be found in Daniel Dennett and Douglas Hofstadter, The Mind’s I (Brighton, UK: Harvester, 1981). See also David Chalmers, “The Matrix as Metaphysics,” in Philosophers Explore the Matrix, edited by Christopher Grau (Oxford, UK: Oxford University Press, 2005).
(26)Alan Turing, “Computing Machinery and Intelligence,” Mind, vol. 59 (1950), p. 433.
(27)A classic being Isaac Asimov’s I, Robot (New York: Genome Press, 1950).
(28)Roger Penrose, The Emperor’s New Mind (New York: Oxford University Press, 1989).
(29)Gordon Moore, cofounder of Intel, predicted decades ago that computing power would double about every one or two years. So far he has been proved correct.
(30)See, for example, Frank Tipler, The Physics of Immortality (New York: Doubleday, 1994).
(31)Interested readers can learn more by visiting Bostrom’s Web site at www.simulation-argument.com.
(32)Martin Rees, Our Final Century (New York: Basic Books, 2004).
(33)John Barrow, “Glitch,” New Scientist (June 7, 2003), p. 44. Reprinted courtesy of New Scientist.
(35)The simulating system need not be an electronic computer. If the assumption of computational universality (see the next paragraph in the main text), on which this entire discussion is based, is correct, then the simulation could be performed using almost any objects, such as beer cans and string, or even something as simple as a classical three-body chaotic system, which is infinitely complex in its behavior. Also, “our” time and time in the simulating system need not be the same. The simulation could be much faster or much slower in its own time than our subjective experience of time within the simulation.
(37)Paul Davies, “A Brief History of the Multiverse,” New York Times, April 12, 2003.
(38)Martin Rees, “In the Matrix,” Edge (www.edge.org), September 15, 2003.
الفصل التاسع: التصميم الذكي، والتصميم غير الذكي
(1)Augustine, City of God, XI, 4, 2, in Basic Writings of St. Augustine, edited by W. T. Oates (New York: Random House, 1948).
(2)Aquinas is famous for his arguments for the existence of God, based on “five ways” of reasoning. The five ways are contained in his Summa Theologica, edited by Timothy McDermott (Westminster, MD: Christian Classics, 2000).
(3)William Paley, Natural Theology (1802), in Paley’s Natural Theology with Illustrative Notes, edited by H. Brougham and C. Bell (London, 1836), chapters 1 and 2.
(4)Richard Dawkins, The Blind Watchmaker (New York: Norton, 1987).
(5)Henry Drummond, The Lowell Lectures on the Ascent of Man (New York: J. Pott & Co., 1894), pp. 427-28.
(6)The term seems to have been coined by C. A. Coulson in Science and Christian Belief (London: Fontana, 1958), although Drummond had already captured the basic idea in The Ascent of Man.
(7)A useful video demonstrating the details, featuring Dan-Erik Nilsson, has been produced by WGBH Educational Foundation and Clear Blue Sky Productions and can be found at www.pbs.org/wgbh/evolution/library/01/1/1_011_01.htm.
(8)Intelligent Design proponents are (for political reasons) frustratingly vague about the non-Darwinian mechanism whereby physical systems such as the bacterial flagellum acquire their designlike structure. It does not have to be an on-the-spot miracle, like a rabbit pulled out of a hat, although that is apparently what their supporters prefer. There could be a designlike law of nature that operates over evolutionary timescales. To establish the meaningfulness of such a law, it is first necessary to provide a rigorous mathematical definition of design. A heroic attempt at just that has been made by William Dembski: see his book No Free Lunch (Lanham, MD: Rowman & Littlefield, 2001).
(9)A robust case for self-organization in biology is made by Stuart Kauffman in his book At Home in the Universe (New York: Oxford University Press, 1995).
(10)Lee Smolin proposed a theory in which black holes create “baby universes” that inherit laws from their “parent universe,” with some random variation. In this theory there is a sort of inheritance and variation, but no selection. Details can be found in his book Life of the Cosmos (New York: Oxford University Press, 1997).
(11)Christoph Schönborn, “Finding Design in Nature,” New York Times, July 7, 2005.
(12)See, for example, Nelson Pike, God and Timelessness (New York: Random House, 1970).
(13)E. W. Harrison, “The Natural Selection of Universes Containing Intelligent Life,” Quarterly Journal of the Royal Astronomical Society, vol. 36, no. 3 (1995), p. 193.
(14)Remember, the landscape is not a physical place or region, but a space of possibilities—a parameter space. The superbeing or supercivilization could create a universe physically close by, but a long way away in parameter space. If the universe containing this being or civilization were already optimal for life, we can imagine that it/they would choose to create baby universes at a similar location in the landscape, to make their product universes fit for life.
(15)Olaf Stapledon, The Star Maker (London: Methuen, 1937).
(16)Fred Hoyle, The Intelligent Universe (London: Michael Joseph, 1983), p. 249.
(17)Andrei Linde, “Stochastic Approach to Tunneling and Baby Universe Formation,” Nuclear Physics, vol. B372 (1992), p. 421.
(18)Heinz Pagels, The Dreams of Reason (New York: Bantam, 1989), p. 156.
(19)James Gardner, Biocosm (Maui, HI: Inner Ocean Publishing, 2003), p. 178.
(20)A clear discussion is given by Richard Swinburne, The Coherence of Theism (New York: Clarendon Press, 1977), part III.
(21)That is, can a being that exists necessarily, is good necessarily, is omnipotent necessarily, and so on, also not create necessarily? Can a necessary being choose to not create?
(22)Isaac Newton, who wrote more about theology than physics, used this argument. He reasoned that space and time at least are necessary because they emanate directly from God’s necessary being. This may have been a factor in Newton’s view that space and time are absolute, universal, and unchangeable. Of course, we now know that this is wrong.
(23)A good place to start is Keith Ward, God: A Guide for the Perplexed (Oxford: Oneworld Publications, 2005).
(24)The unique, no-free-parameters theory is indifferent about whether there is only one representation of the universe or many. If there are many, they will be in identical quantum states—the postulated unique vacuum state of the theory. Because of the inherent uncertainty of quantum mechanics, this does not require the universes to be precise clones. So even the supposedly “unique” universe theory is consistent with a limited form of multiverse.
(25)The original idea for this analogy came from Carl Sagan, who described it in his novel Contact (New York: Simon & Schuster, 1985). It has been used in its present context by Rodney Holder in his book God, the Multiverse, and Everything (Burlington, VT: Ashgate, 2004).
(26)There is also a technical explanation, in terms of the foundations of mathematics and logic, of why a unique final theory is impossible. This has to do with what is known as Gödel’s incompleteness theorem. For a recent discussion of this theorem, see, for example, Gregory Chaitin, Meta Math! The Quest for Omega (New York: Pantheon Books, 2005). It was partly in consideration of Gödel’s theorem that Stephen Hawking, in a much publicized U-turn, recently repudiated the existence of a unique theory of everything.
(27)Stephen Hawking, A Brief History of Time (New York: Bantam, 1988), p. 174.
(28)Leibniz, who was a theist, considered this problem and famously concluded that ours is the best of all possible worlds (for why would an all-good, perfect God create something less than best?). Leibniz’s definition of best refers not to maximum happiness for humans, but more abstractly to mathematical optimization: simplicity consistent with richness and diversity.
(29)Anything that is logically self-consistent, I mean. A round square, for example, could not exist anywhere.
(30)Tegmark was certainly not the first to suggest that all possible universes really exist. The idea was embraced, for example, by the Princeton philosopher David Lewis.
(31)Max Tegmark, “Parallel Universes,” Scientific American (May 2003), p. 31.
(33)Benoît B. Mandelbrot, The Fractal Geometry of Nature (New York: Freeman, 1982).
(34)Tegmark calls it the “ultimate ensemble theory.”
(35)See, for example, Chaitin, Meta Math!, p. 97.
(36)The set of all sets that do not contain themselves is not in fact a set, according to the logical niceties of set theory.
(37)Unless, that is, it can be demonstrated that there is a necessary being that is necessarily unique.
(38)For example, one axiom states that any two points in space can be connected by a straight line.
(39)This is perhaps a simplification. One may have evidential reasons for believing in a particular starting point. For example, support for a multiverse might come from evidence of variations of the “constants” of nature. Support for God might come from religious experience or moral arguments.
(40)Sometimes as “the only one,” but I have already pointed out the dubiousness of that claim.
(41)Martin Gardner, Are Universes Thicker Than Blackberries? (New York: Norton, 2003), p. 3.
(42)Richard Swinburne, The Existence of God (New York: Oxford University Press, 1979), chapter 5.
(43)Richard Dawkins, “The Improbability of God,” Free Inquiry Magazine, vol. 18, no. 3 (1998), p. 6.
(44)Not the Tegmark multiverse: that is simple (well, maybe …).
الفصل العاشر: كيف أتى الوجود؟
(1)Quoted by David Deutsch in The Fabric of Reality (New York: Viking, 1997), pp. 177-78.
(2)Brandon Carter, “Large Number Coincidences and the Anthropic Principle in Cosmology,” in Confrontation of Cosmological Theories with Observational Data, IAU Symposia No. 63, edited by M. S. Longair (Dortrecht, Netherlands: Reidel, 1974), p. 291; “The Anthropic Principle and Its Implications for Biological Evolution,” Philosophical Transactions of the Royal Society of London A, vol. 310 1983, p. 347.
(3)John Barrow and Frank Tipler, The Anthropic Cosmological Principle (New York: Oxford University Press, 1986).
(4)Freeman Dyson, Disturbing the Universe (New York: Harper & Row, 1979), p. 250.
(5)“Evolution’s Driving Force,” discussion between Robyn Williams and Simon Conway Morris, ABC Radio National, December 3, 2005: www.abc.net.au/rn/science/ss/stories/s1517968.htm.
(6)Christian de Duve, Vital Dust: Life as a Cosmic Imperative (New York: Basic Books, 1995), p. 300.
(7)Stuart Kauffman, At Home in the Universe (Oxford, UK: Oxford University Press, 1995).
(8)Deutsch, The Fabric of Reality, p. 181.
(9)Ibid., p. 134. This statement is closely related to the Church-Turing thesis, the claim that defines the basis for the concept of a universal, or general-purpose, computer. Deutsch proposes elevating this thesis to the status of a fundamental principle of the universe.
(10)Another example of an inconspicuous yet fundamental property of quantum systems is entanglement, whereby two or more particles remain subtly linked even though widely separated.
(11)There is increasing evidence that some “junk” DNA, although not part of the genetic coding system, may nevertheless play a role in the operation of the cell.
(12)The crucial and basic distinction between the “easy” and “hard” problems of consciousness was first stressed by David Chalmers in a famous essay, “Facing Up to the Problem of Consciousness,” Journal of Consciousness Studies, vol. 2 (1995), p. 200. Most, but not all, philosophers have since accepted this distinction as valid.
(13)Daniel Dennett, Consciousness Explained (Boston: Little, Brown, 1991).
(14)See, for example, David Chalmers, The Conscious Mind: The Search for a Fundamental Theory (New York: Oxford University Press, 1997).
(15)Just as Schrödinger’s cat is seemingly in a state of “suspended animation” in the absence of an observation, so the quantum universe as a whole remains suspended in a superposition of vastly many “histories.” Readers who want to know more about the disappearance of time in quantum cosmology can find a detailed discussion in The End of Time by Julian Barbour (New York: Oxford University Press, 2001).
(16)Andrei Linde, “Inflation, Quantum Cosmology and the Anthropic Principle,” in Science and Ultimate Reality, edited by John Barrow, Paul Davies, and Charles Harper (New York: Cambridge University Press, 2004), p. 426.
(17)Quoted by Tim Folger, “Does the Universe Exist If We’re Not Looking?” Discover Magazine, vol. 23, no. 6 (June 2002), p. 43.
(18)Some suggestions for how this may be achieved have been made by Charles Lineweaver and myself: see P.C.W. Davies and Charles H. Lineweaver, “Finding a Second Sample of Life on Earth,” Astrobiology, vol. 5, no. 2 (April 2005), p. 154.
(19)Physicists often refer to this as a Boltzmann gas, after Ludwig Boltzmann, who studied how gases approach thermodynamic equilibrium.
(20)I’m referring here to the macroscopic state, defined by averaging over many molecules, not to the micro-states in which the motions of individual molecules are specified.
(21)This point is well recognized by scientists, and attempts have been made to provide a more precise definition of the elusive quality of “organized complexity” that seems to characterize life. One promising definition, introduced by Charles Bennett of IBM, is in terms of the computational labor needed to describe the system. Bennett calls this the “depth” of the system. A related but more physics-based definition of depth was proposed by Seth Lloyd and Heinz Pagels. A popular account of depth can be found in Murray Gell-Mann, The Quark and the Jaguar (New York: Freeman, 1994), pp. 100–105.
(22)See, for example, Stuart Kauffman, Investigations (New York: Oxford University Press, 2000); or Eric Chaisson, Epic of Evolution: Seven Ages of the Cosmos (New York: Columbia University Press, 2005).
(23)Even professional biologists are not immune to backsliding on this issue. In a recent article taking them to task, Charles Lineweaver highlights what he calls the “planet of the apes fallacy.” See Astrobiology, vol. 5, no. 5 (2005), p. 658.
(24)See, for example, Daniel Dennett, Darwin’s Dangerous Idea (New York: Simon & Schuster, 1996).
(25)An interesting case in point is the Gaia theory of life on Earth, according to which our planet’s ecology, geology, and climate form an interconnected dynamic feedback system in which Earth and its biosphere somehow cooperate to perpetuate life, for example, by responding to external changes such as solar variability with compensating climatic changes. In this popular form, the Gaia theory looks decidedly teleological—Earth’s biosphere responds to internal and external threats to secure its future—and it has been roundly criticized as such.
(26)Marx and Engels, Works, vol. 40 (Moscow, 1929), p. 550.
(27)Murray Gell-Mann, “Nature Conformable to Herself,” Complexity, vol. 1, no. 4 (1995), p. 1126.
(28)Gell-Mann, The Quark and the Jaguar, p. 212. As an ironical aside, let me point out that if the extended version of the multiverse theory is considered (the one in which all possible laws are instantiated in a universe somewhere), then included within this multiverse there must be universes with teleological laws. One cannot banish teleological laws by fiat and at the same time argue that all possible laws are permitted in a universe somewhere. So if one embraces the extended multiverse theory, the question then arises as to whether our universe is one of those that actually has teleological laws, or whether it hasn’t but is cunningly cooked up to mimic the genuine article. If universes with teleological laws exist, ours would be an excellent candidate. The universe certainly looks as if it possesses teleological features. Well, perhaps it is teleological!
(29)Heinz Pagels, Perfect Symmetry (New York: Simon & Schuster, 1985), p. 347.
(30)Časlav Bruckner and Anton Zeilinger, “Information and Fundamental Elements of the Structure of Quantum Theory,” in Time, Quantum, and Information, edited by Lutz Castell and Otfried Ischebeck (Berlin: Springer-Verlag, 2003), p. 323.
(31)John Wheeler, “On Recognizing ‘Law Without Law,’” American journal of Physics, vol. 51 (1983), p. 398.
(32)This is not just the emergence of low-energy effective laws via symmetry-breaking, as discussed in Chapter 8. Wheeler proposes that all laws emerge from chaos after the origin of the universe.
(33)John Wheeler, “Information, Physics, Quantum: The Search for Links,” in Proceedings of the 3rd International Symposium on the Foundations of Quantum Mechanics, Tokyo, 1989, p. 354.
(34)John Wheeler, “Frontiers of Time,” in Problems in the Foundations of Physics, edited by G. Toraldo di Francia (Amsterdam: North-Holland, 1979), p. 395.
(35)This is a general statement, but in practice the bits are determined by quantum mechanics, in the form of discrete yes/no answers, such as whether an electron’s spin is up or down.
(36)John Wheeler, At Home in the Universe (New York: AIP Press, 1994), pp. 295–311. An attempt to build all of physics out of information has been made by B. Roy Frieden in Physics from Fisher Information (New York: Cambridge University Press, 1998) For up-to-date comment on “it from bit,” see Science and Ultimate Reality, edited by John Barrow, Paul Davies, and Charles Harper (New York: Cambridge University Press, 2004), part IV. See also Wheeler, “Information, Physics, Quantum.”
(37)Two relevant papers by Rolf Landauer are “Wanted: A Physically Possible Theory of Physics,” IEEE Spectrum, vol. 4, no. 9 (1967), p. 105; and “Computation and Physics: Wheeler’s Meaning Circuit?” Foundations of Physics, vol. 16, no. 6 (1986), p. 551.
(38)Gregory Chaitin, Meta Math! The Quest for Omega (New York: Pantheon Books, 2005), p. 115.
(39)Seth Lloyd’s calculation is described in his paper “Computational Capacity of the Universe,” Physical Review Letters, vol. 88 (2002), p. 237, 901. See also his book The Computational Universe (New York: Random House, 2006).
(40)There may, however, be situations involving complex systems in which the limit of 10120 does matter. See P.C.W. Davies, “Emergent Biological Principles and the Computational Resources of the Universe,” Complexity, vol. 10, no. 2 (2004), p. 1.
(41)Paul Benioff, “Towards a Coherent Theory of Physics and Mathematics,” Foundations of Physics, vol. 32 (2002), p. 989.
(42)Benioff’s proposed consistency criterion is that the theory should maximally describe its own validity and sufficient strength.
(43)Benioff, “Towards a Coherent Theory,” p. 1005.
(44)I have given a popular account in my book About Time (New York: Simon & Schuster, 1996).
(45)F. Hoyle and J. V. Narlikar, Direct Inter-Particle Theories in Physics and Cosmology (San Francisco: Freeman, 1974).
(46)M. Gell-Mann and J. B. Hartle, “Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology,” in Physical Origins of Time Asymmetry, edited by J. J. Halliwell, J. Pérez-Mercader, and W. H. Zurek (New York: Cambridge University Press, 1994), p. 311.
(47)S. W. Hawking, “The No Boundary Condition and the Arrow of Time,” in Physical Origins of Time Asymmetry, edited by J. J. Halliwell, J. Pérez-Mercader, and W. H. Zurek (New York: Cambridge University Press, 1994), p. 346; Hawking subsequently retracted the idea.
(48)Light rays can be bent by material obstacles, such as the edges of the slit. Thus photons do not always travel in precisely straight lines.
(49)Quantum mechanics requires that all particles have a wave aspect. The two-slit experiment has, for example, been successfully carried out with electrons.
(50)In a practical laboratory experiment the photon would take only nanoseconds to pass from the slits to the blind, and no human experimenter could make a decision so finely judged as to take place after the photon had traversed the slits but before it reached the blind. But this is a minor quibble. In principle one could make the distance to the image screen as long as one likes.
(51)W. C. Wickes, C. O. Alley, and O. Jakubowicz, “A ‘Delayed-Choice’ Quantum Mechanics Experiment,” in Quantum Theory and Measurement, edited by John A. Wheeler and Wojciech H. Zurek (Princeton, NJ: Princeton University Press, 1983), p. 457; see also T. Hellmuth, H. Walther, A. Zajonc, and W. Schleich, “Delayed-Choice Experiments in Quantum Interference,” in Physical Review A, vol. 35 (1987), p. 2532.
(52)There are lots of ingenious refinements to this scenario and many actual experiments, including some in which the accomplice can make a record and then erase it. In all cases, no information can be sent back in time by this sort of arrangement.
(53)A rather natural way of considering the delayed-choice experiment comes from the so-called transactional interpretation of quantum mechanics, due to John Cramer of the University of Washington (see Reviews of Modern Physics, vol. 58 , p. 647). The essential idea is that a quantum event, such as the scattering of an electron or the decay of an atom, involves processes that go both forward and backward in time at the speed of light. If the transactional interpretation were applied to the universe as a whole, it might yield a self-consistent description. The challenge would then be to demonstrate that this description was unique.
(54)Wheeler, “Information, Physics, Quantum,” p. 354.
(55)The concept of a self-explanatory loop is reflected in the ancient mystical symbol of the Ouroboros, represented as a snake eating its own tail.
(56)Wheeler’s more precise definition was “a self-referential deductive axiomatic system” (see “Information, Physics, Quantum,” p. 357).
(57)Barrow and Tipler, The Anthropic Cosmological Principle; Frank Tipler, The Physics of Immortality (New York: Doubleday, 1994).
(58)“The Anthropic Universe,” a documentary on the Australian Broadcasting Corporation’s Radio National, The Science Show, February 18, 2006, produced by Martin Redfern and Pauline Newman. A transcript may be found at www.abc.net.au/rn/science/ss/stories/s1572643.htm.
(59)John Wheeler, “World as a System Self-Synthesized by Quantum Networking,” IBM Journal of Research and Development, vol. 32, no. 1 (1988), p. 4.
(60)Quoted by Folger, “Does the Universe Exist If We’re Not Looking?”
(61)Another way to avoid paradoxes is to adopt the many-universes interpretation of quantum mechanics. See Deutsch, The Fabric of Reality, chapter 12.
(62)If this skimpy discussion leaves the reader more confused than before, I can recommend my little book How to Build a Time Machine (New York: Viking, 2002) for more details.
(63)Physicists will recognize this cumbersome description as what is technically termed a closed time-like world line.
(64)J. R. Gott III and L.-X. Li, “Can the Universe Create Itself?” Physical Review D, vol. 58 (1998), p. 023501.
(65)P. C. W. Davies, “Closed Time as an Explanation of the Black Body Background Radiation,” Nature Physical Science, vol. 240 (1972), p. 3.
(66)Other scientists have had similar ideas. For example, Fred Hoyle concluded that “the Universe is seen as an inextricably linked loop … Everything exists at the courtesy of everything else.” The Intelligent Universe (London: Michael Joseph, 1983), p. 248.
(67)Wheeler arrived at a similar position. He insisted that the results of quantum observations must mean something before the universe can be said to be fully actualized. In this “meaning circuit” (depicted in Figure 10-5,), the physical world gives rise to “observership” and “meaning,” while observers and meaning loop back and give rise to the physical world See, for example, Wheeler, “World as a System.”
(68)Landauer, “Computation and Physics.”
(69)S. W. Hawking and T. Herzog, “Populating the Landscape: A Top Down Approach,” hep-th/0602091. A popular account is Amanda Gefter, “Mr. Hawking’s Flexiverse,” New Scientist (April 22, 2006), p. 28.
(70)Memes play the same role in human culture that genes play in genetics. They may be, for example, habits, fashions, or belief systems. Memes replicate, spread within the community, and compete.
خاتمة: التفسيرات الجوهرية
(1)Broadcast in 1948 on the Third Programme of the BBC. Transcript reprinted in Bertrand Russell, Why I Am Not a Christian (New York: Touchstone, 1957), p. 155.
(2)Neil A. Manson, “Introduction,” in God and Design: The Teleological Argument and Modern Science, edited by Neil Manson (New York: Routledge, 2003), p. 18.
(3)Yes, according to the philosopher John Leslie, who has championed the theory that the universe exists because “it is good” that it does so—an idea that goes back to Plato. The challenge is to convince physicists that “ethical requiredness” has causal potency.