FOREWORD
1. Carl Sagan, “Why We Need to Understand Science,” Skeptical Inquirer 14, no. 3 (Spring 1990).
PREFACE
1. Rosenblum and Kuttner, Reference X, p. 5.
2. Ibid., preface, p. 5, p. 116.
3. In a letter to Max Born on March 3, 1947, Einstein wrote: “physics should represent reality in time and space, free from spooky action at a distance.” This is quoted from Max Born, The Born–Einstein Letters 1916–1955: Friendship, Politics and Physics in Uncertain Times, by Manjit Kumar (New York: Macmillan, 2005), p. 155, in Kumar, Reference K, p. 312.
CHAPTER 1: INTRODUCTION TO PARTS ONE AND TWO
1. McEvoy and Zarate, Reference A, p. 3.
2. Scerri, Reference D, p. 229.
3. Gribbin, Reference Z, photo insert, caption for the identical photo shown in Quantum Fuzz, Figure 1.1.
4. Kumar, Reference K.
5. Bortz, Reference B, pp. 212–27. A similar listing (also in order by the year in which the award is presented, and also starting from 1901when the first award was given) can be found in Wikipedia, s.v. “List of Nobel Laureates in Physics,” https://en.wikipedia.org/wiki/List_of_Nobel_laureates_in_Physics (last accessed September 22, 2016).
CHAPTER 2: PLANCK, EINSTEIN, BOHR
1. Andrew Robinson, The Last Man Who Knew Everything (New York: Pi, 2006), p. 96.
2. Kumar, Reference K, p. 56.
3. A listing of all Nobel Prize winners in Physics and the rationale for the award, from the first in 1901 through 2000, is provided in Bortz, Reference B, pages 212–27. An updated list may be found in Wikipedia, s.v. “List of Nobel Laureates in Physics,” https://en.wikipedia.org/wiki/List_of_Nobel_laureates_in_Physics (last accessed September 22, 2016). As mentioned in the preface, all subsequent quotes showing the rationales for the awards are from these sources.
4. Einstein initially did well in his entrance exams in math and physics, but he failed in history and languages. As a result, he was encouraged to finish high school in a small town near Zurich, where he boarded with the family of the school director, had a great time socially, became a gregarious freethinker, and graduated at the head of his class.
5. Kean, Reference R, p. 43.
CHAPTER 3: HEISENBERG, DIRAC, SCHRÖDINGER
1. Bortz, Reference B, p. 55.
2. Kumar, Reference K, p. 150.
3. Moore, Reference M, p. 272.
CHAPTER 5: THE ESSENTIAL FEATURES OF QUANTUM MECHANICS
1. I modify the format and terminology put forward by Chad Orzel in Reference L, p. 59, to recognize that each state may be represented by a wavefunction, and that these wavefunctions for the states may be components of an overall wavefunction.
CHAPTER 6: CLASH OF TITANS
1. Bohr made a distinction between the macroscopic world, for which classical physics would apply, and the submicroscopic world for which quantum theory would apply. But, as you will come to see, ours is a quantum world, micro or macro, and complementarity, a key principle of quantum theory, may apply critically in explaining the nature of even so massive a body as a black hole (see Chapter 9).
2. From Alice Calaprice, The New Quotable Einstein (Princeton: Princeton University Press, 2005), p. 89, as quoted by Kumar, Reference K, p. 278.
3. Kumar, Reference K, p. 256.
4. Ibid., p. 271.
5. Ibid., p. 316.
6. Ibid.
7. Ibid., p. 295.
8. Ibid., p. 338.
9. Orzel, Reference L, p. 149.
10. But the researchers did not report their results in percentages, so we must translate. Orzel, Reference L, reports on page 159: “Physicists like to deal with numbers, and for the specific configuration they used, a local hidden variables treatment predicts that their results should boil down to a number between –1 and 0. When they did the experiment, they measured a value of 0.126, with an uncertainty of plus or minus 0.014.*” (*This uncertainty is based on the accuracy of their measuring apparatus, and having nothing to do with Heisenberg's uncertainty principle.) Orzel goes on: “The difference between the maximum LHV value and their measurement is nine times larger than the uncertainty in the measurement, meaning that there's a one in 1036 probability of this happening by chance. 1036 is a billion billion billion billion, a number so large that it might have made even Carl ‘Billions and Billions’ Sagan blink.” To see how this relates to the percentages of Bell's inequality described earlier, realize that having LHV “boil down to a number between –1 and 0,” corresponds to having a scale with 100 percent at –1 and 33 percent at 0. On this scale, the 25 percent minimum probability (for a filter misorientation of 60 degrees) would be exactly +0.125, very close to the +0.126 that they measured and well within the uncertainty of the measurement.
11. Ibid., p. 162.
12. Kumar, Reference K, p. 354.
13. Wikipedia, s.v. “Interpretations of Quantum Mechanics,” https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics (accessed August 9, 2016).
14. Wikipedia, s.v. “Many Worlds Interpretation,” https://en.wikipedia.org/wiki/Many-worlds_interpretation (accessed August 9, 2016).
15. Kumar, Reference K, p. 358.
16. Wikipedia, s.v. “Interpretations of Quantum Mechanics,” https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics (accessed August 9, 2016).
17. Orzel, Reference L, p. 89.
18. Ibid., p. 101.
19. Greene, Reference C, p. 212; and Greene, Reference AA, p. 224.
CHAPTER 7: WHAT DOES IT ALL MEAN?
1. Galileo Galilei, Il Saggiatore (in Italian) (Rome, 1623); Galilei, The Assayer, translated by Stillman Drake, in Discoveries and Opinions of Galileo (Garden City, NY: Doubleday Anchor Books,1957), pp. 237–38.
2. S. Chandrasekhar, Newton's Principia for the Common Reader (Oxford: Clarendon, 1995), p. 43.
3. Moore, Reference M, p. 196.
4. McEvoy, Reference A, p. 3.
5. As a practical matter for large objects, where a grain of sand is very large, this doesn't make a difference—it doesn't matter. Suppose that you watched a batter hit a baseball. The classical physicist or engineer would say: “If you tell me the exact position of the baseball relative to the bat and the trajectory of the incoming ball and the swinging bat and the rotation on the ball and the wind and the resistance of the air, I will calculate the exact velocity and trajectory of the ball after it is hit.” (After all, through such calculations we put rockets around the moon.) And they would be right. But in principle, to know the underpinnings of our universe, we need to pay attention. The quantum physicist would say: “No, you can't know exactly both the position and velocity of the ball, or its rotation or the movement of the bat in the first place, and so you cannot calculate the exact outgoing trajectory.” And the quantum physicist or engineer would be right! Consider the Heisenberg uncertainty principle described in Chapter 8. The spread-out probability clouds for the location of the electron in the states of the hydrogen atom are just one manifestation of this uncertainty and lack of determinism. And the uncertainty principle does also apply to large objects: we cannot know with absolute certainty both the location and the motion of an object.
6. The Structure of Scientific Revolutions, by Thomas S. Kuhn, Reference T.
7. Because the product of the uncertainty in an object's position multiplied by the uncertainty in its momentum (mass times velocity) is always equal to or greater than a constant (Planck's constant, as discussed in Chapter 8), knowing an object's position exactly would mean that you can't accurately know its velocity, or vice versa. But Planck's constant is very small in relation to the size and momentum of large objects, so uncertainties in size and velocity can be pretty small compared to their actual size and velocity. If, hypothetically (referring to the earlier endnote), we were to measure the position of a baseball at any instant of time to within about a thousandth of the thickness of a human hair, then we can calculate that the minimum uncertainty for the velocity of the baseball would be about a trillionth of a trillionth of one mile per hour. Even at many many times this minimum, the uncertainty in the speed of the baseball would be an extremely small percentage of the velocity of a baseball moving at maybe ninety miles per hour. And at a thousandth of the thickness of a human hair, we know the baseball's position to within a very, very small fraction of a percent of its size. So the uncertainties in position and velocity, though they are there, are of no practical consequence for the baseball, the batter, or the classical engineer.
CHAPTER 8: APPLICATIONS
1. “Krysta Svore on Quantum Computing,” YouTube video, 28:34, originally presented by Microsoft Research Luminaries, posted by Larry Larson on October 28, 2014, https://youtu.be/kK__pbb66ss (October 5, 2016)
2. I remember the objective of the game as determining the identity of physical objects, but he apparently remembers it as identifying a particular word.
3. In December 2007, ASCII was incorporated into a more advanced UTF-8 coding system.
4. Gribbin, Reference Z, p. 34.
5. Steven Rich and Barton Gellman, “NSA Seeks to Build Quantum Computer That Could Crack Most Types of Encryption,” Washington Post, January 2, 2014.
6. “Krysta Svore on Quantum Computing.”
7. The Bell states are the four binary combinations of the qubit states, representing respectively the binary digit combinations: “0, 0,” “0, 1,” “1, 0,” and “1, 1.”
8. Gribbin, Reference Z, pp. 168 and 169.
9. Ibid., pp. 159–68.
10. Ibid., p. 180.
11. Ibid., p. 190.
12. Ibid., p. 188.
13. Jeffrey Kluger, “Teleportation Is Real and Here's Why It Matters,” Time, May 30, 2014.
14. Orzel, Reference L, p. 184.
15. Wikipedia, s.v. “Quantum Cryptography,” September 13, 2016 (accessed October 4, 2016).
CHAPTER 9: GALAXIES, BLACK HOLES, GRAVITY WAVES, MATTER, THE FORCES OF NATURE, THE HIGGS BOSON, DARK MATTER, DARK ENERGY, AND STRING THEORY
1. Parker, Reference CC, particularly Chapter 4.
2. Bojowald. Reference FF, p. 19.
3. Toback, Reference U, p. 56.
4. Bojowald, Reference FF.
5. Greene, Reference AA, p. 19.
6. Ibid., p. 11.
7. Ibid., p. 20.
8. Michael S. Turner, “Origin of the Universe,” in Reference DD, p. 38.
9. Toback, Reference U, p. 122.
10. Greene, Reference AA, p. 22.
11. Toback, Reference U, p. 206.
12. Greene, Reference AA, p. 23.
13. Ibid., p. 21, p. 22.
14. Coles, Reference GG, p. 57.
15. Ibid., p. 58.
16. Ibid.
17. Ibid.
18. Ibid., p. 57.
19. Wikipedia, s.v. “Universe,” last modified September 11, 2016, https://en.wikipedia.org/wiki/Universe (accessed October 14, 2016).
20. Toback, Reference U, p. 125.
21. Ibid., p. 170.
22. Calculated as the distance in miles of the 13.2 billion light-years of the light's travel from the oldest stars that we have seen. Light-years given by David Toback in Reference U, p. 170.
23. Wikipedia, “Universe.”
24. Toback, Reference U, p. 211.
25. Ibid., p. 231.
26. The sizes of objects were mainly taken from Toback in Reference U, Chapters 2 and 3. The time frame in which they appeared is taken from the timeline of Turner's article “Origin of the Universe,” in Reference DD, pages 40 and 41.
27. Turner, in Reference DD, p. 40.
28. Ibid.
29. Richard P. Feynman, Robert B. Leighton, Matthew L. Sands, The Feynman Lectures on Physics, vol. 1 (Reading, MA: Addison-Wesley, 1963), pp. 52–11.
30. Turner, in Reference DD, p. 40.
31. Ibid.
32. Toback, Reference U, p. 211.
33. Ibid., p. 165.
34. Once again, for a good, readable description of gravity and four-dimensional space-time, I suggest that you read Chapter 4 of Barry Parker's book Einstein's Brainchild—Relativity Made Relatively Easy (Reference CC).
35. Toback, Reference U, pp. 170 and 236.
36. Ibid., p. 164.
37. Ibid., p. 188.
38. Ibid., p. 183.
39. John Gribbin, e-mail correspondence with the publisher regarding Quantum Fuzz, September 26, 2016.
40. Gribbin, Reference LL, p. 83.
41. In ibid., Gribbin writes:
An atomic nucleus can exist in what is known as its ground state, with minimum energy, or it can absorb certain precise amounts of energy (quantised, like everything else in the subatomic world) which raise it to different energy levels. Once “excited” in this way, it will, sooner or later, get rid of the extra energy, probably in the form of a gamma ray, and fall back to its ground state. The energy levels are like steps on a staircase, with nuclei jumping from one step to another (first up, then down) if suitably excited (like an excited child). Hoyle's insight was that an excited nucleus of carbon-12 could form from the collision of a helium-4 nucleus with a beryllium-8 nucleus, if (and only if) there was a step on the carbon-12 energy staircase corresponding to the combined energy of a beryllium-8 nucleus and the incoming helium-4 nucleus. It would be like tossing a ball from the bottom of a staircase with just the right speed for it to come to rest on a high step without bouncing; then, it could gently roll back down the stairs. This was the 7.65 MeV resonance that Hoyle predicted. If the resonance existed, the beryllium-helium interaction could manufacture carbon nuclei in the excited state, which could then radiate the excess energy away and settle into the ground state. But if the resonance did not exist, there would be no carbon, and since we are a carbon-based life form, we would not be here.
42. Toback, Reference U, p. 164.
43. Ibid., p. 187.
44. Ibid., p. 188.
45. Ibid., p. 160.
46. Ibid., p. 176.
47. Ibid., p. 189.
48. Parker, Reference CC, pp. 104 and 141.
49. Bortz, Reference B, p. 84.
50. Susskind, Reference BB, p. 118.
51. Hawking, Reference W, p. 87.
52. Toback, Reference U, p. 196.
53. Ibid., p. 4.
54. Ibid., p. 4.
55. Emily Conover, “Gravitational Waves Caught in the Act,” APS News 25, no. 3, March 2016, p. 4. https://www.aps.org/publications/apsnews/201603/waves.cfm (accessed October 14, 2016).
56. Ibid.
57. Hawking, Reference W, p. 105.
58. Ibid., p. 106.
59. Ibid., p. 10.
60. “The Swift Gamma-Ray Burst Mission,” NASA, July 6, 2016, http://swift.gsfc.nasa.gov/ (accessed October 14, 2016).
61. Susskind, Reference BB, p. 21.
62. I say that this was a “quiet” bombshell because, according to Susskind, it was only Hawking, Susskind, and Gerard ’t Hooft who realized the significance of what Hawking was saying. ('t Hooft would in 1999 share the Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman “for elucidating the quantum structure of the electroweak interactions.” Those are to be described briefly later in this chapter.)
63. Susskind, Reference BB, p. 91.
64. Wikipedia, s.v. “Holographic Principle,” last modified October 8, 2016, https://en.wikipedia.org/wiki/Holographic_principle (accessed October 14, 2016). This entry reads as follows: “The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a boundary to the region—preferably a light-like boundary like a gravitational horizon. First proposed by Gerard ’t Hooft, it was given precise string-theory interpretation by Leonard Susskind….”
65. BEC Crew, “Stephen Hawking Just Published a New Solution to the Black Hole Information Paradox: How Black Holes Can Erase Information, But Also Retain It,” Science Alert, January 11, 2016, http://www.sciencealert.com/stephen-hawking-just-published-new-solution-to-the-black-hole-information-paradox (accessed October 14, 2016). Dennis Overbye, “No Escape from Black Holes? Stephen Hawking Points to a Possible Exit,” New York Times, June 6, 2016, http://www.nytimes.com/2016/06/07/science/stephen-hawking-black-holes.html?_r=0 (accessed October 17, 2016).
66. Coles, Reference GG, p. 59.
67. Ibid., p. 60.
68. Ibid., p. 62.
69. Toback, Reference U, p. 156.
70. Ibid., p. 136, n. 2.
71. Ibid., p. 206.
72. Ibid., p. 211.
73. Turner, in Reference DD, p. 40.
74. Barnett et al., Reference HH, p. 214.
75. Toback, Reference U, p. 59.
76. Ibid., p. 61.
77. Wikipedia, s.v. “Gravitational Lens,” last modified October 12, 2016, https://en.wikipedia.org/wiki/Gravitational_lens (accessed October 14, 2016).
78. Ibid.
79. Toback, Reference U, p. 168.
80. Ibid., p. 225.
81. Ibid., p. 210.
82. Ibid., p. 211.
83. Wikipedia, s.v. “Supernova Cosmology Project,” last modified July 25, 2016, https://en.wikipedia.org/wiki/Supernova_Cosmology_Project (accessed October 14, 2016).
84. Turner, in Reference DD, p. 40.
85. Fred Bortz provides a very nice short summary of the development of these machines and the sequence of discovery achieved with them in his book for young readers (which I find to be a quick, informative read well suited to adults) Understanding the Large Hadron Collider, which is part of his series Exploring the Subatomic World (Reference EE).
86. Barnett et al., Reference HH, p. 134.
87. Ibid., p. 124.
88. Bortz, Reference EE, p. 53, mentions these planned circular colliders and the International Linear Collider to be constructed in Japan and presently in design.
89. Except where noted otherwise, this data is taken from Wikipedia, s.v. “Colliders,” last modified October 1, 2016, https://en.wikipedia.org/wiki/Collider (accessed October 14, 2016).
90. Bortz, Reference EE, p. 53. This collider is described as a Chinese “Higgs factory.”
91. Ibid. The “Very” Large Hadron Collider is just in the early stages of discussion.
92. Wikipedia, s.v. “Large Hadron Collider,” last modified October 12, 2016, https://en.wikipedia.org/wiki/Large_Hadron_Collider (accessed October 14, 2016).
93. Barnett et al., Reference HH, p. 226.
94. Ibid.
95. Michael Riordan, Guido Tonelli, and Sau Lan Wu, “The Higgs at Last,” in Reference DD, p. 4.
96. Barnett et al., Reference HH, p. 215.
97. Ibid., p. 212.
98. Many particles of the Standard Model, including quarks, neutrinos, and the Higgs boson, are separately described in a very interesting, readable, and well-illustrated series of books for young people: Exploring the Subatomic World, by Fred Bortz (Reference EE).
99. Bose was known for early work in the 1920s on quantum mechanics. He suggested a “Bose-Einstein condensate” that we now know explains superconductivity, as described in Chapter 19.
100. Wikipedia, s.v. “Elementary Particle,” last modified October 11, 2016, https://en.wikipedia.org/wiki/Elementary_particle (accessed October 12, 2016).
101. Lincoln, “The Inner Life of Quarks,” in Reference DD, p. 15.
102. Ibid., p. 15.
103. Bortz, Reference B, p. 62.
104. Ibid., p. 143.
105. Ibid., p. 62.
106. Ibid., p. 72.
107. Martin Hirsch, Heinrich Päs, and Werner Porod, “Ghostly Beacons of New Physics,” in Reference DD, p. 25.
108. Bortz, Reference B, p. 147.
109. Barnett, et al., Reference HH, p. 212.
110. Bortz, Reference B, p. 145.
111. Barnett et al., Reference HH, p. 212.
112. Ibid.
113. Bortz, Reference B, p. 92–95.
114. Feynman gave a series of lectures to the general public in which he described this method and some of these diagrams. These lectures have been simplified and re-presented in his book QED—The Strange Theory of Light and Matter (Reference Q).
115. Bortz, Reference B, p. 148.
116. Ibid.
117. K. C. Cole, “The Strange Second Life of String Theory,” Quanta Magazine, September 15, 2016, https://www.quantamagazine.org/20160915-string-theorys-strange-second-life/ (accessed October 17, 2016).
CHAPTER 10: INTRODUCTION TO PART FOUR
1. I mean “simple” in the sense that one central concept of the atom explains everything around us.
2. According to Wikipedia, s.v. “Eric Scerri,” last modified September 27, 2016 (accessed October 15, 2016), Scerri is a lecturer at the University of California, Los Angeles, the founder and editor in chief of Foundations of Chemistry (an international peer -reviewed journal), and a world authority on the history and philosophy of the periodic table. In his book The Periodic Table, Reference D, p. 247, Scerri writes: “The aim of this chapter has not been to decide whether or not the periodic system is explained by quantum mechanics tout court, since the situation is more subtle,” essentially defining “reduction” in this context with his words “the periodic system is explained by quantum mechanics tout court.” He goes on to say, “It is more a question of the extent of reduction or extent of explanation that has been provided by quantum mechanics. Whereas most chemists and educators seem to believe that the reduction is complete, perhaps there is some benefit in pursuing the question of how much is strictly explained from the theory. After all, it is hardly surprising that quantum mechanics cannot yet fully deduce the details of the periodic table, which gathers together a host of empirical data from a level far removed from the microscopic world of quantum mechanics.”
3. Wikipedia, “Chemical Element”, last modified October 13, 2016, accessed October 15,2016.
4. Reference D, starting on pp. 183, and p. 205.
CHAPTER 11: ENERGY, MOMENTUM, AND THE SPATIAL STATES OF THE ELECTRON IN THE HYDROGEN ATOM
1. Actually, it is the square of the angular momentum, the angular momentum times itself, that is quantized, and this produces the quantum numbers ℓ that we discuss here. The square of the angular momentum = ℓ (ℓ +1) (h/2π)2. There it is: Planck's constant again!
2. The z component of angular moment is mh/2π, and “m” is confined to the range –ℓ to +ℓ because the vector for m is only that part of the vector for ℓ that lies in the direction of a magnetic field. Since it is only part of the vector for ℓ, m must always be equal to or smaller in magnitude than ℓ. This range for m also results directly from the solutions to Schrödinger's equation: there simply are no solutions which have m outside of this range.
CHAPTER 12: SPIN AND MAGNETISM
1. This is described in Leighton, Reference F, p. 668, as “one of the greatest successes of theoretical physics.”
2. In the same work, Dirac also predicted the existence of the positron, which is like the electron but with positive rather than negative charge. The positron was subsequently discovered. It was the first manifestation of what has come to be called “antimatter,” so called because an electron contacted by a positron would annihilate both of them with the release of great energy. Richard Feynman jokingly carried the idea of antimatter to an extreme, as described in the subsection on antimatter in Chapter 9.
3. And there it is again: Planck's constant; independently the result of the Dirac's calculations!
4. For a more complete description of spin and magnetic moments, see Leighton, Reference F, p. 185.
CHAPTER 13: EXCLUSION AND THE PERIODIC TABLE
1. Leighton, Reference F, Figure 7-5, p. 251.
2. This is further explained in Chapter 14. To the left because the fewer the number of electrons beyond a completed p block subshell, the less tightly each electron is held and the more easily it is lost in reaction. Farther up because, for each atom, exclusion prevents the electrons from occupying the more tightly binding lower energy states, and because the outer, higher energy states (those available particularly to electrons in the heavier atoms farther up the column) are not very tightly binding. That is because the outermost electrons in these left-side atoms are largely screened (by completely filled inner shells of electrons) from the attraction of the protons in the nucleus. The converse applies to the atoms of those elements to the right in the table, whose atoms become more acquisitive in trying to completely fill an energy shell the closer the shell is to being filled, that is for elements further to the right. In this case, the outermost electrons in the lighter atoms have available to them lower and more tightly binding energy states that are closer to the nucleus, and so the atoms are more acquisitive and more reactive for elements located farther down in these right-side columns of the table. These arguments do not apply to the atoms of the inert elements in the rightmost column of the table.
CHAPTER 15: A FEW TYPES OF CHEMICAL BONDS, FOR EXAMPLE
1. The importance of quantum mechanics in providing an understanding of the electronic structure for chemistry is underscored in some modern general chemistry texts, such as Reference H. This text begins its first chapter with a description of Schrödinger's equation and its solutions for the hydrogen atom, which are further utilized to understand the electron structure of the rest of the elements and the formation of molecules.
2. The electronic structure of the isolated carbon atom consists of two occupied spatial 1s states (one with an electron having plus spin and one with an electron having minus spin), two occupied spatial 2s states, and two different half occupied spatial 2p states. But the energies of the 2s and 2p states are so close to each other that these states will sometimes combine, that is, hybridize, to lower overall energies in bonding with other atoms. When they do this, they form the same total number of total states, but some of the spatial states are differently shaped and oriented at different angles than were the spatial states from which they were formed.
3. Pauling, Reference P, p. 111.
4. Private communication with L. Howard Holley, with reference to Martin Chaplin, “Water Structure and Science,” London South Bank University, June 22, 2016, http://www1.lsbu.ac.uk/water/ (accessed October 16, 2016).
5. This hybridization is somewhat similar to that which occurs in the carbon atom, as described above.
CHAPTER 17: INSULATORS AND ELECTRICAL CONDUCTION IN NORMAL METALS AND SEMICONDUCTORS
1. Kittel, Reference V, p. 159. The resistance in a wire or circuit is measured in ohms, which is defined as the volts applied to a wire or circuit divided by the current, as measured in amperes, that flows as a result. The intrinsic resistance to the flow of electrical current in a metal, insulator, or semiconductor is usually measured in ohm-cm, which when multiplied by the length of the material and divided by the area of its cross section provides a measure of the resistance of an actual piece of material.
2. Schrödinger's solution for free electrons is well presented in Chapter 6 of Kittel, Reference V.
3. The number of states occupied up to the Fermi level is directly proportional to the number of atoms in the metallic specimen being considered, literally billions even for a small sample. The bigger the specimen, the smaller the energy difference between the successive energy levels, and the more states available up to any energy level. But at the same time, the number of atoms and electrons is increased, so that the states are occupied by additional electrons to the same Fermi level. Thus the same Fermi level and related physical properties are produced, independent of the size of the metallic specimen.
4. Chapter 7 of Kittel, Reference V.
5. See Ibid., p. 128.
CHAPTER 18: NANOTECHNOLOGY AND INTRODUCTION TO PART FIVE
1. In Rosenblum, Reference X, p. 116.
2. Katherine Bourzac, “Nano-Architecture,” MIT Technology Review 118, no. 2 (March/April): 35.
3. Julie Shapiro, “Breakthrough: ‘A Metal That's (Almost) Lighter Than Air,’” Time, November 2, 2015, p. 25.
CHAPTER 19: SUPERCONDUCTORS I
1. This was John Bardeen's second Nobel Prize. His first is noted in Chapter 23. An avid golfer, he was said to have remarked, as noted in Bortz, Reference B, p. 130: “Well, perhaps two Nobels are worth more than one hole in one.” You may wish to browse further through this excellent history for additional short biographies of many of the physicists mentioned in Quantum Fuzz.
2. “High-temperature” is a relative term. More recently developed “high-temperature” superconductors operate superconducting to temperatures as high as 138 degrees Kelvin,* high enough to be cooled in liquid nitrogen, which boils at 77 Kelvin, and much higher than those of the superconductors presently used in MRI magnet systems. But as discussed in part in Chapter 24, the issue is whether they can be produced in practical forms, and at what cost. (*Wikipedia, s.v. “High-Temperature Superconductivity,” last modified October 20, 2016, https://en.wikipedia.org/wiki/High-temperature_superconductivity (accessed October 22, 2016).
3. Another interesting and somewhat-similar quantum phenomenon, but one of no practical importance at least for now, is superfluidity. Liquid helium, at temperatures just 4 Fahrenheit degrees [2 Celsius degrees] above the absolute zero, transitions into a state that exhibits a loss of viscosity and a much increased ability to conduct heat, in analogy with the ability of superconductors to conduct electricity without resistance. This so-called superfluid helium is marked by a strange quiescence. It boils without producing any bubbles, and it will climb over the walls of its container to reach lower levels, providing only that all surfaces are maintained at sufficiently low temperatures.
4. “Go Ahead for Japanese Maglev,” Maglev, May 16, 2011, http://www.maglev.net/news/go-ahead-for-japanese-maglev (accessed October 24, 2016).
5. Rosenblum and Kuttner, Reference X, p. 126.
6. MRI was originally called “Nuclear Magnetic Resonance (NMR)” because it is the resonance of radio waves of just the right frequency (radio-wave photon energy) that (when transmitted through the body) produces transitions of spins in the nuclei of atoms (e.g., phosphorous atoms) in the body to higher-energy spin states. (Because some patients associated the word “nuclear” with radioactivity, the manufacturers choose to call the devices “MRI machines.”) When these spins then transition back down to lower-energy spin states, they emit radio waves whose frequencies contain information on the type and health of the tissues from which they are emitted. Since the central frequency of these waves depends on the magnetic field that the body is in, by setting the main superconducting background field and then varying it in x, y, and z directions using smaller magnets, the location of these transmitted bits of information can be “tagged” (by small frequency shifts) as to their x, y, and z locations. When this information is assembled using computers, it can be used to provide images showing the location of various tissues and their state of health. The pulsing of these x, y, and z magnets on and off causes sudden forces when they are attracted to the high magnetic field of the superconducting magnet, and one hears the sudden mechanical impacts of these forces as loud staccato bursts or clicks, a more spaced-out series of clicks, or a short, coarse, rumble.
7. A sense of the magnitude of magnetic fields will be provided in Chapter 21.
8. This is not one of the louder types of sounds of the sort described above, which come from the magnets of the machine itself.
9. SQUIDs use the quantum condition that the flux* of a magnetic field within a superconducting ring is quantized. (*Flux is the magnetic field strength times the area that the field passes through.) As each quantum of magnetic flux enters the ring, the ring produces an electrical voltage signal, so that the number of these quanta or even fractions of these quanta can be counted as a measure of the strength of the field. One can detect about two-millionths of a billionth of one tesla (2 × 10–15 T). For comparison, as noted before, a common approximate field used in MRI magnets and the maximum field achieved with ferromagnetic materials in motors and generators is about 2T, common refrigerator magnets produce about 0.2 T, and the earth's magnetic field is about 5 hundred-thousandths of a tesla (5 × 10–5 T).
10. Stefania Della Penna, Vittorio Pizzella, and Gian Luca Romani, “Impact of Superconducting Devices on Imaging in Neuroscience,” Superconductivity News Forum Global Edition (October 29, 2013), http://snf.ieeecsc.org/abstracts/cr36-impact-superconducting-devices-imaging-neuroscience (accessed September 15, 2016); and S. Della Penna, V. Pizzella, and G. L. Romani, “Impact of Superconducting Devices on Imaging in Neuroscience” (presentation of pre-published plenary paper CR36), Superconductivity News Forum Global Edition (January 17, 2014), http://snf.ieeecsc.org/abstracts/crp39-impact-superconducting-devices-imaging-neuroscience-0 (accessed September 15, 2016).
11. Leyna P. De Haro et al.,” Magnetic Relaxometry as Applied to Sensitive Cancer Detection and Localization,” Superconductivity News Forum Global Edition (July 2016), http://snf.ieeecsc.org/abstracts/st518-magnetic-relaxometry-applied-sensitive-cancer-detection-and-localization (accessed October 24, 2016).
12. Carl H. Rosner, Chairman and CEO of Cardiomag, private discussion with the author, September 16. 2016.
13. IEEE/CSC & ESAS European Superconductivity News Forum, no. 3 (January 2008).
14. Intelligence Advanced Research Projects Agency, “IARPA Launches Program to Develop a Superconducting Computer,” IARPA press release, December 3, 2014, through Superconductivity News Forum Global Edition, http://snf.ieeecsc.org/sites/ieeecsc.org/files/HE93_The%20C3%20IARPA%20Program_finally%20announcedfinal%20link.pdf (accessed October 24, 2016).
15. Oleg A. Mukhanov, “Recent Progress in Digital Superconducting Electronics,” Superconductivity News Forum Global Edition (July 2015), http://snf.ieeecsc.org/abstracts/crp54-recent-progress-digital-superconducting-electronics (accessed October 24, 2016).
CHAPTER 20: FUSION FOR ELECTRICAL POWER, AND LASERS ALSO FOR DEFENSE
1. Reported by Marin Lamonica in the magazine of the Institute for Electrical and Electronic Engineers, IEEE Spectrum (North America), April 2015, p. 12, and by Kevin Bulis, MIT Technology Review 118, no. 3 (May/June 2015): 13.
2. Lev Grossman, “A Star Is Born,” Time, November 2, 2015, p. 30.
3. David Kramer, “ITER Cost and Schedule Still Not Pinned Down,” Physics Today, January 2016, p. 30.
4. Thomas Rummel, Beate Kemnitz, Thomas Klinger, and Isabella Milch, “First Plasma in the Superconducting Fusion Device Wendelstein 7-X,” Superconductivity News Forum Global Edition (January 2016), http://snf.ieeecsc.org/sites/ieeecsc.org/files/documents/snf/abstracts/HP104_RummelTh_First%20plasma%20in%20W7-X_012016.pdf, and references therein (accessed October 24, 2016).
5. Grossman, “Star Is Born.”
6. Ibid.
7. Rachel Courtland, “Laser Fusion's Brightest Hope: The National Ignition Facility Houses the World's Most Powerful Laser. Is It Enough to Ignite a Fusion Revolution?” IEEE Spectrum, March 27, 2013, http://spectrum.ieee.org/energy/nuclear/laser-fusions-brightest-hope (accessed October 24, 2016).
8. This is about one thousand times as much power as the United States consumes, on average, at any moment. But, again, remember that power is the rate of delivery of energy, and the energy of these lasers is delivered in just four-billionths of a second. Were their energies delivered much more slowly, say, in one second, the power would still be substantial—about two megawatts—enough, if delivered at this rate continuously, to light a couple of thousand average homes.
9. Wikipedia, s.v. “National Ignition Facility,” last modified September 14, 2016, https://en.wikipedia.org/wiki/National_Ignition_Facility (accessed November 4, 2016).
CHAPTER 21: MAGNETISM, MAGNETS, MAGNETIC MATERIALS, AND THEIR APPLICATIONS
1. Diamagnetic substances are repelled from a place of high field to places of lower field, and the strength of the repulsion depends on how much the field changes with change in distance, what is called the field “gradient.”
2. The tesla is a Standard International, SI, mks (meter kilogram second), unit of what is called “magnetic induction,” what is commonly referred to as “magnetic field.” One tesla is equivalent to 10,000 gauss, where the gauss is a cgs (centimeter, gram, second) unit of this field.
3. Wikipedia, s.v. “Francis Bitter,” last modified July 14, 2016, https://en.wikipedia.org/wiki/Francis_Bitter (accessed October 21, 2016).
4. Solenoids are typically wound as contiguous turns of wire around a structural tube, with additional layers similarly wound back and forth over the first layer.
CHAPTER 22: GRAPHENE, NANOTUBES, AND ONE “DREAM” APPLICATION
1. Wikipedia, s.v. “Graphene,” last modified October 15, 2016, https://en.wikipedia.org/wiki/ Graphene (accessed October 21, 2016).
2. Ibid.
3. Ibid.
4. Warner et al., Reference JJ.
5. Andre K. Geim, “Atomic Scale Legos,” Scientific American 311 (November 18, 2014): 50–51.
6. “Introducing the Micro-Super-Capacitor: Laser Etched Graphene Brings Moore's Law to Energy Storage,” IEEE Spectrum, October 2015, pp. 41–45.
7. Katherine Bourzac, “Bend by Design,” Scientific American 311 (November 18, 2014): 19.
8. John Pavlus, “The Search for a New Machine,” Scientific American 312 (April 14, 2015): 58–63.
9. Wikipedia, s.v. “Graphite,” last modified October 21, 2016, https://en.wikipedia.org/wiki/ Graphite (accessed October 21, 2016).
10. Wikipedia, s.v. “Fullerene,” Wikipedia, last modified October 21, 2016, https://en.wikipedia.org/wiki/ Fullerene (accessed October 21, 2016).
11. Wikipedia, s.v. “Carbon Nanotube,” last modified October 19, 2016, https://en.wikipedia.org/wiki/Carbon_nanotube (accessed October 21, 2016).
12. Ibid.
13. Ibid.
14. Ibid.
15. “Konstantin E. Tsiolkovsky,” Aeronautics Learning Laboratory for Science Technology, and Research (ALLSTAR) Network, March 12, 2004 (retrieved June 10, 2015).
16. Bob Hirschfeld, “Space Elevator Gets Lift,” TechTV, G4 Media, January 31, 2002, https://web.archive.org/web/20050608080057/http:/www.g4tv.com/techtvvault/features/35657/Space_Elevator_Gets_Lift.html (archived from the original on June 8, 2005; retrieved September 13, 2007): “The concept was first described in 1895 by Russian author K. E. Tsiolkovsky in his ‘Speculations about Earth and Sky and on Vesta.’”
17. Wikipedia, s.v. “Space Elevator,” last modified October 11, 2016, https://en.wikipedia.org/wiki/Space_elevator (accessed October 21, 2016).
18. Wikipedia, s.v. “Carbon-Fiber-Reinforced Polymer,” Wikipedia, June 23, 2016, https://en.wikipedia.org/wiki/Carbon-fiber-reinforced_polymer last modified October 20, 2016(accessed October 21, 2016).
19. Wikipedia, s.v. “Boeing 787 Dreamliner,” last modified October 20, 2016, https://en.wikipedia.org/wiki/Boeing_787_Dreamliner (accessed October 21, 2016).
20. Boeing used a new design of lithium-ion battery in its planes, with the result that it overheated and threatened to cause fires. The plane was grounded for a time. Boeing redesigned the battery and overcame the problem. The lithium-ion battery is an excellent example of innovation in chemistry and materials science. It effectively uses that element with the highest per unit weight concentration of electrons outside of a filled valence shell to make a light and powerful accessory for electrical and electronic devices, including electric and hybrid electric vehicles, and now the Dreamliner.
21. Originally available at the IMAX's of the National Air and Space Museum in Washington, DC, and the Henry Ford Museum in the Detroit area (among others); this movie is now available on 3-D Blu-ray and DVD. A trailer for the movie can be viewed on the internet at http://www.youtube.com/watch?v=dpoxMVw1EM4.
22. Wikipedia, “Boeing 787 Dreamliner.” Wikipedia, s.v. “Airbus A350 XWB,” last modified October 21, 2016, https://en.wikipedia.org/wiki/Airbus_A350_XWB (accessed October 21, 2016).
CHAPTER 23: SEMICONDUCTORS AND ELECTRONIC APPLICATIONS
1. There are many different types of transistors, and they operate using various physical mechanisms. I have described just one type, but they all have this characteristic of having the input to one terminal control the flow of current through the other terminals.
2. Reference X, p. 119.
3. Charles Q. Choi, “Nitrogen Supercharges Super-Capacitors,” IEEE Spectrum (North America), February 2016, p. 14.
4. Ibid., p. 9.
5. Ibid., p. 12.
6. “Survival in the Battery Business,” MIT Technology Review 118, no. 4, July/August 2015, p. 35.
7. “SolarCity's ($750 million) Gigafactory,” MIT Technology Review 119, no. 2, March 2016, p. 54.
8. IEEE Spectrum (North America), September 2016, p. 9.
CHAPTER 24: SUPERCONDUCTORS II
1. Liquid nitrogen is available as a by-product of the commercial separation of oxygen from the air by liquefaction. It costs about as much as tomato juice. The boiling point of liquid nitrogen is 77 Kelvin, fully a quarter of the way from absolute zero toward normal room temperatures at around 300 Kelvin.
2. René L. Flukiger, “Advances in MgB2 Conductors,” Superconductivity News Forum Global Edition, October 2014, http://snf.ieeecsc.org/abstracts/crp46-advances-mgb2-conductors-annotated-plenary-slide-presentation (accessed October 24, 2016), on MgB2 wires and the short review of applications therein.
3. Measuring in megavolt-amperes (MVA) is a way of taking into account both resistive and reactive components in the flow of power. Resistive power is like that used to operate incandescent light bulbs or toasters in our homes. Note that one MVA is one megawatt only for resistive power. Reactive power usually involves energy transferred in and out of electric or magnetic fields, and the latter occurs particularly in motors and transformers. One MVA is the time-averaged approximate power needed for about one thousand average American homes.
4. A 10 MVA generator was subsequently built and tested at GE, and other generators have been built and tested variously around the world, most notably in Japan where 70 MVA and then 200 MVA generators were constructed and tested in the 1980s. These machines are of a commercial size for efficient power generation and begin to approach the size of the largest generators in commercial operation, typically on the order of 1000 MVA. But the power industry has yet to install one of these machines for commercial use. For context refer to the section “A Comment on Energy Resources and Global Warming,” which follows this chapter.
5. Mark Stemmle, Frank Schmidt, Frank Merschel, and Matthias Noe, “Ampacity Project—Update on World's First Superconducting Cable and Fault Current Limiter Installation in a German City Center,” Superconductivity News Forum Global Edition, October 2015, http://snf.ieeecsc.org/abstracts/stp475-ampacity-project-%E2%80%93-update-world%E2%80%99s-first-superconducting-cable-and-fault-current (accessed October 24, 2016).
6. For example, faults caused by tree branches (or unlucky squirrels) that short across power lines (making an electrical connection phase-to-phase or phase-to-ground). These faults often cause lights to blink or go out until the fault is cleared.
7. Electrical power is the rate at which electrical energy is generated, transmitted, or utilized. At any instant it is just the phase-to-phase (or, in the home, phase-to-neutral) voltage times the phase-to-phase (or phase-to-neutral) current flow. Because power lines would need to be unreasonably thick and heavy to carry the currents required by tens of thousands of homes at the 110-volt home level, transformers are used to first step up the voltages (from generators) to very high levels (hundreds of thousands of volts) so that only small currents and small-diameter, lightweight lines are needed to carry the same power, tower to tower, across the country. Then large very high voltage transformers, and subsequently, many medium-power transformers are used to step the voltage back down at substations for the distribution to neighborhoods. And then there are many more even smaller, and then smaller yet pole-mounted, transformers to successively step down the voltage to the level that we use in our homes.
8. As for preceding ASC conferences, those papers presented are reviewed and published in the IEEE Transactions on Applied Superconductivity. For example, those for the 2012 conference, which was held in Portland, Oregon, are in vol. 23, no. 3 of these transactions.
APPENDIX A
1. The distance from positive crest to the next positive crest is the same for both the E field and B field sine waves shown in sFigure A.1(c), and this distance is defined as the wavelength, w, of the electromagnetic wave. In the classical view of the electromagnetic wave, the crest value (the amplitude) can have any value down to zero, and the energy of the wave can correspondingly have any value down to zero. But, actually, electromagnetic energy comes in indivisible chunks called quanta. And the energy of each quantum is related to the wavelength of the wave (or its equivalent frequency).
APPENDIX B
1. We now know that the forming of elements from one or more others can happen by nuclear fission or fusion, not by chemical processes. (This is discussed in Chapter 20.)
2. In this book I will often be referring to material written by Eric R. Scerri. Professor Scerri teaches chemistry as well as history and philosophy of science at UCLA. He is the editor in chief of the journal Foundations of Chemistry. Here I cite from his book The Periodic Table (Reference D, p. 45).
3. Ibid., p. 112.
4. The table in Scerri, Reference D, p. 112, has already been redrawn. It's not clear whether the Roman numerals are from Mendeleev or Scerri.
5. Ibid., starting at the bottom of page 112.
6. Kean, Reference R, p. 49.
7. Ibid., p. 50.
8. Scerri, Reference D, p. 101.
9. Ibid., p. xiii.
APPENDIX C
1. Reference Z, p. 159–68.
2. Ibid., p. 161.
3. Philip Schindler et al., “A Quantum Information Processor with Trapped Ions,” New Journal of Physics15 (August 14, 2013): 123012, http://arxiv.org/abs/1308.3096 (accessed October 24, 2016).
4. Nuclear magnetic resonance is the key physical process utilized in the medical diagnostic tool MRI (magnetic resonance imaging). “Nuclear” was considered to be too frightful a word for the naming of this device, the construction and operation of which is described in Chapter 19.
5. Lieven M. K. Vandersypen et al., “Experimental Realization of Shor's Quantum Factoring Algorithm Using Nuclear Magnetic Resonance,” Nature 414, no. 6866 (December 20–27, 2001): 883–87.
6. Nanyang Xu et al., “Quantum Factorization of 143 on a Dipolar-Coupling NMR System,” Cornell University Library, arXiv:1111.3726 (November 16, 2011).
7. Referring to dimensions on the order of one nanometer = 10–9 meters = one millionth of the thickness of a dime, on the scale of the sizes of atoms.
8. Michelle Simmons, “Quantum Computing in Silicon and the Limits of Silicon Miniaturization—Michelle Simmons,” YouTube video, 43:27, from part of discussion meeting on advances in graphene, Majorana fermions, and quantum computation, presented at the International Centre for Theoretical Sciences at the Tat Institute of Fundamental Research, posted by International Centre for Theoretical Sciences, May 22, 2013, https://www.youtube.com/watch?v=gDi3Jl6PuVc (accessed September 16, 2016). This presentation was made as a part of a working discussion group between physicists and materials scientists in this field of work. It is highly technical but worth watching not only for the presentation of the history of development but also just to get an idea of the complexity of the physical systems considered and the scientific tools that are required both to make and characterize materials.
9. In one very much nonstandard part of chip fabrication, the electrostatic attraction of the needlepoint tip of a scanning tunneling microscope (STM) is used for the selective removal of just six adjacent atoms from a protective single-atom-thick layer of hydrogen deposited on the silicon surface. Subsequent exposure to phosphine gas and heating then results in the substitution of just one phosphorous atom for one of the silicon atoms that was exposed by the hydrogen removal. This forms a quantum dot.
10. Michelle Simmons, “Practical Quantum Computing Applications” (public presentation given at Science at the Shine Dome under the auspices of the Australian Academy of Sciences, session “Atomic-Scale Electronics”), the speech is available at “Atomic-Scale Electronics for Quantum Computing: Prof. Michelle Simmons—Science at the Shine Dome 15,” YouTube video, 14:42, posted by the Australian Academy of Science, May 28, 2015, https://www.youtube.com/watch?v=hg2UUdQm26s&index=7&list=PL9DfJTxCPaXIJZgp6kBprILssq_AEAnY8 (accessed September 16, 2016).
11. All photons are electromagnetic in nature and are polarized so that their tiny electric fields alternate in time in one direction in space, as illustrated in Figure A.1(c) of Appendix A, with related discussion. All polarization possibilities can be represented as the combination of any two perpendicular polarization states, for example, vertical and horizontal polarizations.
12. One particular logic gate, the CNOT gate (not possible with classical bits), operates by flipping the state of a target qubit only if (for example) a second control qubit is in a 1 (as opposed to a 0) state. What makes this process special in another way is that the two qubits can become entangled in the CNOT operation, linked together to represent any one of their four so-called Bell states, regardless of how far the qubits may later become physically separated from each other.
13. Reference Z, p. 161.
14. SQUIDs have also been used, for example, for the detection of very small magnetic fields as a way of monitoring heart function, as described in Chapter 19.
15. M. Steffan, D. P. DiVincenzo, J. M. Crow, T. N. Theis, and M. B. Ketchen, “Quantum Computing: An IBM Perspective,” IBM Journal of Research and Development 55, no. 5, paper 13.
16. Press release issued on D-Wave.com by D-Wave: The Quantum Computing Company, “D-Wave Systems Breaks the 1000 Qubit Quantum Computing Barrier,” D-Wave Systems, Inc., June 22, 2015, http://www.dwavesys.com/press-releases/d-wave-systems-breaks-1000-qubit-quantum-computing-barrier.
17. Low temperatures are conveniently represented in Celsius-sized units, but on a Kelvin scale between absolute zero (the lowest temperature attainable), zero degrees Kelvin, and the temperature at which ice freezes, 273 degrees Kelvin. These SQUID-based computers typically operate close to one degree Kelvin, that is, one degree above absolute zero.
18. Jeremy Hsu, “Google's First Quantum Computer,” posted September 12, 2014, published in Superconductivity News Global Edition, September 22, 2014, http://snf.ieeecsc.org/pages/googles-first-quantum-computer (accessed October 24, 2016); and “Progress in Quantum Computer Error Correction,” Superconductivity News Global Edition, June 2, 2014, http://snf.ieeecsc.org/pages/progress-quantum-computer-error-correction (accessed October 24, 2016).
19. Lillian Childress, Ronald Walsworth, and Mikhail Lukin, “Atom-like Crystal Defects: From Quantum Computers to Biological Sensors,” Physics Today, October 2014, pp. 38–43.
20. Ibid., p. 41.
APPENDIX D
1. Richtmyer, Reference G, p. 167.
2. Remember that an atom in its ground state is an atom with all of its lowest energy states occupied by electrons, only one electron per combined spin and spatial state, as required by exclusion.
3. One way that the radius of an atom of an element can be determined is by the diffraction of x-rays from a crystal of that element. At certain angles, x-rays are reflected from the crystal with increased intensity in a way that depends on the wavelength of the x-rays and the spacing between the atoms in the crystal.
4. Though sometimes zinc, cadmium, and mercury are not considered transition metals.