touch-activated computer screens
Townes, Charles H.
transformers, electrical
Transformers (2007)
transistors
transmission of power
transmutation
transportation
automobiles
and energy storage
and jet packs
levitating trains
transporters
tritium
Trokel, Stephen
Twain, Mark
20Leagues Under the Sea (Verne)
Uhlenbeck, George
ULTIVAC
ultraviolet catastrophe
ultraviolet light
and beta rays
and invisible writing
and lasers
and phosphorescence
uncertainty principle
and conductivity
described
and helium
and matter wave equations
and nanostructured materials
and quantum mechanical wave functions
and radioactivity
and semiconductors
UNIVAC (UNIVersal Automatic Computer)
University of Alabama
University of Heidelberg
University of Houston
University of Pennsylvania
uranium
half life of
and nuclear fission
and radioactive decay
and stellar fusion
and the strong force
U.S. Department of Defense
U-238 Atomic Energy Lab
vacuum tubes
valence electrons
Verne, Jules
Village of the Damned (1960)
viscosity
War of the Colossal Beast (1958)
The War of the Worlds (Wells)
warfare. See also nuclear weapons
Warren, Ken
waste heat
Watchmen (Moore and Gibbons). See also Dr. Manhattan (Jonathan Osterman)
water
wave functions
and atomic spectra
and Bose-Einstein condensates
and de Broglie matter waves
and Dr. Manhattan
and intrinsic field
and quantum computers
and quantum entanglement
and Schrödinger’s equation
and spin=0 particles
and superconductors
and transition rates
wave-particle duality
wavelengths
wavepackets
weak force
Wells, H. G.
Werthem, Fredric
Whitmore, James
Wieman, Carl
Wilson, Edward O.
Wolff, Th.
Woman in the Moon (1929)
World Health Organization
“The World of a Hundred Men,”
The World Set Free (Wells)
World War I,
World War II,
World Wide Web
World’s Finest
wrist phones
X: The Man with the X-ray Eyes (1936)
X-Factor
X-Men
X-ray spectroscopy
X-rays
discovery of
and electromagnetic waves
and electron-electron repulsion
and the exclusion principle
and interference patterns
and microscopes
and radioactivity
and the ultraviolet catastrophe
X-ray vision
Xavier, Charles
Xavier, James
Zeilinger, Anton
zero-point energy
PHOTO CREDITS
The copyrighted DC Comics, Marvel Comics, Gold Key Comics, Tribune Media Syndicate, King Features Syndicate, Experimenter Publishing, Stellar Publishing, Teck Publishing, and Dille Family Trust illustrations in this book are reproduced for commentary, critical, scientific, and scholarly purposes. The copyright information and dates adjacent to the illustrations refer to when the illustrations were first published.
All line drawings copyright James Kakalios and Christopher Jones.
Figure 21: Photograph by Alan Richards, courtesy of AlP Emilio Segre Visual Archives.
Figure 25: Data from Figure 1 from “The Natural Distribution of Tritium,” Sheldon Kaufman and W. F. Libby, Physical Review 93, p.1337 (1954); http://link.aps.org/abstract/PR/v93/p 1337.
The copyrights and trademarks in the Challengers of the Unknown, June Robbins, ULTIVAC, Felix Hesse, Floyd Barker, the Atom, Wonder Woman, Plastic Man, Green Lantern, Ken Warren, Dr. Manhattan, Jon Osterman, and related logos and indica are owned by DC Comics Inc.
The copyrights and trademarks in Groot, Leslie Evans, Evans’s wife, town sheriff, bystander, and related logos and indica are owned by Marvel Entertainment Group Inc.
The copyrights and trademarks in Dr. Solar, Dr. Clarkson, and related logos and indica are owned by Random House Inc.
The copyrights and trademarks in Dick Tracy and Sam Catchem, and related logos and indica, are owned by Tribune Media Syndicate Inc.
The copyrights and trademarks in Dagwood Bumstead, dog Daisy and puppies, Alexander (Junior) Bumstead, Cookie Bumstead, Mandrake the Magician, and related logos and indica are owned by King Features Syndicate Inc.
The copyrights and trademarks in Buck Rogers and Wilma Deering, and related logos and indica, are owned by Dille Family Trust Inc.
The cover illustrations of Amazing Stories, August 1928, December 1936; Science Wonder Stories, February 1930; Air Wonder Stories, April 1930; and related logos and indica are owned by their respective copyright holders.
1 Seriously! See Chapter 21.
2 Sorry, ladies, but I’m already married!
3 The largest of the chain of Marquesas Islands in what was known as French Polynesia.
4 That is, our discussion will employ a Quentin Tarantino-esque description of quantum physics—namely, answers first, then questions.
5 In which case, at least, you won’t have to wonder why you aren’t invited to more parties!
6 As light from the sun reaches us through the vacuum of empty space, electromagnetic waves are unique in not requiring a medium in which to propagate.
7 When a nucleus emits an alpha particle, it transmutes into another element, as discussed in detail in Section 3.
8 George Gamow, brilliant physicist and famed practical joker, once added Hans Bethe (pronounced “beta”) as a coauthor of a paper he wrote with his graduate student Ralph Alpher, so that the scientific citation list of authors would read, Alpher, Bethe, Gamow.
9 For an oil slick on water, the thickness needs to be one-fourth the wavelength of light for constructive interference, while for a glass slab with air above and below, the constructive interference criteria call for the thickness to be one-half the wavelength. The difference, involving phase changes at the top reflection surface, is not important for the discussion here.
10 Goddard correctly pointed out that any gravity screen as suggested by Brush would enable one to lift a large mass with little effort. Upon removal of the gravity shield, the mass would then fall as any normal weight and thus could provide a work output greater than the energy required to lift the mass, thereby violating the law of conservation of energy.
11 We must also look for the police!
12 While technically “soot” refers to particulates formed from the incomplete combustion of fuels such as coal, oil, or wood, and is mostly carbon but may contain other elements depending on the nature of the burning material, here I am using the term as a shorthand for “amorphous carbon.”
13 Certainly not if you want them to remain your beloved!
14 There may be a slight difference, owing to technicalities. The electrons scatter most strongly from the top few atomic planes, while the X-rays can penetrate deeper into the crystal. This is because the electron-electron repulsion that governs th
e electron scattering is much stronger than the photon-electron interactions. If the crystal structure of the top surface differs from that of the bulk crystal, a different pattern may be observed. But this is a detail that does not affect the basic point of wave-particle symmetry.
15 We’ll soon see that, although it is a useful metaphor, we should not take the “spinning top” picture literally.
16 When I described Asimov’s suggestion in my 2005 book The Physics of Superheroes, it caught the attention of Tony Stark! In Marvel Comics’s Civil War Files, consisting of background notes dictated by Iron Man’s alter ego, under an entry for “Goliath,” one finds: “My first introduction to Bill Foster (Goliath, Giant-Man, Black Goliath) was his remarkable paper with Jim Kakalios on extra-dimensional manipulations of Planck’s constant, and I quickly had them hired by Stark Enterprises.” Upon reading this, I realized that I needed to update my resumé!
17 This argument still holds, even with the recognition that neutrons (and protons) are themselves composed of electrically charged quarks. As explained, the quarks would have to be rotating faster than light speed to account for the observed magnetic field of these composite particles.
18 Many physicists, when pressed, would confess that the notion of the electron they carry around in their heads involves a particle with a large arrow protruding from it, pointing either “up” or “down,” whenever “spin” comes up. Thus, if you find the image of an electron spinning like a top too compelling to give up—you’re just thinking about it the way we professionals do!
19 Here physicists seem to have anticipated superhero comic books. In X-Factor # 72, when Guido, a superstrong member of a team of superpowered mutants, realized that nearly all other such teams have at least one member whose superpower involves superstrength, he adopted the code name Strong Guy.
20 Some accelerators use electrons or atomic nuclei instead of protons—and some accelerate particles in a straight line—but the idea is the same.
21 In such a world, to quote Krusty the Clown, “the living would envy the dead.”
22 Comic books back in the 1950s, at the height of Fredric Werthem’s Seduction of the Innocent scare, may indeed have been corrupting young readers’ minds (after all, isn’t that what literature is supposed to do?), but one could hardly complain that they weren’t improving readers’ vocabulary or reading comprehension.
23 I’m not kidding! While other pioneers of quantum theory such as Werner Heisenberg and Paul Dirac required extreme solitude in order to develop their theories, Schrödinger needed a more . . . stimulating environment. Historians of science debate to this day the identity of the woman (definitely not his wife!) who kept him company over a long Christmas holiday break, at a friend’s chalet in the Swiss Alps, when he successfully constructed the matter-wave equation that now bears his name. As I tell my students of modern physics, if you are going to learn quantum mechanics, you must remember one key principle: Don’t be a playa’ hata’!
24 Since the mathematical convention is that a positive number multiplied by a negative number yields a negative number, and the product of two negative numbers is a positive number, there is no real number that, when multiplied by itself, would yield a negative number. We can certainly imagine such numbers, but they are not in the set of real numbers we deal with. They are hence termed “imaginary” and are defined to be represented by the lower case letter i, so i × i = -1.
25 We use the letter V for the potential, as the letter p is reserved for mathematical descriptions of the mo-mentum! Sometimes it seems like we physicists deliberately make the equations harder than they need to be.
26 The notation Ψ* is mathematical code that says to change all the terms with i in Ψ to -i. As i × i = -1, (-i) × i = -1 × (i × i ) = -1 × -1 = +1, and we will have a positive, real function in Ψ2. Those who recall their algebra may note that Ψ is actually a “complex” number (Ψ = a + ib, where a and b are regular numbers), so that I should technically use the notation |Ψ|2 instead of Ψ2. We’ll stick with Ψ2, as for us the important point is that Ψ2 is a real, positive number.
27 Technically the average is 50.5 in this case—but you get the idea.
28 I apologize for that joke.
29 At Mars’s closest point to our planet.
30 A nonlinear equation would be something like Ψ2 = 2Ψ, which is a true statement for Ψ = 2, but not foraΨvalue ten times bigger, that is, Ψ = 20.
31 The heat emitted by the reactor causes the water to boil, and the resulting steam turns turbines in the dynamo that generates electricity.
32 And indeed, this student is Charles Misner, who has made many important contributions to the study of cosmology and gravitation over his distinguished career.
33 A “nucleon” is the term physicists use for a particle inside a nucleus, either a proton or a neutron.
34 The sponsor for the Disneyland program Our Friend, the Atom was General Dynamics, manufacturer of, among other things, nuclear submarines.
35 Assuming that the alpha particle is electrically repelled before striking the nucleus.
36 To maintain stability in a nucleus requires a critical balance of the number of neutrons and protons—consequently, isotopes such as hydrogen, with one proton and two neutrons, may be unstable and “decay.” More on this soon.
37 Depending on the detailed decay fragments of the fissioning uranium nucleus. How exactly the unstable uranium nucleus decays into smaller nuclei is a complicated process.
38 There is a process by which, when an electron drops from a high-energy state to a lower level, another electron in the atom is ejected. But for the most part electronic transitions within the atom involve emission or absorption of photons.
39 My track record playing the lottery provides direct empirical evidence of this phenomenon.
40 A nucleus with two neutrons and two protons is called helium, or, when ejected from a larger unstable nucleus, an alpha particle.
41 The full analysis involves studies of meteorites, and is more complicated than summarized here.
42 By the time neutrons were discovered, the identity of nuclear radiation was better understood, and the “ray” nomenclature was no longer employed.
43 That is, one that is sitting still, isolated in space or moving but stationary to us if we moved along in the same speed and direction as the neutron (called the neutron’s “rest frame”).
44 For technical reasons that need not concern us, when neutrons decay they emit a proton, an electron, and an antineutrino (the antimatter version of a neutrino). As I say, we need not worry about this particular detail here.
45 Famed astrophysicist Sir Arthur Eddington was one of the first to recognize that the sun’s energy resulted from nuclear reactions. However, prior to the development of quantum mechanics, many physicists objected that the temperatures at the center of the sun were too low to enable such processes. To this Eddington replied in 1920, “We do not argue with the critic who urges that the stars are not hot enough for this process; we tell him to go and find a hotter place.”
46 Measured relative to a particular axis of rotation.
47 Those who know quantum mechanics will recognize that these two functions are A = Ψm(1)Ψn(2) and B = Ψn(1)Ψm(2), where Ψm(1) is the wave function for an electron at position 1 in quantum state m and Ψn(2) represents the second electron in a quantum state n at position 2. If the positions of the electrons 1 and 2 are interchanged, then the total wave function Ψ = A-B= Ψm(1)Ψn(2) - Ψn(1)Ψm(2) acquires a minus sign. If you understood this footnote—then this book is not for you!
48 As in section 2, since Ψ is a complex number, by “squaring” I mean multiplying Ψ by its complex conjugate. For our purposes this has the same effect as squaring Ψ, so we use the simpler notation of Ψ2.
49 For simplicity, the nucleus in Figure 31 is represented by a single positive charge, while in fact there are multiple protons in all nuclei except hydrogen, from two in helium (Figure 31b) to thirteen in aluminum (F
igure 31e). I have also not attempted to represent the changes in the spacing of the rows for the different elements.
50 This notion that organisms with specialized skills could serve as analogs of sensory organs or other bodily or psychological functions in a gestalt organism was anticipated in Theodore Sturgeon’s 1953 science fiction novel More Than Human.
51 As before in Chapter 12, the functions A and B are products of the one-particle wave functions, with A = Ψm(1)Ψn(2) and B = Ψn(1)Ψm(2), where Ψm(1) is the wave function for a boson at position 1 in quantum state m and Ψn(2) represents the second identical boson in a quantum state n at position 2. If the positions of objects 1 and 2 are interchanged, then the total wave function Ψ = A + B = Ψm(1)Ψn(2) + Ψn(1)Ψm(2) is unchanged.
52 While the illustration with the ribbon does not apply for spin = ħ (or 2ħ, and so on) particles, the mathematical arguments above about symmetric two-particle wave functions for these integral spin particles is identical to the spin = 0 case.
53 Strictly speaking, the transition that helium makes as it forms a superfluid, or when the electrons form Cooper pairs in a superconductor, is not technically an example of Bose-Einstein condensation. The distinctions between a true Bose-Einstein condensate and the superfluid or superconducting state are technical, and for our purposes we may take them to be the same.
54 And that has made all the difference!
The Amazing Story of Quantum Mechanics Page 33
