unitarity, 212
of scattering amplitudes, 138
of the S-matrix, 25–26, 83
violation of, 105
unitary abelian group, in one dimension, 58
universe: becoming increasingly inhomogeneous, 187
as biggest accelerator, 41
as source of radiation, 42
up quark (u), 7
uranium, emitting gamma rays (photons), 16
vacuum, x, 212
energy 68-69
energy density 72, 73, 96, 138
expectation value, 125-126, 213
vacuum tube technology, 34
valence quarks, three basic, 29
van der Meer, Simon, 48, 161
van Hove, Leon, 7
van Nieuwenhuizen, Peter, 72
vapor droplets, surrounding ions in the cloud chamber, 35
Varela, João, 169–170
variable speed of light (VSL): cosmology, 131, 213
increasing the speed of light, 131
models, 187–188
theory, 207
vector, transferring from one point to another distant, 21
vector boson W: charged massive, 142
massive intermediate, 84
mass of charged intermediate, 24
quarks coupled to the charged intermediate, 12. See also W and Z bosons vector boson Z, neutral, 40, 84, 93
current coupled to, 12
vector field, 21, 63, 213. See also scalar field
vector minus axial vector, 28
vectorphobic model, 120
vector potential, in electromagnetism, 22, 62
Veltman, Martinus, 93, 96, 180
Vilenkin, Alexander, 187
violation of parity (left-right symmetry), 28
virtual particle, 100, 117
V minus A (V - A) theory, 28
void cosmology, 131, 132, 213
von Neumann, John, 2
V shape, signature of the neutral Z boson, 41
VSL. See variable speed of light (VSL)
walking Technicolor, 124, 125
Wallace, Alfred Russell, 182
Walton, Ernest, 43
W and Z bosons, xiv, 16, 68, 213
discovery of, 66
Ward, John, 27, 83, 213
Ward identities, 83, 213
Ward-Takahachi identity, 213
warping of spacetime geometry, gravity as, 15
wave and particle, duality of, 63
waves: out of phase, 65
in phase, 64
phase of, 63, 209
W boson, 20, 81
coupling strength to, 156
discovery of, x
existence of, 22
similar problems with mathematical infinities, 21
spoiling QED without Higgs boson, 123
unwanted scalar bosons coupling with, 143. See also vector boson W
W and Z bosons
weak interaction angle, 96
weak anthropic principle, 181–182
weak force or interaction, 16, 17, 205, 213
lack of flavor-changing neutral currents in, 13
presenting a greater need for BSM physics, 123
producing a renormalizable or finite theory of, 96
renormalizable quantum field theory of, 84
weak interaction theory, 122, 123
weak neutral current, 142
Weinberg, Eric, 185
Weinberg, Steven, xiv, 68, 85, 90–91, 93, 96, 124, 142, 146, 161
Weinberg-Salam model, 105, 139, 185
Weisskopf, Victor, 17
Wess, Julius, 71
Weyl, Hermann, 2, 21–22, 62
Wheeler, John, 25
Widerøe, Rolf, 43
Wielers, Monika, 106, 108, 109–110
Wigner, Eugene, 4
Wilczek, Frank, 29, 30
Wilson, Charles, 35
Wilson, Kenneth, 19–20
Wilson, Robert, 48
WIMPs (weakly interacting massive particles), 77, 106
W mass, new measurement by the CDF and D0 detectors, 154
Woit, Peter, 154, 161, 170
Woodard, Richard, 136, 139
Worldwide Web, invented at CERN, 78
W propagator, 143
Wulf, Theodor, 41, 42
X boson, 16-17, 172, 189, 192, 193
Xenon 100 underground experiment, 106
Yamawaki, Koichi, 126
Yang, Chen-Ning, 22, 23–25, 60, 83, 118, 142, 164
Yang and Mills, 65–66
Yang-Mills gauge bosons, 24
Yukawa, Hideki, 2
Yukawa Lagrangian, 186, 193
Z boson, 213
decay of, 100
discovery of, x
paths in the bubble chamber, 40. See also W and Z bosons
Zeldovich, Yakov, 73
zeta boson, 118, 128
decay into a pair of Z bosons, 148
zeta meson, 148
zeta meson resonance, 118, 129
zeta prime boson, 128, 148
Zumino, Bruno, 71
Zweig, George, 1, 6, 7
1. An elementary particle is not composed of other particles bound together by a force; the electron, for example, is an elementary particle, but the proton and neutron are not, being composed of quarks.
2. Leptons are weakly interacting particles such as the electron, muon, and tau, and the neutrinos.
3. In Einstein’s special relativity, energy is equivalent to mass through his famous equation E = mc2. We express particle masses in units of energy, such as electron volts (eV), thousands of electron volts (KeV), millions of electron volts (MeV), billions of electron volts (GeV), and trillions of electron volts (TeV). For example, the electron has a mass of 0.5 MeV, the proton has a mass of 938 MeV, the W boson has a mass of about 80 GeV, and the top quark has a mass of about 173 GeV.
4. Sadly, Robert Brout died in May 2011, which does, however, make the committee’s decision somewhat easier.
5. In modern particle physics, quantum mechanics and relativity are united in quantum field theory. Each elementary particle has an associated field, and this field is quantized so that the particle field is consistent with quantum mechanics and relativity. Quantum field theory is used to do calculations in particle physics.
6. R. Jackiw and K. Johnson, “Dynamical Model of Spontaneously Broken Gauge Symmetries,” Physical Review, D8, 2386–2398 (1973).
1. Several authors have questioned the idea that quarks are the final, basic, and indivisible units of matter by claiming that quarks are composed of “prequarks.” The large hadron collider has searched for such prequarks, or preons, and the possible composite nature of quarks, and so far has not found evidence for them.
2. At this time, particles were identified by “bumps” appearing in the measured cross-sections of particle collisions in accelerators. These bumps had a mass and a width determined by a formula obtained by physicists Gregory Breit and Eugene Wigner, and were called resonances in the cross-sections.
3. M. Gell-Mann, “A Schematic of Baryons and Mesons,” Physics Letters, 8, 214–215 (1964).
4. George Zweig, “Origins of the Quark Model,” in Baryon ‘80: Proceedings of the 4th International Conference on Baryon Resonances, ed. Nathan Isgur, July 14–16, 1980, Toronto. Quoted in Andrew Pickering, Constructing Quarks: A Sociological History of Particle Physics (Chicago, IL: University of Chicago Press, 1984), 89–90.
5. J.D. Bjorken, “Asymptotic Sum Rules at Infinite Momentum,” Physical Review, 179, 1547–1553 (1969).
6. R.P. Feynman, Photon Hadron Interactions (Reading, MA: W.A. Benjamin, 1972).
7. QCD is the currently accepted theory of strong interactions involving quarks and gluons, which will be explained in more detail later.
8. B.J. Bjorken and S.L. Glashow, “Elementary Particles and SU(4).” Physics Letters, 11 (3), 255–257 (1964)
9. J.W. Moffat, “Higher Symmetries and the Neutron-Proton Magnetic-Moment Ratio,” Physical Review, 140 (6B), B
1681–B1685 (1965).
10. Albert Einstein, “Grundlage der allgemeinen Relativitätstheorie,” Annalen der Physik (ser.4), 49, 769–822 (1916).
11. Paul A. M. Dirac, “The Evolution of the Physicist’s Picture of Nature,” Scientific American 53 (May 1963). Cited in Helge Kragh, Dirac: A Scientific Biography (Cambridge, UK: Cambridge University Press, 1990), 184.
12. Richard P. Feynman, QED: The Strange Theory of Light and Matter (Princeton, NJ: Princeton University Press, 1985).
13. K.G. Wilson, “The Renormalization Group: Critical Phenomena and the Kondo Problem,” Reviews of Modern Physics, 47 (4), 773 (1975)
14. M. Gell-Mann and F.E. Low, “Quantum Electrodynamics at Small Distances,” Physical Review 95 (5), 1300–1312 (1954).
15. The phase of a wave is a particular point in the cycle of a waveform, usually measured as an angle.
16. Oskar Klein, “Quantentheorie und Fünfdimensionale Relativitätstheorie,” Zeitschrift fur Physik A, 37 (12), 895–906 (1926).
17. C.N. Yang and R. Mills, “Conservation of Isotopic Spin and Isotopic Gauge Invariance,” Physical Review, 96, 191–195 (1954).
18. “Space” here does not refer to our everyday three-dimensional space, but is a mathematical concept to describe isotopic spin.
19. This scene is described in Robert P. Crease and Charles C. Mann, The Second Creation (New Brunswick, NJ: Rutgers University Press, 1996), 194, with quotations from Yang.
20. This was despite the fact that the predictions of Tomonaga, Schwinger, and Feynman in 1949/1950 for QED, such as the anomalous magnetic moment of the electron and the Lamb shift in hydrogen, were confirmed experimentally with amazing accuracy.
21. Y. Ne’eman, “Derivation of Strong Interactions from a Gauge Invariance,” Nuclear Physics, 26, 222–229 (1961).
22. M. Gell-Mann, “Symmetries of Baryons and Mesons,” Physical Review, 125, 1067–1084 (1962).
1. A black body is an idealized physical system that absorbs all of the electromagnetic radiation that hits it and emits radiation at all frequencies with 100 percent efficiency.
2. Albert Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Annalen der Physik, 17 (6), 132–148 (1905).
3. A Geiger counter is a portable ion counter used to measure radioactivity.
4. An electron has an energy of 1 V when it is accelerated by an electric field with a potential difference of 1 V.
5. R. Wideröe, “Über ein neues Prinzip zur Herstellung hoher Spannungen,” Archiv für Elektrotechnik, 21 (4), 387–406 (1928).
6. ATLAS stands for “A Toroidal LHC apparatus,” and CMS means “compact muon solenoid.”
7. The superconducting supercollider in Texas, the construction of which was canceled in 1993, was to have had a maximum energy of 40 TeV.
1. O(3) is the three-dimensional rotation group of all rotations around the origin of three-dimensional Euclidean space. The group SO(3), a subgroup of O(3), does not include reflections as O(3) does, so rotations reflected in a mirror look the same.
2. In group theory, SU(2) is technically referred to as the double cover of O(3).
3. The vector potential in electromagnetism can be detected according to quantum theory by means of the Bohm-Aharanov phase prescription.
4. Hermann Weyl, Space, Time, Matter (Dover Books on Physics), 4th edition (Mineola, NY: Dover Publications, 1952).
5. H. Weyl, “Electron und Gravitation,” I.Z. Physik, 56, 330 (1929).
6. F. London, “Quantenmechanische Deutung der Theorie von Weyl,” Z. Physik, 42, 375 (1927).
1. Fermions have half-integer spins. For example, the electron has spin ½. Bosons, on the other hand, have integer spins, such as the photon with spin 1.
2. Albert Einstein, “Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie,” Königlich Preussische Akademie der Wissenschaften, 142–152 (1917).
3. The algebra of the operators of string theory for boson strings is only consistent with special relativity in 26 dimensions, thereby satisfying the symmetry of Lorentz invariance.
1. J. Schwinger, “A Theory of the Fundamental Interactions,” Annals of Physics, 2, 407–434 (1957).
2. The range of a force in particle physics is determined by the mass of the particle. For classical electromagnetism, the fact that the photon is massless results in the electromagnetic force having infinite range. On the other hand, in weak interactions, which govern the radioactive decay of particles, the force has to be short-range, so we know that the intermediate vector boson, W, that carries the weak force has to have a mass. The “confined” massless gluon is an exception.
3. F.J. Dyson, “The Radiation Theories of Tomonaga, Schwinger and Feynman,” Physical Review, 75, 486–502 (1949); and “Divergences of Perturbation Theory in Quantum Electrodynamics,” Physical Review, 85, 631–632 (1952).
4. S.L. Glashow, “Partial-symmetries of Weak Interactions,” Nuclear Physics, 22, 579–588 (1961).
5. J. Goldstone, “Field Theories with Superconductor Solutions,” Nuovo Cimento, 19, 154–164 (1961).
6. J. Goldstone, A. Salam, and S. Weinberg, “Broken Symmetries,” Physical Review, 127, 965–970 (1962).
7. W. Gilbert, “Broken Symmetries and Massless Particles,” Physical Review Letters, 12, 713–714 (1964). Physical Review, 125, 397–398 (1962).
8. P.W. Anderson, “Plasmons, Gauge Invariance and Mass,” Physical Review, 130, 439–442 (1963).
9. J. Schwinger, “Gauge Invariance and Mass,” Physical Review, 125, 397–398 (1962).
10. F. Englert and R. Brout, “Broken Symmetry and the Mass of Gauge Vector Mesons,” Physical Review Letters, 13, 321–323 (1964).
11. P.W. Higgs, “Broken Symmetries and the Masses of Gauge Bosons,” Physical Review Letters, 13, 508–509 (1964).
12. G.S. Guralnik, C.R. Hagen, and T.W.B. Kibble, “Global Conservation Laws and Massless Particles,” Physical Review Letters, 13, 585–587 (1964).
13. J. Bardeen, L.N. Cooper, and J.R. Schrieffer, “Theory of Superconductivity,” Physical Review, 108, 1175–1204 (1957).
14. W. Meissner and R. Ochsenfeld, “Ein neuer Effekt bei Eintritt der Supraleitfähigkeit,” Naturwissenschaften, 21 (44), 787–788 (1933).
15. V.L. Ginzburg and L.D. Landau, Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 20, 1064 (1950). English translation in: L.D. Landau, Collected Papers (Oxford: Pergamon Press, 1965), 546.
16. P. Higgs, “Broken Symmetries, Massless Particles and Gauge Fields,” Physics Letters, 12, 132–133 (1964).
17. S. Weinberg, “A Model of Leptons,” Physical Review Letters, 19, 1264 (1967).
18. Elementary Particle Theory: Relativistic Groups and Analyticity, ed. Nils Svartholm. (Stockholm: Almqvist & Wiksell, 1968).
19. P.W. Higgs, “Spontaneous Symmetry Breakdown without Massless Bosons,” Physical Review, 145, 1156–1163 (1966).
1. An important relation in particle physics is the mass shell. It is the relationship between the momentum and energy of a particle of a given mass. If we make a plot, with the single component of momentum (mass multiplied by velocity) along the x-axis, and the energy of the particle represented by the y-axis, we must allow for positive and negative values of the movement of the particle to the right and left. The curve showing the energy dependence with momentum is a parabola that has its minimum at the origin of the x- and y-axes. Because the associated energy in the velocity of the particle is quadratic, then for a given value of momentum, the energy is four times greater if we double the momentum. For the two components of momentum, the parabola becomes a shell shape if we rotate it in three-dimensional space. A particle can be called a virtual particle if its energy is not inside this mass shell. This virtual particle does not violate conservation of energy because of the Heisenberg uncertainty principle—namely, the violation of conservation of energy happens in such a short time that it cannot be measured.
2. The Weinberg–Salam model was the first t
o introduce the Higgs mechanism and Higgs boson in a construction of an electroweak model. Glashow had not included them in his 1961 paper. Consequently, physicists have come to refer to the model as the “Weinberg–Salam” model.
3. J.W. Moffat, “Ultraviolet Complete Electroweak Model without a Higgs Particle,” European Physics Journal Plus, 126, 53 (2011).
4. Cross-sections are measured in units of “barns” (b); a barn is equal to the cross-section of the uranium nucleus, which is 10−28 m2. “Femto” means 10−15, or a thousandth of a millionth of a millionth. Thus, a “femtobarn” (fb) equals 10−43 m2. The “inverse femtobarn” is how many particle collision events there are per femtobarn. The “luminosity” of the proton collisions, measured over time, is the number of collisions per square meter per second. Experimentalists express the integrated luminosity in inverse femtobarns.
5. On July 4, 2012, on the basis of between 5 inverse femtobarns and 6 inverse femtobarns of luminosity, CERN announced the discovery of a new boson decaying into two photons, at about a 4-sigma statistical significance. By combining data from this two-photon decay channel with data from the decay of the new boson into ZZ* and four leptons, they were able to claim a 5-sigma discovery. In November 2012, in Kyoto, on the basis of a luminosity of 12 inverse femtobarns, CERN representatives were able to confirm the statistical significance of the new boson beyond 5 sigma. Again, this was based on the combined data from the two-photon decay channel and the ZZ*–4 lepton decay channel.
1. L.D. Landau, Doklady Akademii Nauk SSSR, 60, 207 (1948); C.-N. Yang, Physical Review, 77, 242 (1950).
2. J.W. Moffat, “Quarkonium Resonance Identified with the 125 GeV Boson,” arXiv.org/1211.2746 [hep-ph]; and “Quarkonium Resonance Model of the 125 GeV Boson,” arXiv.org/1302.5583 [hep-ph].
3. S. Weinberg, “Implications of Dynamical Symmetry Breaking,” Physical Review, D13, 974–996 (1976).
4. L. Susskind, “Dynamics of Spontaneous Symmetry Breaking in the Weinberg–Salam Theory,” Physical Review, D20, 2619–2625 (1979).
5. S. Dimopoulos and L. Susskind, “Mass without Scalars,” Nuclear Physics, B155, 237–252 (1979).
6. V.A. Miransky and K. Yamawaki, “On Gauge Theories with Additional Four Fermion Interaction,” Modern Physics Letters, A4, 129–135 (1989).
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