8. There is a huge amount of sociological literature on deviance and marginality. Robert Ezra Park coined the term “marginal man,” but his usage was different than ours. Also relevant is Georg Simmel’s discussion of “the stranger.” Everett Hagen was one of the first to ask if deviance might be related to innovation. See his On the Theory of Social Change: How Economic Growth Begins (Homewood, IL: Dorsey Press, 1962), 573.
9. Eric Felisbret, “Legal Venues Celebrate Graffiti as an Art Form,” New York Times, July 18, 2014, https://www.nytimes.com/roomfordebate/2014/07/11/when-does-graffiti-become-art/legal-venues-celebrate-graffiti-as-an-art-form.
Chapter 7: What Banged?
1. The expanding universe model was independently discovered by
1. Alexander Friedmann et al., “Über die Krümmung des Raumes,” Zeitschrift für Physik A 10, no. 1 (1922): 377–86.
2. Georges Lemaître, “Expansion of the Universe, A Homogeneous Universe of Constant Mass and Increasing Radius Accounting for the Radial Velocity of Extra-Galactic Nebulæ,” Monthly Notices of the Royal Astronomical Society 91, no. 5 (March 1931): 483–90.
3. H. P. Robertson, “Kinematics and World Structure,” Astrophysical Journal 82 (November 1935): 284–301.
4. A. G. Walker, “On Milne’s Theory of World-Structure,” Proceedings of the London Mathematical Society, Series 2 42, no. 1 (1937): 90–127.
Chapter 8: A Dark Conductor of Quantum Galaxies
1. All observed galaxies have dark matter. See Jim Shelton, “New Studies Confirm Existence of Galaxies with Almost No Dark Matter,” YaleNews.com, March 29, 2019, https://news.yale.edu/2019/03/29/new-studies-confirm-existence-galaxies-almost-no-dark-matter.
2. The spatial anisotropy in the density of baryonic and dark matter deviates by approximately one part in ten thousand from the average homogeneous and isotropic cosmic microwave background thermal bath.
3. It was shown by Kris Pardo and David Spergel that it is difficult to reproduce the effects of dark matter in the CMB fluctuations in the early universe with MOND. See Kris Pardo and David Spergel, “What Is the Price of Abandoning Dark Matter? Cosmological Constraints on Alternative Gravity Theories,” Physical Review Letters 125 (October 19, 2020): https://arxiv.org/abs/2007.00555.
4. To be precise, dark matter is five times the density of baryonic (visible) matter.
5. Kaplan is known for producing the critically acclaimed film about the Large Hadron Collider, Particle Fever, which tells the story of the vision of the LHC and the physicists behind it. Coincidentally, I was the moderator for the world premier for the film at the NeueHouse in New York City.
6. Classical field theories have conserved quantities. For example, in electromagnetism the current is conserved. A quantized theory should also conserve all classical currents. However, there are some currents that are broken upon quantization. The amount of current that is broken is called an anomaly. However, a healthy quantum theory fixes these anomalies by realizing that topology needs to be considered in the quantum theory so as to reinstate the current conservation.
Chapter 10: Embracing Instabilities
1. The uncertainty principle can be conveniently written as , the uncertainty in the position of the particle in a harmonic oscillator is bounded by the size of the system. Therefore, the velocity can never be zero according to the uncertainty relation above.
2. General relativity provides an equation that relates energy and matter to the curvature of space-time. The configuration of the matter and energy should warp the space-time field in a specific dynamical manner dictated by the Einstein field equations similar to how a magnet emanates and bends a magnetic field surrounding it. Microscopically, a magnet emerges from interacting atomic spins in a metal. The cosmological constant interacts with the space-time in a manner that causes it to accelerate in its expansion without bound.
3. The Ashtekar variable is similar to QCD in that the dynamics of both theories are encoded in a gauge field connection. In QCD the connection enjoys a larger symmetry [SU(3)] than that Ashtekar connection, [SU(2)].
4. Stephon Alexander and Raúl-Rubio, “Topological Features of the Quantum Vacuum,” Physical Review D 101, no. 2 (2020); Stephon Alexander, Gabriel Herczeg, and Jinglong Liu, “Chiral Symmetry and the Cosmological Constant,” Physical Review D 102, no. 8 (2020).
Chapter 11: A Cosmologist’s View of a Quantum Elephant
1. I first spoke to Sir Roger Penrose, the inventor of twistor theory, who encouraged me to discuss the idea with Ashtekar. Twistors are maps from events in space-time to the celestial sphere that has close semblance to the symmetries enjoyed by the Ashtekar connection. I first thought that my idea behind parity violation and quantum gravity had to do with twistors.
Chapter 12: The Cosmic Biosphere
1. “John von Neumann Compares the Functions of Genes to Self-Reproducing Automata,” HistoryofInformation.com, http://www.historyofinformation.com/detail.php?id=682.
2. B. Jesse Shapiro et al., “Origins of Pandemic Vibrio cholerae from Environmental Gene Pools,” Nature Microbiology 2, article no. 16240 (2017).
As Salvador Almagro-Moreno communicated to me, “Virulence adaptive polymorphisms (VAPs) circulate in environmental populations and must be present in the genomic background of a bacterium before it can emerge as a successful pandemic clone.”
3. The entropy of a black hole is calculated to be .
4. Ludwig Boltzmann, “The Second Law of Thermodynamics,” in Theoretical Physics and Philosophical Problems, ed. B. F. McGuiness (New York: D. Reidel, 1974).
5. One potential loophole to the low-entropy initial state is that there was a previous state what was actually even more entropic that reduced its entropy. For example, if the big bang started out dominated with black holes, then they could evaporate and produce the CMB radiation. If the massless radiation, such as photons, got homogeneously distributed then decayed into matter, then we would have a lower-entropy situation. However, the original entropy presumably in the form of black holes would have to get diluted. This idea can perhaps be implemented in a mechanism developed by Peter Mészáros and me where we postulated that primordial black holes that form after inflation could explain the CMB and dark matter if they undergo Hawking evaporation.
6. Fred C. Adams et al., “Constraints on Vacuum Energy from Structure Formation and Nucleosynthesis,” JCAP 03 (2017).
Chapter 13: Dark Ideas on Alien Life
1. A similar phenomenon happens with electrons and magnetic fields in the fractional quantum Hall effect.
Chapter 14: Into the Cosmic Matrix
1. Arvind Borde and Alexander Vilenkin demonstrated that even cosmic inflation is geodesically incomplete and does not escape the cosmic singularity. See Arvind Borde, Alan H. Guth, and Alexander Vilenkin, “Inflationary Spacetimes Are Incomplete in Past Directions,” Physical Review Letters 90, no. 15 (April 15, 2003).
2. To be precise, if x and p are position and momenta variables then quantization rules promote their Poisson brackets (curly brackets) to commutation (square brackets) . Classical dynamics of an observable is given by Hamilton’s equation, which states that the time evolution is generated by the Poisson brackets of the Hamiltonian and the observable of interest. For example, the classical time evolution of the position of a particle, x(t) is given by the Poisson bracket between the Hamiltonian and the position.
Whereas the time evolution of the position operator is given by the commutator between the Hamiltonian and position operators.
3. Here we are assuming that the spatial dimensions have the topology of circles whose local products are tori. These topologies admit one-cycles that strings can wind around without collapsing to a point.
4. This initial condition for string cosmology is an extension of the Copernican principle in the standard big bang, which states that there is no preferred vantage point in the universe. The Copernican principle is consistent with assuming homogeneity and isotropy not only in space but in the degrees of freedom that o
ccupy the universe.
5. A cyclic BV mechanism was studied by Brian Greene, Daniel Kabat, and Stefanos Marnerides. They found that the BV mechanism can exhibit a cyclic cosmology if the theory incorporates higher derivative terms in the gravitational theory.
6. In a closed string theory we can add open strings that satisfy both von Neumann and Dirichlet boundary conditions.
The above equation states that the derivate of the string ends on p space-time dimensions. This is a Dirichlet boundary condition. This p-dimensional hypersurface defines the worldvolume of a Dp-brane.
7. The above equation states that the string vanishes in the other dimensions.
Chapter 15: The Cosmic Mind and Quantum Cosmology
1. Deepak Chopra, MD, and Menas C. Kafatos, PhD, You Are the Universe: Discovering Your Cosmic Self and Why It Matters (New York: Harmony Books, 2017).
2. Kimbwandende Kia Bunseki Fu-Kiau, African Cosmology of the Bantu-Kongo: Principles of Life and Living (Brooklyn, NY: Athelia Henrieta Press, 2001), 17–54.
3. In general relativity the Hamiltonian is constrained to be zero. As a result the associated Schrödinger equation will no longer have time dependence. The state of the universe will therefore be timeless, which means that the universe as a whole is changeless. In order to obtain time dependence, one has to introduce an external clock relative to the rest of the universe, and matters of this sort are called the problem of time in quantum gravity.
4. Alexander Vilenkin, “Creation of Universes from Nothing,” Physics Letters B 117, no. 1–2 (November 1982): 25–28.
5. Andrei Linde, “Universe, Life, Consciousness,” https://static1.squarespace.com/static/54d103efe4b0f90e6ca101cd/t/54f9cb08e4b0a50e0977f4d8/1425656584247/universe-life-consciousness.pdf.
6. Vincent Jacques et al., “Experimental Realization of Wheeler’s Delayed-Choice Gedanken Experiment,” Science 315, no. 5814 (February 16, 2007): 966–968, https://arxiv.org/abs/quant-ph/0610241.
ALSO BY STEPHON ALEXANDER
The Jazz of Physics
PRAISE FOR FEAR OF A BLACK UNIVERSE
“The rabbit hole gets wrestled here. An old school saying applies: the more you know, the more you don’t know. Dance along this read into the unknown and find out that this book may be the best ever answer to ‘what is soul?’”
—Chuck D, rapper and co-founder of Public Enemy
“This book reminds me of Hawking’s A Brief History of Time—very brief and very ambitious. It covers an enormous amount of material and offers insights not only into physics but how we do physics and who we are as physicists.”
—David Spergel, winner of the 2018 Breakthrough Prize in Fundamental Physics
“Stephon Alexander has done it again. Fear of a Black Universe opens many dimensions—it’s an endlessly stimulating, hyper-complex overview by a deeply musical scientist and mathematician. From Public Enemy’s classic Fear of a Black Planet hip hop album and what happened before the Big Bang to how consciousness itself is woven into the fabric of space-time, this book will blow your mind. A must-read for anyone who thinks of physics and music as being inseparable.”
—Paul D. Miller aka DJ Spooky
“An expansive and poetic account of not just the theory of physics, but the dreamy processes that lead to its creation, and the opposing forces that support and hinder its progress.”
—Eugenia Cheng, author of x + y
“Einstein famously remarked that mystery is the source of all true art and science. This book explores some of the biggest mysteries of all—dark matter, dark energy, the origin of the universe, and the origin of life—in ways that are unconventional and enthralling, yet down to earth. We go on a journey with a brave adventurer for whom physics is a passionate pursuit of beauty and truth. His passion shines through on every page.”
—Edward Frenkel, author of Love and Math
“Read this book and you’ll feel awe at the grandeur and the remaining mysteries of our world, but you’ll also get a hint of the human side of physics. Science is made of people and is for people; this book revives the humanist project that launched science in the first place.”
—Jaron Lanier, author of Ten Arguments for Deleting Your Social Media Accounts Right Now
“In this courageous and provocative book, Alexander recounts his personal story of overcoming prejudice while offering a hopeful perspective for our future. Discussing the origins of his boldest ideas, from his practice as a professional jazz musician to his explorations of Jungian psychology, is especially inspiring.”
—Lee Smolin, author of Einstein’s Unfinished Revolution
Fear of a Black Universe Page 20