Into the Unknown, page 35
4. I say this with a nod to Descartes and the chapter on epistemology and whether we can actually “know” anything.
5. Admittedly, I have not stopped random people on the street and asked them about whether they thought time was linear, or whether time has loops. My instinct is that such interactions wouldn’t end well for me. This may be fertile ground for an aspiring psychology PhD student.
6. Note that we are only considering a single dimension of space to simplify the visualization.
CHAPTER 8: ARE THERE HIDDEN DIMENSIONS?
1. As an example, the word “algebra” comes from the Arabic al-jabr, which loosely means “the joining of broken parts.”
2. P. Ball, “Islamic Tiles Reveal Sophisticated Maths,” Nature, 2007.
3. M. Gardner, “Extraordinary Nonperiodic Tiling That Enriches the Theory of Tiles,” Scientific American, 1968. This seems like a fine place to point out that there are different sizes of infinities in math. In this case, “uncountable” infinities are larger than “countable” ones.
4. A. C. Clarke, “Hazards of Prophesy: The Failure of the Imagination,” in Profiles of the Future: An Enquiry into the Limits of the Possible, Harper & Row, 1962.
5. J. Horgan, “Why String Theory Is Still Not Even Wrong,” Scientific American, 2017; R. Peierls, “Where Pauli Made His ‘Wrong’ Remark,” Physics Today, 1992.
6. A. F. Ali, M. Faizal, and K. Mohammed, “Absence of Black Holes at LHC Due to Gravity’s Rainbow,” Physics Letters B, 2015.
7. P. Hořava and E. Witten, “Eleven-Dimensional Supergravity on a Manifold with Boundary,” Journal Nuclear Physics B, 1996.
8. Abbott et al., “Tests of General Relativity with GW170817,” Physical Review Letters, 2019.
9. This very book is another case in point; I have to view this book as an experiment, and if I were too afraid to write it because it might not turn out well, I never would have put pen to paper, or fingers to keyboard, as it were.
10. I really hate using the word “never.” However, based on the laws of physics as we currently understand them, the word “never” seems appropriate. That being said, I would love for some far-future reader to pick up this book and laugh at how naive and closed-minded we twenty-first-century humans were.
11. M. Tegmark, “Parallel Universes,” in Science and Ultimate Reality: From Quantum to Cosmos, Cambridge University Press, 2003.
12. A. Guth, “Eternal Inflation and Its Implications,” Journal of Physics A, 2007.
13. P. Steinhardt, “Natural Inflation,” in The Very Early Universe, Cambridge University Press,1983.
14. M. Kramer, “Our Universe May Exist in a Multiverse, Cosmic Inflation Discovery Suggests,” Space.com, 2014, https://www.space.com/25100-multiverse-cosmic-inflation-gravitational-waves.html.
15. S. Hawking and T. Hertog, “A Smooth Exit from Eternal Inflation?,” Journal of High Energy Physics, 2018.
16. “Taming the Multiverse: Stephen Hawking’s Final Theory About the Big Bang,” University of Cambridge, 2018, accessed June 2023, https://www.cam.ac.uk/research/news/taming-the-multiverse-stephen-hawkings-final-theory-about-the-big-bang.
17. J. Brockman, “Smolin vs. Susskind: The Anthropic Principle”; D. Overbye, “About Those Fearsome Black Holes? Never Mind,” New York Times, 2004.
18. The idea of branes took off in the late 1990s with a set of papers by Lisa Randall and Raman Sundrum (called the “RS models”) and Merab Gogberashvili (working on a shell model) (L. Randall and R. Sundrum, “A Large Mass Hierarchy from a Small Extra Dimension,” Physical Review Letters, 1999; M. Gogberashvili, “Hierarchy Problem in the Shell-Universe Model,” International Journal of Modern Physics D, 2002).
19. V. Rubakov and M. Shaposhnikov, “Do We Live Inside a Domain Wall?,” Physics Letters B, 1983.
20. J. Khoury et al., “The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang,” Physical Review D, 2001.
21. C. Collaboration, “Search for Microscopic Black Hole Signatures at the Large Hadron Collider,” Physics Letters B, 2011; L. Visinelli, N. Bolis, and S. Vagnozzi, “Brane-World Extra Dimensions in Light of GW170817,” Physical Review D, 2018.
CHAPTER 9: WHAT DETERMINES THE LAWS OF NATURE?
1. M. Gardner, “The Fantastic Combinations of John Conway’s New Solitaire Game ‘Life,’” Scientific American, 1970.
2. At the time that I am writing this, if you google “Conway’s Game of Life,” the results page will have a Game of Life evolving across it, which is a level of nerdiness I am down for. After this quick search, you should have several online options to choose from. These generally have options you can play around with, like the cell size to zoom out or in, the frame rate, and so on. Just experiment and see what happens.
3. I am sorry to say that, although I went to science camp every summer, I never had the chance to attend metaphysical philosophy camp. I wonder if they debate whether s’mores exist.
4. G. Oppy, “Ontological Arguments,” Stanford Encyclopedia of Philosophy, 2021.
5. A. Franklin, “The Rise and Fall of the ‘Fifth Force’: Discovery, Pursuit, and Justification in Modern Physics,” American Institute of Physics, 1993. Indeed, a fifth force was proposed in the 1980s (Fischbach et al., “Reanalysis of the Eoumltvös Experiment,” Physical Review Letters, 1986), but as researchers went around the empirical inquiry loop, the observations ultimately kicked them onto the path of “Where did our assumptions or method go wrong?”
6. J. C. Maxwell, A Treatise on Electricity and Magnetism, Clarendon Press, 1873.
7. The physicist responsible for the levitating frog, Andre Geim, won the Ig Nobel Prize (which is the satiric version of the Nobel Prize) for this in 2000. And then he went on to win the actual Nobel Prize in physics in 2010 for work on graphene. I imagine his lab is a very interesting place.
8. In modern physics the term of art converted from “force” to “interaction,” which acknowledges that what we perceive as forces really arise from interactions with fields. Frankly, I also happen to think that “interaction” just sounds more friendly and welcoming, so I’m all for it. The strong and weak forces are typically referred to as “interactions,” but for the sake of not being any more confusing I’m just calling everything a “force.”
9. A quick clarification that protons have not been observed to decay when in isolation (outside a nucleus). This is important in the chapter on fine-tuning. Protons can decay by capturing electrons.
10. I occasionally give a homework assignment that involves students dropping drops of ink from different heights onto paper and observing the splatter patterns that are created—which have spectacular symmetries in them. This particular assignment invites a lot of questioning looks. You are welcome to try this experiment, which may well spur some curious conversations with passersby. The resulting ink splatters are stunning.
11. Roughly 1 in 10,000 people have their hearts on the right side, which is known as dextrocardia. Still asymmetric, just with the opposite handedness.
12. A. Salam and J. Ward, “A Treatise on Electricity and Magnetism,” Nuovo Cimento, 1959; S. Weinberg, “A Model of Leptons,” Physical Review Letters, 1967.
13. Yes, I know, sound requires a medium to travel in, and typically we don’t expect there to be sound in outer space given the extremely low density in most of the universe today. But let’s not forget that the early universe, at the time of inflation, was a fair bit more dense. In fact, at that time the universe was a thick hot plasma, and there most definitely was sound, and these ancient sound waves are now frozen into the structure of the cosmic microwave background.
14. R. Descartes, Discourse on Method and Meditations on First Philosophy, Yale University Press, 1996. With modern-day AI, this also turns out to be wrong, and chatbots are giving all manner of replies.
15. B. Voytek, “Are There Really as Many Neurons in the Human Brain as Stars in the Milky Way?,” Nature, 2013. There is urban lore that the brain has more nerve cells than stars in our galaxy. I suspect the origin of this myth is ultimately connected to humans wanting to feel important. If you are so inclined, a quick fact check will tell you that the Milky Way has at least 100 billion stars, and possibly as many as 400 billion. Curiously, this is roughly the same number as there are galaxies in the observable universe. Conspiracy theorists must love this.
16. A. Turing, “Computing Machinery and Intelligence,” Mind, 1950.
17. See, for example, the Illustris simulation and its descendants (Illustris Project [website], accessed June 2022, https://www.illustris-project.org/.)
18. D. A. Grier, When Computers Were Human, Princeton University Press, 2005.
19. N. Bostrom, “Are You Living in a Computer Simulation?,” Philosophical Quarterly, 2003. The original paper by Nick Bostrom is freely available online at https://simulation-argument.com/simulation.pdf.
20. S. Hossenfelder, “The Simulation Hypothesis Is Pseudoscience,” BackReAction, 2021.
21. Far be it from me to throw shade at Descartes, but this issue with self-reference is also embedded in “I think, therefore I am.” Thinking is an action that changes the state of being, so after you have done the thinking, you are no longer the same person you were when you started, which brings into question the nature of “am” and what “am” includes.
22. A. Tarski, “The Semantic Conception of Truth: And the Foundations of Semantics,” Philosophy and Phenomenological Research, 1944; A. Tarski, Logic, Semantics, Metamathematics: Papers from 1923 to 1938, Clarendon Press, 1956.
23. P. Raatikainen, “Gödel’s Incompleteness Theorems,” Stanford Encyclopedia of Philosophy, 2020; K. Gödel, On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover, 1992.
24. S. Hawking, “Godel and the End of Physics,” Stephen Hawking (website), 2002, accessed June 2023, https://www.hawking.org.uk/in-words/lectures/godel-and-the-end-of-physics.
25. R. Penrose, “Gödel, the Mind, and the Laws of Physics,” in Kurt Gödel and the Foundations of Mathematics, Cambridge University Press, 2011.
26. R. Penrose, The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics, Oxford University Press, 1989.
27. P. Raattkainen, “On the Philosophical Relevance of Godel’s Incompleteness Theorems,” Revue internationale de philosophie, 2005.
CHAPTER 10: IS THE UNIVERSE FINE-TUNED?
1. For a deeper overview of the parameters in the universe, see M. Tegmark et al., “Dimensionless Constants, Cosmology, and Other Dark Matters,” Physical Review D, 2006.
2. If you don’t actually have a good physics book, you should have one on your shelf. You never know when you might need it. If nothing else, they are really good for pressing flowers.
3. G. W. Anderson and D. J. Castaño, “Measures of Fine Tuning,” Physics Letters B, 1995.
4. G. Hooft, “Naturalness, Chiral Symmetry, and Spontaneous Chiral Symmetry Breaking,” in Recent Developments in Gauge Theories, NATO Science Series B,1980.
5. In my opinion, this is one of those ridiculous astronomy terms that just don’t make sense—for example, there is nothing “hydro” (which suggests water) about this, and “static” (meaning it isn’t changing) and “equilibrium” strike me as redundant.
6. F. Adams, “Stars in Other Universes: Stellar Structure with Different Fundamental Constants,” Journal of Cosmology and Astroparticle Physics, 2008.
7. H. Kragh, “When Is a Prediction Anthropic? Fred Hoyle and the 7.65 MeV Carbon Resonance,” Philosophy of Science Archive, 2010.
8. Sorry for the jargon. Hopefully, the “triple” clued you in to there being three of something. Those somethings are helium nuclei—so two protons and two neutrons each, which are called “alpha particles.” In other words, the triple-alpha process uses three helium nuclei.
9. F. Hoyle, “On Nuclear Reactions Occurring in Very Hot Stars. I. The Synthesis of Elements from Carbon to Nickel,” Astrophysical Journal Supplement Series, 1954.
10. H. Oberhummer, A. Csótó, and H. Schlattl, “Stellar Production Rates of Carbon and Its Abundance in the Universe,” Science, 2000.
11. How do we do that? You will surely be relieved to know that there are dedicated scientists in labs whose job it is to determine these constants as precisely as possible (for example at the National Institute of Standards and Technology, NIST). You know you want to go read up on these precision lab experiments.
12. As a throwback to the chapter on laws, you might note that the neutron decay uses the weak interaction.
13. Just a quick reminder of note 9 in Chapter 9 and the circumstances under which protons can decay.
14. I don’t think I believe in reincarnation, but if I did, I would not want to come back as a face mite.
15. M. Tegmark, “On the Dimensionality of Spacetime,” Classical and Quantum Gravity, 1997.
16. Just to decode the jargon in case you are interested: the Greek letter σ (sigma) is generally used as a statistical measure of difference in a set of measurements (i.e., standard deviation). The 8 comes from this particular measurement being normalized to units of 8 Mpc/h, and h itself is code for H0/(100 km/s/Mpc).
Sometimes you will also see the letter Q used for the amplitude of primordial fluctuations, which is a straight value of amplitude as observed in the cosmic microwave background and has a value of roughly 10−5.
17. G. Hinshaw et al., “Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results,” Astrophysical Journal Supplement Series, 2013.
18. M. Tegmark, “Why Is the Cosmic Microwave Background Fluctuation Level 10-5?,” Astrophysical Journal, 1998.
19. R. V. Wagoner, “Big-Bang Nucleosynthesis Revisited,” Astrophysical Journal, 1973.
20. As a side note, helium is a nonrenewable resource on Earth, and we are constantly losing it to space. Think about that the next time you are holding a helium balloon.
21. S. Rahvar, “Cosmic Initial Conditions for a Habitable Universe,” Monthly Notices of the Royal Astronomical Society, 2017.
22. M. Tegmark et al., “Dimensionless Constants, Cosmology, and Other Dark Matters,” Physical Review D, 2006.
23. C. H. Bennett, “Logical Depth and Physical Complexity,” in The Universal Turing Machine—a Half-Century Survey, Oxford University Press, 1988.
24. Bennett, “Logical Depth and Physical Complexity.”
25. Note that the orbits are not actually perfect circles, but back in the day it sure seemed like it.
26. I. Newton, Opticks: or, A treatise of the reflections, refractions, inflexions and colours of light (London: Printed for Sam. Smith, and Benj. Walford, 1704), Smithsonian Libraries online, https://library.si.edu/digital-library/book/optickstreatise00newta.
27. C. Darwin, The Origin of Species, William Collins, 2011 (1859).
28. B. Carter, “Large Number Coincidences and the Anthropic Principle,” in Confrontation of Cosmological Theories with Observational Data, D. Reidel, 1973.
29. R. Dicke, “Dirac’s Cosmology and Mach’s Principle,” Nature, 1961.
CHAPTER 11: WHAT IS OUR PLACE IN THE UNIVERSE?
1. A. Casselman, “Strange but True: The Largest Organism on Earth Is a Fungus,” Scientific American, 2007, https://www.scientificamerican.com/article/strange-but-true-largest-organism-is-fungus/.
2. For context, there are other macroscopic living organisms on Earth that have reached ages far surpassing this—including several species of plants believed to be more than ten thousand years old.
3. F. Falchi et al., “The New World Atlas of Artificial Night Sky Brightness,” Science Advances, 2016, https://www.science.org/doi/10.1126/sciadv.1600377. Don’t even get me started on the impending deluge of satellites in Earth orbit. Today as I write this book, global internet providers have submitted applications to launch over half a million satellites into Earth orbit. By comparison, only about five thousand stars are visible to a typical human eye at the darkest locations on Earth. If only a quarter of these planned satellites are ultimately launched, and only one in ten of those are bright enough for the human eye to see, there will be nearly three times more satellites visible and orbiting in the night sky than visible stars.
4. I don’t know that I can say the same of my dogs; I have the sense that they just accept the nature of reality without wondering why it is the way it is. They certainly don’t think about the philosophical implications of quantum mechanics.
5. There are resources online to help you find the darkest night-sky location near you. One of my favorites is https://www.lightpollutionmap.info, which will let you zoom into any location in the world. Also a pro tip: be mindful of the moon phase—the closer to a new moon, the better.
Kelsey Johnson, Into the Unknown
