Einstein's Unfinished Revolution
Page 28
3. Yakir Aharonov and Lev Vaidman, “The Two-State Vector Formalism of Quantum Mechanics: An Updated Review,” in Time in Quantum Mechanics, vol. 1, eds. J. Gonzalo Muga, Rafael Sala Mayato, and Íñigno Egusquiza, 2nd ed., Lecture Notes in Physics 734 (Berlin and Heidelberg: Springer, 2008), 399–447, arXiv:quant-ph/0105101v2.
4. John G. Cramer, “The Transactional Interpretation of Quantum Mechanics,” Reviews of Modern Physics 58, no. 3 (July 1986), 647–87; Cramer, The Quantum Handshake: Entanglement, Nonlocality and Transactions (Cham, Switzerland: Springer International, 2016); Ruth E. Kastner, “The Possibilist Transactional Interpretation and Relativity,” Foundations of Physics 42, no. 8 (August 2012): 1094–113.
5. Huw Price, “Does Time-Symmetry Imply Retrocausality? How the Quantum World Says ‘Maybe,’” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43, no. 2 (May 2012), 75–83, arXiv:1002.0906.
6. Rafael D. Sorkin, “Quantum Measure Theory and Its Interpretation,” in Quantum Classical Correspondence: Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, Drexel University, Philadelphia, USA, September 8–11, 1994, eds. Bei-Lok Hu and Da Hsuan Feng (Cambridge, MA: International Press, 1997), 229–51, arXiv:gr-qc/9507057.
7. Murray Gell-Mann and James B. Hartle, “Quantum Mechanics in the Light of Quantum Cosmology,” in Proceedings of the 3rd International Symposium: Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1989, 321–43; Gell-Mann and Hartle, “Alternative Decohering Histories in Quantum Mechanics,” in Proceedings of the 25th International Conference on High Energy Physics, 2–8 August 1990, Singapore, eds. K. K. Phua and Y. Yamaguchi, vol. 1, 1303–10 (Singapore and Tokyo: South East Asia Theoretical Physics Association and Physical Society of Japan, dist. World Scientific, 1990); Gell-Mann and Hartle, “Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology,” in Proceedings of the NATO Workshop on the Physical Origins of Time Asymmetry, Mazagón, Spain, September 30–October 4, 1991, eds. J. Halliwell, J. Pérez-Mercader, and W. Zurek (Cambridge, UK: Cambridge University Press, 1992), arXiv:gr-qc/9304023; Gell-Mann and Hartle, “Classical Equations for Quantum Systems,” Physical Review D 47, no. 8 (April 1993): 3345–82, arXiv:gr-qc/9210010.
8. Robert B. Griffiths, “Consistent Histories and the Interpretation of Quantum Mechanics,” Journal of Statistical Physics 36, nos. 1–2 (July 1984), 219–72; Griffiths, “The Consistency of Consistent Histories: A Reply to d’Espagnat,” Foundations of Physics 23, no. 12 (December 1993): 1601–10; Roland Omnès, “Logical Reformulation of Quantum Mechanics, 1: Foundations,” Journal of Statistical Physics 53, nos. 3–4 (November 1988): 893–932; Omnès, “Logical Reformulation of Quantum Mechanics, 2: Interferences and the Einstein-Podolsky-Rosen Experiment,” ibid., 933–55; Omnès, “Logical Reformulation of Quantum Mechanics, 3: Classical Limit and Irreversibility,” ibid., 957–75; Omnès, “Logical Reformulation of Quantum Mechanics, 4: Projectors in Semiclassical Physics,” Journal of Statistical Physics 57, nos. 1–2 (October 1989): 357–82; Omnès, “Consistent Interpretations of Quantum Mechanics,” Reviews of Modern Physics 64, no. 2 (April 1992): 339–82.
9. Fay Dowker and Adrian Kent, “On the Consistent Histories Approach to Quantum Mechanics,” Journal of Statistical Physics 82, nos. 5–6 (March 1996): 1575–646, arXiv:gr-qc/9412067.
10. Michael J. W. Hall, Dirk-André Deckert, and Howard M. Wiseman, “Quantum Phenomena Modeled by Interactions between Many Classical Worlds,” Physical Review X 4, no. 4 (October 2014): 041013, arXiv:1402.6144.
11. Benhui Yang, Wenwu Chen, and Bill Poirier, “Rovibrational Bound States of Neon Trimer: Quantum Dynamical Calculation of All Eigenstate Energy Levels and Wavefunctions,” Journal of Chemical Physics 135, no. 9 (September 2011): 094306; Gérard Parlant, Yong-Cheng Ou, Kisam Park, and Bill Poirier, “Classical-like Trajectory Simulations for Accurate Computation of Quantum Reactive Scattering Probabilities,” invited contribution and lead article, special issue to honor Jean-Claude Rayez, Computational and Theoretical Chemistry 990 (June 2012): 3–17.
12. Gerard ’t Hooft, “Time, the Arrow of Time, and Quantum Mechanics” (2018), arXiv:1804.01383.
13. Lee Smolin, “Could Quantum Mechanics Be an Approximation to Another Theory?” (2006), arXiv:quant-ph/0609109.
14. Matthew F. Pusey, Jonathan Barrett, and Terry Rudolph, “On the Reality of the Quantum State,” Nature Physics 8, no. 6 (June 2012): 475–78, arXiv:1111.3328.
Chapter 14: First, Principles
1. Lee Smolin, Time Reborn: From the Crisis in Physics to the Future of the Universe (New York: Houghton Mifflin, 2013); Roberto Mangabeira Unger and Lee Smolin, The Singular Universe and the Reality of Time: A Proposal in Natural Philosophy (Cambridge, UK: Cambridge University Press, 2015); Smolin, “Temporal Naturalism,” invited contribution to special issue on Cosmology and Time, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 52, no. 1 (November 2015): 86–102, arXiv:1310.8539.
2. Fotini Markopoulou and Lee Smolin, “Disordered Locality in Loop Quantum Gravity States,” Classical and Quantum Gravity 24, no. 15 (July 2007): 3813–24, arXiv:gr-qc/0702044.
3. Lee Smolin, “Derivation of Quantum Mechanics from a Deterministic Non-Local Hidden Variable Theory, I. The Two-Dimensional Theory,” IAS preprint PRINT-83-0802 (Princeton: Institute for Advanced Study, August 1983); Smolin, “Stochastic Mechanics, Hidden Variables and Gravity,” in Quantum Concepts in Space and Time, eds. Roger Penrose and C. J. Isham (Oxford and New York: Clarendon Press / Oxford University Press, 1986).
4. Lee Smolin, “Matrix Models as Non-Local Hidden Variables Theories,” in Quo Vadis Quantum Mechanics?, eds. Avshalom C. Elitzur, Shahar Dolev, and Nancy Kolenda, The Frontiers Collection (Berlin and Heidelberg: Springer, 2005), 121–52; Smolin, “Non-Local Beables,” International Journal of Quantum Foundations 1, no. 2 (April 2015): 100–106, arXiv:1507.08576.
5. Stephen L. Adler, Quantum Theory as an Emergent Phenomenon: The Statistical Mechanics of Matrix Models as the Precursor of Quantum Field Theory (Cambridge, UK: Cambridge University Press, 2004); book draft, Statistical Dynamics of Global Unitary Invariant Matrix Models as Pre-Quantum Mechanics (2002), arXiv:hep-th/0206120.
6. Artem Starodubtsev, “A Note on Quantization of Matrix Models,” Nuclear Physics B 674, no. 3 (December 2003): 533–52, arXiv:hep-th/0206097.
7. Markopoulou and Smolin, “Disordered Locality.”
8. Fotini Markopoulou and Lee Smolin, “Quantum Theory from Quantum Gravity,” Physical Review D 70, no. 12 (December 2004): 124029, arXiv:gr-qc/0311059.
9. Gottfried Wilhelm Leibniz, The Monadology, 1714, in Leibniz: Philosophical Writings, ed. G. H. R. Parkinson, trans. Mary Morris and G. H. R. Parkinson (London: J. M. Dent, 1973).
10. Julian Barbour and Lee Smolin, “Extremal Variety as the Foundation of a Cosmological Quantum Theory” (1992), arXiv:hep-th/9203041.
11. Leibniz, The Monadology, paragraph 57, in Leibniz, Philosophical Writings.
12. Lee Smolin, “The Dynamics of Difference,” Foundations of Physics 48, no. 2 (February 2018): 121–34, arXiv:1712.04799; Smolin, “Quantum Mechanics and the Principle of Maximal Variety,” Foundations of Physics 46, no. 6 (June 2016): 736–58, arXiv:1506.02938; Smolin, “A Real Ensemble Interpretation of Quantum Mechanics,” Foundations of Physics 42, no. 10 (October 2012): 1239–61, arXiv:1104.2822.
13. Lee Smolin, “Precedence and Freedom in Quantum Physics” (2012), arXiv:1205.3707.
Chapter 15: A Causal Theory of Views
1. Luca Bombelli, Joohan Lee, David Meyer, and Rafael D. Sorkin, “Space-Time as a Causal Set,” Physical Review Letters 59, no. 5 (August 1987): 521–24; Sorkin, “Spacetime and Causal Sets,” in Relativity and Gravitation: Classical and Quantum (Proceedings of the SILARG VII Conference, held in Cocoyoc, Mexico, December 1990), eds. J. C. D’Olivo et al. (Singapore: W
orld Scientific, 1991), 150–73.
2. Maqbool Ahmed, Scott Dodelson, Patrick B. Greene, and Rafael Sorkin, “Everpresent Lambda,” Physical Review D 69, no. 10 (May 2004): 103523, arXiv:astro-ph/0209274.
3. Ted Jacobson, “Thermodynamics of Spacetime: The Einstein Equation of State,” Physical Review Letters 75, no. 7 (August 1995): 1260, arXiv:gr-qc/9504004.
4. Fotini Markopoulou and Lee Smolin, “Holography in a Quantum Spacetime” (October 1999), arXiv:hep-th/9910146; Smolin, “The Strong and Weak Holographic Principles,” Nuclear Physics B 601, nos. 1–2 (May 2001): 209–47, arXiv:hep-th/0003056.
5. Marina Cortês and Lee Smolin, “The Universe as a Process of Unique Events,” Physical Review D 90, no. 8 (October 2014): 084007, arXiv:1307.6167 [gr-qc]; Cortês and Smolin, “Quantum Energetic Causal Sets,” Physical Review D 90, no. 4 (August 2014): 044035, arXiv:1308.2206 [gr-qc]; Cortês and Smolin, “Spin Foam Models as Energetic Causal Sets,” Physical Review D 93, no. 8 (June 2014): 084039, arXiv:1407.0032; Cortês and Smolin, “Reversing the Irreversible: From Limit Cycles to Emergent Time Symmetry,” Physical Review D 97, no. 2 (January 2018): 026004, arXiv:1703.09696.
6. Smolin, “The Dynamics of Difference,” Foundations of Physics 48, no. 2 (2018): 121–34, arXiv:1712.04799.
Epilogue/Revolutions
Epigraph David Gross, “Closing Remarks,” Strings 2003 Conference, Kyoto, Japan, July 6–11, 2003, slide 17, https://www.yukawa.kyoto-u.ac.jp/assets/contents/seminar/archive/2003/str2003/talks/gross.pdf.
GLOSSARY
Acceleration: The rate of change of velocity.
Angular momentum: A conserved quantity that measures the amount of rotation or angular motion.
Anti-realism: A philosophy according to which either there is no objective, universal reality, or if there is such, human beings cannot have complete knowledge of it.
Atom: The basic unit of matter, consisting of a nucleus, which contains protons and neutrons, surrounded by electrons.
Background: A scientific model or theory often describes only part of the universe. Some features of the rest of the universe may be included as necessary to define the properties of that part of the universe that is studied. These features are called the background. For example, in Newtonian physics space and time are part of the background because they are taken to be absolute.
Background dependent: A theory, such as Newtonian physics, that makes use of a background.
Background independent: A theory that does not make use of a division of the universe into a part that is modeled and the rest, which is taken to be part of the background. General relativity is said to be background independent because the geometry of space and time is not fixed, but evolves in time just like any other field, such as the electromagnetic field.
Bayesian probability: A subjective probability which measures a person’s degree of belief about something.
Bell’s theorem: States that in a world which is local, in the sense that the choice of measurements made on one system never influences the probabilities for the outcome of measurements made on a distant system, certain correlations of measurements are restricted by an inequality. That inequality is violated experimentally. Also called Bell’s relation or Bell’s restriction.
Bohmian mechanics: Another name for pilot wave theory.
Causal set theory: An approach to quantum spacetime based on the hypothesis that the history of the world is made from a discrete set of fundamental events and their causal relations.
Causality: The principle that events are influenced by those in their past. In relativity theory one event can have a causal influence on another only if energy or information sent from the first reaches the second.
Causal structure: Because there is a maximum speed at which energy and information can be transmitted, the events in the history of the universe can be organized in terms of their possible causal relations. To do this, one indicates, for every pair of events, whether the first is in the causal future of the second, or vice versa, or whether there is no possible causal relation between them because no signal could have traveled between them. Such a complete description defines the causal structure of the universe.
Classical physics: That part of physics from Galileo through general relativity, prior to the quantum theory.
Collapse of the wave function: The postulate that immediately after an observer takes a measurement which reveals a definite value for some observable, a quantum system takes on the quantum state associated to that value.
Complementarity principle: Principle proposed by Bohr that quantum systems admit different descriptions, such as particle and wave, that would contradict each other if they had to be imposed simultaneously. However, any given experiment can be described using one or the other.
Conserved quantity: A property of a physical system whose total value never changes in time as the system evolves. Examples are energy, momentum, and angular momentum.
Consistent histories approach: An interpretation of quantum mechanics based on assigning probabilities to sets of histories that decohere from each other.
Contrary state: See Einstein-Podolsky-Rosen state.
De Broglie–Bohm theory: Another name for pilot wave theory, named for its two inventors.
Decoherence: The process by which large quantum systems, containing many degrees of freedom, in contact with an environment which introduces random fluctuations, lose their wave properties, due to the phases of the waves becoming randomized, and so emerge as particles.
Degree of freedom: A variable quantity, describing one way a physical system can change.
Determinism: The philosophy that the future state of a physical system is completely determined by the laws of physics acting on the present state.
Discreteness: The property of some observables of quantum systems, such as the energy of an atom, to take values restricted to a discrete list.
Dynamical collapse theory: A proposal that collapse of the wave function is a real physical process.
Einstein-Podolsky-Rosen (EPR) state: A joint state of two particles which contains no information at all about the individual particles, but indicates that if any measurement is made on both, the results will be opposite. Also called the contrary state.
Energy: A physical quantity giving a measure of the activity of a system, whose value is preserved in time. Energy takes several forms and can be transmuted among them, with the total value always conserved.
Entanglement: A property of a quantum state of two or more systems, where the state indicates a property shared by those systems that is not just the sum of properties held by the individual particles. The EPR or contrary state is an example of an entangled state.
Entropy: A measure of the disorder of a physical system, which is related to the information trapped in the exact values of its microscopic degrees of freedom.
Event: In relativity theory, something that happens at a particular point of space and moment of time.
Exclusion principle: Invented by Wolfgang Pauli, it says that no two fermions can be in the same quantum state.
Field: A physical system spread out in space, with one or more degrees of freedom per spacetime point. The electric and magnetic fields are examples.
Field theory: A physical theory that describes the evolution in time of one or several fields. An example is electrodynamics, where the laws of motion of the fields are called the Maxwell equations.
Force: In Newtonian physics, the change in the momentum in a collision. Also equal to the acceleration of a body times the mass.
Future: The future, or causal future, of an event consists of all those events that it can influence by sending energy or information to them.
Hidden variable: A property or degree of freedom of a quantum system that is not described by quantum mechanics, but is needed to complete the description of an individual system.
> Holographic principle: A conjectured principle which limits the quantity of information crossing a surface to the area of the surface in Planck units.
Information: A measure of the organization of a signal. It is equal to the number of yes/no questions whose answers could be coded in the signal.
Instrumentalism: An approach to science wherein the role of theory is only to provide a description of a physical system in terms of its responses to externally imposed forces conveyed by measuring instruments.
Kochen-Specker theorem: A theorem that shows that quantum mechanics is contextual, which means that the value of an observable can depend on a choice of which other measurements are made at the same time.
Locality: The property of physical law that systems are only directly influenced by what is nearby in space and time.
Loop quantum gravity: An approach to quantum gravity based on a quantization of Einstein’s general theory of relativity.
Many moments interpretation: The hypothesis that what really exists is a vast collection of moments, containing everything that might have happened in the history of the universe.
Many Worlds Interpretation: An interpretation of quantum theory according to which the different possible outcomes of an observation of a quantum system reside in different universes, all of which somehow coexist.
Mass: In Newtonian physics, the inertial mass is a measure of the quantity of matter, which, multiplied by velocity, gives a conserved quantity called the momentum.
Matrix: A table of numbers organized into rows and columns.
Matrix mechanics: An approach to quantum mechanics in which observables are represented by matrices.
Momentum: A quantity defined for moving particles, which is exchanged in collisions so as to conserve the total. In Newtonian physics it is equal to the product of the mass and velocity.
Newtonian physics: A framework for describing and explaining motion, invented by Isaac Newton and presented in his 1687 book Principia Mathematica, which is based on three laws of motion.