This article possibly contains original research. (September 2017)
In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into three areas:
- interpretations of quantum mechanics: mainly concerning issues with how to formulate an adequate response to the measurement problem and understand what the theory says about reality.
- the nature of space and time: Are space and time substances, or purely relational? Is simultaneity conventional or only relative? Is temporal asymmetry purely reducible to thermodynamic asymmetry?
- inter-theoretic relations: the relationship between various physical theories, such as thermodynamics and statistical mechanics. This overlaps with the issue of scientific reduction.
Philosophy of space and time
The existence and nature of space and time (or space-time) are central topics in the philosophy of physics.
Time is often thought to be a fundamental quantity (that is, a quantity which cannot be defined in terms of other quantities), because time seems like a fundamentally basic concept, such that one cannot define it in terms of anything simpler. However, certain theories such as loop quantum gravity claim that spacetime is emergent. As Carlo Rovelli, one of the founders of loop quantum gravity has said: "No more fields on spacetime: just fields on fields". Time is defined via measurement—by its standard time interval. Currently, the standard time interval (called "conventional second", or simply "second") is defined as 9,192,631,770 oscillations of a hyperfine transition in the 133 caesium atom. (ISO 31-1). What time is and how it works follows from the above definition. Time then can be combined mathematically with the fundamental quantities of space and mass to define concepts such as velocity, momentum, energy, and fields.
Both Newton and Galileo, as well as most people up until the 20th century, thought that time was the same for everyone everywhere. The modern conception of time is based on Einstein's theory of relativity and Minkowski's spacetime, in which rates of time run differently in different inertial frames of reference, and space and time are merged into spacetime. Einstein's general relativity as well as the redshift of the light from receding distant galaxies indicate that the entire Universe and possibly space-time itself began about 13.8 billion years ago in the Big Bang. Einstein's theory of special relativity mostly (though not universally) made theories of time where there is something metaphysically special about the present seem much less plausible, as the reference-frame-dependence of time seems to not allow the idea of a privileged present moment.
Some theories, most notably general relativity, suggest that suitable geometries of spacetime, or certain types of motion in space, may allow time travel into the past and future. Concepts that aid such understanding include the closed timelike curve.
Albert Einstein's special theory of relativity (and, by extension, the general theory) predicts time dilation that could be interpreted as time travel. The theory states that, relative to a stationary observer, time appears to pass more slowly for faster-moving bodies: for example, a moving clock will appear to run slow; as a clock approaches the speed of light its hands will appear to nearly stop moving. The effects of this sort of time dilation are discussed further in the popular "twin paradox". Although these results are experimentally observable, an intrinsic aspect of Einstein' theory is an equation applicable to the operation of GPS satellites and other high-tech systems used in daily life.
A second, similar type of time travel is permitted by general relativity. In this type a distant observer sees time passing more slowly for a clock at the bottom of a deep gravity well, and a clock lowered into a deep gravity well and pulled back up will indicate that less time has passed compared to a stationary clock that stayed with the distant observer.
Many in the scientific community believe that backward time travel is highly unlikely, because it violates causality i.e. the logic of cause and effect. For example, what happens if you attempt to go back in time and kill yourself at an earlier stage in your life (or your grandfather, which leads to the grandfather paradox)? Stephen Hawking once suggested that the absence of tourists from the future constitutes a strong argument against the existence of time travel— a variant of the Fermi paradox, with time travelers instead of alien visitors.
Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because there is nothing more fundamental known at present. Thus, similar to the definition of other fundamental quantities (like time and mass), space is defined via measurement. Currently, the standard space interval, called a standard metre or simply metre, is defined as the distance traveled by light in a vacuum during a time interval of 1/299792458 of a second (exact).
In classical physics, space is a three-dimensional Euclidean space where any position can be described using three coordinates and parameterised by time. Special and general relativity use four-dimensional spacetime rather than three-dimensional space; and currently there are many speculative theories which use more than four spatial dimensions.
Philosophy of quantum mechanics
Quantum mechanics is a large focus of contemporary philosophy of physics, specifically concerning the correct interpretation of quantum mechanics. Very broadly, much of the philosophical work that is done in quantum theory is trying to make sense of superposition states: the property that particles seem to not just be in one determinate position at one time, but are somewhere 'here', and also 'there' at the same time. Such a radical view turns many common sense metaphysical ideas on their head. Much of contemporary philosophy of quantum mechanics aims to make sense of what the very empirically successful formalism of quantum mechanics tells us about the physical world.
The uncertainty principle is a mathematical relation asserting an upper limit to the accuracy of the simultaneous measurement of any pair of conjugate variables, e.g. position and momentum. In the formalism of operator notation, this limit is the evaluation of the commutator of the variables' corresponding operators.
The uncertainty principle arose as an answer to the question: How does one measure the location of an electron around a nucleus if an electron is a wave? When quantum mechanics was developed, it was seen to be a relation between the classical and quantum descriptions of a system using wave mechanics.
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light. "Hidden variables" are putative properties of quantum particles that are not included in the theory but nevertheless affect the outcome of experiments. In the words of physicist John Stewart Bell, for whom this family of results is named, "If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local."
The term is broadly applied to a number of different derivations, the first of which was introduced by Bell in a 1964 paper titled "On the Einstein Podolsky Rosen Paradox". Bell's paper was a response to a 1935 thought experiment that Albert Einstein, Boris Podolsky and Nathan Rosen proposed, arguing that quantum physics is an "incomplete" theory. By 1935, it was already recognized that the predictions of quantum physics are probabilistic. Einstein, Podolsky and Rosen presented a scenario that involves preparing a pair of particles such that the quantum state of the pair is entangled, and then separating the particles to an arbitrarily large distance. The experimenter has a choice of possible measurements that can be performed on one of the particles. When they choose a measurement and obtain a result, the quantum state of the other particle apparently collapses instantaneously into a new state depending upon that result, no matter how far away the other particle is. This suggests that either the measurement of the first particle somehow also interacted with the second particle at faster than the speed of light, or that the entangled particles had some unmeasured property which pre-determined their final quantum states before they were separated. Therefore, assuming locality, quantum mechanics must be incomplete, as it cannot give a complete description of the particle's true physical characteristics. In other words, quantum particles, like electrons and photons, must carry some property or attributes not included in quantum theory, and the uncertainties in quantum theory's predictions would then be due to ignorance or unknowability of these properties, later termed "hidden variables".
Bell carried the analysis of quantum entanglement much further. He deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. This constraint would later be named the Bell inequality. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles are able to interact instantaneously no matter how widely they ever become separated.
Multiple variations on Bell's theorem were put forward in the following years, introducing other closely related conditions generally known as Bell (or "Bell-type") inequalities. The first rudimentary experiment designed to test Bell's theorem was performed in 1972 by John Clauser and Stuart Freedman. More advanced experiments, known collectively as Bell tests, have been performed many times since. To date, Bell tests have consistently found that physical systems obey quantum mechanics and violate Bell inequalities; which is to say that the results of these experiments are incompatible with any local hidden variable theory.
The exact nature of the assumptions required to prove a Bell-type constraint on correlations has been debated by physicists and by philosophers. While the significance of Bell's theorem is not in doubt, its full implications for the interpretation of quantum mechanics remain unresolved.
Interpretations of quantum mechanics
In March 1927, working in Niels Bohr's institute, Werner Heisenberg formulated the principle of uncertainty thereby laying the foundation of what became known as the Copenhagen interpretation of quantum mechanics. Heisenberg had been studying the papers of Paul Dirac and Pascual Jordan. He discovered a problem with measurement of basic variables in the equations. His analysis showed that uncertainties, or imprecisions, always turned up if one tried to measure the position and the momentum of a particle at the same time. Heisenberg concluded that these uncertainties or imprecisions in the measurements were not the fault of the experimenter, but fundamental in nature and are inherent mathematical properties of operators in quantum mechanics arising from definitions of these operators.
The term "Copenhagen interpretation" is somewhat loosely defined, as many physicists and philosophers of physics have advanced similar but not identical views of quantum mechanics. It is principally associated with Heisenberg and Bohr, despite their philosophical differences. Features common to Copenhagen-type interpretations include the idea that quantum mechanics is intrinsically indeterministic, with probabilities calculated using the Born rule, and the principle of complementarity, which states that objects have certain pairs of complementary properties that cannot all be observed or measured simultaneously. Moreover, the act of "observing" or "measuring" an object is irreversible, and no truth can be attributed to an object, except according to the results of its measurement. Copenhagen-type interpretations hold that quantum descriptions are objective, in that they are independent of any arbitrary factors in the physicist's mind.: 85–90
The Everett, or many-worlds interpretation of quantum mechanics claims that the wave-function of a quantum system is telling us claims about the reality of that physical system. It denies wavefunction collapse, and claims that superposition states should be interpreted literally as describing the reality of many-worlds where objects are located, and not simply indicating the indeterminacy of those variables. This is sometimes argued as a corollary of scientific realism, which states that scientific theories aim to give us literally true descriptions of the world.
One issue for the Everett interpretation is the role that probability plays on this account. The Everettian account is completely deterministic, whereas probability seems to play an ineliminable role in quantum mechanics. Contemporary Everettians have argued that one can get an account of probability that follows the Born rule through certain decision-theoretic proofs, but there is as yet no consensus about whether any of these proofs are successful.
Physicist Roland Omnès noted that it is impossible to experimentally differentiate between Everett's view, which says that as the wave-function decoheres into distinct worlds, each of which exists equally, and the more traditional view that says that a decoherent wave-function leaves only one unique real result. Hence, the dispute between the two views represents a great "chasm". "Every characteristic of reality has reappeared in its reconstruction by our theoretical model; every feature except one: the uniqueness of facts."
Philosophy of thermal and statistical physics
The philosophy of thermal and statistical physics is that part of the philosophy of physics whose subject matter is an amalgam of classical thermodynamics, statistical mechanics, and related theories. Its central questions include: What is entropy, and what does the second law of thermodynamics say about it? What is the correct resolution of the Maxwell's demon paradox? Does either thermodynamics or statistical mechanics contain an element of time-irreversibility? If so, what does statistical mechanics tell us about the arrow of time? What is the nature of the probabilities that appear in statistical mechanics?
This section's factual accuracy is disputed. (September 2022)
Aristotelian physics viewed the universe as a sphere with a center. Matter, composed of the classical elements, earth, water, air, and fire, sought to go down towards the center of the universe, the center of the Earth, or up, away from it. Things in the aether such as the Moon, the Sun, planets, or stars circled the center of the universe. Movement is defined as change in place, i.e. space.
Every body perseveres in its state either of rest or of uniform motion in a straight line, except insofar as it is compelled to change its state by impressed forces.
"Every body" includes the Moon, and an apple; and includes all types of matter, air as well as water, stones, or even a flame. Nothing has a natural or inherent motion. Absolute space being three-dimensional Euclidean space, infinite and without a center. Being "at rest" means being at the same place in absolute space over time. The topology and affine structure of space must permit movement in a straight line at a uniform velocity; thus both space and time must have definite, stable dimensions.
Gottfried Wilhelm Leibniz, 1646–1716, was a contemporary of Newton. He contributed a fair amount to the statics and dynamics emerging around him, often disagreeing with Descartes and Newton. He devised a new theory of motion (dynamics) based on kinetic energy and potential energy, which posited space as relative, whereas Newton was thoroughly convinced that space was absolute. An important example of Leibniz's mature physical thinking is his Specimen Dynamicum of 1695.
Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense.
He anticipated Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute: "As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions."
- Anthropic principle
- Arrow of time
- Causality (physics)
- Causal closure
- Constructor theory
- Digital physics
- Mind-body dualism
- Field (physics)
- Functional decomposition
- Fundamental interaction
- Laws of thermodynamics
- Mesoscopic scale
- Modal realism
- Physical ontology
- Philosophy of:
- Physics envy
- Quantum theory:
- Symmetry in physics
- Time in physics
- Maudlin, Tim (2012). Philosophy of Physics: Space and Time. Princeton University Press. p. xi. ISBN 978-0691143095. Retrieved 3 October 2017.
...the existence and nature of space and time (or space-time) is a central topic.
- Rovelli, C. (2004). Quantum Gravity. Cambridge Monographs on Mathematical Physics. p. 71.
- Roger Penrose, 2004. The Road to Reality: A Complete Guide to the Laws of the Universe. London: Jonathan Cape. ISBN 0-224-04447-8 (hardcover), 0-09-944068-7 (paperback).
- Bolonkin, Alexander (2011). Universe, Human mmortality and Future Human Evaluation. Elsevier. p. 32. ISBN 978-0-12-415810-8. Extract of page 32
- BristolPhilosophy (19 February 2013). "Eleanor Knox (KCL) – The Curious Case of the Vanishing Spacetime". Archived from the original on 11 December 2021. Retrieved 7 April 2018 – via YouTube.
- Bell, John S. (1987). Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press. p. 65. ISBN 9780521368698. OCLC 15053677.
- Einstein, A.; Podolsky, B.; Rosen, N. (15 May 1935). "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?". Physical Review. 47 (10): 777–780. Bibcode:1935PhRv...47..777E. doi:10.1103/PhysRev.47.777.
- Bell, J. S. (1964). "On the Einstein Podolsky Rosen Paradox" (PDF). Physics Physique Физика. 1 (3): 195–200. doi:10.1103/PhysicsPhysiqueFizika.1.195.
- Parker, Sybil B. (1994). McGraw-Hill Encyclopaedia of Physics (2nd ed.). McGraw-Hill. p. 542. ISBN 978-0-07-051400-3.
- Mermin, N. David (July 1993). "Hidden Variables and the Two Theorems of John Bell" (PDF). Reviews of Modern Physics. 65 (3): 803–15. arXiv:1802.10119. Bibcode:1993RvMP...65..803M. doi:10.1103/RevModPhys.65.803. S2CID 119546199.
- "The Nobel Prize in Physics 2022". Nobel Prize (Press release). The Royal Swedish Academy of Sciences. 4 October 2022. Retrieved 6 October 2022.
- The BIG Bell Test Collaboration (9 May 2018). "Challenging local realism with human choices". Nature. 557 (7704): 212–216. arXiv:1805.04431. Bibcode:2018Natur.557..212B. doi:10.1038/s41586-018-0085-3. PMID 29743691. S2CID 13665914.
- Wolchover, Natalie (7 February 2017). "Experiment Reaffirms Quantum Weirdness". Quanta Magazine. Retrieved 8 February 2020.
- Niels Bohr, Atomic Physics and Human Knowledge, p. 38
- Faye, Jan (2019). "Copenhagen Interpretation of Quantum Mechanics". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University.
- Camilleri, K.; Schlosshauer, M. (2015). "Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts?". Studies in History and Philosophy of Modern Physics. 49: 73–83. arXiv:1502.06547. Bibcode:2015SHPMP..49...73C. doi:10.1016/j.shpsb.2015.01.005. S2CID 27697360.
- Omnès, Roland (1999). "The Copenhagen Interpretation". Understanding Quantum Mechanics. Princeton University Press. pp. 41–54. doi:10.2307/j.ctv173f2pm.9. S2CID 203390914.
Bohr, Heisenberg, and Pauli recognized its main difficulties and proposed a first essential answer. They often met in Copenhagen ... 'Copenhagen interpretation has not always meant the same thing to different authors. I will reserve it for the doctrine held with minor differences by Bohr, Heisenberg, and Pauli.
- Omnès, R. (1994). The Interpretation of Quantum Mechanics. Princeton University Press. ISBN 978-0-691-03669-4. OCLC 439453957.
- David Wallace, 'The Emergent Multiverse', pp. 1–10
- David Wallace, 'The Emergent Multiverse', pp. 113–117
- David Wallace, 'The Emergent Multiverse', pg. 157–189
- Kent, Adrian (2010). "One world versus many: The inadequacy of Everettian accounts of evolution, probability, and scientific confirmation". In S. Saunders; J. Barrett; A. Kent; D. Wallace (eds.). Many Worlds? Everett, Quantum Theory and Reality. Oxford University Press. arXiv:0905.0624. Bibcode:2009arXiv0905.0624K.
- Kent, Adrian (1990). "Against Many-Worlds Interpretations". International Journal of Modern Physics A. 5 (9): 1745–1762. arXiv:gr-qc/9703089. Bibcode:1990IJMPA...5.1745K. doi:10.1142/S0217751X90000805. S2CID 14523184.
- Price, Huw (2010). "Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability?". In S. Saunders; J. Barrett; A. Kent; D. Wallace (eds.). Many Worlds? Everett, Quantum Theory and Reality. Oxford University Press. arXiv:0802.1390.
- Omnès, Roland (2002). "11". Quantum philosophy : understanding and interpreting contemporary science (in French). Arturo Spangalli (transl.) (1st paperback ed.). Princeton: Princeton University Press. p. 213. ISBN 978-1400822867.
- Frigg, Roman; Werndl, Charlotte (10 January 2023). "Philosophy of Statistical Mechanics". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
- Tim Maudlin (2012-07-22). Philosophy of Physics: Space and Time: Space and Time (Princeton Foundations of Contemporary Philosophy) (p. 3). Princeton University Press. Kindle Edition. "Because it is a sphere, Aristotle's universe contains a geometrically privileged center, and Aristotle makes reference to that center in characterizing the natural motions of different sorts of matter. 'Upward', 'downward', and 'uniform circular motion' all are defined in terms of the center of the universe."
- Tim Maudlin (2012-07-22). Philosophy of Physics: Space and Time: Space and Time (Princeton Foundations of Contemporary Philosophy) (p. 4). Princeton University Press. Kindle Edition. "Aristotle adopts the concept of space, and the correlative concept of motion, that we all intuitively employ."
- Tim Maudlin (2012-07-22). Philosophy of Physics: Space and Time: Space and Time (Princeton Foundations of Contemporary Philosophy) (pp. 4–5). Princeton University Press. Kindle Edition. "Newtonian physics is implicit in his First Law of Motion: Law I : Every body perseveres in its state either of rest or of uniform motion in a straight line, except insofar as it is compelled to change its state by impressed forces. 1 This single law smashes the Aristotelian universe to smithereens."
- Tim Maudlin (2012-07-22). Philosophy of Physics: Space and Time: Space and Time (Princeton Foundations of Contemporary Philosophy) (pp. 5). Princeton University Press. Kindle Edition.
- Tim Maudlin (2012-07-22). Philosophy of Physics: Space and Time: Space and Time (Princeton Foundations of Contemporary Philosophy) (pp. 9–10). Princeton University Press. Kindle Edition. "Newton believed in the existence of a spatial arena with the geometrical structure of E3. He believed that this infinite three-dimensional space exists at every moment of time. And he also believed something much more subtle and controversial, namely, that identically the same points of space persist through time."
- Tim Maudlin (2012-07-22). Philosophy of Physics: Space and Time: Space and Time (Princeton Foundations of Contemporary Philosophy) (p. 12). Princeton University Press. Kindle Edition. "...space must have a topology, an affine structure, and a metric; time must be one-dimensional with a topology and a metric; and, most importantly, the individual parts of space must persist through time.
- Ariew and Garber 117, Loemker §46, W II.5. On Leibniz and physics, see the chapter by Garber in Jolley (1995) and Wilson (1989).
- Rafael Ferraro (2007). Einstein's Space-Time: An Introduction to Special and General Relativity. Springer. p. 1. ISBN 978-0-387-69946-2.
- See H. G. Alexander, ed., The Leibniz-Clarke Correspondence, Manchester: Manchester University Press, pp. 25–26.
- David Albert, 1994. Quantum Mechanics and Experience. Harvard Univ. Press.
- John D. Barrow and Frank J. Tipler, 1986. The Cosmological Anthropic Principle. Oxford Univ. Press.
- Beisbart, C. and S. Hartmann, eds., 2011. "Probabilities in Physics". Oxford Univ. Press.
- John S. Bell, 2004 (1987), Speakable and Unspeakable in Quantum Mechanics. Cambridge Univ. Press.
- David Bohm, 1980. Wholeness and the Implicate Order. Routledge.
- Nick Bostrom, 2002. Anthropic Bias: Observation Selection Effects in Science and Philosophy. Routledge.
- Thomas Brody, 1993, Ed. by Luis de la Peña and Peter E. Hodgson The Philosophy Behind Physics Springer ISBN 3-540-55914-0
- Harvey Brown, 2005. Physical Relativity. Space-time structure from a dynamical perspective. Oxford Univ. Press.
- Butterfield, J., and John Earman, eds., 2007. Philosophy of Physics, Parts A and B. Elsevier.
- Craig Callender and Nick Huggett, 2001. Physics Meets Philosophy at the Planck Scale. Cambridge Univ. Press.
- David Deutsch, 1997. The Fabric of Reality. London: The Penguin Press.
- Bernard d'Espagnat, 1989. Reality and the Physicist. Cambridge Univ. Press. Trans. of Une incertaine réalité; le monde quantique, la connaissance et la durée.
- --------, 1995. Veiled Reality. Addison-Wesley.
- --------, 2006. On Physics and Philosophy. Princeton Univ. Press.
- Roland Omnès, 1994. The Interpretation of Quantum Mechanics. Princeton Univ. Press.
- --------, 1999. Quantum Philosophy. Princeton Univ. Press.
- Huw Price, 1996. Time's Arrow and Archimedes's Point. Oxford Univ. Press.
- Lawrence Sklar, 1992. Philosophy of Physics. Westview Press. ISBN 0-8133-0625-6, ISBN 978-0-8133-0625-4
- Victor Stenger, 2000. Timeless Reality. Prometheus Books.
- Carl Friedrich von Weizsäcker, 1980. The Unity of Nature. Farrar Straus & Giroux.
- Werner Heisenberg, 1971. Physics and Beyond: Encounters and Conversations. Harper & Row (World Perspectives series), 1971.
- William Berkson, 1974. Fields of Force. Routledge and Kegan Paul, London. ISBN 0-7100-7626-6
- Encyclopædia Britannica, Philosophy of Physics, David Z. Albert
- Stanford Encyclopedia of Philosophy:
- "Absolute and Relational Theories of Space and Motion"—Nick Huggett and Carl Hoefer
- "Being and Becoming in Modern Physics"—Steven Savitt
- "Boltzmann's Work in Statistical Physics"—Jos Uffink
- "Conventionality of Simultaneity"—Allen Janis
- "Early Philosophical Interpretations of General Relativity"—Thomas A. Ryckman
- "Everett's Relative-State Formulation of Quantum Mechanics"—Jeffrey A. Barrett
- "Experiments in Physics"—Allan Franklin
- "Holism and Nonseparability in Physics"—Richard Healey
- "Intertheory Relations in Physics"—Robert Batterman
- "Naturalism"—David Papineau
- "Philosophy of Statistical Mechanics"—Lawrence Sklar
- "Physicalism"—Daniel Sojkal
- "Quantum Mechanics"—Jenann Ismael
- "Reichenbach's Common Cause Principle"—Frank Artzenius
- "Structural Realism"—James Ladyman
- "Structuralism in Physics"—Heinz-Juergen Schmidt
- "Supertasks"—JB Manchak and Bryan Roberts
- "Symmetry and Symmetry Breaking"—Katherine Brading and Elena Castellani
- "Thermodynamic Asymmetry in Time"—Craig Callender
- "Time"—by Ned Markosian
- "Time Machines" —John Earman, Chris Wüthrich, and JB Manchak
- "Uncertainty principle"—Jan Hilgevoord and Jos Uffink
- "The Unity of Science"—Jordi Cat