HPS 2626 Recent Topics in Philosophy of Physics
Tuesdays, 9:30am-11:55am. Fall term, 2004. G28 CL.
John D. Norton, 1017CL, 4-5896, email@example.com, http://www.pitt.edu/~jdnorton
Department of History and Philosophy of Science
University of Pittsburgh
This site is http://www.pitt.edu/~jdnorton/teaching/philphys
This document may be updated in the course of term.
Updated: September 1, 2004. (Ising simulation link added November 10, 2004)
The Three Principal Problems of Philosophy of Modern Physics
Topics and Readings
Space and Time
The Fine Print
Other course documents
The Three Principal Problems of Philosophy of Modern Physics
While the literature in philosophy of physics is huge, it turns out that a great deal of it is devoted to just three general problems. They arise in the interactions of the three principal elements of modern physics:
1. Mathematical structures.
2. Physical ontology
- First Problem. When do intertransformable mathematical structures represent the same physical ontology?
(Esp. philosophy of space and time.)
- The two ways in which the mathematical structures in question may be related are by symmetry transformations and gauge transformations.
A symmetry transformation leaves the mathematical structure unchanged, e.g. a translation or a rotation in a Euclidean space. This is the strongest form of interrelation. A symmetry transformation expresses a homogeneity of space or a relativity principle. e.g. The Lorentz transformation is a symmetry of a Minkowski spacetime. In the case of a symmetry transformation, we can only say that the original and transformed structures represent something different in the ontology by calling on something outside what is described by the mathematical structures of the theory. e.g. In a Minkowski spacetime free of all other material structures, a Lorentz transformation can be construed as shifting one "God's eye" observer's frame to another in relative motion.
A gauge transformation alters the mathematical structure but in a way for which we have some reason to believe that the physical ontology represented is unchanged. The simplest example is a real valued field in Euclidean space representing a Newtonian gravitational field. Since differences in potential only have physical meaning, we can always add a real constant to the field without changing the physical ontology, although the numerical value of the potential field will be changed throughout. This addition is a gauge transformation. The principal challenge with a gauge transformation is finding grounds for judging that the distinct mathematical structures represent the same thing physically. Two sorts of grounds have been used: verificationism--there is no observable difference between what the two structures represent; indeterminism--if we insist the two structures represent distinct physical ontologies, we gratuitiously visit indeterminism of the theory.
There is an interesting inversion of the general problem with the existence of unitarily inequivalent representations of the commutation relations in algebraic quantum field theory. These are structures that are not intertransformable, but plausibly should somehow represent the same ontology. Or should they?
- Second Problem. What do the mathematical structures of a successful theory represent in the physical ontology?
(Esp. philosophy of quantum theory)
- With any mathematical theory, we must associate the mathematical structures of the theory with something in the physical ontology. Usually this is not so difficult to achieve. Invariant line elements in a metrical space are associated with physical distances in ordinary space. Or the magnetic field strength vector field of electrodynamics is associated with the magnetic field supported by a magnet. One instance of this problem has proven remarkably recalcitrant:
Interpretations of quantum theory Quantum theory has proven enormously successful in dealing with appearances. However the debate rages without evident hope of resolution over just what physical ontology ought to be ascribed to the theory's mathematical structures. The Schroedinger wave of a particle was initially hoped to be some sort of charge distribution; and then perhaps a wave of probability or potentiality, whatever that might mean; and most recently the theory is somehow about "quantum information." The most refractory problems have been presented by superpositions and entangled states. The problems of the latter were paraded in the Einstein-Podolsky-Rosen paper of 1935 and developed later by Bell. The concensus arising from this problem is of an unavoidable non-locality or non-separability in the theory's physical ontology. The problems of the former (superpositions) were emphasized by Schroedinger's "cat" paper also of 1935. Seventy years later, the enormous literature in "interpretations of quantum theory" is largely given over to trying to specifying just what the physical ontology of quantum theory should be.
The measurement problemWhat complicates the problem of interpretation enormously is a possible incompleteness of the theory's formal apparatus. In traditional developments, two types of time development are distinguished: Schroedinger evolution (spreading of the wave packet) and measurement (collapse of the wave packet). Unfortunately we do not have precise rules to decide when one or the other happens. Rather we have pretty good rules of thumb that work well for practical application of the theory. If a wave interacts with something big, it collapses; if it interacts with one or two other particles, or none at all, it spreads. But how are we to handle the intermediate cases?
Some interpretations ("no collapse theories") do away with the measurement problem by seeking to develop the theory entirely from Schroedinger time evolution. Such approaches complicate matters since we no longer have a single fixed theory. Collapse and no-collapse theories differ on just what time evolutions are possible within the mathematical structures.
- Third Problem. How do we reconcile a physical ontology with seemingly incompatible appearances?
(Esp. philosophy of statistical physics)
- In this problem, we face some sort of systematic mismatch between the physical ontology and appearances. Two important instances arise in statistical physics.
The asymmetry of time. Excepting weak interactions, all our microphysics is time reversible. The appearances of the macroscopic world are strongly directed in time, distinguishing past from future. How can this asymmetry arise from the microphysics?
Phase transitions. The interactions of microphysics are represented by differential equations that admit no discontinuities. The appearance of thermal systems is characterized by discontinuous transformations--phase transitions, such as between solid and gaseous state. How can the appearance of discontinuity arise from a continuous ontololgy?
This problem can arise in many other contexts. e.g. Einstein in 1905 worried about how to reconcile the presence of a preferred ether state of rest in then current electrodynamics with appearances that conformed to the principle of relativity. Some versions of no-collapse theories of quantum mechanics must explain how quantities appear to have sharp values when their version of quantum mechanics says that they really do not.
Topics and Readings
Philosophy of Space and Time; Symmetries and Gauges
The classical literature on the principle of relativity
Newton, Leibniz and the debate over absolute space.
Einstein and special relativity
Einstein and the vexed problem of whether general relativity extends the principle of relativity to acceleration.
Mach's Principle and Machian theories of space and time.
The relativity of acceleration in Newtonian cosmology
Newtonian cosmology turns out to host a rather unexpected principle of relativity tha governs uniform acceleration. Because of its unfamiliarity, it is a good place to hone our intutions on the principle of relativity.
Norton, J. D. "The Force of Newtonian Cosmology: Acceleration is Relative" Philosophy of Science, 62 (1995), pp.511-22. Download.
The hole argument
The revival of Einstein's "hole argument" was an early and important element in the development of interest in gauge freedoms in philosophy of physics. One aspect of its importance lies in its clear delineation of the two sorts of physical groundings for the judgment that a transformation represents a non-physical gauge freedom: verificationism and determinism.
Norton, J. D. "The Hole Argument," Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/spacetime-holearg/
Neo-Lorentzians return again
A perennial topic of debate is whether the physical effects of special relativity (e.g. length contraction) require some sort of physical explanation that in turn requires some sort of state of rest such as Lorentz envisaged was supplied by his ether.
Balashov, Y. and Janssen, M. "Presentism and relativity," British Journal for the Philosophy of Science 54 (2003), 32746.
Brown, H, R. and Pooley, O. "Minkowski space-time: a glorious non-entity." 2004 Download from philsci-archive.
Presentism, possibilism, eternalism
Is the reality of time a moving instant of "now," a moving "now" that converts potential futures into an existent past, or an eternal coexistence of all times? Does modern physics have anything to add to this old debate?
Savitt, S. "Being and Becoming in Modern Physics," Stanford Encyclopedia of Philosophyhttp://plato.stanford.edu/entries/spacetime-bebecome/
Earman, J. "Thoroughly Modern McTaggart: Or, What McTaggart Would Have Said if He Had Read the General Theory of Relativity," Philosophers' Imprint, Vol. 2, No. 3. http://www.philosophersimprint.org/002003/
Mauldlin, T. "Thoroughly Muddled McTaggart: Or, How to Abuse Gauge Freedom to Create Metaphysical Monostrosities" With a Response by John Earman Philosophers' Imprint, Vol. 2, No. 4. http://www.philosophersimprint.org/002004/
The exploitation of the notion of symmetry and intertransformability in general philosophy of science.
Much of what is said about symmetries and gauge freedoms is of direct relevance to general problems in philosophy of science.
Ismael, J. and Van Fraassen, B. "Symmetry as a Guide to Superfluous Theoretical Structure," Ch. 23 in K. Brading and E. Castellani, eds., Symmetries in Physics: Philosophical Reflections. Cambridge University Press, 2003.
Norton, J. D. "The Formal Equivalence of Grue and Green and How It Undoes the New Riddle of Induction." Synthese, forthcoming. Download A solution of the "grue" problem.
The Bohm Aharonov Effect.
Initially the affect appeared to show that the gauge field of electrodynamics did matter empirically in the quantum mechanical context, so we seemed to have a splendid example of a mathematical construct migrating to the physically real. Later reflection suggested that this is not so and that what has empirical significance is a gauge indepedent holonomy.
Healey, R. "Nonlocality and the Aharonov-Bohm Effect,"Philosophy of Science, 64(1997), pp. 18-41. (Includes a nice account of the effect.)
Healey, R. "On the Reality of Gauge Potentials," Philosophy of Science, 68 (2001), pp. 432-55.
Batterman, R. "Falling cats, parallel parking, and polarized light", Studies in History and Philosophy of Modern Physics, 34 (2003), pp. 527-57.
Nounou, A. M. "A fourth way to the Aharonov-Bohm Effect." Ch. 10 in K. Brading and E. Castellani, eds., Symmetries in Physics: Philosophical Reflections. Cambridge University Press, 2003.
Deeper reflections on gauge.
Just how should one respond to the discovery of a gauge freedom in a physical theory?
Redhead, M. "The Interpretation of Gauge Symmetry," Ch. 7 in K. Brading and E. Castellani, eds., Symmetries in Physics: Philosophical Reflections. Cambridge University Press, 2003.
Belot, G. "Symmetry and Gauge Freedom," Studies in History and Philosophy of Modern Physics, 34 (2002), pp. 189-225.
Earman, J. Gauge matters. Philosophy of Science, 69 (2002), pp. S209S220.
Earman, J. "Tracking Down Gauge: An Ode to the Constrained Hamiltonian Formalism," Ch. 8 in K. Brading and E. Castellani, eds., Symmetries in Physics: Philosophical Reflections. Cambridge University Press, 2003.
How to use mathematical structures to represent physical systems:
Klein's subtractive strategy and Riemann's additive strategy.
Two distinct strategies emerged in the nineteenth century. One could overdescribe the physical system and then use group theoretic methods to deprive some parts of the description of physical significance; or one would strive to introduce just as much mathematical structure as already had physical significance.
Norton, J. D. "Geometries in Collision: Einstein, Klein and Riemann." in J. Gray, ed., The Symbolic Universe. Oxford University Press, pp.128-144. Download
Philosophy of Quantum Theory
The usual suspects. Proposed interpretations of quantum theory. An interpretation of quantum theory is an attempt to give a cogent account of the physical reality that lies behind the enormously successful mathematical formalism of quantum theory. The debate continues without apparent hope of resolution as to which is the right answer.
Collapse models: von Nuemann's two rules and the GRW (Ghirardi, Rimini, Weber) proposal
Copenhagen Interpretation: Bohr's influential vision
Everett Relative-State formulation/Many worlds interpretation
Many worlds interpretations
This is a recent version of the idea popularly rendered as the notion that a superposition in quantum mechanics is to be associated with many worlds existing in parallel.
Wallace, D., "Worlds in the Everett interpretation," Studies in History and Philosophy of Modern Physics 33 (2002), pp. 637661.
Wallace, D. "Everett and structure," Studies in History and Philosophy of Modern Physics, 34(2003), pp. 87105.
Wallace, D., "Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation," Studies in History and Philosophy of Modern Physics 34(2003), pp. 415439.
Quantum mechanics tells us that, in Schroedinger's famous set up, we create a cat in a superposition of live and dead states. The proposal is that this superposed cat rapidly gets into interaction with many other systems and that, through this chaotic interaction, reverts to the more famililar cat that definitely either alive or dead.
Bacciagaluppi, G "The Role of Decoherence in Quantum Theory"Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/qm-decoherence/
Zurek, W.H., "Decoherence, einselection and the existential interpretation (The Rough Guide)." Philosophical Transactions of the Royal Society of London A356 (1998), pp. 17931820.
Zurek, W.H., "Decoherence, einselection and the quantum origins of the classical." Reviews of Modern Physics, 75 (2003) 3, pp. 715775. Download http://www.arxiv.org/abs/quant-ph/0105127.
A number of characteristically quantum effects can be described in terms of information processing. This has led to the notion that what is distinctive about quantum theory is it harbors a new notion of information, quantum information. The effects are all expressions of entanglement and include quantum teleportation, quantum cryptography and quantum computation
Rae, A. "Quantum Information," Ch. 12 in Quantum Mechanics Institute of Physics Publishing, 2002.
Bub, J. "Quantum Entanglement and Information," Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/qt-entangle/
Jozsa, R.. ``Quantum information and its properties'', In Lo, Hoi-Kwong, L., Popescu, S., Spiller, T. Introduction to quantum computation and information, Singapore: World Scientific, 1998.
Quantum information versus Shannon information.
Whether quantum theory requires a new notion of information, as opposed to that already captured in Shannon's classical theory has been debated.
Brukner, C. and Zeilinger, A., Operationally Invariant Information in Quantum Measurements, Physical Review Letters 83 (2001). pp. 3354-57.
Timpson, C. G. "On a Supposed Conceptual Inadequacy of the Shannon Information in Quantum Mechanics," Studies in History and Philosophy of Modern Physics, 34 (2003), pp. 441-68.
Duwell, A. "Quantum Information Does not Exist," Studies in History and Philosophy of Modern Physics, 34 (2003), pp.479-99.
Kochen Specker Theorem.
This theorem expresses the fundamental limits on which properties may be possessed simultaneously by a quantum system. It is one of the most important of the "no go" theorems that preclude quantum craziness arising merely as an artifact of our ignorance of a hidden but classically well behaved microphysics.
Redhead, M. "The Kochen Specker Paradox," Ch. 4 in Incompleteness, Nonlocality and Realism. Oxford: Clarendon Press, 1987.
Held, Carsten "The Kochen-Specker Theorem," Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/kochen-specker/
Hrushovski, E. and Pitowsky, I "Generalizations of Kochen and Specker's theorem and the effectiveness of Gleason's theorem" Studies in History and Philosophy of Modern Physics 35 (2004), pp. 177-194
Bub-Clifton Uniqueness Theorem
Within the constraints of the Kochen Specker theorem, just how many possessed states may be ascribed to a quantum system? Jeff Bub and Rob Clifton found a nice geometrical answer.
Dickson, M. [Section 3] of "The Modal Interpretations of Quantum Theory," Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/qm-modal/
Bub, J. and Clifton, R. "A Uniqueness Theorem for 'No Collapse' Interpretations of Quantum Mechanics," Studies in History and Philosophy of Modern Physics, 27 (1996), pp. 181-96.
Bub, J. "The problem of interpretation," Ch. 4 in Interpreting the Quantum World. Cambridge University Press, 1997.
Philosophy of Statistical Physics
The asymmetry of time
Brown, H. R. and Uffink, J. "The Origins of Time-Asymmetry in Thermodynamics: The Minus First Law," Studies in History and Philosophy of Modern Physics, 32 (2001), pp. 525-38.
The suggestion is that time asymmetry comes from the postulated notion of equilibrium itself.
The big bang and the low entropy state of the universe.
The temporal asymmetry of familiar processes now is often traced back to the low entropy state of the universe near the big bang. Is this explanation cogent or does it in turn raise problems in need of further explanation?
Price, H. "On the Origins of the Arrow of Time: Why There is Still a Puzzle About the Low Entropy Past,"
Callender, C. "There is No Puzzle About the Low Entropy Past,"
Ch.11 and 12 in C. Hitchcock, ed., Contemporary Debates in Philosophy of Science. Blackwells, 2004. Part VI: Is There a Puzzle about the Low Entropy Past?
Parker, D. (2004) "Thermodynamic Irreversibility: Does the Big Bang Explain what it Purports to Explain?" Proceedings Philosophy of Science Assoc. 19th Biennial Meeting - PSA2004: PSA 2004 Contributed Papers. philsci-archive
Phase transition: how it is done in statistical physics
The best known examples of how discontinuous phase transitions may be wrestled from an apparently continuous microphysics are spin lattices. Here is a brief introduction to how this works. Reading to be determined.
A nice simulation of a 2D Ising model.
Asymptotic explanation and the renormalization group
A short introduction to notions that now dominate statistical physics and have enabled considerable clarification of the nature of phase transitions. Phase transitions are recovered by taking limits of infinitely many components. The renormalization group enables us to map out the behavior of systems at their critical points.
"Asymptotic Explanation," Chapter 4 in R. W. Batterman, The Devil in the Details. Oxford University Press, 2002.
Phase transitions and the thermodynamic limit
Should we dispense with the idea that phase transitions involve discontinuities in thermodynamic quantities so that we need not take the thermodynamic limit of infinitely many particles?
Callender, C. "Taking Thermodynamics Too Seriously," Studies in History and Philosophy of Modern Physics, 32 (2001), pp. 501-635.
Batterman, Robert (2004) Critical Phenomena and Breaking Drops: Infinite Idealizations in Physics. Download from philsci-archive
Information and entropy.
A long standing tradition maintains that proper attention to information theory explains why Maxwell's demon must fail to reverse the second law of thermodynamics. John Earman and I (Norton) have long argued that this explanation depends on question beginning. More recently I've pointed to systematic misapplications of statistical physics that seriously compromise Landauer's principle, the notion that memory erasure must be accompanied by an entropy cost.
Earman, J. and Norton, J. D. "Exorcist XIV: The Wrath of Maxwell's Demon." Studies in the History and Philosophy of Modern Physics, Part I "From Maxwell to Szilard" 29(1998), pp.435-471; Part II: "From Szilard to Landauer and Beyond," 30(1999), pp.1-40. Download
Norton, J. D. "Eaters of the Lotus: Landauer's Principle and the Return of Maxwell's Demon." Prepared for New Directions in the Foundations of Physics, American Institute of Physics, College Park, MD. April 30-May 2, 2004. Download from http://www.pitt.edu/~jdnorton/homepage/cv.html
Platonism in mathematical physics.
Is there some kind of unreasonable miracle is the immense fertility of mathematics in physics?
Wigner, E., "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Communications on Pure and Applied Mathematics, 13 (1960), pp. 1-14.
Davey, K. "Unresaonable Effectiveness: Historical/Aesthetic" and "Unreasonable Effectiveness: Descriptive" Chs. 7-8 in Problems in Applying Mathematics: On the Inferential and Representational Limits of Mathematicsin Physics. PhD. Dissertation, Dept. of Philosophy, University of Pittsburgh, 2003. http://etd.library.pitt.edu/ETD/available/etd-10292003-081734/
Norton J. D. "'Nature in the Realization of the Simplest Conceivable Mathematical Ideas?: Einstein and the Canon of Mathematical Simplicity," Studies in the History and Philosophy of Modern Physics, 31 (2000), pp.135-170. Download
Supertasks. Zeno's revenge.
Zeno thought that the idea of completing an infinity of operations was deeply problematic. It is now becoming clear that the completion of an infinity of actions is not just a logical possibility but is licensed by quite a few respectable physical theories and with some curious outcomes. But is the license really licit?
Alper, J. S., Mark Bridger, M. , Earman, J. and Norton, J. D. , "What is a Newtonian System? The Failure of Energy Conservation and Determinism in Supertasks," Synthese, 124(2000), pp. 281-293. Download
NB. The list is not exhaustive. It just has items that happened to cross my desk while I was preparing this page!
Albert, D., 1992, Quantum Mechanics and Experience, Cambridge, MA: Harvard University Press.
Barrett, J. The Quantum Mechanics of Minds and Worlds. Oxford University Press, 1999.
Brading, K. and Castellani, E. , eds., Symmetries in Physics: Philosophical Reflections. Cambridge University Press, 2003.
Bub, J. Interpreting the Quantum World. Cambridge University Press, 1997.
Cushing, J. T. and McMullin, E., eds., Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem. University of Notre Dame Press, 1989.
Hughes, R. I. G. The Structure and Interpretation of Quantum Mechanics Cambridge, MA: Harvard University Press, 1989.
Norton, J. "Introduction to the Philosophy of Space and Time, " in Introduction to the Philosophy of Science. Prentice-Hall, 1992. Reprinted Hackett, 1999.
Preskill, J., Quantum Computation (Lecture Notes for Physics 219, California Institute of Technology) 1998.Download
Rae, A. Quantum Mechanics Institute of Physics Publishing, 2002.
Redhead, M. Incompleteness, Nonlocality and Realism. Oxford: Clarendon Press, 1987.
Sklar, L. Philosophy of Physics Westview, 1992.
Sklar, L. Physics and Chance Cambridge University Press, 1993.
Stanford Encyclopedia of Philosophy http://plato.stanford.edu
Torretti, R. The Philosophy of Physics Cambridge University Press, 1999.
Mathematical background for quantum theory.
Bub, J. Appendix to Interpreting the Quantum World. Cambridge University Press, 1997.
Clifton, Rob, Introductory Notes on the Mathematics Needed for Quantum Theory. 1996. Download from philsci-archive
Ismael, Jenann, "Quantum Mechanics," The Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/qm/
The fine print. Participants in this seminar are expected to attend regularly, read the assigned readings and take their turn in presenting material. The final grade is based on these presentations and on written work consisting of:
EITHER (at least) ten weekly written responses to the readings, a couple of pages that argue some point arising in the weekly seminar reading. The written responses are due on the day the relevant reading will be discussed in class. Only one will be accepted each week. No late submissions will be accepted since the written responses are intended to prepare you to discuss the reading in the seminar and keep you up with the readings. Since there are 14 class meetings (not counting the first meeting), this means that you will be forgiven 4 omissions--no questions asked.
OR an essay to be submitted on Thursday 16th December in 1017CL by noon. My policy is NOT to issue incomplete grades, excepting in extraordinary circumstances. I really do want your essays completed and submitted by the end of term. I do not want them to linger on like an overdue dental checkup, filling your lives with unnecessary worry and guilt. In return for the rigidity of the deadline, the seminar will not meet in the final week of term (Tuesday December 14). The essay may be on any subject of relevance to the seminar. To assist you in commencing work, I ask you submit an essay proposal to me by Tuesday 16th November. The proposal need only be brief. It should contain a short paragraph describing the topic to be investigated and give a brief indication of the sources you intend to use. Do talk to me about possible topics!