Professor of Physics

Ph.D. (1985) California Institute of Technology.
Professor (since 2001).
Associate Professor (1996-2001).
Assistant Professor (1992-1996).
Research Associate, IPST, Univ. of Maryland (1990-92).
Visiting Scientist, NIST (1990-92).
Assistant Professor, Instituto de Física, UNICAMP, Brazil (1987-91).
Post-doctoral position, Physics Dep., Univ. of Utah (1985-87).

Entropy and Probability as tools for Inductive Reasoning; Information Geometry.
Foundations of Quantum Mechanics, Statistical Mechanics and General Relativity.
X-Ray Optics: Theories of the diffraction, scattering and emission of x rays.

My recent work explores whether the laws of physics might be derivable from principles of inductive reasoning. These principles - consistency, objectivity, universality and honesty - are sufficiently constraining that they lead to a unique set of rules for processing information: these are the rules of probability theory and the method of maximum relative entropy.

Among various forms of dynamics thermodynamics holds a special place because it provided the first clear example of a fundamental physical theory that could be derived as a procedure for processing relevant information using general principles of probable inference.

My work suggests that a second example is provided by quantum mechanics. Many features of the theory that are traditionally considered as postulates follow from the correct identification of the subject matter plus general principles of inference. Briefly, the variables that encode the information relevant for prediction are the amplitudes or wave functions assigned to experimental setups. These ingredients plus a requirement of consistency (namely, that if there are two ways to compute an amplitude, the two results should agree) supplemented by entropic arguments are sufficient to derive most of the standard formalism including Hilbert spaces, a time evolution that is linear and unitary, and the Born probability rule.

One can also approach these problems from a different direction. Instead of asking 'Can dynamical laws be derived as examples of inference?' we ask 'What sort of dynamics can one derive from the rules of inference?' More explicitly: Given an initial and a final state, what trajectory is the system expected to follow? The answer is a equation of motion obtained, not from a law of nature, but from a rule of inference - the principle of maximum entropy. The resulting “entropic” dynamics turns out to be elegant: it is time reversible and the system moves along a geodesic in the space of states. This is simple but not trivial: the geometry of the space of states is curved and possibly quite complicated. The many formal similarities with the theory of general relativity suggest that the latter might be a form of entropic dynamics.

An interesting by-product of this research program has been a clarification of the role played by relative entropy as a tool for reasoning for both classical and quantum theories of inference.

“Relative Entropy and Inductive Inference,” arXiv.org/abs/physics/0311093.

“Maximum entropy approach to the Theory of Simple Fluids,” Chi-Yuan Tseng and A.C., arXiv.org/abs/cond-mat/0310746.

“Maximum Entropy and Bayesian Data Analysis: Entropic Priors,” A.C. and R. Preuss, arXiv.org/abs/physics/0307060.

“Towards a Statistical Geometrodynamics,” to appear in “Decoherence, Information, Complexity and Entropy” ed. by H.-T. Elze (Lecture Notes in Physics, Springer, 2004); arXiv.org/abs/gr-qc/0301061.

“Entropic Dynamics,” in “Bayesian Inference and Maximum Entropy Methods in Science and Engineering” ed. by R. L. Fry, A.I.P. Vol. 617, p. 302 (2002), arXiv.org/abs/gr-qc/0109068.

“Yet another resolution of the Gibbs paradox: an information theory approach,” Chi-Yuan Tseng and A.C., in “Bayesian Inference and Maximum Entropy Methods in Science and Engineering” ed. by R. L. Fry, A.I.P. Conf. Proc. Vol. 617, p. 331 (2002), arXiv.org/abs/cond-mat/0109324.

“Change, time and information geometry,” in “Maximum Entropy and Bayesian Methods in Science and Engineering” ed. by A. Mohammad-Djafari, A.I.P. Vol. 568, p. 72 (2001), arXiv.org/abs/math-ph/0008018.

“Maximum Entropy, fluctuations and priors,” in “Maximum Entropy and Bayesian Methods in Science and Engineering” ed. by A. Mohammad-Djafari, A.I.P. Vol. 568, p. 94 (2001), arXiv.org/abs/math-ph/0008017.

“Insufficient reason and entropy in quantum theory,” Found. Phys. 30, 227 (2000), arXiv.org/abs/quant-ph/9810074.

“Consistency, amplitudes and probabilities in quantum theory,” Phys. Rev. A57, 1572 (1998), arXiv.org/abs/quant-ph/9804012.

“Consistency and linearity in quantum theory,” Phys. Lett. A244, 13 (1998), arXiv.org/abs/quant-ph/9803086.

Selected Publications in X-Ray Physics:

“An asymptotic form of the reciprocity theorem with applications in x-ray scattering,” Phys. Rev. B62, 3639 (2000), arXiv.org/abs/physics/0001005.

“A Fabry-Perot interferometer for sub-meV x-ray energy resolution,” A.C., K. Aliberti and S. Caticha-Ellis, “Synchrotron Radiation Instrumentation '95”, Conf. Proc., Rev. Sci. Instrum. 67, No. 9 (1996).

“A thermal neutron interferometer of the Fabry-Perot type,” A.C. and S. Caticha-Ellis, Phys. Stat. Sol. (a)153, 29 (1996).

“Reflection and transmission of x rays by graded interfaces,” Phys. Rev. B52, 9214 (1995).

“The diffraction of x rays at the far tails of the Bragg peaks. II. The Darwin dynamical theory,” Phys. Rev. B49, 33 (1994).

“The diffraction of x rays at the far tails of the Bragg peaks,” Phys. Rev. B47, 76 (1993).

“Quantum theory of the dynamical Cerenkov emission of x rays,” Phys. Rev. B 45, 9541 (1992).

“Phenomenological quantum electrodynamics in periodic dielectric media,” A.C. and Nestor Caticha, Phys. Rev. B46, 479 (1992).

“A Fabry-Perot interferometer for hard x rays,” A.C. and S. Caticha-Ellis, Phys. Stat. Sol. (a) 119, 643 (1990).

“Dynamical diffraction of x rays by thin crystals at Bragg angles near pi/2,” A.C. and S. Caticha-Ellis, Phys. Stat. Sol. (a) 119, 47 (1990).

“Transition-diffracted radiation and the Cerenkov emission of x rays,” Phys. Rev. A40, 4322 (1989).

“A resonant cavity for the stimulated emission of x rays,” A.C., N. Caticha and S. Caticha-Ellis, Appl. Phys. Lett., 54, 887 (1989).

“Dynamical Diffraction of x rays at Bragg angles near pi/2,” A.C. and S. Caticha-Ellis, Phys. Rev. B25, 971 (1982).