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Time: Poincaré Seminar 2010

Bertrand Duplantier, editor
Publication Date: 
Number of Pages: 
Progress in Mathematical Physics 63
[Reviewed by
Tom Schulte
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The eleventh volume in proceedings from the Poincaré Seminars explores perspectives on time, specifically its directionality. The authors here explore the universe’s time-asymmetry through five articles. Contributing is Fields medalist Cédric Villani, theoretical physicists Thibault Damour and Christopher Jarzynski, experimentalist Christophe Salomon, and philosopher of science Huw Price. There is a concluding, one-page whimsical musing by Catherine de Mitry on a mythic Time in self-reflection.

The first, Damour’s piece “Time and Relativity”, has an aptly introductory tone. It explores broadly the issues at play. This includes reviewing Boltzmann’s ideas on the physical origin of Newton’s Second Law, the entropy time-gradient, and implications of Special and General Relativity. English and original French versions of Villani’s “(Ir)reversibility and Entropy” explore the basic issues in classical mechanics (pre- and post-collision) in a style that alternates between the lively logic of an engaging discussion of these matters to the crisp mathematics of entropy. This hallmark piece of the collection concludes with a paragraph each on eleven paradoxes related to time’s arrow and kinetic equations, including Maxwell’s Demon and Loschmidt’s Paradox.

In “Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale”, Jarzynski explores the idea that it is due to scale that we never observe violations of the Second Law, from the statistical near impossibility of seeing significant deviations from the mean. At small enough scale, Jarzynski finds thermodynamic inequalities become equalities. Salomon describes the incredible precision of modern chronometry in “Time’s Measurement in the XXIst Century”. This includes atomic clocks and optical ones allowing for precisions to one picosecond per day. Aptly for so evasive a topic, the conclusion from Price is a logical, clarifying, and philosophical exploration of the enigma of time asymmetry in thermodynamics. This suitable ending piece is “Time’s Arrow and Eddington’s Challlenge”.

Tom Schulte at times contents himself with the time inferred from sense-impressions at Oakland Community College in Michigan.


​Time and Relativity, Thibault Damour

(Ir)reversibility and Entropy, Cédric Villani

(Ir)réversibilité et entropie, Cédric Villani

Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale, Christopher Jarzynski

Time Measurement in the XXIst Century, Christophe Salomon

Time’s Arrow and Eddington’s Challenge, Huw Price

Image of Time’s Irreversibility, Catherine de Mitry

Image de l'irréversibilité du Temps, Catherine de Mitry