An Alternative Interpretation of Statistical Mechanics

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics

Emergence: Key physical issues for deeper philosophical inquiries

A sketch of three senses of emergence and a suggestive view on the emergence of time and the direction of time is presented. After trying to identify which issues philosophers interested in emergent phenomena in physics view as important I make several observations pertaining to the concepts, methodology and mechanisms required to understand emergence and describe a platform for its investigation. I then identify some key physical issues which I feel need be better appreciated by the philosophers in this pursuit. I end with some comments on one of these issues, that of coarse-graining and persistent structures.Comment: 16 pages. Invited Talk at the Heinz von Foerster Centenary International Conference on Self-Organization and Emergence: Emergent Quantum Mechanics (EmerQuM11). Nov. 10-13, 2011, Vienna, Austria. Proceedings to appear in J. Phys. (Conf. Series

Emergence: Key physical issues for deeper philosophical inquiries

A sketch of three senses of emergence and a suggestive view on the emergence of time and the direction of time is presented. After trying to identify which issues philosophers interested in emergent phenomena in physics view as important I make several observations pertaining to the concepts, methodology and mechanisms required to understand emergence and describe a platform for its investigation. I then identify some key physical issues which I feel need be better appreciated by the philosophers in this pursuit. I end with some comments on one of these issues, that of coarse-graining and persistent structures.Comment: 16 pages. Invited Talk at the Heinz von Foerster Centenary International Conference on Self-Organization and Emergence: Emergent Quantum Mechanics (EmerQuM11). Nov. 10-13, 2011, Vienna, Austria. Proceedings to appear in J. Phys. (Conf. Series

Probing impulsive strain propagation with x-ray pulses

Pump-probe time-resolved x-ray diffraction of allowed and nearly forbidden reflections in InSb is used to follow the propagation of a coherent acoustic pulse generated by ultrafast laser-excitation. The surface and bulk components of the strain could be simultaneously measured due to the large x-ray penetration depth. Comparison of the experimental data with dynamical diffraction simulations suggests that the conventional model for impulsively generated strain underestimates the partitioning of energy into coherent modes.Comment: 4 pages, 2 figures, LaTeX, eps. Accepted for publication in Phys. Rev. Lett. http://prl.aps.or

Less is Different: Emergence and Reduction Reconciled

This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction. In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each of them a model or a framework for modelling, from well-established mathematics or physics. I take emergence as behaviour that is novel and robust relative to some comparison class. I take reduction as, essentially, deduction. The main idea of my first rebuttal will be to perform the deduction after taking a limit of some parameter. Thus my first main claim will be that in my four examples (and many others), we can deduce a novel and robust behaviour, by taking the limit, N goes to infinity, of a parameter N. But on the other hand, this does not show that that the infinite limit is "physically real", as some authors have alleged. For my second main claim is that in these same examples, there is a weaker, yet still vivid, novel and robust behaviour that occurs before we get to the limit, i.e. for finite N. And it is this weaker behaviour which is physically real. My examples are: the method of arbitrary functions (in probability theory); fractals (in geometry); superselection for infinite systems (in quantum theory); and phase transitions for infinite systems (in statistical mechanics).Comment: 75 p

Infinitesimal Idealization, Easy Road Nominalism, and Fractional Quantum Statistics

It has been recently debated whether there exists a so-called “easy road” to nominalism. In this essay, I attempt to fill a lacuna in the debate by making a connection with the literature on infinite and infinitesimal idealization in science through an example from mathematical physics that has been largely ignored by philosophers. Specifically, by appealing to John Norton’s distinction between idealization and approximation, I argue that the phenomena of fractional quantum statistics bears negatively on Mary Leng’s proposed path to easy road nominalism, thereby partially defending Mark Colyvan’s claim that there is no easy road to nominalism

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems