Update on entropy and memory loss

June 21, 2010

A while back I noted an interesting paper about the arrow of time and memory loss in quantum mechanics. Unfortunately for that idea a new commentary by Jennings and Rudolph [PRL 104:148901, 2010] refutes it by exhibiting a counter-example.

Questionable military research on gauge invariance

December 30, 2009

Checking for new eprints, three papers by P. J. Cote and M. A. Johnson caught my attention: (A) New perspectives on classical electromagnetism (arXiv:0903.4104v2), (B) On the peculiarity of the Coulomb gauge (arXiv:0906.4752v1), (C) Groupthink and the blunder of the gauges (arXiv:0912.2977v1). The main point of these papers seems to be that the exploitation of gauge freedom in electromagnetism is questionable. Specific objections are raised to steps in standard derivations using Lorentz and Coulomb gauges. For example, the title of paper B refers to the non-locality of potentials in the Coulomb gauge and some remarks on the matter quoted from J. D. Jackson’s classic textbook.

The papers themselves border on crankery, which is a bit alarming since the authors are affiliated with the army, but are at least wrong in instructive ways. Electromagnetism is manifestly gauge invariant and there are no genuine causality problems in the Coulomb gauge since the non-local potentials are not physically meaningful quantities in and of themselves. Read the rest of this entry »

A condensed matter interpretation of the Standard Model

December 29, 2009

Condensed matter physics provides mathematical analogies with particle physics. Quasiparticles, i.e. particle-like excitations of a given ground state, often share many physical properties with more fundamental particles. Among the many attempts to find deeper insights into the Standard Model is the exportation of analogies in the other direction: from condensed-matter physics to fundamental physics. Here’s one such line of work:

I. Schmelzer. A condensed matter interpretation of SM fermions and gauge fields. arXiv:0908.0591

Abstract: We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.

A recent follow up paper focuses on neutrinos:

I. Schmelzer. Neutrinos as pseudo-acoustic ether phonons. arXiv:0912.3892

Abstract: Recently [arXiv:0908.0591] the author has proposed a condensed matter model which gives all fermions and gauge fields of the standard model of particle physics. In the model, the inertness of right-handed neutrinos is explained by an association with translational symmetry. We argue that this association may be used as well to explain the small neutrino masses. They appear to be pseudo-Goldstone particles associated with an approximate translational symmetry of a subsystem. Then we propose to explain the masslessness of SU(3)_c x U(1)_em with an unbroken SU(3)x U(1) gauge symmetry of the model. We also detect a violation of a necessary symmetry property in the lattice Dirac equation and present a fix for this problem.

Convex analysis and thermodynamics

November 23, 2009

A previous post briefly reviewed convex analysis. Here I’ll review the application of convexity in basic thermodynamics.

Equilibrium states

The concept of thermodynamic equilibrium is a generalization of mechanical equilibrium, where all forces and torques cancel each other. Informally, the idea is that a system in thermodynamic equilibrium has stable, unchanging macroscopic properties, which may be characterized by an n-tuple of extensive variables. Read the rest of this entry »

Entropy decrease results in memory loss

September 2, 2009

I found a fun arrow-of-time paper in PRL, arguing that dynamical decreases in the entropy of an isolated system are not at all impossible, just impossible to remember!

L. Maccone. Quantum Solution to the Arrow-of-Time Dilemma, Phys. Rev. Lett. 103:080401 (2009), arXiv:0802.0438

Abstract: The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

While interesting, I wonder if this approach is really promising. Basically, the author proves his Eq. (2), stating that the sum of entropy changes in a system A containing the observer and another system C equals the entropy change in a reservoir plus the change in the total amount of correlations (i.e., mutual information) between A and C. In the most interesting case when the entropy of the reservoir is constant, any entropy decreases in A and C must come at the expense of decreasing the amount/strength of correlation between A and C. This, according to the author, means that an entropy decrease in C automatically results in the observer in system A losing any memories or records (a memory/record is a kind of correlation) of C’s previous higher entropy state. However, very little correlation (a very small memory/record) is needed to retain, say, just the numerical values of C’s entropy at different times. Entropy decreases in C could, for all we know, come at the expense of other, more detailed, correlations between A and C, while leaving memories of measured entropies intact. Thus, it seems that much more work is needed to actually establish that entropy decreases are unobservable (due to being impossible to remember). The Phys. Rev. Focus commentary also hints at this problem.

Is information, or constraints on inference, all there is?

July 26, 2009

“What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds.” — Ariel Caticha (eprint: 0710.1068)

“Perhaps physics is nothing but inference after all.” — Ariel Caticha (eprint: 0808.1260)

“Physics is the ability to win a bet.” — Attributed to J. R. Buck by C. A. Fuchs (eprint: quant-ph/0105039, p. 125)

Some theories present us with intruiging conceptual puzzles. This is the case with probability theory and statistics. Originally the notion of ‘probability’ was introduced in the study of games of chance, where players who are uncertain about outcomes in a game need to decide on a strategy. Read the rest of this entry »

Thermodynamics and statistical mechanics of self-gravitating systems

July 13, 2009

It is not uncommon among scientists to consider philosophy of science to be an uninteresting distraction from more important matters. When it comes to the foundations of thermodynamics and statistical mechanics, however, some philosophers have made genuinely useful contributions, doing an excellent job of summarizing the current situation and bringing clarity to the strengths and weaknesses of different foundations. Jos Uffink’s article on what, strictly speaking, is asserted by the second law of thermodynamics comes to mind—it has been well received by both philosophers and physicists. To specialists in the field, there may not be much new, but philosophers have at the very least managed to provide clear presentations of successes and problems to a potential wider audience of philosophers, physicists, and lay-men.

I’d like to highlight two preprints by Callender and Wallace, respectively, on the subject of thermodynamics of self-gravitating systems. Read the rest of this entry »