Condensed concepts

Time has a direction. Microscopic equations of motion in classical and quantum mechanics have time-reversible symmetry. But this symmetry is broken for many macroscopic phenomena. This observation is encoded in the second law of thermodynamics. We experience the flow of time and distinguish past, present, and future. The arrow of time is manifest in phenomena that occur at scales covering many orders of magnitude. Here are some of these different arrows of time, listed in order of increasing time scales. These are discussed by Tony Leggett in chapter 5 of The Problems of Physics. Elementary particle physics. CP violation is observed in certain phenomena associated with the weak nuclear interaction, such as the decay of neutral kaons observed in 1964. The CPT symmetry theorem shows that any local quantum field theory that is invariant under the “proper” Lorentz transformations must also be invariant under combined CPT transformations. This means that CP violation means that time-rever

Working in quantum many-body theory, I slowly learned that many key concepts and techniques have predecessors and analogues in classical systems and one-body quantum systems. Examples include Green's functions, path integrals, cumulants, the linked cluster theorem, Hubbard-Stratonavich transformation (completing the square), mean-field theory, localisation due to disorder, and BBGKY hierarchy . Learning a full-blown quantum many-body version is easier if you first understand simpler analogues. This post is about effective theories in classical systems and one-body quantum systems, following my earlier post about effective theories in quantum field theories of elementary particles . Michèle Levi  has a pedagogical article Effective field theories of post-Newtonian gravity: a comprehensive review This is motivated by the use of EFTs to describe gravitational waves produced by the inspiraling and merging of binary black holes and neutron stars . She discusses the different scales invo

The Netflix series, 3-body Problem , features physics and physicists throughout. I am not a big fan of science fiction, but watched the first episode, to try and get a sense of why the series is attracting so much attention. The opening scene (in the video above) is rooted in history. It depicts a "struggle session" during the Cultural Revolution , featuring the denunciation and killing of a physics professor, who is the father of the main character in the series. For some more on the intellectual and political background see Organized criticism of Einstein and relativity in China, 1949–1989 , by Danian Hu

 Over the last hundred years, there has been a fruitful cross-fertilisation of concepts and techniques between the theory of condensed matter and the quantum theory of elementary particles and fields. Examples include spontaneous symmetry breaking, renormalisation, and BCS theory. Sometimes, these efforts have occurred in parallel and only later did people realise that two different communities were doing essentially the same thing but using different language. Other times, one community adopted ideas or techniques from the other. Central to condensed matter theory are ideas of emergence, a hierarchy of scales, and effective theories that are valid at a particular scale. Elementary particle theorists such as Steven Weinberg often distinguish themselves as reductionists with different goals and approaches. I only recently became aware that effective field theories have become a big thing in the elementary particle community, and Weinberg has been one of the leaders of this! There is a h

Stimulated by discussions about the physics of learning machines with Gerard Milburn, I have been wondering about biomolecular machines such as proteins that do the transcription and translation of DNA in protein synthesis.  These are rather amazing machines. I found an article which considers a problem that is simpler than learning, computation. The thermodynamic efficiency of computations made in cells across the range of life Christopher P. Kempes, David Wolpert, Zachary Cohen and Juan Pérez-Mercader It considers the computation of translating a random set of 20 amino acids into a specific string for a specific protein.  Actual thermodynamic values are compared to a generalised Landauer bound for computation .  Below is the punchline. (page 9) Given that the average protein length is about 325  amino acids for 20 unique amino acids, we have that  p i = p =1/20 325 =1.46×10 −423 , where there are 20 325  states, such that the initial entropy is    , which gives the free energy chang