Condensed concepts

 Spontaneous symmetry breaking is a fundamental concept in condensed matter and quantum field theory. Amongst philosophers of science the concept is receiving increasing attention, particularly in the context of discussions about emergence. How do we understand the following two observations about a system at zero temperature? At zero temperature for a finite-sized system there is no symmetry breaking. The ground state transforms as the trivial representation of the symmetry group of the Hamiltonian. It is non-degenerate. In the thermodynamic limit, there is a family of degenerate ground states. They are related to one another by a transformation of the symmetry group. This concept is captured in picture below of the Mexican hat potential. Motion around the trough is associated with the Goldstone mode. Motion perpendicular to the trough is associated with the "Higgs boson". How does this picture connect with a finite system? An intuitive picture is that the ball in the trough

 It is natural to assume that scientists need to probe a system at the microscopic scale to learn about what is happening at that scale. If we take this view we will necessarily be pessimistic about the "bottom-up" research strategy for quantum gravity advocated by Bei Lok Hu.  It goes from macro- to micro-, the opposite to the more popular approaches of string theory and loop quantum gravity. However, the history of science shows that we can learn a lot about microscopics from probing systems at much greater length scales. Here are some examples. Following Perrin's experiments and Einstein's theory of Brownian motion, almost all scientists believed that atoms were not just a mathematical convenience but did exist and were the basic constituents of liquids and solids. All this was before X-ray diffraction allowed the more direct study of crystals at the atomic scale. Crystallography was pretty much settled as a field before there was any direct evidence of the atomic

The good news is that if you read books on Kindle, my book Condensed Matter Physics: A Very Short Introduction can now be purchased as an e-book on Amazon  for US$7.50.  It seems to only be available on the USA site but I used my USA Amazon account and downloaded it. I am no fan of Amazon and minimise my purchases from them. They are my shop of last resort. I understand that some readers will not want to go this route. The bad news is that the production of print copies continues to progress slowly. Depending on the country, different sites advertise it being available at various dates over the next three months...   I look forward to readers feedback.

 Emergence in condensed matter physics may provide some valuable insights into the elusive search for a quantum theory of gravity. There was a helpful discussion by Bei Lok Hu   in  Emergent/quantum gravity: macro/micro structures of spacetime Hu makes a distinction between two approaches that he characterises as "bottom-up" and "top-down". Both have the common goal of understanding how space-time and Einstein's classical theory of gravity can emerge from some more "fundamental" theory that describes physics at higher energies and shorter distances, such as the Planck scale. 1. Going from the micro- to the macro- Examples of this approach are string theory (a la Schwarz, Green, and Witten) and loop quantum gravity. The respective microscopic entities are strings and spin foam. This approach is motivated by the success of the standard model of elementary particles and gauge fields. One starts with a well-defined "classical" action inspired by

What is real? What is true? These big questions are central to philosophy and issues in the philosophy of science. Emergent properties of complex systems raise similar philosophical questions such as  "What is fundamental?" and "Are quasiparticles real?". Robert Batterman is a philosopher of science who is the author of the book, The Devil in the Details: Asymptotic Reasoning in Explanation, Reduction, and Emergence In 2017 Batterman wrote an article in an edition of the Journal of Statitiscal Physics that was in memory of Leo Kadanoff.  Philosophical Implications of Kadanoff’s Work on the Renormalization Group Below I reproduce some of the text as it provides a helpful (and disturbing) summary of how the philosophy of science has evolved. There are very few natural philosophers anymore. The fields of philosophy and science parted company at the end of [the nineteenth] century. Philosophers more and more began to turn toward the disciplines of logic and the analysi