Foam As Granular Matter: Fill & Download for Free

Almost everything. Unlike Quantum Mechanics or Classical Mechanics, Statistical Mechanics (SM) is an exact science; it is the science of counting. If you can count correctly, you get the correct answer. This enables us to tackle many problems which are almost intractable through direct applications of Classical or Quantum Mechanics. I'll give a historical account of the application of Statistical Mechanics.1. 19th Century: The big questions of this time were understanding the properties of ideal gas and the radiation from a black body ( objects which absorb and emit light perfectly.). Application of statistical mechanics in its earliest form led to the theory of Van Der Waals gas. Concepts from that theory was then successfully applied to understand liquefaction of gas.Black Body Radiation was a big problem. Rayleigh gave a formula which was unable to account for the observed radiation profile. Planck tried to tackle the problem and figured out the Quantum Theory of Radiation. The tool he mainly used was Thermodynamics.Boltzman is the founding father of the Statistical Mechanics. He applied his theory to understand the entropy. temperature in a much better way. Also, he worked on transport theory. How energy, momentum etc is transported from one place to another place in a system which is out of equilibrium: Boltzmann equation.Statistical Mechanics was applied to understand the chemistry of colloids, gel etc.2. First half of 20th Century Einstein and Debye used Planck's quantum hypotheses and Equilibrium Statistical Mechanics to understand the heat capacity of the solids. Einstein, Smoluchowski also described Brownian Motion.Later Debye and Nernst successfully applied SM to understand different electro-chemical phenomena: Peter Debye. Nernst equationArrhenius applied SM to understand Chemical Kinetics which is now famously known as Arrhenius Law.Bose and Fermi discovered their eponymous statistics which is widely used in modern day research. Discovery of Fermi Dirac Statistics ushered the electronics age.Around the same time S. Chandrasekhar applied FD statistics to understand the physics of White Dwarf stars. The famous result is now known as Chandrasekhar limit.Frits Zernike used SM to understand physics of liquids around this time.Landau and Ginzburg started describing phase transition using SM which is now known as Ginzburg–Landau theory of phase transition.Claude Shannon used SM to understand what do we mean by information. We now know this as Information Theory.Lars Onsager used SM to solve the 2D Ising model, a simple model which shows ferro/para-magnetic phase transition.3. Second half of 20th Century A lot of impetus was given to understand the physics of phase transition. Leo Kadanoff, Michael Fisher and Kenneth G. Wilson elucidated the mechanism of phase transition.Richard Feynman, Pyotr Kapitsa etc applied SM to understand low temperature physics particularly Superfluidity.People tried to understand other materials like Polymer, Liquid Crystals, Foam etc. Pierre-Gilles de Gennes, Sam Edwards, Robert B. Meyer etc applied SM to understand these objects. It is due to their research that we have LCD, LED display.Ilya Prigogine applied it to understand complex non equilibrium phenomenon and thus ushered a new age of non-equilibrium SM.Presently almost each and every research that is being done involves some amount of SM. Wilson actually showed that a Statistical field theory in d+1 dimension is equivalent to a Quantum Field Theory in d dimension. This enables us to apply SM to virtually any place in science. In recent days people tried to understand exotic forms of matter like High Temperature Superconductivity, Plasma, Neutron Star, Granular Matter. Turbulence, Social Network etc is analyzed using this tool. Like I said initially, it is applied everywhere.Edit 1: A big achievement in Biophysics was to understand the mechanism of mRNA production (commonly known as transcription). A simple SM model can describe what is possibly happening at the cellular level. These calculations have led to new experimental discovery which were previously thought to be impossible.Also, around 1975 John Hopfield and Jacques Ninio figured out how protein is synthesized within cell with less than 0.01% error. They figured out a mechanism completely through theoretical calculation which was later proved to be true. This mechanism is known as Kinetic proofreading.Clearly, this list is not exhaustive, but I tried to give some highlights on the application of SM. Please google for further information.

Absolutely right, there is no need to imagine that space and time is quantised, in the sense of being granular. However spacetime is bent by matter, and this curvature will have to be quantised, producing Wheeler-foam. https://en.wikipedia.org/wiki/Quantum_foam​

Not as molecules but there is a different when we refer to materials, there is a difference between hard materials and soft materials or soft matter.From Nature Materials:[1]Soft materials are materials that can be easily deformed by thermal stresses or thermal fluctuations at about room temperature. Soft materials include liquids, polymers, foams, gels, colloids, granular materials, as well as most soft biological materials.Using the more colloquial explanation from Soft Matter Physics: ‘all things squishy’.It’s is improper to say that there are “hard” molecules vs. “soft” molecules since soft matter characteristics don’t arise at the molecular regime. Instead, it arises in the mesoscopic regime based on how those molecules are organized and interact with each other. This isn’t a molecular property as much as it is a material property. Thus, you probably can’t conclude that there are “hard” and “soft” molecules. There are however, “hard” and “soft” materials.Footnotes[1] Soft materials - Latest research and news