2/2 I just explained that classical vacuum has an important property: it is uniformly empty at every scale. It therefore has the maximum possible entropy, bec

2/2 I just explained that classical vacuum has an important property: it is uniformly empty at every scale. It therefore has the maximum possible entropy, because a chunk of classical vacuum is indistinguishable from any other similar chunk of classical vacuum, whether one measures the chunks in cubic picometres or in cubic lightyears. The smallest microstates can be arbitrarily shuffled and you will observe no changes in any observable features of the largest macrostate. But maybe a quantum vacuum (or string vacuum) is different from a classical vacuum at some level: as you make more and more vigorous swaps at the tiniest scales, perhaps there is a transition from the macrostate of apparent vacuum to something with real particles inside (that might radiate away, for instance, with some striking a detector outside the m^3, similarly to how our nucleon-swapping in water produces unstable isotopes that decay and radiate in the process). We could then ascribe a measure of entropy to such a false vacuum that is different from the perfect entropy of classical vacuum. That in turn has some interesting consequences. That false vacuum is (usually) the source of the entropic force in entropic gravity theories. As one makes the false vacuum purer, by moving dust and gas and light and so forth out of it, its entropy decreases. The decrease in entropy generates an entropic force trying to pull radiation, dust, gas, stars, and so forth back into it in order to return to a higher-energy state. By analogy with the rubber band, lifting matter out of a system stretches the vacuum; the stretched vacuum then generates an entropic force on the nearby vacuum and matter trying to relax into a less-stretched state. False vacuum therefore is in effect very slightly attractive. (One sees the problem: an expanding universe has more and more of this false vacuum appearing, doesn't it? So we need a counter-term, which could be a form of dark energy, or a phase transition at which a sufficiently empty patch of false vacuum becomes very slightly repulsive, but a merely-very-very-empty patch of false vacuum remains more attractive than the patches of interplanetary space inside our solar system out at least as far as Pluto.) A few years ago Erik Verlinde, a well-known theoretical physicist and string theorist, was very excited about being able to describe a model of a spherically symmetrical galaxy in his entropic gravity theory, and the entropic force binding this model galaxy arising from interactions at the scale of strings (as in string theory). The galaxy at some levels resemble elliptical galaxies in our sky, whose outermost stars move faster than would be allowed without some inward pull. In his theory, the inward pull is entropic throughout the modelled galaxy, so gravitation falls off more slowly than the inverse square law for the outermost stars. Thus there was -- at first glance -- no need for dark matter in a halo "suspending" the outermost stars. It was clever, especially as he made a connection with a version of MOND. This programme seems to have stalled since not long after it was presented in 2011. But then so have many other theories that seek to explain the fine details of galaxy rotation curves compared to what one expects with General Relativity where only the Standard Model particles generate the stress-energy tensor. Verlinde's approach noteworthily would also have generated the Standard Model particles out of the same strings that the false vacuum arose from, "just like that", as soon as the "string landscape problem" were solved, and he hoped that one could get there not all at once but by a process of small extensions upon a model that worked for the perfectly spherical galaxy model. Dark matter approaches do not depend on the shape of a galaxy or number of individual galaxies within a cluster but rather the distribution of dark energy, governed by a few key features: it does not move relativistically ("cold"), and it does not radiate or clump ("dark" and "collisionless"). CDM (cold dark matter) approaches explain whole clusters of galaxies (of different shapes and sizes) moving around within a cluster, and one generally only has to set down an initial distribution of CDM from the time before galaxies first formed [1]. It is also not sensitive to the exact details of the vacuum, merely that its bulk property is that it is not attractive of matter. Verlinde's programme turned out to be sensitive to the spherical symmetry, and did not work well with spirals and other shapes, much less arbitrarily-populated galaxy clusters; I do not think much progress was made on an initial-values formulation for the individual-galaxy model(s) that were eventually proposed by his team. Additionally, there was as far as I know no traction on explanations for why galaxy clusters stay gravitationally bound but much larger scale clusters do not, except by directly importing the cosmological constant. As far as I know there aren't many people working on the dynamics of galaxy clusters who are convinced that Verlinde's work will do any better (or be at least as easy to work with as) General Relativity equipped with some bulk behaviour model of dark matter. While Verlinde's team's work -- or some other entropic gravity theory -- might produce a clear connection between the very very very small scale physics of strings and the bulk behaviour of galaxies in an expanding universe, it looks less and less likely to do so without importing some bulk behaviour from the standard cosmology. - -- [1] https://map.gsfc.nasa.gov/universe/bb_cosmo_struct.html https://map.gsfc.nasa.gov/universe/bb_cosmo_struct.html