On Fri, Oct 16, 2020 at 5:37 AM Lawrence Crowell < [email protected]> wrote:
> On Thursday, October 15, 2020 at 5:51:13 PM UTC-5 Jason wrote: > >> I noticed that Victor Stenger's position on entropy, as described here: >> https://arxiv.org/pdf/1202.4359.pdf on page 7, appears to be the same as >> described by the cosmologist David Layzer in a 1975 issue of Scientific >> American: >> https://static.scientificamerican.com/sciam/assets/media/pdf/2008-05-21_1975-carroll-story.pdf >> >> The basic idea, which is described graphically here: >> https://www.informationphilosopher.com/solutions/scientists/layzer/arrow_of_time.html >> >> It is a counter-argument to the commonly expressed idea that the universe >> began in a low entropy state. Rather, it explains how the expansion of the >> universe increases the state of maximum possible entropy. If the universe >> expands more quickly than an equilibrium can be reached, then there is room >> for complexity (information / negative entropy) to increase. >> >> Why is it that the "low entropy" myth is so persistent, and this >> alternate explanation is so little known? Some physicists, such as Penrose >> are still looking for alternate explanations for the special low entropy >> state. What fraction of physicists are aware of Stenger's/Layzer's view? >> Does it appear in any physics textbooks? Has it been refuted? >> >> Jason >> > > With quantum fields in spacetime there is no equilibrium. Think of a > black hole of mass M and temperature T = ħc^3/8πkGM = 1/8πm in a background > region with equal temperature. The black hole can absorb or emit a unit of > mass δm m → m ± δm so the temperature changes as T → T ∓ δT. This means the > temperature will always drift away from any equilibrated temperature. There > is then no thermal equilibrium or maximum entropy. > > The only way to prevent a black hole from this sort of runaway situation > is to place it in a box so if it emits Hawking radiation it is reflected > back to the black hole and reabsorbed. The only ideal box is the anti-de > Sitter spacetime. This then leads to the black hole quantum states in an > entanglement with the boundary fields of the AdS which are by the Maldecena > AdS/CFT result dual to a quantum conformal field theory (CFT) of one > dimension less. If the AdS is three dimensions this is AdS_3 ≃ CFT_2, which > is the Virasoro algebra of the bosonic string. For AdS_4 we have CFT_3 that > is an N = 2 supersymmetric Yang Mills CFT. This corresponds to the BTZ > black hole in and AdS_3. For AdS_5 this is CFT_4 for the N = 4 SYM CFT. > > This leads to a bit of a conundrum. The AdS has Λ < 0, which in the case > of the bosonic string defines its negative vacuum plus tachyon state. Yet > clearly, we do not live in this sort of universe. I published a paper > recently though that illustrates how the vacuum between two black holes in > near collision is approximately AdS_4. We live in a spacetime with Λ ≥ 0, > with equality only a local approximation. This is the Vafa swampland > situation, where the de Sitter (like) spacetime we observe, say FLRW, is > some broken symmetry physics from the AdS. Now interestingly this involves > some increase in vacuum energy. An AdS spacetime has causal regions > separated by timelike boundaries, and on these boundaries are CFTs. These > may include gauge-like gravity with the emergence of an induced metric with > Λ ≥ 0. Also, hyperbolic subsets in AdS, analogous to arcs in the Poincare > ½-plane or disk, may be defects with Lanscoz junction condition for a > positive vacuum there. This would then be a holographic screen > corresponding to de Sitter spacetime. This might then be the dS spacetime > of eternal inflation. > > This leads then back to the entropy condition of the early universe. The > entropy of the inflationary spacetime is determined by the area of the > local horizon. This is really very small ≃ 10^{10} Planck areas at most. > Remember that in QFT in curved spacetime area of a horizon or holographic > screen = entropy. A local region of this spacetime then quantum tunnels > into a false vacuum of much lower energy corresponding to the cosmological > constant we observe. The entropy of fields then was much smaller than the > horizon scale expanded to 10^{10} light years. This gives entropy lots of > room to grow, and this is reflected in the mass-gap between the > inflationary false vacuum and the physical vacuum and sets in reheating. > This generates radiation and particles. So the upshot is that the entropy > of the early universe set by the inflationary dS spacetime, but quantum > transitioned into a region that had much lower temperature. Hence there was > a huge disequilibrium situation that defined the resulting big bang. > > > Thanks Lawrence for your detailed reply. It is helpful, though I was not familiar with most of the terminology, the last paragraph made sense to me. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUid%3DmpCx%2B-g0weM9_NYJN6HfMMKwDCGO_-noBAvBehssg%40mail.gmail.com.
