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.
LC
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