Intuitively, there is a competition between the / = 0 FRW metric cosmological redshift effect and the / > 0 de Sitter cosmological blue shift effect. But de Sitter wins the race in the end. FRW is the Hare, de Sitter is the Tortoise. Remember the energy densities of real quanta keep going down as space expands - not so the virtual zero point quanta!
Rocky Kolb SLAC Summer School
Remember there is NO finite future event horizon when / = 0 in the old FRW standard big bang cosmology prior to the 1999 discovery of dark energy in the anomalous redshifted spectra of Type 1a supernovae.
area of future event horizon ~ /^-1 ~ 1/(dark energy density in past light cone)
Also remember that in Wheeler-Feynman/Hoyle-Narlikar a pure FRW cosmology gives the wrong answer for the Arrow of Time - there is no net retarded causality for / = 0, only for dS / > 0.
We need the dark energy density in order for the 2nd Law of Thermodynamics to work! Sean Carroll does not seem to know this in his book From Eternity to Here.
On Jul 26, 2010, at 1:39 PM, james f woodward wrote:
"Jack, I repeat, a photon emitted, necessarily into the future, gets
cosmologically redshifted as it travels along. It does not get
That's what I used to think also. But it's wrong. Sure the universe is expanding so the wavelengths stretch that's the standard argument and it works for / = 0, but it does not work as our universe approaches the de Sitter (dS) metric
gtt ~ 1 - / ^2 asymptotically in the future
in static LNIF representation where we are located at r = 0
There is, of course, a competition between the cosmic redshift stretching of the wavelengths for the / = 0 contribution, but eventually the / > 0 wins.
Remember in Newtonian terms the repulsive gravity force (per unit test mass)
is g = +2c^2/ (universal anti-gravity repulsion accelerating expansion rate of 3D space)
and this does work on the photon increasing its energy relative to the static LNIF detectors (actually does work on any real particle).
This is in contrast to a photon leaving a black hole where
g = - c^2rs/2r^2
here r = rs is the event horizon and we are at r ---> infinity
therefore a photon must do work to get out of the gravity well in Newtonian terms.
also a photon falling into the gravity well has work done on it by the gravity field and blue shifts
Note the duality in the effective Newtonian potentials
VdS = -c^2/ ^2 repulsive field toward inside future cosmological dS event horizon that we are inside of!
we at r = 0
therefore work done on retarded test particle falling toward the dark energy dS horizon from the inside.
Vbh = - c^2rs/2r attractive field toward black hole event horizon - we are outside black hole horizon
we at r ---> infinity
therefore work done on retarded test particle falling toward the black hole event horizon from the outside.
the inside/outside topology difference and the r^2 vs 1/r difference, and the inversion r = 0 <--> r = infinity are a kind of duality here.
"So, as it approaches the horizon of the source, it cannot
excite e-p pairs out of the vacuum to act as an absorber. If the
expansion is accelerating, I suppose you might try to argue that the
acceleration at the horizon produces a Unruh-Davies thermal bath of
photons of sufficient energy to excite the e-p pairs out of the vacuum
that would then act as an absorber. But that's a completely different
scenario than the one you are pushing here. And to be convincing, it
would have to be fleshed out in much greater detail. Besides, if there
is an accelerating expansion, you automatically get a cosmic horizon
without invoking the vacuum at all."
On the contrary, to my intuition it's obvious that the future de Sitter horizon is a static LNIF detector i.e. Kip Thorne's electrical membrane, where any real on shell charged particle or photon that couples to charged particles has so much energy relative to it, that it will excite real pairs out of the virtual vacuum sea and thus in effect be the desired total absorber of last resort restoring the Arrow of Time (2nd Law of Thermodynamics) and the net past to future retarded causality - that is broken only when we have post-quantum signal nonlocality as in living matter - as Fred Hoyle clearly saw back in the 1980s.