Can horizon complementarity apply to a horizon between de Sitter and Minkowski space?
Minkowski space has no horizon. I don't know what you mean.
Well, what it is, is that Boddy, Carrol, and Pollack have a recent paper out on the web, called "De Sitter Space Without Dynamical Quantum Fluctuations".
The premise seems to be that a lot of other physicists have confused "vacuum fluctuations", which Boddy et al. define as non-dynamical features of quantum states resulting from "radiative corrections of virtual particle pairs", with "Boltzmann fluctuations", which they define as "fluctuations which arise when the microstate of a system is time-dependent, even through the coarse-grained macrostate may be stationary". (The authors associate the latter with "downward fluctuations" in the microstate's entropy.) Their correction of this error in "the conventional wisdom" would include drastic reductions in the possibilities both for Boltzmann brains, and for the usual versions of inflation as a process eternal to the future.
They do specify two "outs" that could rule out their revision of inflationary cosmology. One is the use of one of the other interpretations of quantum mechanics, instead of the "Many Worlds" interpretation which they employ. The other, which is the one I was asking about in my opening post, is described on their p.25, which says that, "With horizon complementarity, this picture changes somewhat....Boltzman fluctuations will lead to true transitions [including up-tunneling to higher densities of energy] between states concentrated at different minima of the potential. If the true vacuum is Minkowski,on the other hand", the limitations on Boltzmann brains and on eternal inflation would apply, with the latter limited to no more than a minority of the branches of the wavefunction.
I've heard of horizon complementarity as referring to the strong possibility that a single horizon might look very different from one side of it than from the other, but the wording on Boddy's p.25 was such that I couldn't tell whether the crux of the matter lay in that complementarity, or, rather, in the prevalence of the inherently-expanding deSitter space both within the true vacuum and within the false one. (The English parts of the paper are very clear, but my ignorance of the QM notations is almost total.) I had thought that Minkowski space was a totally flat space without gravity, serving nowadays as a teaching prep for the current gravitational theory (General Relativity), but the way Boddy et al. mention it left me thinking it might be conceivable as a real setting within which the false vacuum would do its repulsive gravity thing.
Discussion might be made easier if you'd link the paper:
Horizon complementarity refers to the conjecture that it is possible to describe all of the degrees of freedom of the universe beyond the horizon solely using degrees of freedom defined on the horizon. The horizon itself is a holographic representation of everything beyond it. With this picture, it is possible to describe a universe where the true vacuum is de Sitter as a fully-finite system with just the degrees of freedom within the horizon and the degrees of freedom on the horizon.
But if the de Sitter vacuum is a false vacuum, and the true vacuum is Minkowski space, then the vacuum will eventually decay to Minkowski space and has an infinite number of degrees of freedom (assuming no non-trivial topology). The breakdown of what this implies is laid out pretty well on pages 4-5 where the sections are summarized.
So, just to see if I'm getting this right, the horizon required to recover the generically future-eternal inflation and the numerous possibilities for Boltzmann brains would be one separating a de Sitter false-vacuum from a true vacuum--that would also be de Sitter-- IF horizon complementarity would BE a valid concept, whereas Minkowski space (totally flat because it would remain unaffected by any gravity) is what the de Sitter space of the false-vacuum would become, EVEN if its spatial surroundings would have also been de Sitter, if horizon complementarity would NOT be a valid concept? (What I'm wondering here is how a spot of flat space would suddenly appear in a region of space that's curved, however gently, and how its duration--even if ultra-brief--could fail to be "time-dependent", i.e., "dynamical".)
The horizon doesn't separate different vacuum states. It's just an event horizon. An observer crossing my cosmological horizon wouldn't experience anything special at all: they just wouldn't be able to communicate with me any longer, while for me the information that represents them would forever be imprinted on the horizon I observe.
Oh, right, the true and false vacuums would be separated by a bubble wall carrying considerable energy potential, not by a horizon.
I should say that I'm much more an amateur historian by education than I am even the rankest of amateur physicists, and am trying to figure out how BCP perhaps got things right, after everyone else got them wrong for about 35 years.
While I'm re-reading the parts of their paper I can understand, let me just be verifying that there is some issue (as per their p.25) as to whether a false-vacuum bubble tunnels from de Sitter space into Minkowski space or into higher-energy deSitter space; that Minkowski spacetime is flat and zero energy; and that de Sitter spacetime is faintly curved and consequently has some gravity in its repulsive form, which (like its more familiar attractive form) comprises negative energy; also, that they may've brought horizon complementarity into their picture only because it increases our potential for understanding its difference from the picture drawn earlier by such physicists as Vilenkin and Linde, cited on BCP's p.3.
I'm sorry to be hitting you with 4 separate questions in this one post, but your answers are usually comprehensible, and I don't want to lose you.
Well, before the last fish unpacks his slide rule & starts however many mos. of work their paper took BCP (-did I finally get the initials in the right order?) just helping me get through the mourning period for eternal inflation, I've got to say that I think I've got a (totally paranoid) alternative combo worked up: It's not that I mind the "horrendous ontological cost" I've heard attributed to the Many Worlds Interpretation, it's that that cost just went up quite a bit & the log jam at the door to the next replicated reality was making me plainly nervous. (I sincerely hate ontology--its zone got me where I am today--so, let its grant money burn! However, I'm finding the Ghirardi-Rimini-Weber alternative looking really swell (with each particle serving as its own clock! Can you beat that, for an out from something that sure looks random but has its predetermined persona already replicatEverythingReady? I mean, its batteries are charged! Did Carroll get out the word, or Watt?))
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