On Sunday, September 15, 2019 at 1:03:06 PM UTC-6, Jason wrote: > > > > On Sun, Sep 15, 2019 at 12:05 PM Alan Grayson <agrays...@gmail.com > <javascript:>> wrote: > >> >> >> On Sunday, September 15, 2019 at 9:58:53 AM UTC-6, Jason wrote: >>> >>> >>> >>> On Sun, Sep 15, 2019 at 7:36 AM Alan Grayson <agrays...@gmail.com> >>> wrote: >>> >>>> >>>> >>>> On Sunday, September 15, 2019 at 1:01:23 AM UTC-6, Jason wrote: >>>>> >>>>> >>>>> >>>>> On Sun, Sep 15, 2019 at 12:02 AM Alan Grayson <agrays...@gmail.com> >>>>> wrote: >>>>> >>>>>> >>>>>> >>>>>> On Saturday, September 14, 2019 at 4:34:28 PM UTC-6, Jason wrote: >>>>>>> >>>>>>> >>>>>>> >>>>>>> On Sat, Sep 14, 2019 at 3:06 PM Alan Grayson <agrays...@gmail.com> >>>>>>> wrote: >>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> On Saturday, September 14, 2019 at 7:46:27 AM UTC-6, Jason wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> On Sat, Sep 14, 2019, 4:36 AM Alan Grayson <agrays...@gmail.com> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> On Saturday, September 14, 2019 at 12:34:18 AM UTC-6, Jason wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> On Friday, September 13, 2019, Alan Grayson <agrays...@gmail.com> >>>>>>>>>>> wrote: >>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> On Friday, September 13, 2019 at 4:42:00 PM UTC-6, Jason wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> On Fri, Sep 13, 2019 at 8:25 AM Alan Grayson < >>>>>>>>>>>>> agrays...@gmail.com> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> On Friday, September 13, 2019 at 5:24:11 AM UTC-6, Bruno >>>>>>>>>>>>>> Marchal wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> On 13 Sep 2019, at 04:26, Alan Grayson <agrays...@gmail.com> >>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> On Thursday, September 12, 2019 at 11:01:54 AM UTC-6, Alan >>>>>>>>>>>>>>> Grayson wrote: >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> On Thursday, September 12, 2019 at 7:45:22 AM UTC-6, >>>>>>>>>>>>>>>> Lawrence Crowell wrote: >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> On Thursday, September 12, 2019 at 4:20:46 AM UTC-5, >>>>>>>>>>>>>>>>> Philip Thrift wrote: >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> On Wednesday, September 11, 2019 at 11:45:41 PM UTC-5, >>>>>>>>>>>>>>>>>> Alan Grayson wrote: >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> https://www.wired.com/story/sean-carroll-thinks-we-all-exist-on-multiple-worlds/ >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Many Worlds is where people go to escape from one world >>>>>>>>>>>>>>>>>> of quantum-stochastic processes. They are like vampires, but >>>>>>>>>>>>>>>>>> instead of >>>>>>>>>>>>>>>>>> running away from sunbeams, are running away from >>>>>>>>>>>>>>>>>> probabilities. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> @philipthrift >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> This assessment is not entirely fair. Carroll and Sebens >>>>>>>>>>>>>>>>> have a paper on how supposedly the Born rule can be derived >>>>>>>>>>>>>>>>> from MWI I >>>>>>>>>>>>>>>>> have yet to read their paper, but given the newsiness of this >>>>>>>>>>>>>>>>> I might get >>>>>>>>>>>>>>>>> to it. One advantage that MWI does have is that it splits the >>>>>>>>>>>>>>>>> world as a >>>>>>>>>>>>>>>>> sort of quantum frame dragging that is nonlocal. This >>>>>>>>>>>>>>>>> nonlocal property >>>>>>>>>>>>>>>>> might be useful for working with quantum gravity, >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> I worked a proof of a theorem, which may not be complete >>>>>>>>>>>>>>>>> unfortunately, where the two sets of quantum interpretations >>>>>>>>>>>>>>>>> that >>>>>>>>>>>>>>>>> are ψ-epistemic and those that are ψ-ontological are not >>>>>>>>>>>>>>>>> decidable. There >>>>>>>>>>>>>>>>> is no decision procedure which can prove QM holds either way. >>>>>>>>>>>>>>>>> The proof is >>>>>>>>>>>>>>>>> set with nonlocal hidden variables over the projective rays >>>>>>>>>>>>>>>>> of the state >>>>>>>>>>>>>>>>> space. In effect there is an uncertainty in whether the >>>>>>>>>>>>>>>>> hidden variables >>>>>>>>>>>>>>>>> localize extant quantities, say with ψ-ontology, or >>>>>>>>>>>>>>>>> whether this localization is the generation of information in >>>>>>>>>>>>>>>>> a local >>>>>>>>>>>>>>>>> context from quantum nonlocality that is not extant, such as >>>>>>>>>>>>>>>>> with >>>>>>>>>>>>>>>>> ψ-epistemology. Quantum interprertations are then >>>>>>>>>>>>>>>>> auxiliary physical axioms or postulates. MWI and within the >>>>>>>>>>>>>>>>> framework of >>>>>>>>>>>>>>>>> what Carrol and Sebens has done this is a ψ-ontology, and >>>>>>>>>>>>>>>>> this defines the Born rule. If I am right the degree of >>>>>>>>>>>>>>>>> ψ-epistemontic >>>>>>>>>>>>>>>>> nature is mixed. So the intriguing question we can address is >>>>>>>>>>>>>>>>> the nature of >>>>>>>>>>>>>>>>> the Born rule and its tie into the auxiliary postulates of >>>>>>>>>>>>>>>>> quantum >>>>>>>>>>>>>>>>> interpretations. Can a similar demonstration be made for the >>>>>>>>>>>>>>>>> Born rule >>>>>>>>>>>>>>>>> within QuBism, which is what might be called the dialectic >>>>>>>>>>>>>>>>> opposite of MWI? >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> To take MWI as something literal, as opposed to maybe a >>>>>>>>>>>>>>>>> working system to understand QM foundations, is maybe taking >>>>>>>>>>>>>>>>> things too >>>>>>>>>>>>>>>>> far. However, it is a part of some open questions concerning >>>>>>>>>>>>>>>>> the >>>>>>>>>>>>>>>>> fundamentals of QM. If MWI, and more generally postulates >>>>>>>>>>>>>>>>> of quantum interpretations, are connected to the Born rule it >>>>>>>>>>>>>>>>> makes for >>>>>>>>>>>>>>>>> some interesting things to think about. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> LC >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> If you read the link, it's pretty obvious that Carroll >>>>>>>>>>>>>>>> believes the many worlds of the MWI, literally exist. AG >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Carroll also believes that IF the universe is infinite, then >>>>>>>>>>>>>>> there must exist exact copies of universes and ourselves. This >>>>>>>>>>>>>>> is >>>>>>>>>>>>>>> frequently claimed by the MWI true believers, but never, >>>>>>>>>>>>>>> AFAICT, proven, or >>>>>>>>>>>>>>> even plausibly argued. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> The idea comes from Tegmark, and I agree with you, it >>>>>>>>>>>>>>> necessitate more than an infinite universe. It requires also >>>>>>>>>>>>>>> some >>>>>>>>>>>>>>> assumption of homogeneity. >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> Our universe is, on a large scale, homogeneous. But it can't >>>>>>>>>>>>>> be infinite since it has only been expanding for finite time, >>>>>>>>>>>>>> 13.8 BY. I >>>>>>>>>>>>>> had a discussion with Brent about this some time ago, and he >>>>>>>>>>>>>> claimed finite >>>>>>>>>>>>>> in time doesn't preclude infinite in space. I strongly disagree. >>>>>>>>>>>>>> Perhaps I >>>>>>>>>>>>>> am missing something. Wouldn't be the first time. AG >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> I think what you may be missing is that in popular (but >>>>>>>>>>>>> misleading) accounts of the BB they often say everything >>>>>>>>>>>>> originated from a >>>>>>>>>>>>> point, rather than everywhere at once. To say "everything came >>>>>>>>>>>>> from a >>>>>>>>>>>>> point" is at best only valid for describing the observable >>>>>>>>>>>>> universe (or any >>>>>>>>>>>>> finite portion of the universe) but is invalid to extrapolate it >>>>>>>>>>>>> to the >>>>>>>>>>>>> whole universe, which may be spatially infinite. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> I am not assuming our universe began from a mathematical point, >>>>>>>>>>>> but I do assume that 13.8 BYA it was very very small, the >>>>>>>>>>>> observable and >>>>>>>>>>>> unobservable parts. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Why do you assume this? Most cosmologists make no such >>>>>>>>>>> assumption. Under the concordance (standard assumed) model of >>>>>>>>>>> cosmology, >>>>>>>>>>> space is infinite. >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> I don't think there is an implied disconnect between our >>>>>>>>>>>> measurements of the CMBR and what an observer would measure in >>>>>>>>>>>> parts we >>>>>>>>>>>> have no access to. It was everywhere hot and dense, and very very >>>>>>>>>>>> small. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> There's no observational motivation for the universe being very >>>>>>>>>>> very small at the beginning. It could have been small, large or >>>>>>>>>>> infinite, >>>>>>>>>>> for all we know. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> I've never read a description of inflation where the universe is >>>>>>>>>> described as very large spatially when it initiates. Never. It's >>>>>>>>>> always >>>>>>>>>> claimed it begins a few Planck durations (10^-43 seconds) after the >>>>>>>>>> BB, at >>>>>>>>>> which time the spatial diameter is many orders of magnitudes smaller >>>>>>>>>> than >>>>>>>>>> the diameter of a proton. It then expands to the diameter of the >>>>>>>>>> Earth or >>>>>>>>>> the Solar System before terminating, all this occuring within the >>>>>>>>>> first >>>>>>>>>> second after the BB. AG >>>>>>>>>> >>>>>>>>> >>>>>>>>> I think we need to clearly distinguish between three periods, >>>>>>>>> which are frequently confused: >>>>>>>>> >>>>>>>>> 1. "quantum vacuum phase" Size: ??? Time: ??? >>>>>>>>> If inflation began as a fluctuation in the vacuum, the vacuum was >>>>>>>>> a pre-existing initial condition. We can say nothing of it's size or >>>>>>>>> how >>>>>>>>> long it has existed. Alternatively, this vacuum may have already >>>>>>>>> been in a >>>>>>>>> state of exponential expansion and required no fluctuation to get >>>>>>>>> started. >>>>>>>>> >>>>>>>>> >>>>>>>>> 2. "Inflation start" Size: (min = Planck size, max = ???) Time: >>>>>>>>> (min = fraction of second before hot stage of BB, max = finite but >>>>>>>>> otherwise unlimited time ago). >>>>>>>>> If inflation started as a fluctuation it could have started very >>>>>>>>> small, but it would then grow exponentially forever. How big it was >>>>>>>>> when >>>>>>>>> it stopped for us we can't say, but we can guess it had to have gone >>>>>>>>> on for >>>>>>>>> at least 10^-32 seconds to fit with observations. This is only the >>>>>>>>> minimum >>>>>>>>> time, there's no known upper bound. There's not necessarily any >>>>>>>>> cooling >>>>>>>>> during this time as the heat doesn't enter the picture until >>>>>>>>> inflation >>>>>>>>> begins to stop somewhere. >>>>>>>>> >>>>>>>>> 3. "Local inflation end", Size of inflating space: (undefined but >>>>>>>>> ever growing), Size of pocket from outside: (finite but growing), >>>>>>>>> Apparent >>>>>>>>> size of pocket from inside: (finite or infinite depending on shape of >>>>>>>>> the >>>>>>>>> universe), Time: 13.8 BY ago. >>>>>>>>> >>>>>>>>> The "T = 0 of the BB" no longer makes sense in the inflation >>>>>>>>> picture, the only place we can begin to speak of absolutes with time >>>>>>>>> is >>>>>>>>> when we speak of the local end to inflation in our pocket. >>>>>>>>> >>>>>>>>> Jason >>>>>>>>> >>>>>>>> >>>>>>>> I'll say it again. One the main reasons to posit inflation is to >>>>>>>> explain the observable large scale homogeneity of a universe that is >>>>>>>> now >>>>>>>> NOT causally connected. If the universe was very very tiny when >>>>>>>> inflation >>>>>>>> started, it WAS then causally connected, >>>>>>>> >>>>>>> >>>>>>> The *observable* part of the universe is posited to have once been >>>>>>> causally connected to come to thermal equilibrium but not necessarily >>>>>>> the >>>>>>> entire universe. >>>>>>> >>>>>> >>>>>> OK, but based on our best measurements, we live in a closed, >>>>>> accelerating and expanding hypersphere, since the curvature is NOT zero >>>>>> and >>>>>> NOT negative. >>>>>> >>>>> >>>>> Do you have a citation for this? All the estimates I am familiar with >>>>> assume a flat or slightly open shape. >>>>> >>>>> >>>>>> I prefer to go with what we think we know, rather than with a model >>>>>> which is completely speculative. AG >>>>>> >>>>> >>>>> Which is what? >>>>> >>>> >>>> I am looking for a citation, but I recall that someone on this thread >>>> stated the measured curvature is close to zero, but POSITIVE. AG >>>> >>> >>> Okay. >>> >>> >>>> >>>>> >>>>>> >>>>>>> >>>>>>>> and inflation preserved the homogeneity. This is what Guth was >>>>>>>> trying to solve with inflation, among other problems, such as no >>>>>>>> detectable >>>>>>>> monopoles. This entire logic breaks down if one assumes an infinite >>>>>>>> universe at the time of inflation. >>>>>>>> >>>>>>> >>>>>>> Correct, using inflation and previous causal connectedness does not >>>>>>> produce for homogeneity of temperature to all parts of the universe if >>>>>>> the >>>>>>> universe is infinite. >>>>>>> >>>>>> >>>>>> So far, as I just stated, our best evidence >>>>>> >>>>> >>>>> There's no evidence either way, as far as I am aware, which is why i >>>>> is still considered an open question. If you can point me to some >>>>> evidence >>>>> I would be interested. >>>>> >>>>> >>>>>> does NOT suggest an infinite universe. AG >>>>>> >>>>> >>>>> What are you calling as the universe here? How are you defining it? >>>>> >>>> >>>> I am referring to our bubble, which arose with the BB, and refers to >>>> the observable and UNobservable regions (not to the possibly infinite >>>> substrate from which it arose). AG >>>> >>> >>> Alright. Then you also need to clarify which perspective you are >>> using. Since the bubble may be finite from the outside, but can appear >>> infinite from the inside. >>> >> >> Since there's no way to observe the bubble from the outside, I don't see >> this as productive way to analyse the situation. AG >> >>> >>> >>>> >>>>> >>>>>> >>>>>> >>>>>>> At best it can only extend to some finite region of that >>>>>>> universe. But once you are working in an inflationary model, you >>>>>>> already >>>>>>> have accepted there is a large scale where the universe is not >>>>>>> homogenous >>>>>>> (pocket regions vs. the rapidly inflating regions of vacuum). >>>>>>> >>>>>> >>>>>> I don't see why assuming inflation implies acceptance of large parts >>>>>> of the UNobservable universe which is NOT homogeneous. AG >>>>>> >>>>> >>>>> Because decay events of the vacuum do not happen everywhere at once, >>>>> this leads to isolated "pocket universes" separated by exponentially >>>>> expanding space. The inhomogenity I am referring to are the different >>>>> parts of the vacuum in different energy states. >>>>> >>>>> >>>>>> >>>>>>> >>>>>>>> In this case, the infinite universe was always homogeneous even >>>>>>>> though it was never causally connected. >>>>>>>> >>>>>>> >>>>>>> That is another possibility that avoids inflation as an explanation >>>>>>> of homogeneity: To simply assume everything at all places began at the >>>>>>> same temperature and density. >>>>>>> >>>>>> >>>>>> If so, why did Guth think homogeneity needed an explanation? On its >>>>>> face, thermal equilibrium for a non causally connected universe seems >>>>>> improbable. AG >>>>>> >>>>> >>>>> It came for free, with the other explanations. On its own, I am not >>>>> sure it would be justified to trade one assumption for another, but >>>>> inflation replaced 4 or 5 assumptions with a single one, which is its >>>>> main >>>>> strength. >>>>> >>>>> >>>>>> >>>>>>> >>>>>>>> Further, how could it have been so hot 380,000 years after the BB >>>>>>>> if it wasn't dense at that time? >>>>>>>> >>>>>>> >>>>>>> Actually the universe was not very dense at the time of 380,000 >>>>>>> years. It was billions of times more sparse than Earth's atmosphere. >>>>>>> Each >>>>>>> time the scale factor >>>>>>> <https://en.wikipedia.org/wiki/Scale_factor_(cosmology)> halves >>>>>>> going backwards in time, the temperature doubles, and the density >>>>>>> increases >>>>>>> by a factor of 8 (2 cubed). You can follows this backwards at least >>>>>>> until >>>>>>> the temperature is about 10^27 K, far far hotter and denser than >>>>>>> 380,000 >>>>>>> years, back to a time just a fraction of a second after inflation ended. >>>>>>> >>>>>> >>>>>> Yes, it was far hotter and denser just after the BB, than at 380,000 >>>>>> years. >>>>>> >>>>> >>>>> Okay. >>>>> >>>>> >>>>>> But contrary to what you allege above and below, it must have far >>>>>> hotter and denser at 380,000 years, than it is today, 2.7 deg K, so hot >>>>>> and >>>>>> dense that it was opaque to light. >>>>>> >>>>> >>>>> I'm not sure how this is contrary to what I say above and below... I >>>>> agree it was hotter and denser the farther back you go. >>>>> >>>> >>>> And smaller as well? (BTW, "smaller" can't be a property of a spatially >>>> infinite universe.) >>>> >>> >>> Smaller is not implied by the big bang model, only things being >>> "previously closer". >>> >> >> True, but if *inflation* is to solve the large scale homogeneity >> property of our present universe, which it does, inflation had to occur >> when the universe was exceedingly small. See my previous post on this >> issue. AG >> > > I would make this correction: > > True, but if inflation is to solve the large scale homogeneity property > of our present universe, which it does, inflation had to occur when the > *OBSERVABLE* universe was exceedingly small. See my previous post on this > issue. AG >
OK, but I would include the *UNOBSERVABLE* part of our bubble, because as far as we know it became unobservable because of the expansion. AG > > >> >> >>> I know many popular accounts of the BB say the universe was once >>> smaller, but this is sloppy writing. They are referring to some fixed part >>> of the universe being smaller, such as the observable part. But to say the >>> universe in total was smaller is to assume one knows if it is infinite or >>> finite, open/flat or closed. This is not known, so no accurate account of >>> the BB would implicitly assume it to be known. >>> >>> >>>> It had to have gotten smaller to explain its present homogeneity. I >>>> want to avoid the assumption that homogeneity can arise spontaneously in a >>>> causally DIS-connected universe, the one we observe. >>>> >>> >>> But to explain that rather than assuming it, then you need inflation, >>> but below you call this "totally speculative". Which is it? >>> >>> >>>> And I don't believe that at 380,000 years it was less dense than our >>>> atmosphere (as you earlier alleged). AG >>>> >>> >>> The present density of the universe is about 5 hydrogen atoms per cubic >>> meter. At the time of 380,000 years, things were ~1100x closer together >>> (the scale factor is ~1/1100) compared to today. This is a simple >>> calculation of the temperature difference. If it's 2.73K now, and it was >>> 3000K then, then the scale factor growth from then to now is 3000/2.73 = >>> 1098. >>> >>> If each dimension changed by a factor of 1,000, this means the density >>> back then would have been 1,000 x 1,000 x 1,000 or a billion times what it >>> is now. So instead of 5 hydrogen atoms per cubic meter, you get 5 billion >>> hydrogen atoms per cubic meter. This is many many orders of magnitude less >>> dense than atmospheric pressure. A cubic meter of air at sea level weighs >>> 1.3 kilograms ( https://hypertextbook.com/facts/2000/RachelChu.shtml ). >>> Compare this weight to the weight of 5 billion hydrogen atoms. A Hydogen >>> atom weighs 1.67 × 10^-24 g, 5 billion of them would get you to 8.37 × >>> 10^-18 kilograms. >>> >>> So I was wrong, it wasn't a billion times less dense, it was closer to a >>> billion billion times less dense than the atmosphere. >>> >>> >>>> >>>>> >>>>>> I am just saying that it does seem to be cooling as it expands, >>>>>> >>>>> >>>>> Yes. >>>>> >>>>> >>>>>> and the curvature data seems to imply smallness just after the BB. >>>>>> >>>>> >>>>> What curvature data are you referring to? The latest Planck data say >>>>> the curvature is flat to within the limits of our measurement accuracy. >>>>> Is >>>>> there a new result that indicates positive curvature? >>>>> >>>> >>>> "Flat" means curvature is exactly zero; that is, flat like a Euclidean >>>> plane. But if we measure slightly positive, which I think is the case, it >>>> must be a closed hyperspace, but HUGE. Physicists tend to equate "almost >>>> flat", which if true would mean a huge spherical hyperspace, with >>>> Euclidean >>>> flat. This is a persistent error. AG >>>> >>>> What I don't understand is why, a universe with accelerating expansion, >>>> must be open, like a saddle. >>>> >>> >>> The shape (closed, flat, open), depends on how much gravitating stuff is >>> in the universe compared to how much anti-gravitating stuff is in the >>> universe, and the current expansion rate and density. A closed universe >>> implies gravitational attraction wins out in the end and things eventually >>> collapse. In a universe where there is more gravitating stuff then anti >>> gravitating stuff, the speed of expansion ought to be slowing down. If it >>> is slowing down in a way that only after infinite time the expansion rate = >>> 0 (loosely analogous to throwing something upwards at exactly the escape >>> velocity) then the geometry is flat. But the only way for the universe >>> expansion to be accelerating now is if the anti-gravity stuff exceeds the >>> gravitating stuff. In this case, (should the condition persist), then the >>> universe will not recollapse (can't be closed), nor will it come to a rest >>> after infinite time (can't be flat), so the alternative is that it must be >>> open. >>> >> >> That's what the books say. But suppose the universe was a spherical >> expanding hyperspace at some point in its history, closed, and then the >> expansion rate started to increase. Would that closed universe somehow >> "tear" and become open? AG >> > > I'm not sure, it is a good question if the shape can evolve over time. > Perhaps someone on this list more familiar with GR can answer. > > >> >>> >>>> Why can't a spherical hyperspace retain its closure if its expansion is >>>> accelerating? AG >>>> >>> >>> Mathematically you can of course imagine an ever expanding hypersphere, >>> but the reason it is not possible physically is comes down to general >>> relativity, which informs of us of a relationship between the spatial >>> curvature and the ultimate fate of the universe. So if anti-gravity stuff >>> wins out such that the universe expands forever in an accelerating or >>> constant rate, then GR requires that the spatial curvature be negative. It >>> would not allow for a positive curvature. >>> >> >> I find this rather dubious. Can you show me how GR requires this? AG >> > > It is made clear in the Friedmann equations, which are derived from the > field equations of GR: > https://en.wikipedia.org/wiki/Friedmann_equations > Where they contain a parameter k which is either -1, 0, or 1, > corresponding to the curvature of space. The value of k determines how the > expansion rate changes over time. > The problem may lie in the fact that the Friedmann equations are idealizations and not physically realizable. As I see it, one can get transitions between flat and open universes in both directions, but a closed universe cannot became flat or open; nor can the reverse occur. AG > > Jason > > >> >>> >>>> >>>>> >>>>>> Moreover, applying the Cosmological principle, it couldn't have been >>>>>> homogeneous on large scale in the finite observable region, and at the >>>>>> same >>>>>> time infinite and non-homogeneous in regions we can't observe. AG >>>>>> >>>>> >>>>> It all comes down to scale. At the scale of stars or galaxies, the >>>>> universe is non homogeneous, on the scale of super clusters and above it >>>>> is, but at larger scales of inflating vacuums and pocket universes, again >>>>> it is non homogeneous, but perhaps if you zoom out far enough the picture >>>>> becomes homogeneous again. The non-homogeneous part I am referring to >>>>> can >>>>> be seen as the spiky image, a rendering of eternal inflation: >>>>> https://www.preposterousuniverse.com/blog/2011/10/21/the-eternally-existing-self-reproducing-frequently-puzzling-inflationary-universe/ >>>>> >>>> >>>> I would forget about inflating vacuums and pocket universes, which are >>>> totally speculative, >>>> >>> >>> They're more or less a direct consequence of inflation. Inflation is a >>> little bit more than totally speculative. I would go so far to saying it >>> is at least weakly confirmed. >>> >>> >>>> and focus on what we can observe -- which, on a large scale, is >>>> homogeneous. Why trash the Cosmological Principle by appealig to >>>> unobservable phenomena? AG >>>> >>> >>> The cosmological principle is not a firm rule or law, it is a rule of >>> thumb which works under the assumption that the same laws operate >>> everywhere and same conditions hold everywhere, and therefore things should >>> be roughly the same everywhere. Inflation tells us that at certain scales >>> the conditions are not the same everywhere, so we should not expect >>> everything to seem homogeneous at those scales. >>> >> >> The same laws must operate everywhere; otherwise we can't do physics. But >> obviously, within those laws, whatever they are, different events can occur >> in different locations. AG >> >>> >>> 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 everyth...@googlegroups.com <javascript:>. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/c7b2d6c8-41f4-4588-a668-a1ae824a2c06%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/c7b2d6c8-41f4-4588-a668-a1ae824a2c06%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> > -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/edfb70a1-adba-481d-9af4-3b614527e548%40googlegroups.com.
