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 <[email protected] > <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 <[email protected]> >>> 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 <[email protected]> >>>>> 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 <[email protected]> >>>>>>> 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 <[email protected]> >>>>>>>>> wrote: >>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> On Saturday, September 14, 2019 at 12:34:18 AM UTC-6, Jason wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> On Friday, September 13, 2019, Alan Grayson <[email protected]> >>>>>>>>>>> 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 < >>>>>>>>>>>>> [email protected]> 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 <[email protected]> >>>>>>>>>>>>>>> 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 [email protected] <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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/edfb70a1-adba-481d-9af4-3b614527e548%40googlegroups.com.
