Of course, there is such a frame. It is not "absolute" because physics works the same in all frames. Relativity never said that one frame has to look like another, only that the laws of physics don't care.
Correct. This also means it is not "radially streaming".
Actually, it stems from imagining it originated from a particular point, rather than everywhere. It is a very common error, so it's a good one to make so it can get corrected.The "momentum state" is to have zero momentum, with expansion. In GR, these are not contradictory. It is dynamic, not static because it changes with age, not because it has a nonzero "momentum state".

I guess this could expose a difference in views: space is being created or space is just there being filled.

Considering the size differential between a grapefruit** and the universe it seems like I could claim the universe originated from a "point".

** - the size of the universe after inflation.

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My invisible elf ??? Why he is made of dark matter and lives off of dark energy !!!
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Acutally, I think most cosmologists acknowledge that the issue is still unresolved, and that it could be either way. The actual data leans just slightly to the side of a finite, closed universe, but the fact that it's hard to tell at all leads to some decent theoretical arguments that it's infinite.

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Conserve energy. Commute with the Hamiltonian.

The "leaning" is not statistically significant, I think inflation more or less guarantees that. I expect we'll never know what the deviation from flatness is, and even if we did, we'd have no way of assuming that deviation stays constant outside the observable horizon. I'm pretty confident that we'll never have any hard evidence that the universe is either finite or infinite, I'm just saying that it's theoretically cleaner not to impose a boundary where there is no evidence for one, or curvature where there's no statistically significant evidence for that either. I do think the "truth" will never be available to us, just yet another of science's intrinsic limitations, handed to us by inflation or some analogous process, and a universe of finite age.

In the sense that the error margin is enough that it could still be either way. That's why I described it only as a slight leaning, not any kind of definite result.

Inflation is just a theoretical explanation for the observation that it's particularly close to flat. A future observation with narrower error margins that pointed one way or the other would trump that kind of theoretical argument.

Maybe, maybe not. Which is why most cosmologists acknowledge the question as unsettled, rather than making an assumption that there isn't any.

Certainly true. However, we're always forced to assume that regions we can't observe are more or less like the regions that we can observe, so that's not unique to this question or even to cosmology. If a future observation were to show, say, that there is a definite negative curvature, I would say it would make more sense to conclude that the universe probably has negative curvature overall than to insist that the universe must be flat, but that we live in an enormous negatively curved bubble.

I don't think anyone thinks there is a boundary. All models of finite universes I've seen are still unbounded. And maybe it's theoretically cleaner to you, but that's a value judgment. Not all cosmologists share it.

Perhaps. But actually, I see no particular reason why more refined measurements cannot reduce the error margin on the measurement of curvature further. Astronomers are certainly designing experiments and equipment to do exactly that. If that happens, either the value will be constrained to be even closer to unity than it is now, lending further support to the conclusion that it is flat, or instead showing that it is slightly curved one way or the other. If we were sure which way it would turn out, astronomers wouldn't be so eager to test it further.

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Conserve energy. Commute with the Hamiltonian.

Grey,

Could you please describe the differences between a finite, bounded
Universe and a finite, unbounded Universe?

-- Jeff, in Minneapolis

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http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

A bounded universe would actually have an edge somewhere. You go far enough, and you come to the boundary of the universe. I'm not sure quite what that would be like, but it would not be possible to travel any further in that direction (otherwise, it's not really a boundary, is it? ), and there would be no light or anything else coming from beyond the boundary. Who knows what would happen if you tried to shine light across the boundary? Maybe it would be reflected, maybe just absorbed, maybe something weirder would happen. No serious cosmologist that I'm aware of thinks the universe is like this, perhaps partly just because having an edge to reality seems really bizarre.

A finite but unbounded universe wraps around and connects to itself so that, while there is only so much space, you still never reach an edge. The typical example is the surface of the Earth. There is only so much surface area, but no matter how far you walk in any direction, you'll never reach an edge. It's hard to envision that in three dimensions, but it still works in principle. If you went far enough, you'd come back to where you started. It doesn't have to be a simple connectivity like a sphere, either. It could be a torus, or something weirder. Of course, the evidence that we have at this point suggests that even if the universe is finite but unbounded, the radius of curvature is at least 70 billion light years, so circumnavigating it isn't actually a possibility. And if the expansion rate is accelerating, as it appears to be, then that situation is not going to get any better in the future.

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Conserve energy. Commute with the Hamiltonian.

Thanks, Grey.

Neither of your descriptions describes a universe of finite size and
quantity of matter in an infinite space, which is the easiest for me
to visualize. What label would you put on a universe like that?
Is it bounded or unbounded?

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

If space is infinite, then such a universe would be described as open. If the matter in it is confined to some finite extent (the rest is presumably just empty), that's just an unusual distribution of matter. For what it's worth, there aren't any serious cosmologists who think that's a good model of the universe, either. I'd place that in the same category as Ken G's suggestion that the curvature might be different outside the observable universe. That is, our observations are consistent with a universe that is isotropic and homogeneous at the largest scales, so to assume otherwise without some decent evidence doesn't seem like a good plan.

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Conserve energy. Commute with the Hamiltonian.

I know, but this is not a standard kind of result, because of the instability of the non-flatness. It's like if you see a pencil balanced on its point, and you know it's been there for a long time, and you measure which way it is "leaning" and got a statistically small result, you would not use normal statistics on that to guess which way it will fall-- you'd look for the string holding the pencil up. In cosmology, that string is, in effect, inflation (or some similar idea), and it makes it seem philosophically very unlikely that any non-flatness is just now emerging, just below our ability to measure. Statistical analyses make assumptions that don't seem very applicable to the flatness measurement, unless we have the whole idea completely wrong.
Indeed, but I'm arguing that we'll never see such a future observation. It would throw physics into a complete tizzy if we did, which is possible, but at this point the observations are more likely interpreted as unmeasurably flat.
But we make assumptions like that in physics all the time. Tomorrow we might discover that the uncertainty principle is unnecessarily restrictive, or that the speed of light varies. I would think either of those would do less philosophical violence to physics than a measurable curvature, yet we have included those postulates in our assumptions, primarily out of familiarity by now. So it will be with flatness, we just don't have the same familiarity yet. Maybe there's a law that says the generation that discovers a particular result never really believes it, but the next one does!

But we've seen pretty much all we'll see, from the CMB. The rest are just minor details, or maybe something exotic like dark matter or neutrinos or gravity waves. Who knows what we'll infer from them, but it's not terribly likely we can do better than what light tells us.
Familiarity will eventually replace those hangers-on.
The same could be said for statistically marginal results in ESP and astrology. Maybe there's a tiny real effect there too, it would be no more revolutionary. But some things are not purely statistical issues, until there's real proof.
As are ESP researchers, and I feel the same way about it-- I'm glad someone is doing it, but not if it costs a lot. I realize one difference is the ESP stuff has been going on a long time, but maybe they've been looking in the wrong places, or with insufficient sensitivity. The point is, it's not news, until it's news!

Yup. Those were exactly the sort of arguments that I was referring to when I said "but the fact that it's hard to tell at all leads to some decent theoretical arguments that it's infinite".

I don't think it would cause a tizzy at all. I don't think it would necessarily invalidate inflation. After all, if inflation is what really happened, then the universe probably does have some nonzero curvature, and from the argument above, even the slightest deviation will increase over time. If we measured some nonzero curvature, that would certainly constrain some parameters for inflation and the big bang in general, but the model could handle that just fine.

Not a chance. All of our current cosmological models can handle curvature easily. So much so, that any reasonable cosmology text talks in detail about all of the possibilities. The other changes you suggest would require major modifications to quantum theory or relativity. We assume that the speed of light is constant because we can think of a great many things that would be measurably different if it varied, and when we check, those things are consistent with a constant speed. We assume that the uncertainty principle holds because it's a simplification that can be easily derived from more detailed treatments of quantum theory, which have been tested out to about eight decimal places.

Neutrinos would let us push back a couple hundred thousand years from the CMB. That would give us a lot more data. Heck, someone was working on what we could determine of the cosmoic neutrino background from effects it should have on the cosmic microwave background, even without being able to detect it directly. And of course that's not the only source of information here. More analysis of distant supernovae would give us further information

Now that's a low blow, especially to the astronomers involved. We've got one good theoretical argument why the universe should be flat, and observations that say that it's at least really close to it, but I can't think of any good reason why we should simply assume that's the case. And of course it will cost a lot of money, but there will also be other discoveries made from spending that money.

It's a bold prediction, and you're welcome to that as an opinion. But it is simply false to claim, as you seemed to, that cosmologists all (or even mostly) assume an infinite universe since they don't have positive evidence to the contrary.

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Conserve energy. Commute with the Hamiltonian.

The huge problem would be the specialness of our time. Remember, the very reason inflation is a popular idea is because it resolves problems like the flatness problem. It would be trying to have one's cake and eat it too to say "inflation made the universe so flat that it could stay nearly flat for 10^10 years instead of the expected 10^(-32) seconds" and also say that "oh yeah, it's just starting to show up as nonflat now, 10^60 or so inflationary epochs later."

On the ther hand, there is a possibility that could allow this, which is along the lines of the anthropic principle. Perhaps of all the possible universes, only very special ones last long enough to build intelligence like ours, and the vast majority of those don't do it with a lot of unnecessary time to spare. In other words, intelligence always appears in the "end times", speaking logarithmically. If so, then perhaps it is natural for curvature to begin to appear with intelligence. The same might be said for the acceleration by dark energy. But why both of those at the same time? Too many coincidences, it's still ESP in my book.

And those are all behind the times! If I were writing a cosmology text, the first thing I'd do is throw out all the "k different from zero" business. It adds a lot of complexity for no payoff at all-- what does nonflat curvature tell us about our universe? Nothing-- our universe is still indistinguishable (in terms of what happens in it, not the measurements you're talking about) from a flat one. Since all of physics is an "effective theory", the universe is "effectively flat". The rest is just angels on a pin, it doesn't mean anything even if we can measure it. For example, I see no reason to assert that the curvature is constant-- if it is not flat, we could be on any shape at all, the bridge of God's nose-- why not? It's angels on a pin still.

True, but those were still just metaphysical hiccups, and modifications are just that. It's just physics, it could be any way one can dream of. But if we find that the universe's parameters are set up such that space is just now "unraveling", I think that would have huge impact. The convergence of the acceleration and the non-flatness would tell us something very philosophically odd about our universe as a whole, perhaps moreso than even the measurement theory of quantum mechanics or the reference frames of relativity. It would be up there, anyway.
But somewhere there is a "marginally significant result" that it varies, I'm sure-- that's the law of marginally significant results! The flatness is no different.
But what happens in the ninth? We can always imagine that great surprises are waiting in the next factor-of-two error reduction, just like for the flatness issue. Granted, that's a lot of what science does, but my point is we carry on assuming this will not happen-- that is also natural for science to do.
But that's because they are so undetectable. Just to see cosmological neutrinos would be a challenge, let alone see anisotropies like in the CMB. That might already rule out a dramatic neutrino signal, you might need "precision neutrino astronomy". Not gonna happen. And they are working on ESP too, with similar likelihood of success. I can't imagine how an anomalous CMB signal would not be attributed to a dozen other factors prior to fingering a weird neutrino flux! I could be wrong there, not being a neutrino expert, but the point is, people are doing all kinds of pretty farfetched things. They all have a tiny chance of a Nobel prize (which is more than I can say), but a big chance of squat. That's also true about ESP and ghost research, it's just the nature of the beast.
That's all post-CMB, it can't blow the lid off.
I admit that its prospects might be better than ESP or astrology, because they both seem kind of ridiculous, but I still think that to have both acceleration and non-flatness just now appearing on our radar screens would require such a spectacular fine-tuning of parameters that science as we know it would pop a gasket. Even string theory is not gonna answer that one, it's working hard enough just to get an interesting universe to result. But I suppose one could turn that argument around and use it to motivate the observation, and I'll certainly admit it's a Nobel prize for anyone who can prove our neck of the universe is measurably unflat. I wish I could place bets on it though.
I'm not really saying what cosmologists believe when they go to bed at night, I'm talking about what they have any business calling a scientific result as they push forward the "effective theories" of physics. I'm also not saying the universe is infinite, I'm just saying that's the natural effective theory. For example, what if the curvature is measured to be very slightly positive? Are they going to have basis for assuming the universe is finite? Every surface looks flat at some scale, and starts to look unflat with enough precision, but it still doesn't allow you to map the whole surface. I would claim that if the observable universe is measurably nonflat, the natural assumption is that it is a local perturbation to the overall flatness, in terms of an effective theory-- that certainly is just as good as assuming the curvature is constant everywhere. It's science run amok, we are never going to know the true global shape of our universe, so we shouldn't build effective theories that pretend otherwise.

I don't think that you can escape the anthropic principle, at least in it's weak forms anyway. There are a fair number of physical parameters that need to be pretty close to what they are for the universe to have things like stars and planets and people. So, possibly one more coincidence. It seems strange to insist on utterly rejecting this particular one.

And that attitude (perhaps combined with laziness ) is probably why you haven't had a cosmology textbook published. It's extremely useful when trying to understand cosmology to look at, not just what our universe is like, but what it could be like, if certain parameters are different. And to make it clear what we really know about the constraints on those parameters, rather than the way we think it should be, based on our current theories.

As an example of just this kind of thing, long after Einstein had removed the cosmological constant form general relativity and called it a mistake, texts on gravitation and cosmology still included an explanation of it, and what the effects of it would be. If they had similar attitudes to yours about flatness, they would have said "why bother keeping this in at all, when it's obvious that the universe has a cosmological constant of zero?". And now we know that understanding how a universe with a nonzero cosmological constant works is a very good thing if you want to study cosmology.

No, actually. We expect that as we probe deeper we'll find some discrepancies, and those are the most active areas of experiment. We specifically look for places where the observations don't match our theories, because that's where new physics lies. The very last thing we should do is what you're suggesting: we have a theory that says the universe should be like thus-and-such, and we've confirmed it to within a percent or so, so we should just assume that we're pretty much right about it and go look at other things.

Not any time soon, certainly. It may even be impossible. For example, I think I recall seeing someone work out some rough estimates, and you might need a planet-sized detector. Then again, I've also seen a well-writeen paper that was able to determine the temperature of the CMB in the past experimentally, by looking at its effect on distant galaxies. I wouldn't have expected that was possible, but someone else was more clever than I probably would have been.

Frankly, I find this continual comparison to parapsychology really insulting to some serious astonomers, and it's making me lose respect for you. It's a clear straw man, too, Ken. It's tantamount to saying that anything that we don't currently have direct evidence for is all equally unlikely, so that if we're going to imagine that we might be able to do neutrino astronomy, we might just as well believe in anything.

I disagree. By itself, the CMB only constrains the flatness to about 6%. It's further data that's brought us down to a couple percent. And looking at other cosmological parameters along with flatness provides constraints to any inflationary model, so we know if that particular idea works or not. Sure, maybe there's a string holding the pencil up, but we want to know what the string actually is, not just assume that we've got it figured out. Just because inflation provides one possible explanation for what we see does not mean that it's the only possibility.

Nah. Science has handled plenty of startling discoveries that have completely changed how we thought about the universe before. It just keeps on chugging.

Hawking bets on things like that all the time. And we really are always making observations on the edge of things, looking for exactly the places where what we see is different then what our current models say we should see. That's always the most interesting stuff!

Hey, you get to decide what your own opinion of cosmologists is, and you can think they are all goofballs if you'd like. However, when presenting a mainstream opinion, you should still present the actual mainstream opinion, not what you think it should be. And for any cosmologist that I've seen, when asked whether the universe is infinite or flat, the answer is "well, we know it's really close to flat, which we think would mean that it's infinite, and there are some good reasons to think it might be, but we're not sure; we at least know that it's really, really big".

Sure, there are locally curved regions; that's why we have gravity. But that's not the kind of measurement we're doing here. If you're trying to measure the curvature of the Earth, you can tell the difference between mountains and overall curvature. If the Earth were a lot bigger, it might be hard to deduce the curvature, but it's still possible in principle, even if it's very slight and there are a lot of mountains.

Now this seems completely nonsensical. If everything we can observe looks one way, we should assume the universe beyond what we can obseve is a different way, just because you think it's more "natural"? Why is a flat infinite universe a more natural assumption than a curved (finite or infinite, depending on which way) universe? Because we're used to Euclidean geometry? Why is it better to assume that the unobservable part of the universe is the way you think it should be, rather than the way the observable part is? What something unobservable is like must obviously be a complete assumption, but assuming that it's different from what you can observe does not seem like the best choice.

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Conserve energy. Commute with the Hamiltonian.

Perhaps so, we are already in a pretty narrow window of parameter space, but with most parameters you can point to why they had to be the way they are-- it's not just a surprising coincidence like it would be with curvature. But there does seem to be a potential for some kind of anthropic element to this too, so perhaps I'm judging too quickly.
Laziness, for sure . But I'm speaking hypothetically. Do cosmology texts include the cosmology of a 2D universe in their core explanation? It would be equally informative, if not more so. Or what if the speed of light wasn't constant? More grist for the mill, but not viewed as relevant to the cosmology of our universe. We now know that nonzero k is equally irrelevant to anything important, so it should also be dropped from the "critical stream". Sure, it can be in there somewhere, just as those other things could, but it's time to re-evaluate the standard approach of putting k in right from the start as if it was a fundamentally unknown parameter. It no longer is, not in any important way.Yes, that's just what they should have done. And what if they had? No big deal, the cosmological constant would have been back just as quickly. It's not uncommon in physics to do a more general calculation just because you can, and then project onto a simpler subspace for applications to particular problems, but that is generally only done when you might very well also be doing the more general problem for some other real application. When there's simply no known real application, the excess machinery is not included in the core description.
So when we teach the uncertainty principle, we should embed it in a more general theory that allows for minor deviations in some situations, even though those situations don't appear in reality? No, the theory does not anticipate the observation, it awaits the observation-- a statistically significant observation.
That is not what I suggested, I said that we assume the simplest theory is correct until observation shows otherwise, that's just Occam's Razor. Why should we not do that with cosmology?

Actually, I think that's insulting to parapschologists (real ones, not kooks). Don't get me wrong, parapsychology is a science without a result to analyze, but it's still a science. How can you say that ESP is not possible, but positive curvature is? They are both living at the realm of marginal statistical significance, and either could emerge as real with a somewhat better observation. How do you know which one will win the race? Personally, I'd bet half my savings that neither will, that's my point.

I think there's some truth to that-- all marginally significant results are created equal. What basis can we have to decide differently? I'd say the only criterion is the history of the pursuit-- if efforts keep beating down the error and still the signal stays at the marginal level, that's the red flag. I think we are starting to see that with curvature, but perhaps not quite the extent to which we've seen it with ESP.That's interesting, I didn't realize that supernova data was better than the CMB at determing flatness. I guess that's because flatness involves a sense of "depth perception", which the CMB is not very good at producing.Oh I agree, that wasn't my point-- my point was when the curvature is very nearly flat, and is highly unstable, the real issue is what is holding it up. The actual deviation from flat is irrelevant, it's just not the interesting part of the story, especially since it could never be globally extrapolated with confidence.
The difference I see is that it's not just a new theory that would explain it-- that's no problem at all for science. The problem for science would be a hint that the scientific method won't be able to answer an observation that science can make. That's the problem with fine tuning of parameters that aren't needed to be fine tuned to have a natural explanation. It makes you wonder if the explanation isn't purely natural, whatever that means, and the anthropic approach is not clearly a scientific principle-- it's already a bit of a departure from the philosophy of science. But on further thought, it does seem like a pretty natural explanation that there could be local instabilities that have bits of the universe showing curvature after awhile, and the places that show it fairly quickly can't make galaxies for some reason, and the ones that take a very long time are rare, so intelligence tends to show up in ones that are just beginning to show it. But again, the acceleration is a separate issue, it's not clear how they would be united.


One should not characterize my point as being that there's nothing interesting to look for at the edge of what's known, it's that some edges are more likely to reveal an interesting result than others. That's why I brought in ESP, as an example of an unlikely avenue. It would be nice to characterize our observable curvature, but it's very likely to be flat, and even if it isn't it really won't change cosmology a whit, except for the philosophical types who unnecessarily extrapolate that to a globally closed universe (and note that my anthropic argument would allow the curvature to not be global, because then you don't need a "many universe" approach).
But why did you leave out "is the curvature constant or varying on scales larger than we can observe"? What would cosmologists say to that? Same kind of thing, I'd expect.
Why not? How do you establish a scale where gravity can no longer vary?

On the contrary, I'm not assuming anything, I'm merely pointing out an alternative picture which is every bit as valid as a constant curvature view. Indeed, I would argue that it is more natural to expect that just because we live on a mountain, and that's everything we can observe, the entire Earth is not ten miles around. I would say on probabilistic grounds, if one is going to apply an anthropic approach (and there's little alternative, as we've agreed), infinite universes with variable curvature are infinitely more likely than finite ones with constant curvature.
I repeat the mountain analogy-- if you know your vision is limited, it makes more sense to apply whatever logic you can to the rest, or at least just say "I have no idea", than to extrapolate without justification.