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#81 |
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Philosopher
Join Date: Feb 2005
Location: Shanghai
Posts: 7,095
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"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov |
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#82 |
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Join Date: Sep 2007
Posts: 5,785
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#83 |
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Philosopher
Join Date: Feb 2005
Location: Shanghai
Posts: 7,095
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To be clear: you agree with both "I am sitting under the tree" and "the tree is over me" describe the situation accurately and that both models are true. But you suggest that while that's the case in this very simple example, it's not the case with respect to the choice of coordinates in GR, correct?
(I'm just looking for clarity, there's a good chance the the above is incorrect and you're saying something else, but I'm not sure if your are or what that other thing could be)
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"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov |
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#84 |
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Philosopher
Join Date: Feb 2005
Location: Shanghai
Posts: 7,095
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__________________
"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov |
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#85 |
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Join Date: Sep 2007
Posts: 5,785
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I specifically do not agree that that is analogous to the Earth/Sun situation at all. Not even close. That's like saying that from a certain POV that when the Sun is currently to the left of the Earth, the Earth is currently to the right of the sun. Just because 2 valid models are equally accurate in one situation does not mean that all valid models in all situations are equally accurate. |
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#86 |
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Join Date: Sep 2007
Posts: 5,785
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#87 |
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Join Date: Sep 2007
Posts: 5,785
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#88 |
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Philosopher
Join Date: Feb 2005
Location: Shanghai
Posts: 7,095
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I didn't ask you if you agreed that it was analogous. I basically said "You agree that both of those statements are true, yes or no?" you haven't answered that question.I then said that I think you don't agree that it's a good analogy (so you seem to be agreeing with me about that), because while some models can be indistinguishable and both true, in the specific case of the earth/sun system and rotation, you feel there's other evidence that we can draw on to distinguish them. Rather than arguing with the above, which isn't an argument, can't you just answer the actual questions I'm asking? I'm only trying to clarify what you're saying. |
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"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov |
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#89 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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First of all, I want to make clear that I'm not joking about the tree.
The main point of the analogy is this: There is a physical occurrence that can be described as: 1. H'ethetheth sitting under a tree 2. A tree standing above H'ethetheth 3. H'ethetheth and a tree rotating at 15°/hour and moving east at 1000 km/h. 4. H'ethetheth, a tree, more trees, a planet, and a star in a galaxy moving on a complicated sinusoidal path through intergalactic space at 30 km/s Which of these really describes the the actual physical occurrence? A secondary point is that it's not an analogy so much as a simpler example of exactly what you are describing. |
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#90 |
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Philosopher
Join Date: Feb 2005
Location: Shanghai
Posts: 7,095
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I'll take that as "I think it's more complicated than that presented in the post you quoted, so can't answer yes or no." Because answering either yes or no would have been much easier than posting what you just posted.
I'm seriously not trying to be argumentative. Anyway, I'll take a look at your last post when I get a chance, late for work!
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"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov |
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#91 |
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Philosopher
Join Date: Oct 2007
Location: Nova Roma
Posts: 8,419
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#92 |
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Philosopher
Join Date: Feb 2005
Location: Shanghai
Posts: 7,095
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Okay, I'm no expert on this. Just an interested layman, which is why I didn't answer. I figured you were looking for the answers of the experts (like sol). But since you asked I'll do my best.
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If you are trying to model the entire universe I think that as Zig said, the CMB rest frame is the most convenient. I honestly don't know if one can be said to be more complicated than the other, since they can be transformed into each other. But I honestly don't know.
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"... when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." Isaac Asimov |
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#93 |
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Philosopher
Join Date: Aug 2007
Posts: 8,565
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Knock the tree over relative to what?
ETA: Pick frame of reference--any frame of reference. Figure the current forces on the tree, in that frame. Apply a new force to the tree. Figure the outcome, in that frame. Do the same thing in another frame. It's the same outcome, every time. Pick one of the frames. Declare it to be the "best" frame, or the "correct" frame. Explain why. |
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#94 |
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Graduate Poster
Join Date: Mar 2008
Location: Poole, UK
Posts: 1,960
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Relative to the ground.
Because it's the simplest, and because it helps us to understand the world. Which is why we do physics. And when we do, we are reminded that a reference frame is merely an artefact of measurement. Stars exist, galaxies exist, planets exist, and other things too. These things exist in the universe, and they move. They are real and so is their motion. But you cannot point up to the clear night sky and say "look, there's a reference frame". We understand reference frames, we use them as appropriate, but we do not allow an artefact that has no actual existence to cloud our understanding of the things that do. All maps are equally valid, but the map is not the territory. The Sun does not "go round the Earth in a suitable reference frame", just as the Earth is not rectangular whatever the map. That reference frame is not something that actually exists, so the Sun and the Earth are not "in it". They're in space. They exist, and their motion exists, in this universe which also exists. And in that universe, the Earth goes round the Sun. |
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#95 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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I agree with almost your entire post, except this sentiment.
This is just your preference, just as it is your preference to evaluate me knocking over a tree in a reference frame in which the universe is rotating, and the cosmic background radiation is shifted by about 30 km/s, if I recall correctly. |
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#96 |
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Graduate Poster
Join Date: Mar 2008
Location: Poole, UK
Posts: 1,960
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It's kind of like the buck stops with the universe, H'ethetheth. We say motion is relative, but we can use the CMBR dipole anisotropy to gauge our motion with respect to the universe. Different people moving in different ways might all try to claim that it's "perfectly valid" to say that the universe is moving instead. But when you put them together in a room and let them fight it out, they soon realise that they can't all be right, and then they end up seeing sense.
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#97 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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Yes, it's kind of like that, but not really, because the buck almost always stops well before that, depending on what you're describing, and what the most intuitive description is.
People sitting under a tree never say they're closely accompanying a tree on its polycycloid path in the general direction of the constellation hydra at about 300 (I recalled incorrectly) km/s. There is no need for the buck to stop if we can stop it anywhere we prefer. In fact, general relativity states that all the people in your room can all be right, and if they did their homework correctly, they are all right. |
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#98 |
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Graduate Poster
Join Date: Mar 2008
Location: Poole, UK
Posts: 1,960
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No probs re usage of a coordinate system appropriate to your situation. But in the end the buck really does stop with the universe. You just can't say that the universe is moving with respect to something else, because the universe is everything there is.
Yes, the people in the room can be all right. The idea is that they compare notes and make allowance for their different coordinate systems, then reach a consensus. That's what the coordinate-independence of general relativity is like, something like you take a step back and see the big picture. For example if you're moving fast towards a star, and you say it's length-contracted like this |, and if I'm heading towards it from an orthogonal direction and say it's length-contracted like this ―, we don't fight like cat and dog. We compare notes and we recognise that we each see the world in a different fashion, and then we step back and see the big picture of how the world really is, and how we see it different when our motion through it is different. |
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#99 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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#100 |
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Graduate Poster
Join Date: Nov 2007
Posts: 1,553
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__________________
When I look up at the night sky and think about the billions of stars out there, I think to myself: I'm amazing. - Peter Serafinowicz |
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#101 |
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Philosopher
Join Date: Oct 2007
Location: Nova Roma
Posts: 8,419
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That may or may not be true. But it's also irrelevant, because we cannot see the entire universe. Indeed, the current standard cosmological model posits an infinite universe of which we can (obviously) only see a finite part, and in fact - although this is little discussed - it's a universe in which the portion we can see is guaranteed to be rapidly rotating with respect to any other distant portion.
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#102 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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#103 |
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Philosopher
Join Date: Oct 2007
Location: Nova Roma
Posts: 8,419
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Well, in the standard cosmological model the universe is flat (meaning basically that it's infinite in spatial extent). Moreover, it underwent a period of so-called inflation in its very early evolution shortly after the big bang.
Inflation causes regions of the universe to expand away from each other very rapidly, and it produces random fluctuations in density and pressure. It is those fluctuations that seeded the stars and galaxies we see around us. There are essentially two possibilities regarding inflation - it last forever going back into the past, in which case any two distant regions were close together at some point during inflation and the region in between them was filled by inflationary fluctuations produced after they separated, or it lasted for a finite time. If it lasted for a finite time, sufficiently distant regions were never close together. Because the period before inflation was extremely inhomogeneous and anisotropic, one expects very large fluctuations in the characteristics of such distant regions, including large relative rotation. If it lasted forever, the perturbations produced during inflation accumulated indefinitely. That means that sufficiently distant regions are again disconnected in the sense that one expects no correlation in their characteristics. |
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#104 |
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Graduate Poster
Join Date: Mar 2008
Location: Poole, UK
Posts: 1,960
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I would urge posters to do their own research at this juncture.
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#105 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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I think I sort of get that, superficially. Though you are talking about the rotation of regions of spacetime, right? I don't think I know what that actually means, but I'll just allow it as something that I may come to grasp one day.
ETA: Something I just thought of that could help me grasp it: Is rotating spacetime at all comparable to vorticity in fluid dynamics? |
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#106 |
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Muse
Join Date: Apr 2012
Location: Montana, USA
Posts: 576
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I don't want to put words in sol invictus's mouth, but I don't think that's what he's saying. It's more that massive objects close together in the early universe had rotation and, as the universe expanded, these "portions of space" (i.e. the massive objects within that volume) continued to rotate relative to other portions of space. Of course, there is something like vorticity in space-time as well: http://science.nasa.gov/science-news...11/04may_epic/.
sol invictus, I've really only heard that inflation lasted for a finite period of time. Is this more accepted than the other view? Or is the other view new and I just haven't heard of it yet? If inflation is always occurring, is there something that weakened/diffused that repulsion so today it is negligible? Or is this a possible candidate for dark energy? |
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#107 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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#108 |
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Muse
Join Date: Apr 2012
Location: Montana, USA
Posts: 576
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No, I'm not sure. I think that's accurate for the scenario in which inflation is finite, but I bet sol invictus will correct me if I'm wrong. In the example of infinite inflation, I think the unique rotations are introduced by the random fluctuations, but I'm not at all familiar with this hypothesis.
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#109 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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Okay, I'll just sit back and wait, save for the occasional dumb question.
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#110 |
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Graduate Poster
Join Date: Mar 2008
Location: Poole, UK
Posts: 1,960
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This is an interesting one. Strictly speaking the answer is no. However there is a relationship between spacetime and vorticity, see this NASA article on gravity probe B. Note though that it's the Earth that's rotating, whilst spacetime is "twisted" rather than rotating:
"If Earth were stationary, that would be the end of the story. But Earth is not stationary. Our planet spins, and the spin should twist the dimple, slightly, pulling it around into a 4-dimensional swirl". Whilst a gravitomagnetic field and indeed a magnetic field is a "turn" field in that gyroscopes precess or a compass needle rotates to point North, this occurs because motion through a twisted region results in a rotation. Not because the region is rotating. A region of spacetime rotating bodily with respect to another would be a magnetic monopole, which doesn't exist in nature. People do speculate that they might, but an electron has an electromagnetic field. It doesn't have an electric field. A particle cannot have an electric field all on its own, and in similar vein a particle cannot have a magnetic field all on it own. It's the same for a region of space, because space is "connected", something like elastic. The region cannot rotate freely like some roller bearing disconnected from surrounding regions. Also note re an earlier post that a flat universe does not imply an infinite universe, and that inflation is thought to have been of brief duration, and responsible for smoothing out fluctuations rather than causing them. |
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#111 |
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Philosopher
Join Date: Oct 2007
Location: Nova Roma
Posts: 8,419
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Yes, it's comparable. Spacetime is strange stuff in GR; it's not like an aether because it has no rest frame, but it can "wave" (i.e. waves of spacetime exist), and it can rotate and drag things along with it. Sound waves in a fluid with vorticity behave in ways that are quite analogous to light in a rotating spacetime. You do have to be careful with this analogy (it's mathematically precise, but in a slightly tricky and non-obvious way) because there's no rest frame.
It's both. Objects will tend to rotate with the spacetime locally, because they get dragged along with it. At the same time a rotating mass sources rotating spacetime around it (and inside it). Going back to the fluid analogy, if you had a porous object in a fluid, it would both drag fluid with it and get dragged along by it. You might expect distant parts of the fluid to slow each other down until they cease to rotate with respect to each other. Something like that happens in the universe too, but only if the regions are close enough together that they've been able to interact (in a fluid, if the regions are separated by a distance longer than the time the system has existed times the sound speed, they can't have affected each other).
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As for dark energy, if that's due to a vacuum energy/cosmological constant it means a new phase of inflation has just begun in our region of the universe - but it's a different phase, with a much slower acceleration rate, than the one in our past. |
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#112 |
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fishy rocket scientist
Join Date: Aug 2004
Location: among the machines
Posts: 2,340
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#113 |
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Muse
Join Date: Apr 2012
Location: Montana, USA
Posts: 576
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Thanks for the information! I've been reading this post over and over for a while and it still has not registered fully. Please forgive my ignorance, but if inflation is an accelerating expansion, wouldn't that mean our universe ought to be expanding faster than it ever has in the past? And isn't it true that the inflationary epoch was the most rapid expansion of space-time in our universe's history? Or am I conflating something here?
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#114 |
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Illuminator
Join Date: Jul 2006
Posts: 4,648
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Let's separate two things: (a) the inflationary epoch and (b) "dark energy". The inflationary epoch (or so this well-tested hypothesis says) was an era when the vacuum energy density was huge, and drove a period of wild acceleration. There was a particular field (the "inflaton") responsible for this energy density, and after the field had decayed, the inflationary behavior ended.
Modern dark energy has an inflation-like behavior, and, yes, it drives an accelerating expansion. Unlike the inflaton, its energy density is very low. Also, dark energy's acceleration has to fight against the gravitational pull of normal matter (baryons + dark matter), which together work to decelerate the expansion. In the past, when the universe was smaller and attractive-gravity better able to work, the deceleration effect was more important. In the present and future, the normal matter is spread out and its mutual-attraction-acceleration is small, so the inflation-y effects of dark energy are just now starting to dominate. So, yes, in the future dark-energy acceleration will drive an ever-increasing rate of expansion, just as inflaton-acceleration it did in the early universe. |
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#115 |
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Muse
Join Date: Apr 2012
Location: Montana, USA
Posts: 576
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ben m, that's how I've always understood it: the inflationary epoch is something entirely distinct from dark energy. What has me confused is this notion of an infinite inflation. If inflation is an accelerating expansion and it is infinite (continuously occurring?), it would seem to me that there must be some force/pressure that either counteracts it or dilutes its effects to a large degree. I say this because I was always led to believe that inflation was a finite process in which the universe expanded greatly for a short period of time, and then returned to a "normal" expansion rate (the graphs I've seen show a kind of saddle-like curve for this period). After this, as you said, we have periods in which matter dominates and, now, dark energy.
So, does the inflaton field still affect us? If so, is there something negating this effect? Or am I misusing the term infinite? |
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#116 |
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Illuminator
Join Date: Jul 2006
Posts: 4,648
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If I understand this correctly, you should think of the inflaton as as short-lived high-energy particle. For a short while this particle existed, and then it decayed into a low-energy state, and having decayed it's now not there any more---so, no, it doesn't affect us any more.
The tricky part is understanding why "a high energy particle exists", or "a high-energy particle is decaying", would look like vacuum energy. The answer is that the particle needs to be a vacuum condensate, sort of like the Higgs boson, so that its energy density does not dilute as the universe expands. Combine the two pictures, and roughly what you have is that *the vacuum itself* was in a high-energy state, then the vacuum decayed completely to the modern-day low-energy state, and inflation occurred only during this short-lived decay process. |
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#117 |
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Muse
Join Date: Apr 2012
Location: Montana, USA
Posts: 576
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ben m, great info! And the best part... I get it!
Inflation always bugged me because even though it seemed like just a way of writing off the magnetic-monopole problem, it was so widely accepted in Cosmology. I watched some Cosmology lectures that helped boost my confidence a bit, but I still didn't understand it that well. This concept of a high-energy vacuum really makes sense though, so thank you very much!
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#118 |
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Philosopher
Join Date: Oct 2007
Location: Nova Roma
Posts: 8,419
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In theories of eternal inflation, inflation is always occurring somewhere - just not around here. The way it works is that once inflation starts somewhere, it ends locally in patches, but other patches are still inflating and producing yet more volume. Then in those new volumes inflation ends in some patches, but in others it's still going and produces even more, etc.
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#119 |
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Muse
Join Date: Apr 2012
Location: Montana, USA
Posts: 576
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sol invictus, thank you very much, that's making sense now. One more question, if you would indulge me.
Where do these patches of inflation occur, or are they a yet-unobserved prediction of the inflationary model?
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#120 |
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Graduate Poster
Join Date: Mar 2008
Location: Poole, UK
Posts: 1,960
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Get yourself a stress-ball, squeeze it down in your fist, then let go. It would be neat if you could find a black one with little white specks on it. Einstein didn't talk about stress-energy for nothing. And if they'd had stress-balls in his day, he wouldn't have made his greatest blunder.
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