Post by: Ron Maxwell on 13/08/2013 17:59:29
Post by: Bill S on 13/08/2013 20:25:35
The reason I tend to leap in early in threads like this is not because I necessarily think I have the answer; rather, it is in the hope of testing my ideas. Unfortunately, it does not always work, which I assume is either because I am absolutely right, or my idea is so silly it does not merit a response.
Anyway, once again, this is my understanding.
Currently, the majority view is that the Universe is flat (or as near as makes no real difference), and is infinite. If this is right, a hypothetical craft could travel for ever without visiting the same point twice. It would also mean that there was no centre to the Universe. This is not just because we can’t find one, but because there is no centre, in the same way that there is no central number between zero and infinity.
If you have been following other threads you will be aware that I have as serious problem with the suggestion that something that is finite can become infinite. The main reason why I distinguish between the Universe and the cosmos is that the Universe could be just that part of the cosmos we can detect, so it could be the cosmos that is infinite.
The reason I tend to leap in early in threads like this is not because I necessarily think I have the answer; rather, it is in the hope of testing my ideas. Unfortunately, it does not always work, which I assume is either because I am absolutely right, or my idea is so silly it does not merit a response.
Anyway, once again, this is my understanding.
Currently, the majority view is that the Universe is flat (or as near as makes no real difference), and is infinite. If this is right, a hypothetical craft could travel for ever without visiting the same point twice. It would also mean that there was no centre to the Universe. This is not just because we can’t find one, but because there is no centre, in the same way that there is no central number between zero and infinity.
If you have been following other threads you will be aware that I have as serious problem with the suggestion that something that is finite can become infinite. The main reason why I distinguish between the Universe and the cosmos is that the Universe could be just that part of the cosmos we can detect, so it could be the cosmos that is infinite.
Post by: Pmb on 14/08/2013 01:42:56
I agree with Bill in that I too think the cosmos as being different than the universe. I think of the cosmos of all that exists while the universe is the set of all places which can be connected to each other by a continuous set of points. Nice thinking Bill!!! :)
Post by: Ron Maxwell on 15/08/2013 12:18:26
Post by: Bill S on 15/08/2013 15:51:27
Quote from: Pmb
You can think of the spatial geometry of the universe in one of three ways; a sphere, a flat sheet or shaped like an infinitely large saddle. In all cases there is no center.
Let’s take the spherical universe as an example, because it’s the easiest – I think.
If it is finite and spherical, how can it not have a centre?
If it is infinite, how could anyone possibly know it is a sphere? I accept that if one can discover that it is positively curved, one can consider that it must be spherical, and that that sphere might be considered to be unbounded, in which case it can extend in every direction without limit, but infinite implies that it has already done that. If it is infinite, it must already be infinity, and must always have been infinite. It has no centre, but in what sense can it be said to be a sphere?
Wow! Post 666 - "the Number of the Beast". :D
Post by: Pmb on 15/08/2013 17:30:32
Quote from: Bill S
If it is finite and spherical, how can it not have a centre?Because we're talking only about the geometry of the surface. Only the space consisting of the surface of the sphere is part of the "space" that we're talking about. Remember that this is an analogy and not a physical representation of the space. An analogy is defined as something which is similar in some ways but not in all ways. In this case the analogy does not apply to two dimensional surface of the sphere being "embedded" in three dimensional space. Two dimensional beings who live on the surface could travel everywhere on the surface but none of them would ever run into a place which they could call the center since all places on the surface are identical to all other places.
If the geometry of the universe is closed then it's finite, not infinite. The spherical universe is bounded.
Post by: Bill S on 15/08/2013 23:01:59
Would I be right in thinking that in order to apply this analogy to physical, 3D, space, the sphere would actually have to be a 4D hypersphere? If so, this is where I run into difficulty. I cannot visualise a hypersphere, much less its 3D surface. As a result, useful though the analogy is in some respects, it fails me when I try to connect the dots to apply it to our Universe. I end up seeing a spherical (3D) Universe bounded by a (2D) surface.
Post by: Pmb on 15/08/2013 23:28:04
Pete, as you rightly point out, the surface of a sphere has no central point. You also point out that this is an analogy and not a physical representation of the space.I dthink so.
Would I be right in thinking that in order to apply this analogy to physical, 3D, space, the sphere would actually have to be a 4D hypersphere?
Pete, as you rightly point out, the surface of a sphere has no central point. You also point out that this is an analogy and not a physical representation of the space.Think about it like this. In 3-space which has the geometry of a closed universe, if you set rulers end to end in a line parallel to each other each starting off in a straight line they will end up leading right back too where they started out from but not coming back parallel but crossing each other. This happens no matter which direction they lead out from. Now appl;y this to the surface of a sphere and you'll see that the same thing happens. That's how to use the analogy.
Would I be right in thinking that in order to apply this analogy to physical, 3D, space, the sphere would actually have to be a 4D hypersphere? If so, this is where I run into difficulty. I cannot visualise a hypersphere, much less its 3D surface. As a result, useful though the analogy is in some respects, it fails me when I try to connect the dots to apply it to our Universe. I end up seeing a spherical (3D) Universe bounded by a (2D) surface.
Post by: Bill S on 16/08/2013 19:03:25
Post by: yor_on on 22/08/2013 21:40:39
Just compress.
Post by: Ron Maxwell on 12/01/2015 04:04:29
Post by: jeffreyH on 12/01/2015 05:37:02
Post by: CliffordK on 12/01/2015 05:47:30
Can we estimate the shape and dimensions of the visible universe? Does it have a three dimensional form? If so, where is the centre?Shape of the visible universe: spherical, 3 dimensional.
Radius: About 13 billion lightyears.
Center: EARTH.
We don't know how big the unseen portion of the Universe is, and don't have a good idea to its form and shape. But, the visible portion is roughly a sphere with Earth at the center.
Post by: jeffreyH on 12/01/2015 06:25:35
Can we estimate the shape and dimensions of the visible universe? Does it have a three dimensional form? If so, where is the centre?Shape of the visible universe: spherical, 3 dimensional.
Radius: About 13 billion lightyears.
Center: EARTH.
We don't know how big the unseen portion of the Universe is, and don't have a good idea to its form and shape. But, the visible portion is roughly a sphere with Earth at the center.
You can't argue with that. [:D]
Post by: Ophiolite on 12/01/2015 12:35:08
I've done some checking and it seems to be centered on me, although it is influenced by which way I turn my head.Can we estimate the shape and dimensions of the visible universe? Does it have a three dimensional form? If so, where is the centre?But, the visible portion is roughly a sphere with Earth at the center.
Post by: dlorde on 12/01/2015 12:58:44
As I understand it, there is - in principle - no reason why even an expanding universe could not be infinitely large - if it started off infinitely large. An infinite extent can expand, as Hilbert's Hotel (http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel) illustrates. I'm told that this is the default assumption of standard cosmology.
I've been told that inflation theory gives an estimate for the size of the universe beyond the observable horizon (very large), but I'm waiting for a reference on this.
Post by: PmbPhy on 12/01/2015 16:34:15
Quote from: CliffordK
Shape of the visible universe: spherical, 3 dimensional.I assume this is a joke?
Radius: About 13 billion lightyears.
Center: EARTH
Post by: chiralSPO on 12/01/2015 18:21:12
Post by: PmbPhy on 12/01/2015 19:37:09
No joke--the Earth is very close to the center of the OBSERVABLE universe.Ah! I see what you mean now. Thanks.
Post by: PmbPhy on 12/01/2015 19:38:29
When I first tried to comprehend the topology of the universe as a potentially finite but non-bounded volume, I found it helped to think of the old arcade game of Asteroids (http://www.freeasteroids.org/), where whatever disappeared off the screen in one direction, reappeared on the opposite side, moving in the same direction - a finite but unbounded 2D surface.Right. It had the topology of a cylinder.
Here's something interesting. The space around a cosmic string is flat. The geometry is that of a cone.
Post by: jccc on 12/01/2015 19:48:05
Post by: JohnDuffield on 12/01/2015 19:54:14
With (hopefully) the intelligence to follow the arguments but not the education to understand the Maths, I go a bit lost with some of this. If the Big Bang theory is correct then surely the universe cannot be infinite.Correct. There's this huge non-sequitur wherein people say WMAP found that the universe is "flat" and therefore the universe must be infinite. Here's a NASA website for example: shape of the universe (http://map.gsfc.nasa.gov/universe/uni_shape.html). But it just doesn't follow. And it doesn't tie in with big bang cosmology. When you challenge the people who say the universe is infinite, they duck and dive and say the universe has always been infinite. It's a cop-out.
Is Pmb correct that if it is infinite, it must always have been so?Yes. But he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand.
The replies here seem to suggest the universe (or cosmos) is located on the edge of an expanding shape whether a sphere or not. I had imagined, wrongly it seems, that it was of a 3D form.Wrongly? There is no evidence of any "higher dimensions". There's no evidence that the universe is located on the surface of some shape. The only evidence we have is that the universe is an expanding ball of space dotted with galaxies as per the raisin-cake analogy.
It's like the analogy to a balloon. Is the space within akin to the universe or is it the balloon?The space within is akin to the universe because we live in 3D space. People will tell you the universe is like the surface of the balloon, but there's absolutely no scientific evidence that supports that assertion. None whatsoever. Zip. Zero. Zilch.
* See the energy-pressure diagonal in the stress-energy-momentum tensor (https://en.wikipedia.org/wiki/Stress%E2%80%93energy_tensor).
Post by: jeffreyH on 12/01/2015 20:04:09
Is Pmb correct that if it is infinite, it must always have been so?Yes. But he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand.
I disagree.
Post by: chiralSPO on 12/01/2015 20:08:17
Is Pmb correct that if it is infinite, it must always have been so?Yes. But he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand.
I disagree.
I don't think that having an infinite universe would preclude expansion. Using JohnDuffield's logic, wouldn't the energy pressure also "cancel out" if the universe were finite and unbounded?
Post by: dlorde on 12/01/2015 20:10:05
More of a sphere - top and bottom were also contiguous; perhaps I should have said 'edge' rather than 'side'...When I first tried to comprehend the topology of the universe as a potentially finite but non-bounded volume, I found it helped to think of the old arcade game of Asteroids (http://www.freeasteroids.org/), where whatever disappeared off the screen in one direction, reappeared on the opposite side, moving in the same direction - a finite but unbounded 2D surface.Right. It had the topology of a cylinder.
Quote
Here's something interesting. The space around a cosmic string is flat. The geometry is that of a cone.Ooh-er, I don't think I can visualise a flat cone...
Post by: dlorde on 12/01/2015 20:11:39
Me too.... he also says the universe is infinite. Only it can't be infinite if it's expanding. If it was infinite the energy-pressure* would be counterbalanced at all locations. It couldn't expand.
I disagree.
Post by: JohnDuffield on 12/01/2015 20:34:16
I don't think that having an infinite universe would preclude expansion. Using JohnDuffield's logic, wouldn't the energy pressure also "cancel out" if the universe were finite and unbounded?No. Imagine you've got a vacuum, and I introduce a 10cm sphere of air at 14psi. It will expand. However if introduce the sphere of air into the room you're in, it won't. Because it's surrounded by air at 14psi. Take a look at the energy-pressure diagonal in the stress-energy tensor, and think of space as something like the ball of air:
(https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/StressEnergyTensor_contravariant.svg/236px-StressEnergyTensor_contravariant.svg.png)
Note though that a ball of space isn't surrounded by anything. There is no space around it or beyond it. The ball of space is all there is. This is a tricky concept. Which is why I think people talk about an infinite universe.
Post by: chiralSPO on 12/01/2015 21:36:11
Post by: JohnDuffield on 12/01/2015 22:04:37
but the Universe isn't expanding into anything--it's just expanding. The space within it is growing.Agreed. Like I said, there is no space around it or beyond it.
I don't know how good an analogy gas pressure is to "energy pressure" (but if there is a reference that explains why it is a good analogy, please direct me there--I would rather be wrong now and right later!)Einstein talked about it. The Einstein digital papers are now online, see this (http://einsteinpapers.press.princeton.edu/). There's a search function, though I'm not sure it picks up every instance. But anyway, see this (http://einsteinpapers.press.princeton.edu/vol6-trans/72?highlightText=pressure) and this (http://einsteinpapers.press.princeton.edu/vol6-trans/200) for starters. The thing that people don't appreciate about the stress-energy tensor is that it "describes the density and flux of energy and momentum in spacetime". And it's got a pressure diagonal, and a shear stress term. Space is like some ghostly gin-clear compressed elastic! IMHO when the penny drops with this, it's really sad that Einstein didn't predict the expanding universe. If they'd had stress balls in his day, I imagine he would have done.
Post by: chiralSPO on 13/01/2015 04:03:22
Post by: jeffreyH on 13/01/2015 05:05:19
Post by: Ron Maxwell on 14/01/2015 00:11:57
Post by: jeffreyH on 14/01/2015 00:37:56
http://en.wikipedia.org/wiki/Great_Attractor
This means that not only is the universe expanding but something else is stretching it in a particular direction. Was this mysterious source part of a big bang or was it there prior to the event? There may be many other great attractor type sources that are just too far away to detect.
Post by: PmbPhy on 14/01/2015 01:36:39
Quote from: Ron Maxwell
jeffreyH, what is your definition of infinity?Jeff is not one to create his own definitions but uses the ones which are universally defined in math and physics. I.e.
[ Invalid Attachment ]
Post by: petm1 on 14/01/2015 03:21:24
Post by: JohnDuffield on 14/01/2015 09:23:46
OK John define the pressure gradient of a black hole. Do it with mathematics and not mumbo jumbo.
Jeffrey: broadly speaking the pressure is proportional to the gravitational time dilation (https://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere) so the expression
serves us adequately. The pressure increases as you approach the black hole, and the potential and coordinate speed of light decreases. The force of gravity at any location depends on the local gradient in the potential or coordinate speed of light. However when you get to the event horizon r = r0 and the expression gives an undefined result. This corresponds to a coordinate speed of light of zero. It can't go lower than this. In similar vein the potential can't go lower and the pressure can't go higher, and there's no more gravitational gradient. What you're left with is Oppenheimer's original "frozen star" black hole. You don't hear much about this, but see The Formation and Growth of Black Holes (http://mathpages.com/rr/s7-02/7-02.htm) where Kevin Brown says it's one of two alternative interpretations. He doesn't favour it, but I think it's right. Here's a depiction:
Post by: dlorde on 14/01/2015 10:45:13
jeffreyH, what is your definition of infinity? Is not the result of subtracting any number still infinity? How then can you get back to a 'big bang'?The idea is that the big bang may have been an expansion of an infinite expanse of very hot dense stuff. This seems to potentially allow for a version of a multiverse (as it's hard to see how an infinite expanse can evolve uniformly).
As I understand it, there's no clear evidence to rule out the infinite hypothesis, so it must remain on the table (unless some new analysis has ruled it out).
Post by: JohnDuffield on 14/01/2015 11:09:05
As I understand it, there's no clear evidence to rule out the infinite hypothesis, so it must remain on the table (unless some new analysis has ruled it out).I think the clear evidence that rules it out is the universe is expanding. An infinite universe can't expand because at every location the spatial pressure is counterbalanced on all sides. What surprises me is that people dismiss that, even though the stress-energy tensor has an energy-pressure diagonal. They don't say what's that all about? even when they've got a physics PhD. And they never seem to notice that there's one hell of a problem reconciling big bang cosmology with a universe that's always been infinite. Or that saying a flat universe is infinite is a total non-sequitur. Or that the infinite universe is just a turtles all the way down non-answer.
Post by: dlorde on 14/01/2015 16:44:45
I can only assume that they don't agree that your pressure argument is valid.As I understand it, there's no clear evidence to rule out the infinite hypothesis, so it must remain on the table (unless some new analysis has ruled it out).I think the clear evidence that rules it out is the universe is expanding. An infinite universe can't expand because at every location the spatial pressure is counterbalanced on all sides. What surprises me is that people dismiss that, even though the stress-energy tensor has an energy-pressure diagonal. They don't say what's that all about? even when they've got a physics PhD.
Quote
And they never seem to notice that there's one hell of a problem reconciling big bang cosmology with a universe that's always been infinite.What problem is that?
Quote
Or that saying a flat universe is infinite is a total non-sequitur. Or that the infinite universe is just a turtles all the way down non-answer.It may not be intended as a sequitur; i.e. the logic may be that if the universe is flat, it could also be infinite (implying that flatness is necessary). I don't think it's intended as an answer, it's an option that, in their opinion, hasn't yet been ruled out. At present, all current origin options seem unsatisfactory, whether turtles-all-the-way-down, creation ex-nihilo, or 'it just is'.
Post by: PmbPhy on 14/01/2015 17:27:18
Quote from: jccc
If the universe has mass, then there is a center of the total mass.No. That is incorrect. Not only is it wrong but there is no justification in any sense for it to be right. That this is so follows from the fact that an infinitely large universe does not have a finite total mass. Consider an infinitely large sheet which has a uniform mass density. Such a sheet wouldn't have a center of mass.
Post by: PmbPhy on 14/01/2015 17:30:56
Quote from: JohnDuffield
An infinite universe can't expand because at every location the spatial pressure is counterbalanced on all sides.What in the name of God do you mean by this? What justification do you have that the pressure is always balanced and that because of this the universe can't expand? The equations of motion for an expanding universe certainly does hold true for our universe, that's for sure.
Post by: jccc on 14/01/2015 20:13:02
What do you want to bet Pete?Quote from: jcccIf the universe has mass, then there is a center of the total mass.No. That is incorrect. Not only is it wrong but there is no justification in any sense for it to be right. That this is so follows from the fact that an infinitely large universe does not have a finite total mass. Consider an infinitely large sheet which has a uniform mass density. Such a sheet wouldn't have a center of mass.
Post by: CliffordK on 14/01/2015 22:26:43
Quote from: CliffordKShape of the visible universe: spherical, 3 dimensional.I assume this is a joke?
Radius: About 13 billion lightyears.
Center: EARTH
No joke--the Earth is very close to the center of the OBSERVABLE universe.
Yes & No.
The original question was about the observable universe, I.E. What we can see, which is roughly a sphere around Earth, with the most distant objects that we can see being about 13-14 billion light years away.
I'm not saying that there isn't more Universe out there that we can't observe (and undoubtedly the most distant stars have already changed from what we're seeing today), and we are likely far from the middle of the universe as a whole, assuming a middle or edge exists.
However, we are in the middle of what we can observe. This is one of the few geocentric things left in Astronomy. Even if humanity manages to visit more stars in the Milkyway, it is unlikely we'll ever exit from the Milkyway (unless Andromeda does a close flyby, and we can spread to that galaxy in a few billion years. We should probably start planning the jump soon. So, over time we may extend the range of our telescopes, or stars from which the light hasn't reached us may come into view (unless they are going in the wrong direction too fast). But, or observable universe will still remain more or less a sphere around Earth and the Milkyway.
In a sense, it is like looking at a single cell in the Human body and trying to figure out what the rest of the body looks like.
What I will say is that there are some things one can learn from what is observable about stuff that we either don't see, or can't see. For example, Neptune was actually predicted before it was found (http://en.wikipedia.org/wiki/Discovery_of_Neptune). Perhaps order will be found within the universe that will predict the form of what lies beyond. Unfortunately, we may never be able to confirm or deny anything about the universe beyond the sphere which we can see.
Post by: jeffreyH on 14/01/2015 23:22:56
OK John define the pressure gradient of a black hole. Do it with mathematics and not mumbo jumbo.
Jeffrey: broadly speaking the pressure is proportional to the gravitational time dilation (https://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere) so the expression
serves us adequately. The pressure increases as you approach the black hole, and the potential and coordinate speed of light decreases. The force of gravity at any location depends on the local gradient in the potential or coordinate speed of light. However when you get to the event horizon r = r0 and the expression gives an undefined result. This corresponds to a coordinate speed of light of zero. It can't go lower than this. In similar vein the potential can't go lower and the pressure can't go higher, and there's no more gravitational gradient. What you're left with is Oppenheimer's original "frozen star" black hole. You don't hear much about this, but see The Formation and Growth of Black Holes (http://mathpages.com/rr/s7-02/7-02.htm) where Kevin Brown says it's one of two alternative interpretations. He doesn't favour it, but I think it's right. Here's a depiction:
Well John I would like to know the path you took in deriving your equations. What steps did you go through?
Post by: PmbPhy on 15/01/2015 04:36:39
Quote from: jccc
What do you want to bet Pete?I don't make bets on principle. State your argument and I'll show you where your error is.
Post by: jccc on 15/01/2015 04:54:09
I bet there is a center of the mass of the universe. Just for a dollar.Quote from: jcccWhat do you want to bet Pete?I don't make bets on principle. State your argument and I'll show you where your error is.
Post by: PmbPhy on 15/01/2015 05:11:24
Quote from: jccc
I bet there is a center of the mass of the universe. Just for a dollar.Nope. No bets. One of the problems with bets like this is that you'll post what you think is a proof and then when I've proved it to be flawed you'll be unable to understand what I've said and refuse to pay.
The fact is that I really don't care what you have to say in a rebuttal because I know as a fact that it'd be wrong. I've been studying this for years. What kind of shmuck studies cosmology for years and misses basic well-known facts of the field? That fact is that the universe is unbounded and an unbounded universe has no center. That's even true for a universe with a finite amount of mass.
Post by: jccc on 15/01/2015 05:27:46
Post by: CliffordK on 15/01/2015 06:56:07
Any center may well like outside of the sphere we are able to visualize. One may not ever be able to disprove a "center", and proving it may be quick, or it could take centuries or millennia of observations and calculations.
Post by: dlorde on 15/01/2015 10:38:14
Post by: JohnDuffield on 15/01/2015 13:43:46
Quote from: jeffreyh
Well John I would like to know the path you took in deriving your equations. What steps did you go through?I didn't. It's a well-known Schwarzschild-metric equation.
Quote from: PmbPhy
What in the name of God do you mean by this? What justification do you have that the pressure is always balanced and that because of this the universe can't expand? The equations of motion for an expanding universe certainly does hold true for our universe, that's for sure.Yes, our universe is expanding. I'm saying the pressure isn't counterbalanced and that's why it expands. If the universe was infinite, space couldn't expand because the pressure is counterbalanced at all locations. See the stress-energy-momentum tensor, note the energy-pressure diagonal. There's a "spatial pressure gradient" around the Earth. In the universe overall there's no pressure gradient, just pressure. Space has this innate pressure. It expands. Provided it isn't infinite.
(https://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/StressEnergyTensor_contravariant.svg/236px-StressEnergyTensor_contravariant.svg.png)
Post by: jeffreyH on 15/01/2015 20:36:42
Quote from: jeffreyhWell John I would like to know the path you took in deriving your equations. What steps did you go through?I didn't. It's a well-known Schwarzschild-metric equation.
[/quote]
You do realize of course that the equation is for a special situation involving a non-rotation body. This is one of the solutions for a black hole and not very realistic. The other is the Kerr solution for a rotating mass.
http://en.wikipedia.org/wiki/Kerr_metric
You have 4 solutions listed, all of which involve perfect spheres as far as I can remember.
Now this shows you how difficult your position is in this argument.
https://www.physicsforums.com/threads/equation-for-time-dilation-of-body-in-orbit-around-kerr-black-hole.781691/
Note that the ergosphere is the real danger point. What this shows is you can't make glib statements without reviewing all the maths. You may think physicists get 'lost in the maths' but without the maths there is no physics.
Post by: PmbPhy on 16/01/2015 07:12:10
Quote from: dlorde
Ooh-er, I don't think I can visualise a flat cone...We're talking about the intrinsic curvature, not the extrinsic curvature here. See:
http://mathworld.wolfram.com/IntrinsicCurvature.html
Quote
A curvature such as Gaussian curvature which is detectable to the "inhabitants" of a surface and not just outside observers. An extrinsic curvature, on the other hand, is not detectable to someone who can't study the three-dimensional space surrounding the surface on which he resides.
Post by: PmbPhy on 16/01/2015 07:34:06
Quote from: JohnDuffield
There's no evidence of any unbounded topology or any higher dimensions.The term scientific evidence is defined as http://en.wikipedia.org/wiki/Scientific_evidence
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Scientific evidence is evidence which serves to either support or counter a scientific theory or hypothesis. Such evidence is expected to be empirical evidence and in accordance with scientific method. Standards for scientific evidence vary according to the field of inquiry, but the strength of scientific evidence is generally based on the results of statistical analysis and the strength of scientific controls.As such there is plenty of evidence that the universe might be infinite. But we're talking about the various models of the universe and the ramifications of what is implied when one of the models is true. My comments applied to the situation where we assumed that the universe is spatially infinite. It didn't apply to what it "really" is since that can't be known.
Post by: JohnDuffield on 17/01/2015 14:02:03
As such there is plenty of evidence that the universe might be infinite.No there isn't. None whatsoever. If you beg to differ, show me some.
But we're talking about the various models of the universe and the ramifications of what is implied when one of the models is true. My comments applied to the situation where we assumed that the universe is spatially infinite. It didn't apply to what it "really" is since that can't be known.Don't assume what you don't know. Instead, be scientific. Think about the alternatives.
Post by: JohnDuffield on 17/01/2015 14:28:54
You do realize of course that the equation is for a special situation involving a non-rotation body. This is one of the solutions for a black hole and not very realistic. The other is the Kerr solution for a rotating mass.At the event horizon the coordinate speed of light is zero. So the Kerr black hole is spinning faster than the local speed of light. That doesn't seem too realistic to me.
Now this shows you how difficult your position is in this argument.Oh dear, it starts with the science of Interstellar. This movie features time travel. I'm afraid it's science fiction masquerading as serious science. Because yes, physicists do get "lost in maths". See where Jesse says the time dilation goes to infinity as you approach the Schwarzschild radius. Think of a light clock. When it goes slower, it isn't because "time goes slower". It's because "light goes slower". And when time dilation goes to infinity, it's because light stops. This is what I was referring to when I said the coordinate speed of light is zero. And for a Kerr black hole to exist, the black hole has to be spinning faster than light. That can't happen, but Jesse and the guys he's talking to have missed this. See in post #23 (https://www.physicsforums.com/threads/equation-for-time-dilation-of-body-in-orbit-around-kerr-black-hole.781691/page-2) where he refers to a non-rotating black hole? You think Ahah! Now we're talking! But then he brings in Kruskal-Szekeres coordinates. These involves a cringeworthy schoolboy error, wherein you put a stopped observer in front of a stopped light-clock and claim he sees it ticking normally. Even though light is stopped. Then in post #24 Smithers refers to the "river model" (aka waterfall analogy) in which space is thought of as being like flowing water that "drains" through black holes. This is just junk. A gravitational field alters the motion of light and matter through space. It doesn't suck space in. It just goes from bad to worse.
https://www.physicsforums.com/threads/equation-for-time-dilation-of-body-in-orbit-around-kerr-black-hole.781691/
Note that the ergosphere is the real danger point. What this shows is you can't make glib statements without reviewing all the maths. You may think physicists get 'lost in the maths' but without the maths there is no physics.
Post by: yor_on on 24/01/2015 21:02:02
You could simplify it to asking how something already infinite can be allowed to become more 'infinite' in a expanding acceleration. Then again, that depends on your definitions of what infinite should be. You can turn that around, ignoring 'dimensions' for now, asking yourself if it all is about 'communication', then what defines a universe. Its ability to communicate between 'points'? And those points, do they have a 'background', or do they create it?
Post by: yor_on on 24/01/2015 21:13:55
Post by: yor_on on 24/01/2015 23:51:47
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From https://math.stackexchange.com/questions/345297/why-is-mean-curvature-extrinsic
Post by: jeffreyH on 25/01/2015 02:29:22
See where Jesse says the time dilation goes to infinity as you approach the Schwarzschild radius. Think of a light clock. When it goes slower, it isn't because "time goes slower". It's because "light goes slower". And when time dilation goes to infinity, it's because light stops.
Your reference to light is a total red herring. Everything slows down, not just light. Rates of change slow down and what do we use to measure rates of change? Come on John you know the answer to this one. You can see this in the shifting wavelengths. How do you measure a frequency? You'll have to remind me it has slipped my memory.... Begins with a T I think.
Post by: Atomic-S on 25/01/2015 05:38:47
Quote
More of a sphere - top and bottom were also contiguous; perhaps I should have said 'edge' rather than 'side'...No, a torus (doughnut).
Post by: JohnDuffield on 25/01/2015 13:22:40
Your reference to light is a total red herring.It isn't. It gets to the heart of the matter.
Everything slows down, not just light.Because everything has an electromagnetic nature. We make electrons (and positrons) out of light in pair production.
Rates of change slow down and what do we use to measure rates of change? Come on John you know the answer to this one. You can see this in the shifting wavelengths. How do you measure a frequency? You'll have to remind me it has slipped my memory.... Begins with a T I think.You measure it with a clock. The most precise clocks are optical clocks.
Post by: jeffreyH on 25/01/2015 17:15:04
Your reference to light is a total red herring.It isn't. It gets to the heart of the matter.Everything slows down, not just light.Because everything has an electromagnetic nature. We make electrons (and positrons) out of light in pair production.Rates of change slow down and what do we use to measure rates of change? Come on John you know the answer to this one. You can see this in the shifting wavelengths. How do you measure a frequency? You'll have to remind me it has slipped my memory.... Begins with a T I think.You measure it with a clock. The most precise clocks are optical clocks.
You are dancing around here. You mention a clock. What do clocks measure?
Post by: jeffreyH on 25/01/2015 17:33:16
Post by: JohnDuffield on 25/01/2015 22:31:30
You are dancing around here. You mention a clock. What do clocks measure?A clock "clocks up" some kind of regular cyclical local motion and displays a cumulative result that we call the time. If it's a grandfather clock the regular cyclical local motion is a swinging pendulum. If it's a mechanical watch it's the motion of a sprung rocker. If it's a quartz watch it's the vibration of a piezo-electric crystal. If it's an atomic clock it's the motion of the microwaves emitted by a hyperfine spin-flip. A clock doesn't actually measure the flow of time. It isn't some kind of cosmic gas meter with time flowing through it instead of odorized methane. Time doesn't literally flow or pass, that's just a figure of speech. Things move, including things in clocks.
John you said, "Because everything has an electromagnetic nature. We make electrons (and positrons) out of light in pair production." There is an electromagnetic field which arises because of mass. The problem you have is that you first need to determine what is slowing down and exactly why. This may sound like a bizarre statement at first read but it cuts to the heart of the matter. Does the intrinsic spin slow down.Yes. But note that conservation of energy applies. The internal kinetic energy of a falling electron is converted into its macroscopic kinetic energy. When you get rid of this you're left with a mass deficit.
Post by: yor_on on 26/01/2015 17:20:26
So light speed is a constant, defined locally and true everywhere, even at a event horizon. The best clock would be one able to measure lights speed at Planck scale, 'one Planck step at one Planck time'. You can get one theoretically by splitting 'c' to that scale, doing so you will notice that your measurement of local time and lights 'propagation' fits perfectly. So 'c' is the ultimate clock, and depending on whether you want to stop there also a limit for our universe.
Post by: JohnDuffield on 26/01/2015 17:50:11
"Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable".
This Baez article (http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html) is pretty good too. The locally measured speed of light is always 299,792,458 m/s because we use the local motion of light to define our second and our metre. However the "coordinate" speed of light varies with gravitational potential. At the event horizon, it's zero. The observer at the event horizon is said to observe everything happening normally, but the infinite time dilation means it hasn't happened yet. See the formation and growth of black holes (http://mathpages.com/rr/s7-02/7-02.htm) where Kevin brown says this:
"Historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock asymptotically approaches "full stop" (i.e., running at a rate of zero). It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. In contrast, according to the geometric interpretation, all clocks run at the same rate, measuring out real distances along worldlines in curved spacetime. This leads us to think that, rather than slowing down as it approaches the event horizon, the clock is following a shorter and shorter path to the future time coordinates. In fact, the path gets shorter at such a rate that it actually reaches the future infinity of Schwarzschild coordinate time in finite proper time."
Note that where he mentions Einstein he used to mention Wheeler, and still should IMHO. Einstein would have had no truck with a clock reaching future infinity. That's the end of time. It hasn't got there yet, and never ever will.
Post by: yor_on on 26/01/2015 22:40:59
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Where it gets questioned is mostly from the aspect of assuming some sort of 'container universe', containing us all. Naively also assumed to be both 'infinite', as well as having some sort of boundaries, as in examples where you can walk out of a universe to the right, just to find yourself to appear at the left. Myself I'm not happy about those ones, I like the universe to be infinite and 'bound less' in all ways you can define it, assuming it to build itself up through the 'protocols' used, laws, constants, etc, defining it. That means that you won't find that sort of situation in 'my' idea of a :) isotropic and homogeneous universe. Instead every other place you look out from, at the universe, it will look the same, no boundaries and no 'seams'. And it treats a inflation the same way as a expansion. Happening in 'all points'. In short, the 'protocol' (heh, some sf writer that likes that one? Feel free to use it) is the universe, and there is no way for me to step outside it, as the universe should be what communicate.
The difference is subtle, but there are no 'seams' in my sort of universe. Instead communication defines its limits. Which can be interpreted as where there is no communication my universe 'ends'. But on the other tentacle also should be understood as 'limits' doesn't exist, not for us at least inside it, if we by that means something defining 'seams' or the universes possible 'size', etc. With such a universe any definitions of a 'size' becomes questionable. A little like wanting to prove a universe to 'rotate', relative what?
But there are 'limits' if we by it mean constants, laws, rules, statistics etc. And 'c' is one of them. And another thing, the size of such a universe may be questionable, but scales, as QM use, is not, as far as I know. And that sort of scaling should hold true wherever you go, just as I would expect conservation laws to do. You can translate that one (scaling) into the one defining your local measurement of a length as belonging to a constant too. Your ruler never change its length, and the measurements (experiments) you make on a microscopic scale should be repeatable, as well as using a 'same scale', throughout a universe. Those are all ideal definitions naturally, as we consist of constituents of mass, acting and being acted on by mass. But Einstein has already defined the clock and the ruler ideally so I hope we can jump that one here.
also, as I use a strict local definition a black hole is communicative locally defined, in the sense that you can join it, on your own peril naturally, and so locally defined describe it (communicate with it). If we instead define communication as in the constant sending and receiving of information throughout a 'whole universe', a black hole may as per Hawking radiation, or may not, be 'communicative'. In the last definition where it is not it becomes a cosmic censorship, but it doesn't define a outside. Possibly one could look at it as another 'inside' though :) if we look at how I defined it here, two out of three possibilities define it as communicative, so maybe it is? I don't know :)
Well, actually I think I do know, if I stay with strict locality you can go into a black hole and communicate with it. That the local definition I like, avoiding ideas of a universe as described through 'container models' needing higher dimensions.
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And yes, I think Einstein wanted a 'container universe'. He used 'dimensions' and as I understand kept searching for a way to define a fifth that would join observer dependencies into one perfect description of the 'real universe'. He also had a faith of sorts it seems, not in a 'God' creating men into his image, but of something more than just the universe, unless, maybe he thought of the universe as being just that? I don't know there but I wish I did.
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btw: I don't think Einstein used a geometric definition originally, he adopted it after some initial irritation from Minkowski
"By 1907 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented. The beginning part of his address delivered at the 80th Assembly of German Natural Scientists and Physicians (21 September 1908) is now famous:
"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
Einstein himself at first viewed Minkowski's treatment as a mere mathematical trick, before eventually realizing that a geometrical view of space–time would be necessary in order to complete his own later work in general relativity"
And that geometrical way gives different 'paths of propagation' to a ray, depending on mass, acting and being acted on, as I understands it. Einstein used Algebra for SR, and I suspect he trusted more to that than the geometrical definition in his later works too, which may bring some light to him saying as he did in your citation. That is unless you can prove that a 'curved path' (geometrically defined), due to mass, can't be translatable into a longer path, equivalent to a longer time for the ray to reach the observer.
Post by: Ron Maxwell on 24/12/2015 12:26:13
I don't know what distortion of the usual meaning of 'centre' would allow an unbounded topology to have one; does a loop or circle have a centre? or the surface of a sphere? or an unbounded volume? if so, how does one calculate it?We are considering three dimensions of space so yes, they all have a centre.
Post by: puppypower on 24/12/2015 13:53:21
In other words, if all the matter/energy of the early universe was contained in a volume of say one light year in diameter, something that small, in the context of the entire modern universe; billions of light years in diameter, would occupy a very tiny angle of view from the earth. Such a tiny angle of view can't be both behind us and in front of us or all around us, since the angle of view; due to size, is less than 1 second arc, and not more than 180 degrees.
If the argument is light bends due to relativity and expanding space-time, so there is no center, then do we the oldest ancient quasar, both behind and in front of us, due to the same light bending affect? Would the light bending affect make one ancient star look like millions of ancients stars all around us, just like we assume of the BB event is all around us?
Have we found the center point; observation of the 1 light year universe. I assume a center since nobody says the oldest observations we see, can be viewed by looking out in any angle due to light bending; same exact thing is everywhere.
Say our earth reference, was inside of the 1 light year sized early universe. If we are not in the center of the expansion, shouldn't there be more universal matter/energy on one side of us, compared to the other side? Should this asymmetry of matter relative to us, in terms of GR and SR, create asymmetry in the microwaves we see? Some of the microwaves has to travel longer, on the long side, thereby altering the energy density since there is not enough time for the farthest end to reach us when all the close side is counted.
Post by: dlorde on 25/12/2015 22:35:06
We are considering three dimensions of space so yes, they all have a centre.So how does one identify the centre of an unbounded 3D space?
Post by: dlorde on 25/12/2015 22:48:47
If we reverse the expansion of the universe and space-time; play it backwards, this leads us to the singularity of the BB. If we could see energy burst, from that original event, shouldn't that event appear as a single point in space; center of the universe?It may be worth pointing out that if you reverse the observed expansion of any explosion by extrapolation, you'll get back to an apparent origin smaller than whatever it was that exploded; so there's really no compelling reason to suppose there actually was a singularity at the BB.
Also, given that spacetime seems to be topologically flat, it's apparently possible that it was not finite in extent at the BB, i.e. it was an infinite expanse of hot, dense stuff that started expanding. The part we see, the observable universe, would have been a tiny part of that infinite extent. This isn't a scenario I'm particularly comfortable with, but I'm told it can't yet be ruled out; I'm not particularly comfortable with quantum 'weirdness' either, but it's a demonstrable fact, suggesting that reality doesn't care what I'm comfortable with [8D]
Post by: Ron Maxwell on 26/12/2015 01:26:57
We are considering three dimensions of space so yes, they all have a centre.So how does one identify the centre of an unbounded 3D space?
I can't see why one would want to as there is,as far as I'm aware, no such thing. The idea that the universe is infinite makes no sense to me.
Post by: dlorde on 29/12/2015 00:43:23
It doesn't have to be infinite, I'm asking about an unbounded finite 3D volume, i.e. closed in 4 dimensions, so it is unbounded in 3 - in the same way the surface of a sphere is an unbounded but finite 2D area, closed in 3 dimensions. It's one of the more popular topological models for a finite 3D universe.So how does one identify the centre of an unbounded 3D space?I can't see why one would want to as there is,as far as I'm aware, no such thing. The idea that the universe is infinite makes no sense to me.
Post by: Ophiolite on 29/12/2015 02:13:45
I can't see why one would want to as there is,as far as I'm aware, no such thing. The idea that the universe is infinite makes no sense to me.Your lack of understanding is probably not a sound basis upon which to reach such definitive conclusions.
Post by: Ron Maxwell on 29/12/2015 15:36:25