How large is the universe?

[Kwalish Kid]

I know Wheeler's dead, and you know I know, so stow the wisecrack comments. This is the Kip Thorne article on time travel that's junk.

What's the problem with the universe being an expanding ball of space? Space has its vacuum energy. The "empty space" of a gravitational field comprises energy that "shall act gravitatively in the same way as any other kind of energy". On the large scale the universe is "flat", so you don't you go thataway and come back thisaway. To the best of our knowledge the universe has been expanding from a small size for 13.7 billion years, so it can't be infinite. Doesn't leave much room for manoeuvre, does it?

Why would you say these things that are so clearly contradicted in the popular literature, even in the very links that you provide?

 

[sol invictus]

I am not a physicist. Looking at this as a mathematician, it looks easy, even trivial.
....
Solution 1: The subspace of solution 0 with t > 0.

I suppose you're right, technically - but as you point out, that's geodesically incomplete, and we need to know what happens at (or beyond) the boundaries to be able to do physics.

 

[W.D.Clinger]

This is the Kip Thorne article on time travel that's junk.

As I have already noted:

That article is uncontroversial. It says travel backwards in time is probably impossible, but the so-called Twin Paradox makes it theoretically possible for a resident of earth to travel away from earth at high speed and then to revisit earth arbitrarily far into earth's future but only a few years into the traveller's future.

You haven't been able to explain why you think the article is junk. As Thorne explains, forward time travel is a consequence of relativistic time dilation, which has been observed in numerous experiments.

Given your history of denying the basics of relativity, I can only assume your objection to Thorne's article is that you think relativistic time dilation is junk.

What's the problem with the universe being an expanding ball of space?

An expanding ball of Euclidean (flat) space has a boundary. sol invictus has already explained the problems with that.

The cosmic microwave background radiation is very nearly isotropic. Many other astronomical observations also suggest space is isotropic. If space were an expanding ball, it wouldn't look isotropic unless we were near its exact center.

That seems unlikely. If you want us to believe the universe is an expanding ball of space, you'll have to explain why you think humans occupy a very special position within the universe.

 

[Farsight]

Nope - the data simply says that if it's a hypersphere (or hyperbolic 3-space, or anything else with uniform curvature), the radius of curvature is about 10x the current Hubble radius. And if the curvature is not assumed uniform, it tells us almost nothing about what's beyond the Hubble horizon.

No it doesn't. Go and look at references to WMAP. Here's a mention on wiki:

"Analysis of data from WMAP implies that on the scale to the surface of last scattering, the density parameter of the Universe is within about 0.5% of the value representing spatial flatness.[7]"

See that 0.5%? That's one two-hundredth. And the Hubble radius is 13.7 billion light years whilst the particle horizon is circa 46 billion light years. The data absolutely rules out a hypersphere with a radius of curvature of 10x the Hubble radius.

Nonsense...

More nonsense.

You don't know what you're talking about. And huff puff and nonsense just doesn't cut it.

 

[sol invictus]

No it doesn't. Go and look at references to WMAP. Here's a mention on wiki:

"Analysis of data from WMAP implies that on the scale to the surface of last scattering, the density parameter of the Universe is within about 0.5% of the value representing spatial flatness.[7]"

See that 0.5%? That's one two-hundredth. And the Hubble radius is 13.7 billion light years whilst the particle horizon is circa 46 billion light years. The data absolutely rules out a hypersphere with a radius of curvature of 10x the Hubble radius.

Nonsense. The contribution of curvature to the density parameter (in the appropriate units) is 1/(HR)^2, where R is the radius of curvature and H is the Hubble parameter. 1/200~1/10^2.

You don't know what you're talking about. And huff puff and nonsense just doesn't cut it.

Look in a mirror.

 

[John Jones]

infinite.

What is?

Links or it never happened.

 

[Farsight]

You haven't been able to explain why you think the article is junk. As Thorne explains, forward time travel is a consequence of relativistic time dilation, which has been observed in numerous experiments. Given your history of denying the basics of relativity, I can only assume your objection to Thorne's article is that you think relativistic time dilation is junk.

I've explained why the article is junk, and you know it. And you know I don't deny the the basics of relativity, or time dilation. See post 30 on this thread where I explained why time dilation isn't time travel. Now pack it in, you do yourself no credit defending time travel and attacking me. Stick to the physics.

An expanding ball of Euclidean (flat) space has a boundary. sol invictus has already explained the problems with that.

He hasn't explained them, he's mentioned them, and if there's problems, we deal them.

The cosmic microwave background radiation is very nearly isotropic. Many other astronomical observations also suggest space is isotropic. If space were an expanding ball, it wouldn't look isotropic unless we were near its exact center.

Wrong. When you see the CMBR you aren't seeing the edge of the universe. You're seeing the electromagnetic equivalent of mist. It's like you're inside a cloud, and all you see is white. It's isotropic when the surrounding cloud extends further than the distance you can see.

That seems unlikely. If you want us to believe the universe is an expanding ball of space, you'll have to explain why you think humans occupy a very special position within the universe.

I don't think they do. And I don't want you to believe anything. But can you explain how the universe can be infinite when it's been expanding from a small size for 13.7 billion years? No. Or how it can be a hypersphere in the light of the WMAP data? No. So like I said, there's not much room for manoeuvre. When you have eliminated the impossible, whatever remains, however improbable, must be the truth.

 

[Farsight]

Nonsense. The contribution of curvature to the density parameter (in the appropriate units) is 1/(HR)^2, where R is the radius of curvature and H is the Hubble parameter. 1/200~1/10^2.

You really don't know what you're talking about. When the density is uniform, light travels in straight lines, and there is no curvature.

 

[ctamblyn]

You really don't know what you're talking about. When the density is uniform, light travels in straight lines, and there is no curvature.

And in that situation, R (the radius of curvature) would be infinite, and the contribution given by sol's formula would be zero.

What sol is saying is that, if the universe is (spatially) non-flat (i.e. spherical or hyperbolic) and R happens to be sufficiently large, the contribution will be indistinguishable from zero due to experimental uncertainties. And, with our current data at least, "sufficiently large" turns out to be 10 times larger than today's Hubble radius.

 

[W.D.Clinger]

You haven't been able to explain why you think the article is junk. As Thorne explains, forward time travel is a consequence of relativistic time dilation, which has been observed in numerous experiments. Given your history of denying the basics of relativity, I can only assume your objection to Thorne's article is that you think relativistic time dilation is junk.

I've explained why the article is junk, and you know it.

Au contraire. You'd like for the more gullible readers of this thread to believe you've explained why the article is junk, but you haven't even made a serious attempt to do so. Readers of this thread can confirm for themselves that my characterization of Thorne's article was accurate.

And you know I don't deny the the basics of relativity, or time dilation.

Au contraire. For the past several years, you've been using this forum to deny basic facts of relativity, notably Einstein's equivalence principle and the legitimacy of coordinate transformations.

If you could demonstrate genuine understanding of relativity and cosmology, your argument wouldn't consist of lying about what you've accomplished in your previous posts while telling ctamblyn and sol invictus they don't know what they're talking about.

 

[sol invictus]

You really don't know what you're talking about. When the density is uniform, light travels in straight lines, and there is no curvature.

That is not even wrong, and a non-sequitor. In GR, assuming it doesn't directly interact with anything, light always travels in "straight" lines (null geodesics) - uniform density or not. Furthermore, uniform density (even when combined with isotropy) does not imply no curvature. It implies constant curvature.

 

[Farsight]

In GR and in the real world, light curves in a gravitational field. Hence gravitational lensing, and I quote:

"A gravitational lens refers to a distribution of matter (such as a cluster of galaxies) between a distant source (a background galaxy) and an observer, that is capable of bending (lensing) the light from the source, as it travels towards the observer. This effect is known as gravitational lensing and is one of the predictions of Albert Einstein's general theory of relativity".

...If you could demonstrate genuine understanding of relativity and cosmology, your argument wouldn't consist of lying about what you've accomplished in your previous posts while telling ctamblyn and sol invictus they don't know what they're talking about... For the past several years, you've been using this forum to deny basic facts of relativity, notably Einstein's equivalence principle and the legitimacy of coordinate transformations.

I'm demonstrating genuine understanding, I'm not lying, it's me who quotes Einstein whilst you dismiss it as "cherry picking", and I haven't replied to ctamblyn yet. Now stop carping and get on with the discussion.

 

[W.D.Clinger]

By denying basic facts of relativity, Farsight is arguing against Einstein.

You really don't know what you're talking about. When the density is uniform, light travels in straight lines, and there is no curvature.

That is not even wrong, and a non-sequitor. In GR, assuming it doesn't directly interact with anything, light always travels in "straight" lines (null geodesics) - uniform density or not. Furthermore, uniform density (even when combined with isotropy) does not imply no curvature. It implies constant curvature.

sol invictus is right about this, and Farsight is wrong.

Einstein's static universe is an example of an isotropic model with uniform density and constant but nonzero spatial curvature.

ETA:

That's hardly the only example. All of the FLRW models are isotropic with uniform density, and almost all of them have nonzero curvature. Einstein's static universe is one of the FLRW models.

The FLRW models are part of the foundation for any modern answer to the question posed by this thread. Farsight's ignorance of those models (and much of relativity in general) is the foundation for his quarrels with modern cosmology (and much of modern physics).

In GR and in the real world, light curves in a gravitational field. Hence gravitational lensing, and I quote:

"A gravitational lens refers to a distribution of matter (such as a cluster of galaxies) between a distant source (a background galaxy) and an observer, that is capable of bending (lensing) the light from the source, as it travels towards the observer. This effect is known as gravitational lensing and is one of the predictions of Albert Einstein's general theory of relativity".

Wikipedia's current article on gravitational lensing speaks of "bending", but a more accurate explanation would explain that spacetime is non-Euclidean in the sense that Euclid's fifth postulate does not hold. Straight lines (e.g. null geodesics, rays of light) that are locally parallel may eventually diverge or meet. That's what really happens with gravitational lensing.

Most of us can understand why a Wikipedia article written for lay persons would speak of light being bent instead of discussing non-Euclidean (and pseudo-Riemannian) manifolds. Einstein himself used such casual metaphors at times.

To understand more precisely what is going on, you must look to the mathematics. Farsight's antipathy toward mathematics is well-documented and ongoing.

 

[Puppycow]

I saw a couple interesting Horizon programs on the size of the universe last night, and I recommend them.

How Big is the Universe?

How Small is the Universe?

 

[Puppycow]

nm