Are we located at the core of the Universe?

[Strange]

Think of it as a mobius strip.

 

Does that help? I don't think you can describe that in terms of intrinsic curvature; it needs to be embedded in a higher dimensional space.

[dimreepr]

 

Does that help? I don't think you can describe that in terms of intrinsic curvature; it needs to be embedded in a higher dimensional space.

 

 

I thought it might since “The Möbius strip has the mathematical property of being non-orientable.”.

[Mordred]

 

Thanks for the articles.

With regards to the curvature;

http://cosmology101.wikidot.com/universe-geometry

 

It is stated:

"In a flat curvature the three angles of a equilateral triangle will add up to 180⁰. A positive curvature will add up to greater than 180⁰, a negative curvature will add up to less than 180^0"

 

Please advice if you agree with the following:

In a flat curvature - The Universe has only three dimensions.

In a positive/negative curvature - The Universe has more than three dimensions.

 

Now, on what kind of curvature our mathematics had been developed for.

In other words, could it be that Einstein' and Friedman' equations had been developed only for a flat curvature Universe?

If so, does it mean that new/updated formulas should be used for any type of curvature which is not flat (positive/negative curvature)?

The reason the paper shows the metrics for 2d to 3d to 4d.

 

Is to teach the metrics involved as well as assist in understanding 4 dimensional curvature. Which in itself is extremely difficult to visualize

 

It is not saying we live in a 2d universe. We obviously live in a 4d universe. If one simply tried using a 4d coordinate system without understanding the 2d and 3d coordinates. They would have an extremely difficult time.

[David Levy]

The reason the paper shows the metrics for 2d to 3d to 4d.

 

Is to teach the metrics involved as well as assist in understanding 4 dimensional curvature. Which in itself is extremely difficult to visualize

 

It is not saying we live in a 2d universe. We obviously live in a 4d universe. If one simply tried using a 4d coordinate system without understanding the 2d and 3d coordinates. They would have an extremely difficult time.

 

I didn't claim that we are living in a 2D Universe.

It is very clear to me that the curvature should add one more dimension.

So, with the following explanation about the curvature, they speak clearly about the radius of curvature.

http://mathworld.wolfram.com/Curvature.html

 

"The curvature of a two-dimensional curve is related to the radius of curvature of the curve's osculating circle. Consider a circle specified parametrically by…"

 

So, in a flat paper, there is no radius.

In a ball there is a radius.

Therefore, although they are discussing about the surface (which is only 2D) this surface is part of a three dimensions shape - which has a radius.

As you can see, the calculation is similar to a surface of a ball.

We can't set a real calculation of the surface of a ball without knowing its radius. So there in one more dimension. Can we set a calculation of the surface of a ball without knowing its radius?

Hence, in principal, the radius of curvature is like added spatial to the 2D.

Why do you disagree about it?

 

In the same token, if we have to add a curvature to a universe, than somehow we must add the radius of curvature factor to our formulas about the Universe.

I will call it one more spatial.

You can call it at any name which you like.

However, without information about that radius of curvature of the Universe, our calculations aren't accurate.

Therefore, as usual we must take a decision:

If we believe that the Universe has no curvature, than all our current formulas are perfectly O.K.If we believe that the universe has a curvature, than we must add the impact of the radius of curvature to our formulas and calculations.

Why that message is incorrect?

 

With regards to the expantion -

I didn't get you answer about the impact of the curvature on the expansion.

How could it be that the curvature affects the light but it doesn't affect the expansion?

Sorry, but we can't add the curvature just when it can help us.

If we add it, we must consider its impact from the first moment of the Universe.

Hence, we have to consider how the expansion should be under the impact of the curvature.

Edited March 10, 2016 by David Levy

[Strange]

 

I didn't claim that we are living in a 2D Universe.

It is very clear to me that the curvature should add one more dimension..

 

And you are wrong. There are centuries of mathematics behind this which you need to catch up on.

In the same token, if we have to add a curvature to a universe, than somehow we must add the [/size]radius of curvature[/size] factor to our formulas about the Universe.[/size]

 

You cannot describe the curvature of space-time in terms of a radius.

 

The Riemann curvature tensor is a way to capture a measure of the intrinsic curvature. When you write it down in terms of its components (like writing down the components of a vector), it consists of a multi-dimensional array of sums and products of partial derivatives (some of those partial derivatives can be thought of as akin to capturing the curvature imposed upon someone walking in straight lines on a curved surface).

 

https://en.wikipedia.org/wiki/Riemann_curvature_tensor

 

 

By extension of the former argument, a space of three or more dimensions can be intrinsically curved. The curvature is intrinsic in the sense that it is a property defined at every point in the space, rather than a property defined with respect to a larger space that contains it. In general, a curved space may or may not be conceived as being embedded in a higher-dimensional ambient space; if not then its curvature can only be defined intrinsically.

https://en.wikipedia.org/wiki/Curvature#Higher_dimensions:_Curvature_of_space

 

 

Reinterpreted theory: the sheet of space-time displayed in the spacetime diagram is intrinsically curved. The trajectories followed by the bodies in free fall are simply the straightest lines of this new curved geometry.

 

Don't even try to imagine this as extrinsic curvature, the bending of a surface into a higher dimensioned space. That way leads to madness! Think of the curvature intrinsically, that is, as a geometrical effect arising entirely within the surface.

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/general_relativity/

[michel123456]

The universe is 4D because we have 3D of space and 1D of time.

And we are ate the edge of this 4D universe in the sense that we can only observe the past of the universe. We cannot observe its present, we cannot observe its future. It is much like standing on the surface of a expanding sphere and being able to see the internal part of it.

And even worse, we cannot observe all its interior. We can only observe the surface of a peculiar scheme that looks like a flame.

From Ned Wright's tutorial, imagine the red curve revolving around its vertical axis.

 

From a little area of the down part of this surface we get an image like that of the Extreme Deep Field.

 

----------

And we call that the Observable Universe

[David Levy]

What about expansion -

How could it be that the curvature affects the light but it doesn't affect the expansion?

Sorry, but we can't add the curvature just when it can help us.

If we add it, we must consider its impact from the first moment of the Universe.

Hence, we have to consider how the expansion should be under the impact of the curvature.

[Mordred]

 

I didn't claim that we are living in a 2D Universe.

It is very clear to me that the curvature should add one more dimension.

So, with the following explanation about the curvature, they speak clearly about the radius of curvature.

http://mathworld.wolfram.com/Curvature.html

 

"The curvature of a two-dimensional curve is related to the radius of curvature of the curve's osculating circle. Consider a circle specified parametrically by"

 

So, in a flat paper, there is no radius.

In a ball there is a radius.

Therefore, although they are discussing about the surface (which is only 2D) this surface is part of a three dimensions shape - which has a radius.

As you can see, the calculation is similar to a surface of a ball.

We can't set a real calculation of the surface of a ball without knowing its radius. So there in one more dimension. Can we set a calculation of the surface of a ball without knowing its radius?

Hence, in principal, the radius of curvature is like added spatial to the 2D.

Why do you disagree about it?

 

In the same token, if we have to add a curvature to a universe, than somehow we must add the radius of curvature factor to our formulas about the Universe.

I will call it one more spatial.

You can call it at any name which you like.

However, without information about that radius of curvature of the Universe, our calculations aren't accurate.

Therefore, as usual we must take a decision:

If we believe that the Universe has no curvature, than all our current formulas are perfectly O.K.If we believe that the universe has a curvature, than we must add the impact of the radius of curvature to our formulas and calculations.

Why that message is incorrect?

 

With regards to the expantion -

I didn't get you answer about the impact of the curvature on the expansion.

How could it be that the curvature affects the light but it doesn't affect the expansion?

Sorry, but we can't add the curvature just when it can help us.

If we add it, we must consider its impact from the first moment of the Universe.

Hence, we have to consider how the expansion should be under the impact of the curvature.

Along with the other posts. I've already stated expansion is related to curvature via the critical density formula. (Though the cosmological constant confuses this aspect).

 

Prior to the discovery of the cosmological constant a negative curved universe has insufficient mass to stop expansion so would expand forever.

 

A flat universe would expand but would eventually slow down and start to collapse. However is also infinite

 

A positive curved universe would also gradually collapse but is finite (again there is no edge, Remember the geometry of a sphere).

 

If the cosmological constant remains constant the Universe will never collapse.

[MigL]

Who says curvature and expansion are not related ?

You have little understanding of how expansion works ( from other posts ), and even less about geometry/topology of higher dimensional non-Euclidian spaces.

How can you make these assertions ?

[Strange]

What about expansion -[/size]

How could it be that the curvature affects the light but it doesn't affect the expansion?[/size]

It does. Why do you think it doesn't.

 

Sorry, but we can't add the curvature just when it can help us.

We don't. It is just arbitrarily added in. It is measured (as you have been told but have chosen to ignore).

 

Unlike you, science doesn't just make stuff up. It uses the evidence.

[David Levy]

It does. Why do you think it doesn't.

Thanks

 

So you agree that curvature affects the expansion as it affects the light. Both should move in the same pattern due to the influence of the curvature.

However, when we have started the discussion it was stated that the Universe has no edge as the light travels in some sort of a loop (as on the surface of a basketball).

 

The surface of a basketball has a size, please show me it's edge.

 

Hence, if the light moves in a loop, than the expansion should also move in a loop.

However, that contradicts the main idea of the expansion. How could it be that there is any expansion if it moves in a loop (as on the surface of a basketball)?

 

So, how did we calculate that the radius of the current observable Universe is 46 Bly? Did we assume a straight forward expansion? If so, than it is a severe mistake.

The curvature must force almost a zero expansion. How can we explain this new paradox?

Edited March 10, 2016 by David Levy

[Mordred]

You keep thinking there is a paradox simply due to lack of your knowledge.

 

That's really a bad habit

You keep thinking curvature has a preffered frame.

 

No matter what location or direction you fire the light beam it will curve the same amount. That follows the geometry of a homogeneous and isotropic expansion.

 

If you think about what we OBSERVE via light paths. How can it not match what we observe for expansion?

 

It's impossible not to match. You cannot observe a location without following the light path influence due to expansion

Edited March 10, 2016 by Mordred

[David Levy]

You keep thinking there is a paradox simply due to lack of your knowledge.

 

That's really a bad habit

You keep thinking curvature has a preffered frame

 

Please,

 

If you claim that there is a curvature - than I fully agree.

 

If you claim that there is no edge - than I fully agree.

 

You set the frame for the curvature.

 

However, as agree, there must be one frame for all.

 

So, under the same frame, how could it be that the expansion can work (expand), while light must stay in the loop???

 

Don't you see the paradox?

 

[Mordred]

Why would you think there is a preferred frame for all?

 

There isn't that is the whole point behind the term homogeneous and isotropic expansion. No matter where your located or direction you look in you will see the same curvature constant

Here maybe the raisin bread analogy may help.

 

http://www.astronomy.ohio-state.edu/~ryden/ast162_9/notes38.html

[Strange]

Hence, if the light moves in a loop, than the expansion should also move in a loop.

 

What does it mean for expansion to move in a loop? How can multiplying all distance by a constant factor "move in a loop"? You are talking nonsense.

 

So, how did we calculate that the radius of the current observable Universe is 46 Bly?

 

 

This has been explained to you so many times already. Do you really need to be told again? You appear to be incapable of learning anything.

 

The curvature must force almost a zero expansion.

Please show the mathematics to support this claim.

Don't you see the paradox?

 

All I see is meaningless nonsense from someone with zero knowledge.

Edited March 10, 2016 by Strange

[ACG52]

Whenever David writes 'so you agree' you can be sure that what follows is his misunderstood crap.

[David Levy]

O.K.

 

There is no edge.

However:

 

What shall we see at the end of the 46 Gly radius?

I assume that in the direction of Earth we should see galaxies. But, what shall we see at the opposite direction?

What shall we see at a distance (radius) of 50 Gly or even 100 Gly?

Edited March 11, 2016 by David Levy

[ACG52]

We would see galaxies. From any point in the universe we would see a spherical volume of space 96 blys in diameter.

[Strange]

What shall we see at the end of the 46 Gly radius?

I assume that in the direction of Earth we should see galaxies. But, what shall we see at the opposite direction?

What shall we see at a distance (radius) of 50 Gly or even 100 Gly?

 

There is absolutely no reason to think you wouldn't see exactly the same sort of thing we see from here: gas, dust, stars, galaxies, galaxy clusters, large scale structure...

[swansont]

O.K.

 

There is no edge.

However:

 

What shall we see at the end of the 46 Gly radius?

I assume that in the direction of Earth we should see galaxies. But, what shall we see at the opposite direction?

What shall we see at a distance (radius) of 50 Gly or even 100 Gly?

 

 

In the direction of earth? The is no "in the direction of Earth". There is no "opposite direction". We're at the center of this particular sphere*. We look out from that point.

 

*and any other observer would be at the center of their visible universe.

 

We don't see anything at distances >46 Gly

[David Levy]

Thanks

 

 

*and any other observer would be at the center of their visible universe.

 

 

Do you mean that our observable universe is 46Gly while someone which is located 10Gly away will also have the same size of observable universe?

Therefore, each observer should be at the center of his visible Universe, regardless from its location.

Is it correct?

 

If so, than technically, we can add more and more observable points. For each point, the observable universe will be 46Bly.

Hence, if we add infinite observable points, than we should get an infinite Universe.

Is it correct?

If so, then why don't we say that the size of the universe in infinite?

Did I miss something?

Edited March 11, 2016 by David Levy

[Strange]

Do you mean that our observable universe is 46Gly while someone which is located 10Gly away will also have the same size of observable universe?

Therefore, each observer should be at the center of his visible Universe, regardless from its location.

Is it correct?

 

Yes. That is what "visible universe" (more commonly, "observable universe") means.

 

If so, than technically, we can add more and more observable points. For each point, the observable universe will be 46Bly.

Hence, if we add infinite observable points, than we should get an infinite Universe.

Is it correct?

Remember my suggestion before? When you feel like saying "Is it correct" stop yourself and remember that it almost certainly isn't. It is just some nonsense you have made up.

If so, then why don't we say that the size of the universe in infinite?

Because it might not be.

Did I miss something?

The fact that all this was explained a few posts previously. And, from what I remember, about 100 times before that.

Does the phase "finite but unbounded" ring any bells? No?

http://www.bartleby.com/173/31.html

Edited March 11, 2016 by Strange

[swansont]

Do you mean that our observable universe is 46Gly while someone which is located 10Gly away will also have the same size of observable universe?[/size]

Therefore, each observer should be at the center of his visible Universe, regardless from its location.[/size]

Yes. It's what I meant the previous time I said it, too.

 

 

If so, than technically, we can add more and more observable points. For each point, the observable universe will be 46Bly.[/size]

As far as I know, yes.

 

Hence, if we add infinite observable points, than we should get an infinite Universe.[/size]

Is it correct?[/size]

[/size]

If so, then why don't we say that the size of the universe in infinite?[/size]

Did I miss something?[/size]

No that's not correct. Yes, you missed something (probably several somethings). This would happen in an infinite universe, but it would happen in one that curves in upon itself, too.

[Airbrush]

David: "Today, that same spot is 46 billion light-years away, making the diameter of the observable universe a sphere around 92 billion light-years."

 

So, the radius of the whole Universe is 46 BLY."

 

Why does your argument bait and switch from "observable" to "whole" universe? That is a logical error.

Edited March 11, 2016 by Airbrush

[David Levy]

So, the following statement is correct:

technically, we can add more and more observable points. For each point, the observable universe will be 46Bl

 

As far as I know, yes.

 

While the following one is incorrect:

if we add infinite observable points, than we should get an infinite Universe

 

No that's not correct. .

 

Why can't we add infinite number of observer points?

Is there any limitation for that?

If there is no limitation, than why the Universe can't be infinite?

 

Edited March 11, 2016 by David Levy