Is the Universe Really Expanding?

[ThomasT]

The universe has no edge.

What does that mean, and how is it known?

 

[DaveC426913]

What does that mean, and how is it known?

Examining the balloon analogy, we can see that the surface of the balloon has no edge. It is suspected that the universe's geometry is in 3-dimensions what the balloon's is in 2 - a volume of space that is finite yet has no boundary. Presumably, if you were able to travel far enough in one direction for long enough, you would arrive back at your starting point.

 

[ThomasT]

Examining the balloon analogy, we can see that the surface of the balloon has no edge. It is suspected that the universe's geometry is in 3-dimensions what the balloon's is in 2 - a volume of space that is finite yet has no boundary. Presumably, if you were able to travel far enough in one direction for long enough, you would arrive back at your starting point.

Thanks Dave, but I don't like the balloon analogy. If we talk about the universe as a complex 3D wave structure, then it's either bounded or it isn't. So, if someone says that the universe has no edge, then I take that to mean that they're saying that it isn't bounded (ie., that it's infinite in extent). So, my question is how can we know that the universe is or isn't bounded.

What does it mean to say that something is finite yet has no boundary? Obviously, a balloon has an 'edge', ie., it's obviously finite and bounded.

By the way, my apologies, but I have nothing else to do right now and can't go to sleep.

 

[DaveC426913]

it isn't bounded (ie., that it's infinite in extent).

The second statement does not follow from the first.

What does it mean to say that something is finite yet has no boundary? Obviously, a balloon has an 'edge', ie., it's obviously finite and bounded.

A balloon's 2 dimensional surface has a finite area, yet it has no boundary.The 3D equivalent is a 4D shape whose 3D volume is finite, yet it has no boundary. If you head in any direction X,Y or Z, you would arrive back where you started.

 

[ThomasT]

The second statement does not follow from the first.

Why not? If a 3D structure has a boundary, then it's finite in extent. If it doesn't have a boundary, then it's infinite in extent.

A balloon's 2 dimensional surface has a finite area, yet it has no boundary.

The problem is that a balloon is a 3D (bounded and finite) structure.

So I guess I just don't get why such a strange analogy is necessary. If the universe is a 3D structure, and if it's expanding like an inflating balloon, then it's both bounded and finite. And we're not on its surface, we're inside it.

But how might we know if it's like an inflating balloon, ie., bounded and finite?

 

[Chronos]

Stephen Hawking gave a good discussion on a universe that is finite, but, unbounded in 'A Brief History of Time'.

 

[bapowell]

So I guess I just don't get why such a strange analogy is necessary. If the universe is a 3D structure, and if it's expanding like an inflating balloon, then it's both bounded and finite. And we're not on its surface, we're inside it.

The balloon analogy is a 2D example of our 3D world. In the balloon analogy, we live on the surface -- there is no inside! The actual universe would be the surface of a 3-sphere.

 

[ThomasT]

The balloon analogy is a 2D example of our 3D world. In the balloon analogy, we live on the surface -- there is no inside!

That makes no sense.

If we're assuming that the universe is 3D and bounded and expanding isotropically, more or less like an inflating balloon, then we'd be part of all the stuff that's happening inside the balloon, not on its surface, since the surface of the balloon, the boundary of the universe in our analogy, would represent the oldest part of the universe.

If our universe is an expanding 3D volume, then why can't it be talked about in those terms? Why the 2D stuff?

 

[DaveC426913]

That makes no sense.

If we're assuming that the universe is 3D and bounded and expanding isotropically, more or less like an inflating balloon, then we'd be part of all the stuff that's happening inside the balloon, not on its surface,

No. You're not getting that the balloon is a 2D analogy of a 3D space.

For an ant living on the surface of the balloon, it is not expanding from its centre - he knows nothing of a "centre" of a 3D balloon, he knows only the 2D surface he lives on - and the surface he lives on is simply getting larger in all directions equally.

In our 3D universe, the same thing happens - the volume expands without a boundary. As it turns out though, there does not actually need to be a 4th dimension for this curvature to happen in. The mathematics work out anyway.

 

[eah2119]

Why not use the Earth as an analogy if the balloon is obviously too hard to understand?

Let's say, for a moment, that the Earth is flat. We can easily find a good pic of this on google. http://go.hrw.com/atlas/norm_map/world.gif
That is the surface of the Earth (a sphere) unrolled so that it is a flat plane. After all, you can't tell the Earth is round by standing from its surface. It appears flat always. Now, it only seems that there are boundaries to the 2D world because it doesn't continue on. But we know that if we sailed a boat from north america, across the pacific, and toward the edge that we would not hit a wall, or fall off an edge, or continue to sail on an endless ocean. If you've been living on this Earth long enough, you should know that you would eventually end up on the coast of Asia. How can this be? You've just been transported from one edge of the world to the other! It's 2 dimensional and has a finite area. Yet, there's no boundary. Walking in a straight line on the surface of the Earth will lead you to the same place you started. This is the same logic that those pioneers long ago went through when they ended up in the same location. It's not rocket science.

Applying this to 3D space, it's the same thing. If you traveled in any straight line, you would eventually end up in the same place you started. How can this be? It's the same thing that went on 600 to 800 years ago. 3D space must be curved in on itself to form a strange 4D sphere just like a 2D plane curves inward to form a 3D sphere. Of course, this is only one of many theories of the shape, size, and nature of the universe.

If you want a similar analogy for the inflating balloon/expanding universe, just extend the size of the world map. Each location on the Earth is moving away from a neighboring location at the same rate. The finite size is increasing, yet, there is still no boundary. Unlike the balloon analogy, the inside of the Earth is completely disregarded as we can only exist on its surface.

 

[ThomasT]

No. You're not getting that the balloon is a 2D analogy of a 3D space.

I get that. I just don't understand why it's necessary.

For an ant living on the surface of the balloon, it is not expanding from its centre - he knows nothing of a "centre" of a 3D balloon, he knows only the 2D surface he lives on - and the surface he lives on is simply getting larger in all directions equally.

Yes, but if we're assuming that we live inside an expanding 3D volume, then I don't get why it's necessary to talk about it in terms of us living on the surface of a 2D sphere. Is it generally thought that this makes the expansion and what it entails easier to understand? Why isn't it understandable (or less understandable) describing it in 3D terms?

In our 3D universe, the same thing happens - the volume expands without a boundary.

That's what I'm asking. How is it known that the 3D volume that's our universe doesn't have a boundary? What does it mean, in 3D terms not a 2D analogy, to say that a volume is finite but not bounded? Is it actually known that traveling in a straight line will bring one back to the point of origin, or is this just a byproduct of the geometry that's used? Is it possible that our universe can be described in 3D Euclidian geometry? Because that's is how I'm thinking about it. I think of the curved space geometry as a simplification of the effects of wave mechanics happening in a 3D Euclidian space. Is it possible that the boundary of our universe is an expanding wave shell (maybe more or less spherical) in 3D Euclidian space, and that the material universe of our experience is the more or less persistent wave structures that have emerged in its wake?

 

[bapowell]

Yes, but if we're assuming that we live inside an expanding 3D volume, then I don't get why it's necessary to talk about it in terms of us living on the surface of a 2D sphere.

Because it's easier to visualize a 2-sphere expanding in 3-space than to visualize the actual universe, which would be the surface of a 3-sphere expanding in 4-space (although as DaveC pointed out -- you don't actually need this higher dimensional space). The surface of a 3-sphere is finite but unbounded.

I don't know about you, but I have a hard time visualizing 4 dimensional objects.

 

[ThomasT]

Because it's easier to visualize a 2-sphere expanding in 3-space than to visualize the actual universe, which would be the surface of a 3-sphere expanding in 4-space (although as DaveC pointed out -- you don't actually need this higher dimensional space).

How is it known that the 'actual universe' is in 4D Euclidian space? Why not just the regular, visualizable 3D Euclidian space of our experience, where we would be part of the interior volume bounded by a 2D shell?

I don't know about you, but I have a hard time visualizing 4 dimensional objects.

But not 3 dimensional ones, right? So why can't we envision our universe as a 3 dimensional object expanding in the 3 dimensional space of our experience, while regarding the 4-space as a mathematical contrivance for the purpose of calculating and predicting gravitational behavior.

 

[bapowell]

Because *if* the universe is a sphere, then it does not have the topology of ordinary 3D Euclidean space. It has the topology of a sphere, a 3-sphere to be exact. Most people have a hard time visualizing the surface of a 3-sphere, since it is 3D space with nontrivial topology. Hence the balloon analogy -- it let's us visualize the correct topology of the universe by reducing the dimensionality to something the brain can digest.

 

[ThomasT]

Because *if* the universe is a sphere, then it does not have the topology of ordinary 3D Euclidean space. It has the topology of a sphere, a 3-sphere to be exact. Most people have a hard time visualizing the surface of a 3-sphere, since it is 3D space with nontrivial topology. Hence the balloon analogy -- it let's us visualize the correct topology of the universe by reducing the dimensionality to something the brain can digest.

Thanks for your input/feedback, but this isn't addressing my questions. Please see my previous post (#43).

 

[math4math]

Definitely expanding. It is same true as the Sun is hot. Spots on the expanding balloon just is an analogy not a theory; as said by DaveC.

I think the red shift is enough proof to simulate the moving away stars to spots on the balloon.

 

[bapowell]

I did address your previous post. Let me be more clear (also, keep in mind that this discussion assumes from the outset that the universe is globally positively curved...it might not be.) Here:

How is it known that the 'actual universe' is in 4D Euclidian space? Why not just the regular, visualizable 3D Euclidian space of our experience, where we would be part of the interior volume bounded by a 2D shell?

Because the region you are proposing does not have spherical topology. A positively curved 3D universe has the shape of a 3-sphere, with the 3D universe corresponding to the surface of the sphere.

But not 3 dimensional ones, right? So why can't we envision our universe as a 3 dimensional object expanding in the 3 dimensional space of our experience, while regarding the 4-space as a mathematical contrivance for the purpose of calculating and predicting gravitational behavior.

The 4-space is indeed mathematically superfluous, but it helps us visualize. Here's an example: a torus is readily visualized as the 2D surface of a donut. We can easily visualize the torus by picturing a donut in everyday 3D space. But we don't need the 3rd dimension -- we can define a torus using only 2 dimensions by starting with a 2D surface and assigning rules for how the edges are to be connected (think of the Asteroids Atari game -- that is an example of bona fide toroidal topology, and it is perfectly defined on just your 2D screen.) So, getting back to the universe. Supposing that the universe is positively curved and has 3 spatial dimensions, then we are dealing with a 3D volume that has spherical topology. Geometrically, this is the surface of a 3-sphere. Now, we don't need the 4th dimension to fully define the topology or geometry (just as we didn't need the 3rd for the torus), but it helps us visualize -- especially since the 4D space becomes the 3D ambient space when we consider the balloon analogy.

 

[ThomasT]

... keep in mind that this discussion assumes from the outset that the universe is globally positively curved ...

That clarifies why we've been sort of 'talking past' each other.

... it might not be.

Ok, so can we assume that our universe is described by flat 3D Euclidian space -- the interior volume of an expanding wave shell?

If so, then it would seem to be visualizable with no need for spherical surface analogies.

 

[WannabeNewton]

That clarifies why we've been sort of 'talking past' each other.

Ok, so can we assume that our universe is described by flat 3D Euclidian space -- the interior volume of an expanding wave shell?

If so, then it would seem to be visualizable with no need for spherical surface analogies.

If the curvature index is zero then you can assume the universe is described by Euclidean 4 - space but, even if it is the most likely, this is still an assumption as there are other 4 - manifolds that are flat but do not have the same topology as Euclidean 4 - space.

 

[bapowell]

If the curvature index is zero then you can assume the universe is described by Euclidean 4 - space but, even if it is the most likely, this is still an assumption as there are other 4 - manifolds that are flat but do not have the same topology as Euclidean 4 - space.

Except you don't need the 4-space -- Euclidean 3-space is sufficient to describe a flat expanding cosmology (with trivial topology).

 

[WannabeNewton]

Except you don't need the 4-space -- Euclidean 3-space is sufficient to describe a flat expanding cosmology (with trivial topology).

That is what I don't get. The Friedmann metric with k = 0 involves Euclidean 4 - space and Euclidean 3 - space would be a space - like hypersurface of it so how is it sufficient to describe an expanding cosmology with nothing but that space - like hypersurface?

 

[bapowell]

That is what I don't get. The Friedmann metric with k = 0 involves Euclidean 4 - space and Euclidean 3 - space would be a space - like hypersurface of it so how is it sufficient to describe an expanding cosmology with nothing but that space - like hypersurface?

We've been discussing the spatial part of the geometry in this discussion! Sorry if that was not made clear. But yes, good catch!

 

[GODISMYSHADOW]

You need not know how big the universe is to realize it is expanding. Einstein deduced the universe could not be static, it had to either be expanding or contracting. Hubble confirmed it was indeed expanding, causing Einstein to commit his biggest blunder - withdrawing his cosmological constant idea.

Does that say anything about the Schwarzschild radius? If we observe the universe is expanding, does that mean we're not sitting in a black hole?

 

[Physics_Kid]

Does that say anything about the Schwarzschild radius? If we observe the universe is expanding, does that mean we're not sitting in a black hole?

interesting point you make. i was pondering the "is expanding" statement that is made about the Uverse. i find galaxy red shift to be not enough info that the Uverse itself is expanding as it only suggests the item is moving away from the observer (or the "moving" object isn't moving relative to its localize space-time, but space-time itself is) . my argument is that you must be able to measure the current "size" of the Uverse and then take same measurement at some time in the future then read the diff to be able to conclude "is expanding", etc. but my argument suggests a instantaneous finite universe. even with the balloon argument (the expanding fabric of space-time) has a finite "area" or "volume" at any given time. i may be completely wrong but to me it makes more sense that the Uverse is not infinite, how can it be if space-time started at a single point?

 

[Physics_Kid]

sorry for bringing back an old thread, but its relevant.

so if the theory of "big bang" is correct and we agree the uverse is expanding, this implies the density of uverse is also decreasing at a fixed rate (unless we can show acceleration in the expansion).

are there any consequences (in math or physics) for space-time to become infinitely less dense?

is it possible that the uverse (however its mechanics are defined) has fixed density?

 

[bapowell]

are there any consequences (in math or physics) for space-time to become infinitely less dense?

What does it mean for space-time to have density?

 

[Drakkith]

are there any consequences (in math or physics) for space-time to become infinitely less dense?

is it possible that the uverse (however its mechanics are defined) has fixed density?

Note that when we say the density of the universe is decreasing we are talking about the density of matter and radiation within the universe.

 

[Chronos]

What does it mean for space-time to have density?

It means nothing.

 

[Physics_Kid]

It means nothing.

are we sure? i mean, if you lasso the uverse you are essentially lasso'ing what we know as space-time. perhaps time itself has no relationship to "density", but it is related to the universe as a whole? can time extend past the edges of the unverse?

but, to my question, any implications for density to become infinitely small?

 

[Drakkith]

are we sure? i mean, if you lasso the uverse you are essentially lasso'ing what we know as space-time.

You cannot lasso the universe so your comparison isn't meaningful.

perhaps time itself has no relationship to "density", but it is related to the universe as a whole? can time extend past the edges of the unverse?

There are no edges to the universe as far as we know.

but, to my question, any implications for density to become infinitely small?

Sure, it just means density becomes zero and you have a vacuum.