Is the Universe Really Expanding?

[Physics_Kid]

so, many shows on tv today that keep suggesting our universe is expanding. is it really?

1. if you can say "it is expanding" doesn't that imply you 1st have to know how big it is now, then make a observation (measurement)? so if the universe is already infinite in size how can anyone say its expanding (we can't measure infinity)...?

2. if the universe was a cube of space with the 2-dimensional sides increasing in size at the known max speed limit of C (speed of light), this seems possible, but as an observer inside the cube observing the edge where any two cube surfaces meet the observer would observe the edge moving away faster than C (the vector)! so to me a cube doesn't make sense.

3. going on #2, the universe is a sphere with radius increasing at C ?

4. and to wrinkle the math some, if the universe itself is not expanding at speed of C doesn't this imply that light itself can indeed reach the edge of the universe? and if it does what happens?

just wondering...

 

[Trevormbarker]

1. Yes its expanding
2. It CAN expand faster then the speed of light
I believe there is a FAQ on this in cosmology somewhere

 

[milkomeda]

Although I'm still new to this, I believe I can help out a bit.
The universe is expanding, but that does NOT imply we know the current size or shape of the entire universe. We know the size of the observable universe (a diameter of 93 billion light years), but depending on your model of the universe, that could very well be a drop of water in an ocean.

The farther a galaxy is from the milky way (our point of reference), the faster it is moving away from us. This was determined via the Doppler Effect, with Hubble discovering a correlation between the redshift of a galaxy and the distance it was from the milky way. This type of event (with objects farther away from a center moving faster than those closer to the center) is seen all the time on Earth, as it occurs during an explosion. I believe through this and other discoveries/theories (which I am not qualified to explain), scientists where able to determine that the universe was at one time in an extremely hot and condensed sate, and then started to expand rapidly (The Big Bang, or perhaps more fittingly, The Big Expansion).

Galaxies cannot by themselves travel faster than the speed of light, but will eventually move away from us faster than the speed of light. This is due to the fact that space-time is expanding at an increasingly faster rate due to the propulsive force that is dark energy. So eventually, with the ever increasing rate of expansion, the galaxies will be moving away from us faster than the speed of light, and will disappear from the night sky, as the light from those galaxies can no longer reach us.

I myself am just starting a B.S. in physics, so I would welcome any critique or corrections to my statements/understandings that some of the other posters may have.

 

[granpa]

google 'baloon analogy'.

 

[Chronos]

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.

 

[bapowell]

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.

Einstein's biggest blunder was his introduction of the cosmological constant -- not it's removal from the theory. I don't think Einstein ever "deduced" anything about the expansion of the universe -- he simply felt that aesthetics mandated a static cosmology. Hence, his introduction of the CC to render the universe static.

 

[Chronos]

Agreed. Just a little tongue in cheek humor. The cosmological constant was introduced in an effort to model a static universe, which was the prevailing [and Einstein's] belief of the time. Einstein was certainly aware his theory did not model a static universe without the cosmological constant. After Hubble's discovery, Einstein called the cosmological constant his greatest blunder. As we now know denouncing the cosmological constant was his only blunder. see http://www.jb.man.ac.uk/~jpl/cosmo/blunder.html

 

[Physics_Kid]

in regards to post #3, galaxies and stuff is matter (mass). just because we can observe that mass moving away from us does not mean that the universe itself is expanding. what I'm asking is if the the "box" of space-time is expanding and if so at what speed? can we even measure space-time?

i don't know an answer, but i know if its not expanding at min C then we need to come up with the physics/math that explains what happens when light reaches the edge of the universe...

 

[granpa]

when light reaches one end of the box it reappears at the opposite side of the box.

 

[Physics_Kid]

when light reaches one end of the box it reappears at the opposite side of the box.

hmmm, this is indeed one theory, like the old asteroids game where spaceship leaves one side and reappears on the other. a theory that needs much explaining, a theory that suggests a finite universe or one that is expanding slower than C.

 

[DaveC426913]

in regards to post #3, galaxies and stuff is matter (mass). just because we can observe that mass moving away from us does not mean that the universe itself is expanding. what I'm asking is if the the "box" of space-time is expanding and if so at what speed? can we even measure space-time?

It is that the farther something is, the faster it is moving away. At the very edge of the observable universe things are moving away quite quickly. i.e. the universe seems to be expanding.

i don't know an answer, but i know if its not expanding at min C then we need to come up with the physics/math that explains what happens when light reaches the edge of the universe...

The universe has no edge. As granpa says: Google balloon analogy. A balloon's surface expands yet it has no edge.

 

[-Job-]

It is that the farther something is, the faster it is moving away.

Ah this reminds me, i had a question recently when watching some documentary on the topic, this is not my field so bear with me.

If stars that are farther away are also farther back in time, then wouldn't the fact that the fastest moving stars are the farthest away from us mean that stars were moving faster a long time ago, suggesting that the universe is deaccelerating?

 

[bapowell]

If stars that are farther away are also farther back in time, then wouldn't the fact that the fastest moving stars are the farthest away from us mean that stars were moving faster a long time ago, suggesting that the universe is deaccelerating?

A given object that today is moving away from Earth with the expansion was once closer to earth, and hence, receding more slowly.

 

[DaveC426913]

Ah this reminds me, i had a question recently when watching some documentary on the topic, this is not my field so bear with me.

If stars that are farther away are also farther back in time, then wouldn't the fact that the fastest moving stars are the farthest away from us mean that stars were moving faster a long time ago, suggesting that the universe is deaccelerating?

No. Again, turn to the balloon analogy.

Glue a bunch of pennies to a balloon. Inflate the balloon. The speed at which any two pennies diverge is directly proportional to the distance between those two pennies. Farthest pennies diverge fastest ,despite the fact that the inflation rate has not increased.

 

[Physics_Kid]

i am still having a hard time understanding how the galaxies (mass) are linked to space itself. if we can observe mass moving by doppler then we can say "that mass is moving at speed xyz", but how does that infer that the universe is expanding?

the balloon theory seems flawed... this balloon theory is more like a balloon inside a infinitely sized box, this seems more analogous to the observable mass moving away from all other observable mass.

 

[DaveC426913]

i am still having a hard time understanding how the galaxies (mass) are linked to space itself. if we can observe mass moving by doppler then we can say "that mass is moving at speed xyz", but how does that infer that the universe is expanding?

"linked to space itself"? Don't know what you mean.

If the sum total of the mass that expanded from the BB is growing in volume, then ipso facto, the universe is getting larger.

the balloon theory seems flawed... this balloon theory is more like a balloon inside a infinitely sized box, this seems more analogous to the observable mass moving away from all other observable mass.

It is not a theory; it is an analogy. It is designed to help one grasp an elusive concept. "flawed" gives it more credit than its due; it's just a simple analogy.

 

[zonde]

i am still having a hard time understanding how the galaxies (mass) are linked to space itself. if we can observe mass moving by doppler then we can say "that mass is moving at speed xyz", but how does that infer that the universe is expanding?

We describe observations using some coordinate system. In that coordinate system average distance between galaxies grows over time. That's our current choice to describe observations this way.

Basically statement that universe itself is expanding is just a way of saying that it is not a big explosion type of expanding. So it says what it is not but do not rally says what it is.

 

[bapowell]

i am still having a hard time understanding how the galaxies (mass) are linked to space itself. if we can observe mass moving by doppler then we can say "that mass is moving at speed xyz", but how does that infer that the universe is expanding?

Galaxies are not linked to space itself. There are two important motions to understand here: there is the expansion of the space itself -- this is the rubber in the balloon analogy. Then you have the motions of the galaxies relative to this space (in the balloon analogy, the galaxies are "painted" onto the surface and don't move relative to it, but this is just a simplification.) The motion of a galaxy relative to the expansion is called its peculiar velocity. Now, one can show that in an expanding universe, objects moving relative to the expansion experience a drag force (called Hubble drag) that causes them to asymptotically come to rest relative to the expansion. In any case, peculiar velocities are really quite small in comparison to the recession velocity due to the expansion.

Now, your point about whether the galactic redshifts we observe are due to the Doppler effect or have a cosmological origin is one that has been debated here on these forums at length. I recall the solution is that these two choices are empirically identical, although a universe in which all galaxies happen to have peculiar velocities that agree with Hubble's Law sounds like a very contrived and special universe indeed.

 

[eah2119]

So, is our observable universe shrinking?

I've always thought that our observable universe is expanding because every day more and more light is reaching us. As a result, more and more distant galaxies are being revealed. But when I think about it, considering the constantly acceleration expansion of space, is our observable universe shrinking? If so, at the time before the great expansion, was the observable universe equal to the entire universe? Will we, one day, be limited to view only our own galaxy or less?

 

[Octonion]

I've always thought that our observable universe is expanding because every day more and more light is reaching us. As a result, more and more distant galaxies are being revealed. But when I think about it, considering the constantly acceleration expansion of space, is our observable universe shrinking? If so, at the time before the great expansion, was the observable universe equal to the entire universe? Will we, one day, be limited to view only our own galaxy or less?

When we look through telescopes, the average velocities of all the objects distant from our galaxy are pointed radially away from us. Indicating that either (a) the milky way is the center of the universe (which it is not), or (b) the universe is itself expanding, where every single point in space-time is getting further from away from one another. On top of this as we look further and further away from the milky way we see things moving faster and faster away from us. Thus, the velocity you can attribute to the expansion of the universe of a galaxy with respect to our observatories here on Earth is proportional to the distance it is away. So when we look at it we can subtract those effects of expansion and study how it is moving with respect to space-time itself. And eventually things are so far away that the space-time they are occupying is expanding away from us faster than the speed of light and thus, the photons from those galaxies can never reach us! This is called the cosmological horizon and because space is expanding everyday more and more things move out of our view. Less and less light is in our viewable portion of the universe.

 

[bcrowell]

so, many shows on tv today that keep suggesting our universe is expanding. is it really?

We have a FAQ on this topic: https://www.physicsforums.com/showthread.php?t=506993

2. if the universe was a cube of space with the 2-dimensional sides increasing in size at the known max speed limit of C (speed of light), this seems possible, but as an observer inside the cube observing the edge where any two cube surfaces meet the observer would observe the edge moving away faster than C (the vector)! so to me a cube doesn't make sense.

We also have a FAQ entry that addresses this question: https://www.physicsforums.com/showthread.php?t=508610

4. and to wrinkle the math some, if the universe itself is not expanding at speed of C doesn't this imply that light itself can indeed reach the edge of the universe? and if it does what happens?

Standard cosmological models don't have edges. You may find this article helpful: http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

 

[Chronos]

The observable universe ends abruptly about 380,000 years after the big bang. We will never see anything older than the universe [13.7 billion years at present]. There are no presently unobservable galaxies that will some day suddenly pop into view, nor any that will suddenly vanish in the future. It appears distant galaxies will eventually redshift beyond detectability over time.

 

[zadignose]

... Indicating that either (a) the milky way is the center of the universe (which it is not)...

I'm not objecting or anything, but seeking to learn. What's the evidence/proof that the milky way is not the center of the universe?

 

[zonde]

I'm not objecting or anything, but seeking to learn. What's the evidence/proof that the milky way is not the center of the universe?

I doubt that there is any serious evidence/proof of that. Because nobody seriously considers this possibility following http://en.wikipedia.org/wiki/Copernican_principle" .

 

[bapowell]

I'm not objecting or anything, but seeking to learn. What's the evidence/proof that the milky way is not the center of the universe?

The Milky Way being the center of the universe is not ruled out by current observations. In fact, a universe in which the Cosmological Principle holds and one in which the Milky Way lies at the center are not empirically distinct. Modern cosmology embraces the Cosmological Principle because it is simpler and requires no assumptions that are not empirically testable (homogeneity and isotropy). If the Milky Way were at the center, scientists would need to understand why we happen to occupy this restricted and privileged location.

EDIT: Also, compare Copernican and Cosmological Principles. The current working assumption is the latter.

 

[Thiago]

I tried to remember about the local group to post here, I found it in the wiki but it fits with the astrophysics class I've done, so I quote:

The Milky Way and the Andromeda Galaxy are a binary system of giant spiral galaxies belonging to a group of 50 closely bound galaxies known as the Local Group, itself being part of the Virgo Supercluster.

these findings are empiric so the milk way can't be the center of universe.

The full articles : http://en.wikipedia.org/wiki/Local_Group
http://en.wikipedia.org/wiki/Milky_Way#Environment

 

[bapowell]

these findings are empiric so the milk way can't be the center of universe.

Why not?

 

[Thiago]

You are PHD in physics, I just assume that you understand it very much more than me, but let me say why ,I think, not.

ok, the local group are real, and we know that we all are rotating at a center near milk way and Andromeda (let's say that once the universe has a center and it's center was milk way) to remain in this way all the gravitational forces done by the other galaxys need to cancel each others as in the local group we have another center of gravity different of milk way the pull of the others will suffice to pull us from the center even if the milk way mass is much more than all the others.

As the probable shape or universe is more like a torus than a rubber ball the probable center of universe is kind of out of it... since I believe that the milk way is in the universe...

if we use philosophy to argue that in one infinite universe there is no center but every location is the center... so I can be much more precise, the center of the universe is in the milk way, better, it is (for now) in earth, in the Americas, in Brazil, in Rio de Janeiro in my bellybutton ^^

and for least using the Occam blade the universe will be much more complex to fit the milk ways as its center thus being much more improbable that it is true.

when I was writing this post I saw the problem, we can change all the points of view to render us the center of universe, but is extremely more complex than the other kind of universe
did I say too many dumb things?

 

[bapowell]

when I was writing this post I saw the problem, we can change all the points of view to render us the center of universe, but is extremely more complex than the other kind of universe
did I say too many dumb things?

Absolutely not! In fact, you reasoned precisely the way I hoped you would. Indeed, it is extremely more complex to develop a model in which the milky way lies at the center of the universe. In fact, my initial post regarding the empirical equivalence of a milky way-centric and a universe adhering to the cosmological principle was based on the large scale homogeneity and isotropy of the universe. Your point, regarding the local inhomogeneity of the galactic neighborhood, clearly complicates any attempt at formulating a Milky Way-centric universe. At the end of the day, we must consider the simplest, most sensible, most predictive model that describes our universe to be the most correct one.

 

[ViewsofMars]

Regarding the topic Is the universe expanding?, the ESA states:


1. "One of Hubble's initial 'core' purposes was to determine the rate of expansion of the Universe, known to astronomers as the "Hubble Constant". After eight years of Cepheid observations this work was concluded by finding that the expansion increases with 70 km/second for every 3.26 million light-years you look further out into space."

2. "For many years cosmologists have discussed whether the expansion of the Universe would stop in some distant future or continue ever more slowly. From the new supernova results it seems clear that the expansion is nowhere near slowing down. In fact, due to some mysterious property of space itself, called dark energy, the expansion is accelerating and will continue forever. This surprising conclusion came from combined measurements of remote supernovae with most of the world’s top-class telescopes, including Hubble. Furthermore recent supernova results indicate that cosmos did not always accelerate, but began accelerating when the Universe was less than half its current age [around 13.7 billion years]."

http://www.spacetelescope.org/science/age_size/

Hope that helps.

 

[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).