Does a finite universe make sense to you?

[epkid08]

If the basketball was expanding at the speed of light (or greater depending on th emodel you prefer) then you would have great difficulty getting from the centre of the ball to the surface of the ball. To get from the centre to the surface you would also have to be sure you were traveling in a straight line to avoid moving in large circles and it turns out that is not as easy as it seams. If you shone a laser beam outwards and followed that, how could you be sure that the beam is not curved by the mass of the universe? If you actually got to the edge of the universe it would be very hard to tell that you were actually there because of gravitational and possibly relativistic abberation that makes light appear to be coming towards you from regions where there are no galaxies, so you would not actually see a void beyond the edge of the universe.

If the universe had an edge, what would lie beyond that edge? There either has to be an explanation of what is beyond the edge, or an explanation of why we cannot physically cross it.

 

[LowlyPion]

We do not have the mental horsepower to translate this 2-D analogy to a 3-D universe, and that is the source of a lot of questions and confusion about the analogy.

No possibility that it's not a matter of our mental horsepower, but a fundamental flaw of the analogy to attempt to use 2 space constructs in 3 land?

If the analogy fails to satisfy our actual experience, then I have to question its utility.

Thanks for the explanation.

 

[cristo]

No possibility that it's not a matter of our mental horsepower, but a fundamental flaw of the analogy to attempt to use 2 space constructs in 3 land?

If the analogy fails to satisfy our actual experience, then I have to question its utility.

Thanks for the explanation.

This is only an analogy. The reason that cosmologists use such an analogy is so that people can imagine the scenario, and thus paint a picture in their head. Of course, we all know that this has a dimension missing, and that the equivalent "real" model would be the three dimensional surface of a higher dimensional sphere (i.e. S^3, in maths terms).

Note that we are not attempting to use a 2D analogy in "3 land", as you say in your post, but are rather reducing the higher dimensional topology into one that can be pictured by throwing away a dimension.

 

[turbo]

Note that we are not attempting to use a 2D analogy in "3 land", as you say in your post, but are rather reducing the higher dimensional topology into one that can be pictured by throwing away a dimension.

Exactly! And throwing away a dimension is something that is either misunderstood or poorly explained (or both). The person hearing the analogy misses that and imagines that there are three degrees of freedom (not just two) because a balloon is a 3-D object.

 

[LowlyPion]

Of course, we all know that this has a dimension missing, ...

Ok I get that and it's helpful to know that it's a simple minded analogy and all, but if I might ask then what is this missing dimension?

 

[sketchtrack]

This is only an analogy. The reason that cosmologists use such an analogy is so that people can imagine the scenario, and thus paint a picture in their head. Of course, we all know that this has a dimension missing, and that the equivalent "real" model would be the three dimensional surface of a higher dimensional sphere (i.e. S^3, in maths terms).

Note that we are not attempting to use a 2D analogy in "3 land", as you say in your post, but are rather reducing the higher dimensional topology into one that can be pictured by throwing away a dimension.

Isn't a sphere a 3d object anyways?

Why should we picture in our heads something that isn't relevant to physics?

 

[cristo]

Ok I get that and it's helpful to know that it's a simple minded analogy and all, but if I might ask then what is this missing dimension?

I'm not sure I get your question: when transforming from the model to the 2D analogy, we discard one spatial dimension.

Isn't a sphere a 3d object anyways?

Technically, no; a 2-sphere is the two dimensional surface of the three dimensional object.

Why should we picture in our heads something that isn't relevant to physics?

What do you mean why should you? I'm simply saying that, if you wish to picture how such a closed universe could look, then you can use the analogy of the surface of an inflating balloon, by considering only two spatial dimensions. If not, and you are comfortable dealing with the model of the 3-sphere, then that is fine.

 

[sketchtrack]

Yeah, but the universe isn't a surface of a sphere, and that is pretty easy to prove, so what is the point? You could say if the universe is a strait line that never ends, then it would look like that, but it isn't.

 

[LowlyPion]

... when transforming from the model to the 2D analogy, we discard one spatial dimension.

OK. I think I got that a space dimension was discarded. I guess my question is what is the 4th dimension of this presumed 4 space on which the 3-space is mapped so as to be able to represent it as the "surface" of a giant inflating balloon?

 

[MeJennifer]

OK. I think I got that a space dimension was discarded. I guess my question is what is the 4th dimension of this presumed 4 space on which the 3-space is mapped so as to be able to represent it as the "surface" of a giant inflating balloon?

Actually you should think of a 4 dimensional space being mapped onto a closed surface.

GR deals with curved 4 dimensional spacetimes.

 

[LowlyPion]

Actually you should think of a 4 dimensional space being mapped onto a closed surface.

GR deals with curved 4 dimensional spacetimes.

Not to be tedious about this but when the analogy is employed of using the expanding balloon and a space dimension is dropped out for this purpose, then what you are saying should be visualized is a 2-space that is mapped on the surface of this balloon and the third dimension is "time". Implying solely in the case of the analogy that the balloon is visualized which captures a single instant, as a spherical surface with radius representing the age of the universe from the big bang? That a picture of all time from the big bang by extension would be a layered solid onion of all the accumulated instants piled one upon another?

 

[NYSportsguy]

No possibility that it's not a matter of our mental horsepower, but a fundamental flaw of the analogy to attempt to use 2 space constructs in 3 land?

If the analogy fails to satisfy our actual experience, then I have to question its utility.

Thanks for the explanation.

Okay simply put, the analogy is similar to the reason why Columbus was able to travel across the globe by sea in 1492 and circumnavigate his way back to wherever it was he sailed from. He saw an "edge" however wasn't able to go over that "Edge" becasue there was more land and sea there. It revolves around forever becasue the surface on which he traveled on (our Earth) is in sphere form. HOwever we do knownthere is an "edge" between our upper atmospshere and space. This is similar to the "edge" we see between "space" and whatever lays on the other side.

For us, so far, it is humanly impossible to detect this "outer boundary". It may not exist for all we know. The laws of physics might prevent us from ever getting that far.

Nobody knows.

 

[yuiop]

If the universe had an edge, what would lie beyond that edge? There either has to be an explanation of what is beyond the edge, or an explanation of why we cannot physically cross it.

Beyond the edge is nothing, an infinite amount of nothing.

To explain why we can not cross it we first have to define what would be classified as the edge of the universe. Do we consider where the universe runs out of stars and galaxies as the edge or is the edge the surface created by the expanding ball of light from the big bang? To cross that boundary you would have to exceed the speed of light. The expanding surface of light and gravity leads the ways in virginal space preparing the way for matter that follows. Of course there is no way to be sure that are not other island universes out there O:

Can we detect anything about the what is beyond our visible universe? I believe the answer is yes. If the universe is larger than our visible horizon yet finite and if we are not exactly at the centre of that larger universe then we should detect some small anisotopy between two hemispheres of the CMB after the small anisotropy of the CMB redshift due to our peculiar motion has been allowed for.

Very accurate measurements of supernova, CMB and cluster data will eventually get all the data to agree with each other and give us an anser to whether the universe if infinite or not. The current best guess is that the universe is finite but not the infinite case is not elliminated by the current error bars.

For what it worth, Einstein felt quite strongly that an infinite universe is not compatible with General Relativity.

 

[yuiop]

Why do we need to drop a dimension to find an analogy? For example a solid cannon ball is a 4D object. It has 3 spatial dimension and one of time. So the challenge is explain why creatures living inside the cannon ball can not leave it and why the cannonball has no edge.

 

[LowlyPion]

The current best guess is that the universe is finite but not the infinite case is not elliminated by the current error bars.

For what it worth, Einstein felt quite strongly that an infinite universe is not compatible with General Relativity.

Since I have no theory in the hunt, for my money I'll take infinite.

If it's finite what's the count?

Before anyone may want to win such a bet though, keep in mind I will demand a recount.

 

[epkid08]

Beyond the edge is nothing, an infinite amount of nothing.

To explain why we can not cross it we first have to define what would be classified as the edge of the universe.

Any finite amount of matter has an edge. If there is no physical edge to cross, the matter cannot be finite, but infinite. (if you have an example to prove this statement wrong, say it)

Even if a finite amount of matter was expanding at a constant acceleration,a<\infty, a particle traveling at a=a_{m}+1 given infinity time would reach an edge of the matter.

Edit: The only explanation I can come up with that goes against what I said, is as you approach the edge of the universe, some undiscovered force, that is applied to you towards the center of the universe, is approaching infinity. Why else would it be impossible to reach the edge of a finite universe?

 

[yuiop]

Since I have no theory in the hunt, for my money I'll take infinite.

If it's finite what's the count?

Before anyone may want to win such a bet though, keep in mind I will demand a recount.

By count, do you mean count the number of galaxies for example? Are there an infinite number of galaxies in the universe? You do realize how big infinite is? Think of the biggest number you can possibly think of, square it, add it to iteself, cube it, multiply by 10^999999999999999999999999, double it again, and one, cube it again and so on and you still haven't got to an infinite number and you could continue cubing it every second for the next 14 billion years you still would not have an infinite number. Are there really an infinite number of galaxies in the universe? Now if you are saying there is an infinite amount of nothing beyond the matter universe I wouldn't exclude that as a possibility.

 

[BoomBoom]

... then what you are saying should be visualized is a 2-space that is mapped on the surface of this balloon and the third dimension is "time".

I believe the "3rd dimension" as you refer to it as is actually the physical curvature of the 2-D surface...not time.

In the real 3-D universe this ( http://en.wikipedia.org/wiki/3-sphere" ) is what they refer to as a 3 sphere. Its application seems to me to be purely mathematical...which is why there is no analogy to describe it.

 

[LowlyPion]

By count, do you mean ...

Just to keep it simple for you make it the number of quarks ... oh and say any photons now in transit.

You needn't count the virtual particles. That might be too tedious.

 

[yuiop]

Just to keep it simple for you make it the number of quarks ... oh and say any photons now in transit.

You needn't count the virtual particles. That might be too tedious.

I would say a rough estimate is that all the quarks in the universe, plus all the photons in transit, plus all the photons that have ever been emitted since the big bang is a big number, but less than infinite ;)

 

[LowlyPion]

I would say a rough estimate is that all the quarks in the universe, plus all the photons in transit, plus all the photons that have ever been emitted since the big bang is a big number, but less than infinite ;)

So you will go with the uncountably finite option then?

 

[sketchtrack]

Edit: The only explanation I can come up with that goes against what I said, is as you approach the edge of the universe, some undiscovered force, that is applied to you towards the center of the universe, is approaching infinity. Why else would it be impossible to reach the edge of a finite universe?

Maybe as you approach the edge, gravity overcomes momentum form the big bang, and you slow and eventually get sucked back inward, but as this happens, you start to get closer to the younger bodies, and cause them to accelerate outwards faster. Then what you have is something liken to an orbit. At some depth into the shell is the point where the momentum from the big bang of mass going outward meets and interacts with the mass being sucked back in, and so the universe isn't really expanding as far as edges go, but mass is being added to that area where those "orbits go". Then eventually, the shell would get so massive that a collapse happens, and boom big bang all over again.

 

[junglist]

while everyone is stuck on the balloon analogy, it appears to me that the discussion is going round in circles - reinforcing confusion and misunderstanding.

now to add more confusion, ill throw my hat in the ring.

the baloon analogy has 2-spacial dimensions and one time dimension. the curvature is undetectable in 2-dimensions. someone looking tangential to the surface would see it as flat as all light, matter, everything in this universe is contained in this plane and also infinite (well they could look out and see the back of their 2d head). whether you want to leave it at that, or complete the analogy by accepting that the 2-d universe experienced by one if its inhabitants actually sits in a greater 3-d space to allow the curvature, its upto you.

now, add another spatial dimension to obtain our universe and viola! we have a 3d (spacial) universe that is infinite in 3-dimensions but sits in a greater 4-d universe (im just talking about spatial dimensions here). to the inhabitants, the 4th spatial dimension is completely hidden and the universe appears spacially infinite.

 

[yuiop]

So you will go with the uncountably finite option then?

I prefer that to Cantor's countably infinite

 

[junglist]

Maybe as you approach the edge...

my understanding is that the big bang happened everywhere at once and there is no 'edge' to it.

the light we see from the cmb is the inside surface of a spherical void in infinite space.

 

[marcus]

...

now to add more confusion, ill throw my hat in the ring.

the baloon analogy has 2-spacial dimensions and one time dimension. the curvature is undetectable in 2-dimensions. someone looking tangential to the surface would see it as flat

as all light, matter, everything in this universe is contained in this plane

and also infinite (well they could look out and see the back of their 2d head).

whether you want to leave it at that, or complete the analogy by accepting that the 2-d universe experienced by one if its inhabitants actually sits in a greater 3-d space to allow the curvature, its upto you.

now, add another spatial dimension to obtain our universe and viola! we have a 3d (spacial) universe that is infinite in 3-dimensions but sits in a greater 4-d universe (im just talking about spatial dimensions here). to the inhabitants, the 4th spatial dimension is completely hidden and the universe appears spacially infinite.

that's a pretty clear commonsense discussion. I agree 90 percent with what you say. And it leaves room for people to adopt the attitude they prefer about the unseen spatial dimension.

What you've done, that a lot of people in this thread didn't do, is carefully imagine the experience of 2D creatures in a curved 2D world.
Who don't see a 3rd spatial dimension and as far as they know one does not exist. It may or it may not.

Slight problem with your saying
someone looking tangential to the surface would see it as flat
since they could measure the interior angles of a triangle and find the excess above 180 degrees.

 

[junglist]

Slight problem with your saying
someone looking tangential to the surface would see it as flat
since they could measure the interior angles of a triangle and find the excess above 180 degrees.

very true.

it is of course still an analogy.

some people like the raisin / bread analogy better, but i don't like it as much as the balloon because it implies a finite distance to the crust/edge of the bread/universe unless you assume the bread is infinite.

the balloon allows a seemingly infinite universe containing a finite amount of matter/energy.

...and all it requires is an additional dimension.

:)

 

[malawi_glenn]

I guess you misunderstood me. Take a basketball for example; Let's call it a sphere. It would be possible for a particle to travel from the center of the ball to the very edge of the ball, but also, it could travel out of the ball. So we can say that because the particle was able to pass the edge of the ball, it then has a normal sized radius. When you say we can't pass the edge of our universe, you have to assume that the radius, or the length from any point to the 'edge' is infinite.

Of course this is if, and only if, we cannot physically pass the edge of the universe. What would lie outside the edge anyways?

You are still only restricting yourself to geometries that we can imagine with our sense. The space and time are 'curved'.

 

[junglist]

while not strictly on the discussion of an infinite universe this will assist in people's understanding of the supplied analogies somewhat.

- I'd suggest that people familiarise themselves with the concept of 'mobius strip', 'klein bottle' and a 'hypercube' to at least gain an understanding of what can be done/visualised with geometries, dimensions, and surfaces.

 

[sketchtrack]

So according to big bang, it happened all at once everywhere. Then everywhere is now getting bigger. Some people told me that the big bang just means the universe was once more dense, if it was just more dense, then big bang isn't really a creation event is it?