An infinite universe with shape?

[Chase]

Please excuse my ignorance on the topic but I just thought of something which seems to make sense to me but then again I have no experience in cosmology.

Just some points I want to clarify. Because the universe had a starting point, can it's size be infinite? If so could the universe be a sphere? Here is why I ask.

An object that is infinite in size doesn't have a shape. Take a hexagon for example, if you increased it's size to infinite then it would no longer have a shape. So if the universe was a sphere when it was created and is now infinite in size. Does that explain why the observable universe doesn't have a curve?

If I draw a circle on a piece of paper and then a larger circle next to it, I can clearly see that the curve of the circle decreases. If you increase the size of the circle to infinite then it would become a flat line with each unique point being infinitely long... Basically if you put two people on the circle at different points, they can never meet up with each other and likewise they will always be stuck in their little unique space coordinate. So if you did the same with a sphere you'd end up with an infinite "shape" where you can go in any direction forever and never meet the part where it starts to curve.

Could it be that we are trapped in our own little space-time coordinate where we can travel forever in any given direction and never move into another coordinate because to do so would imply that we can travel around the universe, like we can with Earth. But if the universe is infinite then we'd never get back to where we started because we can't even leave our own unique coordinate?

Sorry if this is a stupid question

 

[Mordred]

a finite object cannot become infinite, neither can an infinite object become finite. The flat universe described in cosmology is a comparsion between its actual density as compared to its critical density.
This relation affects how light travels through space. In a flat universe the light path is straight and angles of a triangle add up to 180 degrees. In a curved relation this wouldn't be the case as light would curve.

When cosmologists refer to the universe they are usually describing the observable universe. The observable universe is finite. We do not know if the universe was finite or infinite at the time of the BB. We can only ever see and measure our observable portion,this recent post contains several articles that better address your questions on Universe geometry, as well as cover universe geometry in greater detail

https://www.physicsforums.com/showthread.php?t=736246#post4649459

edit: noticed the other posts while I was making this one. In the finite universe scenario, the answers supplied are accurate by Bapowell and Marcus

 

[bapowell]

A spherical universe is necessarily finite. However, as we make the sphere bigger and bigger, as you say, the curvature becomes less and less. The observable universe has been measured to be flat to within 1%, it could be that the observable universe is just a small patch on a very much larger spherical universe.

 

[marcus]

...If I draw a circle on a piece of paper and then a larger circle next to it, I can clearly see that the curve of the circle decreases. If you increase the size of the circle to infinite then it would become a flat line with each unique point being infinitely long... Basically if you put two people on the circle at different points, they can never meet up with each other and likewise they will always be stuck in their little unique space coordinate. So if you did the same with a sphere you'd end up with an infinite "shape" where you can go in any direction forever and never meet the part where it starts to curve...

This seems like pretty good intuitive thinking. You express it in your own words. Mathematicians would say "curvature" and as you increase the size of a circle the "curvature" decreases.
You say "I can clearly see that the curve of the circle decreases.

It is pretty much the same thinking, but put in different words.

You are talking about "taking the limit" (a math idea).

When you increase the size of a circle or a sphere the curvature gets less and less but it never actually reaches zero. The circle never actually becomes a straight line. But the curvature approaches zero in the limit.

Well right now I'm not saying anything, that you didn't already say. Just letting you know I hear you and putting it in different words.

 

[marcus]

Heh heh, three people answered almost simultaneously. Mordy and Brian Powell already said what i wanted to say. All three posts posted at 10:17 Pacific Time, IOW 1:17 PM Eastern.
Mordy pointed out that you can measure the curvature of a sphere *from the inside* by making triangles (say with stretched string or lightrays) and adding up the angles to see if they come to exactly 180, or just slightly greater than 180.

You don't have to "step outside" of space in order to detect and measure the curvature (the "curved-ness") of space.

There is an analogous idea with 3D space. It could be very slightly curved, or it could be perfectly flat. We don't know yet. People are working on measuring the overall average curvature of the part of the universe we can see, but so far they only have a small RANGE of numbers that includes zero as a possibility. They know it is NEARLY zero, but they don't know the exact figure.

The important thing is you can measure "shape" or more exactly curvature *from the inside*, without there necessarily being any outside to it, and also that people doing their best to measure it. They are working diligently and with considerable ingenuity and they are getting better estimates as time goes by.

 

[Chase]

When you increase the size of a circle or a sphere the curvature gets less and less but it never actually reaches zero. The circle never actually becomes a straight line. But the curvature approaches zero in the limit.

I'm confused, I thought this was the whole idea of infinity. $\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\cdots=1$ but the only reason it equals 1 is because it goes on for infinite.

So if you're saying that a circle never becomes a straight line, is that not the same as saying that the above sum doesn't actually equal one it just gets closer and closer to one?

So basically no matter how much I increase the size of a circle, it will always have some value for it's curvature? Even if the circle is infinite in size?

 

[bapowell]

The curvature approaches zero in the limit that the radius of the circle goes to infinity; the sum of your series approaches 1 in the limit that the number of terms goes to infinity. Seems analogous to me...

 

[Chase]

The curvature approaches zero in the limit that the radius of the circle goes to infinity; the sum of your series approaches 1 in the limit that the number of terms goes to infinity. Seems analogous to me...

So why does the curvature never actually reach 0 if the size of the circle is infinitely large? Because by saying that the curve never reaches 0 implies that you could, with enough time travel around the circumference of the circle and get back to where you started which would mean the circle is not infinitely large

 

[bapowell]

So why does the curvature never actually reach 0 if the size of the circle is infinitely large? Because by saying that the curve never reaches 0 implies that you could, with enough time travel around the circumference of the circle and get back to where you started which would be the circle is not infinitely large

How would you travel around the circumference of a circle with infinite diameter?

 

[Chase]

How would you travel around the circumference of a circle with infinite diameter?

But that's the point... If it has an infinite diametre then its curvature must be 0.

 

[bapowell]

Are you familiar with limits?

 

[ViperSRT3g]

I'm confused, I thought this was the whole idea of infinity. $\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\cdots=1$ but the only reason it equals 1 is because it goes on for infinite.

So if you're saying that a circle never becomes a straight line, is that not the same as saying that the above sum doesn't actually equal one it just gets closer and closer to one?

So basically no matter how much I increase the size of a circle, it will always have some value for it's curvature? Even if the circle is infinite in size?

As was stated before, a finite quantity cannot become infinite. Your example shows that you can get as close to 1 as possible, but it will never be 1 BECAUSE it is infinite.

The is the exact same idea as the curvature of your circle. You can increase the size of the circle infinitely, and it will get as close to being perfectly flat as you want. But it will NEVER be perfectly flat because it started out as a circle, which had a finite shape and size.

 

[Chase]

But it will NEVER be perfectly flat because it started out as a circle, which had a finite shape and size.

Now this makes sense and I remember a previous statement saying that a finite object cannot become infinite and vice versa.

Also I am not familiar with limits but I was thinking about this as a physical idea, not so much a mathematical concept.

 

[bapowell]

Also I am not familiar with limits but I was thinking about this as a physical idea, not so much a mathematical concept.

Well, you've just discovered how the two are related :tongue:

 

[madboy]

Please excuse my ignorance on the topic but I just thought of something which seems to make sense to me but then again I have no experience in cosmology.

Just some points I want to clarify. Because the universe had a starting point, can it's size be infinite? If so could the universe be a sphere? Here is why I ask.

An object that is infinite in size doesn't have a shape. Take a hexagon for example, if you increased it's size to infinite then it would no longer have a shape. So if the universe was a sphere when it was created and is now infinite in size. Does that explain why the observable universe doesn't have a curve?

If I draw a circle on a piece of paper and then a larger circle next to it, I can clearly see that the curve of the circle decreases. If you increase the size of the circle to infinite then it would become a flat line with each unique point being infinitely long... Basically if you put two people on the circle at different points, they can never meet up with each other and likewise they will always be stuck in their little unique space coordinate. So if you did the same with a sphere you'd end up with an infinite "shape" where you can go in any direction forever and never meet the part where it starts to curve.

Could it be that we are trapped in our own little space-time coordinate where we can travel forever in any given direction and never move into another coordinate because to do so would imply that we can travel around the universe, like we can with Earth. But if the universe is infinite then we'd never get back to where we started because we can't even leave our own unique coordinate?

Sorry if this is a stupid question

i am new to this forum but this question is quite interesting actually i don't know physics much but i tried to draw the scenario you mentioned as a cubic block taking three coordinate axis and i can see that if we take two universe one possitive and one exactly the mirror image then the two meet to form a cube perfect cube hope that helps.

 

[madboy]

Now this makes sense and I remember a previous statement saying that a finite object cannot become infinite and vice versa.

Also I am not familiar with limits but I was thinking about this as a physical idea, not so much a mathematical concept.

i don't understand how can a circle start to describe the universe we should maybe use a sphere. no offense just want to know .

 

[Chase]

i don't understand how can a circle start to describe the universe we should maybe use a sphere. no offense just want to know .

I used a circle as an example simply because it's easiest to draw on a piece of paper. A circle and a sphere hold the same principle that I was trying to explain.

Doesn't matter now though because I understand what marcus, bapowell and viper were saying so it cleared up any confusion.