Can Two Infinitely Sized Objects Exist in an Infinite Space?

[LT07]

Spare me the ridicule for asking a stupid question, I'm just your average guy trying to comprehend his environment. I do my best to understand the origins and workings of the universe but no matter what path I take I will end up facing an infinity of one form or other.

Ok here goes.

I have always assumed that it is impossible to have two infinitely sized objects since each would occupy space that the other should be existing in. If any infinite sized object ever existed then it would consume all 3D space and there would be no room for anything else to exist.

Now I'm not so sure.

I assume that 3D space is infinite in all directions.

Floating around in this space is a hosepipe of infinite length (infinite to the point it has no ends)

If its infinite in length then it can hold an infinite volume of water.

Any infinite volume should consume all of space but now I find I can have an infinite number of infinite volumes in an infinite amount of space.

It also occurs to me that I can walk up to the hosepipe and cut it in half creating a different type of infinite length, before it had no beginning or end and now I have two infinite lengths both with a beginning but no end.

Am I barking up the wrong tree, should I stick to my idea that an infinitely sized object is impossible or does an infinite amount of space allow for an infinite number of infinitely sized objects?

Don't blame me for asking such stupid questions I'm not the one dumping singularities all over the universe.

 

[pervect]

You might want to read about Hilbert's hotel

The situtation with infinite space is similar - an infinite set can have subsets that are the same size (i.e. can be put into a 1:1 correspondence with) the original set.

 

[LT07]

You might want to read about Hilbert's hotel

The situtation with infinite space is similar - an infinite set can have subsets that are the same size (i.e. can be put into a 1:1 correspondence with) the original set.

Thank you for the reply, yes I have read that particular paradox but am still no closer to understanding infinity. The hosepipe being cut in half has just thrown further confusion at me. I can cut it in half once but never again, it has no middle that I can reach, all I can do now is cut off finite lengths.

So confusing.

 

[Hurkyl]

If any infinite sized object ever existed then it would consume all 3D space

This is clearly false, as your counterexample demonstrates.

(I assume by "size", you mean volume)

 

[LT07]

This is clearly false, as your counterexample demonstrates.

(I assume by "size", you mean volume)

Yes I mean that an infinitely sized object would have infinite volume, however the hose pipe is not of infinite size (only length) yet by my reckoning it contains an infinite volume of water.

Something is desperately wrong with the way I perceive infinity.

 

[Hurkyl]

If you are not using "size" as a synonym for volume, then please explain what you mean by that word.

Also, you seem to suggest that the hosepipe doesn't have infinite volume; why do you think that?

 

[TR345]

Hmm. Is 2i>i? That is a tough one. I guess if you are talking about two infinite spaces, then they are both part of the same infinate space, so 2 infinate spaces can't exist because in the case of infinite space, there are no spaces only one infinite space.

As for the hose idea, I don't know what to say. I guess you could have infinite amounts of different objects and objects could be less frequently, or less densely organised through an infinite space.

If space and time are infinite, then maybe ultimately their is only one fundimental thing that makes up everything and it is infinite in amount and all things and spaces are a part of it in its' infiniteness.

 

[LT07]

If you are not using "size" as a synonym for volume, then please explain what you mean by that word.

Also, you seem to suggest that the hosepipe doesn't have infinite volume; why do you think that?

See note in first post about average guy, the average guy is pretty stupid.

Yes I equate size to be the same thing as volume, that is anything with size has volume! clearly this is something I need to read up on as you seem to know something I don't. I can imagine something like a flat sheet with no thickness but has width and height, it could have a surface area but no volume.

As for whether the hosepipe has infinite volume is the thing I'm trying to understand, if its infinite in length then it must contain an infinite volume of water, but if the volume of water is infinite then how come its not occupying all of space?

I have always considered that something of infinite volume must occupy all available space. I hardly understand the question never mind the answer. :)

 

[Feonix12]

You cannot have an infinite number of infinitely sized objects. Why? Because if there were infinite number of atoms to create these objects then there would be no space in the universe. There is a limited number of atoms in the universe, even though its a bigger number then we can ever comprehend.

 

[Hurkyl]

Because if there were infinite number of atoms to create these objects then there would be no space in the universe.

Why would you think that?

There is a limited number of atoms in the universe,

Or that?

 

[Feonix12]

Why would you think that?


Or that?

If you believe in the big bang theory...
If there was an infinite number of atoms then we couldn't move or exist in the first place. At night when you look up in the sky and see all that blackness, that's empty space. If there were infinite atoms to occupy the universe there would be no blackness, there would be nothing except a solid object, atoms touching atoms throughout the entire universe. Take snow for a rough example, when its falling from the sky you can see inbetween each snowflake, there's space between them(dont get technical with me about gases and particles), but when it compresses on the ground its just a solid hunk of snow. If you believe in the big bang theory then there is no way in hell there are infinite number of atoms, and there is not infinite energy to be consumed. Sure we can harness chemical reactions and keep energy going indefinetly, but fact is we won't be able to keep that reaction going indefinetly in the first place, the sun will colapse on itself some year. All the suns will, or will be engolfed within black holes and the black holes will eventually eat each other up. Then supposedly explode again like another "big bang". This reaction keeps going forever. Just my theory on OUR universe. Thats not including parallel universes or other dimentions. Everything basicly boils down to me as everything is balanced, for every action there is a reaction, + -.

Damn i spew a lot of crap out.

 

[TR345]

Your reasoning involves infinate objects in finite space. How could infinate space be full? There can be no max capacity because there is infine room, never ending. If this space never ends, and there is a snowflake every two inches, then mathematically there is still infanite snowflakes.

 

[TR345]

Besides this is a hypothetical question. The hypothetical isn't: If the big bang theory is true, then could there be infinate objects in an infinate space? Big bang theory cannot rule out infinate space anyways. There could be an infinate amount of big bangs and an infinate amount of universes for all we know.

 

[JesseM]

Big bang theory cannot rule out infinate space anyways. There could be an infinate amount of big bangs and an infinate amount of universes for all we know.

Actually, the basic Big Bang model already assumes that space would be infinite if the density of matter is at or below a certain critical value known as Omega--you don't need an infinite number of Big Bangs, just the one is enough. See my last post (#8) on this thread.

 

[Feonix12]

Your reasoning involves infinate objects in finite space. How could infinate space be full? There can be no max capacity because there is infine room, never ending. If this space never ends, and there is a snowflake every two inches, then mathematically there is still infanite snowflakes.

Ummm i don't know how you interperated my posts as but i never ment it to apear as my reasoning involved infinite objects in finite space. It was Finite objects in infinite space.
And if there was a snowflake every two inches spanning across the infinity of space then you would still have a 2 inch gap were more snowflakes COULD be. This just goes into a big mess because if you can have MORE than infinity it wasnt infinity to begin with which is why it supports there is not a infinite amount of atoms to fill the universe. Its like saying Infinity + Infinity. double infinity? no

 

[TR345]

I'm just saying that mathematically there would still be infinate snowflakes. I'm not saying that makes sense. All your saying is that it doesn't make sense to you. So maybe you ought to not believe in an infinate space.

 

[Feonix12]

I'm just saying that mathematically there would still be infinate snowflakes. I'm not saying that makes sense. All your saying is that it doesn't make sense to you. So maybe you ought to not believe in an infinate space.

It doesn't make sense to anyone, nobody knows any of these idea's. I thought/think that all matter came/comes from the big bang theory and the "dark universe" was already there before this event.

 

[Chronos]

I'm surprised no mention has been made of Olber's Paradox. The universe cannot be infinitely large, old, and homogenous.

 

[Garth]

I'm surprised no mention has been made of Olber's Paradox. The universe cannot be infinitely large, old, and homogenous.

Actually the universe cannot be both infinitely large and old and also static if the sky is dark at night.

The red shift of light from distant stars in an expanding and infinitely large and old universe may be enough to attenuate the light flux below observable limits.

Garth

 

[JesseM]

Ummm i don't know how you interperated my posts as but i never ment it to apear as my reasoning involved infinite objects in finite space. It was Finite objects in infinite space.
And if there was a snowflake every two inches spanning across the infinity of space then you would still have a 2 inch gap were more snowflakes COULD be. This just goes into a big mess because if you can have MORE than infinity it wasnt infinity to begin with which is why it supports there is not a infinite amount of atoms to fill the universe. Its like saying Infinity + Infinity. double infinity? no

How is it relevant that you'd have gaps where more snowflakes "could" be? The universe has no obligation to fill up all of space, in the real world we can see that there is a certain density of hydrogen atoms even in deep space, so there's plenty of empty space where more hydrogen atoms could be, but aren't. There is nothing illogical or contradictory about the idea that the universe continues on this way forever, giving you an infinite number of hydrogen atoms but plenty of empty space, with a similar average density everywhere.

If you think there's something mathematically impossible about the idea that you can add to infinity and still get infinity, you're wrong. For example, the number of odd numbers is infinite, and the number of odd+even numbers is also infinite.

 

[TR345]

Yeah but numbers aren't physical, and don't really exist.

Also if empty space isn't physical and is truly nothing, then it doesn't exist either. Right? Can nothing exist?

 

[JesseM]

Yeah but numbers aren't physical, and don't really exist.

Math is used to model reality in physics though, so it shouldn't surprise you that physicists have no problem with the notion of an infinite universe. And infinity itself is a mathematical concept. Why do you think that it would be impossible to have an infinite number of physical objects, or that it should be impossible to have room to add more objects if the number was already infinite, when this isn't true of the mathematical notion of infinity? If every star was assigned a number and there were an infinite number of them, wouldn't it be true that there'd be an infinite number of odd-numbered stars, and an infinite number of even-numbered stars?

Also if empty space isn't physical and is truly nothing, then it doesn't exist either.

What does "nothing" mean? This seems like a word-game. Empty space can have meaningful properties of its own in physics, such as curvature.

 

[TR345]

It doesn't surprise me mathematically, but when trying to comprehend it as reality it doesn't make sense to me.

I just also think that the idea of the vacuum being just space and having no substance is equally confusing. How can something that doesn't exist have properties. It's a similar confusion to comprehending infinty.

I'm not trying to prove any point as my opinion is that an infinate amount of objects can exist in infinate space without filling it up completely. I'm just trying to hit the question with all angles to try and make sense of it.

 

[Theinvoker]

Hiya,

I'm just starting out my travel down the road of physics and the universe, but maybe that might be to my advantage here :)
Lets use a infinatly long hollow steel bar instead of a hose as it makes my "explanation" easier to understand.

Assumming every dimension universe is infinate, then to calculate its volume you would have to calculate something along the lines of;

Infinity x Infinity x Infinity = Infinity

Your bars volume will be;

2cm x 2cm x Infinity = Infinity

You only fill 2 of the dimensions. The universe would only be full if all dimensions were filled (including dimensions such as time), your tube only fills a 2cm by 2cm wide area at a point in space.

This leaves you saying, yes but I still have an infinate volume in the tube. True but try not to think of infinity as a number as such, more as a description of something that does not end. Your infinate amount of water is contained within the pipe that goes on forever, You could attach a tap to it and fill the universe with your infinate supply of water (though it would also take an infinate amount of time, as this is dimension needs to be filled with infinity aswell), but you could also turn the tap off again and contain it withing the 2cm tube.

*Puts on his flame proof suit expecting posts about how there are more than 3 dimensions to space and other flaws* :)

 

[keinve]

if it is infinate, it would take up all space. if space is infinate, then the infinate object would increase proportionally. it is impossible for there to be more than 1 infinate object, as they would have to be increasing inside each other, resulting in higher density, resulting in possible collapse, resulting in an infinate black hole, resulting in it being destroy by it's taking in the universe, resulting in nothing. morbid, no?

 

[jonmtkisco]

Hi folks,

I am quite certain that, in cosmology theories where it matters, it is believed that there can be an infinite number of infinite universes. (For example, the mainstream theory of inflation assumes that there is eternal inflation and an infinite number of "pocket" universes". One infinite universe simply can't exclude the existence of others, because no matter how much content you put in, there's always room for more.

While it's fun to speculate, it's pretty useless to try to tear into this issue. I suppose mathematicians could have defined infinity to mean something other than what they did. But they didn't, so we're just stuck with a truly infinite infinity.

Jon

 

[FunkyDwarf]

Theres also the concept of cardinaility and 'big' and 'small' infinity that perhaps should be dealt with here, although that's more to do with the countability of sets and such. Saying that you can't have an infinite number of things in a finite space isn't true for the simple fact they can be infinitely small which is effecively how we model point particles and use the delta function and whatnot. Interesting discussion ill be watching it closely :)

 

[Hurkyl]

if it is infinate, it would take up all space.

Why?

if space is infinate, then the infinate object would increase proportionally.

What do you mean by "increase"?


keinve, did you read this thread at all before you decided to chime in? :grumpy:

 

[Ariste]

if it is infinate, it would take up all space. if space is infinate, then the infinate object would increase proportionally. it is impossible for there to be more than 1 infinate object, as they would have to be increasing inside each other, resulting in higher density, resulting in possible collapse, resulting in an infinate black hole, resulting in it being destroy by it's taking in the universe, resulting in nothing. morbid, no?

No.

Consider a universe with 3 infinite dimensions, and consider a 2 inch x 2 inch plank with infinite length. The plank has infinite volume and yet does not occupy all the volume in the infinite universe.