How do we know the universe is infinite?

[bcrowell]

But what is actually expanding, if space is infinite anyway?

Have you considered the analogy I suggested in #28?

And why doesn't the above just mean that two points are moving away from each other?

When we describe space as expanding, it's just an optional interpretation. General relativity doesn't actually say whether space is expanding or not. It makes predictions about directly observable quantities, such as redshifts. Another good example is that if a supercluster of galaxies is unbound or weakly bound, cosmological expansion can disrupt it and break it up. Whether you want to label the effects in these two examples as expansion of space is up to you.

 

[Rupert Young]

Have you considered the analogy I suggested in #28?

I didn't understand the relevance.

When we describe space as expanding, it's just an optional interpretation. General relativity doesn't actually say whether space is expanding or not. It makes predictions about directly observable quantities, such as redshifts. Another good example is that if a supercluster of galaxies is unbound or weakly bound, cosmological expansion can disrupt it and break it up. Whether you want to label the effects in these two examples as expansion of space is up to you.

An optional interpretation doesn't sound very scientific. If space is not expanding wouldn't that mean that light travels faster then we thought; traveled 46 billion light years in 13.7 billion years?

 

[bcrowell]

I didn't understand the relevance.

It's a similar example because it's an infinite thing expanding.

In any case, if you think that it's inherently illogical for an infinite thing to expand, then the burden is really on you to explain why. It may feel uncomfortable to you, but that's not a logical argument.

An optional interpretation doesn't sound very scientific. If space is not expanding wouldn't that mean that light travels faster then we thought; traveled 46 billion light years in 13.7 billion years?

General relativity doesn't have a way of defining the velocity of an object relative to a distant object. Therefore the prohibition on motion faster than c can't even be defined except on a local basis.

 

[William White]

It's a similar example because it's an infinite thing expanding.

In any case, if you think that it's inherently illogical for an infinite thing to expand, then the burden is really on you to explain why. It may feel uncomfortable to you, but that's not a logical argument.

the distance between two points moving apart, where one is at infinity, cannot be defined; therefore you cannot define the velocity at which the points are moving apart; nor the time it takes. Everything becomes undefined. Unless you wave your hands in the air and say its "infinte", but that's not a logical argument.

 

[Finny]

We observe that the universe is homogeneous and isotropic on large scales, and we also assume by default that it has a trivial topology (i.e., it doesn't do anything funny like wrapping around on itself like a torus).

Are you excluding the possibility of wormholes? Those seem 'non trivial'...but maybe not technically??

BTW, your user icon looks like a clone of my terrier mutt -- very cute!

Thanks. Ebony was 'senior doggie' among our three until a few weeks ago. Smartest for sure. She was almost 15 ...we really miss her. What's almost worse, my wife now talks to me instead of the dog! So I am trying to hang out in these forums and appear busy, hoping not to be noticed.

...But what is actually expanding, if space is infinite anyway?

Distances grow. The easiest way to think about infinity or an 'infinite anything' is describing something without limit. Without bounds. I'm sure any mathematicians here will cringe...they have dozens of different concepts for infinity. I stumbled onto one discussion about infinity not so long ago in these forums...and got a headache in reward.
Physics is like peeling an onion...every layer reveals another layer...more questions emerge when one appears answered...sigh...

 

[bcrowell]

the distance between two points moving apart, where one is at infinity, cannot be defined; therefore you cannot define the velocity at which the points are moving apart; nor the time it takes. Everything becomes undefined. Unless you wave your hands in the air and say its "infinte", but that's not a logical argument.

Nobody said anything about a point at infinity.

 

[William White]

Nobody said anything about a point at infinity.

no you are playing philosopical games

you said an infinite "thing" is expanding (which is wooly in the extreme)

if this thing has no points at infinity, it is not a thing nor is it infinite. You said somebody was being illogical, yet use words like "thing" to describe something with a size (infinite) but no points.

you can of course, use other nouns instead of thing, and instead of points, but the principle is the same

 

[bcrowell]

Are you excluding the possibility of wormholes? Those seem 'non trivial'...but maybe not technically??

The general term for this sort of thing is topology change. There are both kinematic and dynamical reasons why we don't expect topology change to be possible. Two examples of topology change are: (1) a closed universe becoming open (or vice versa), and (2) creating a wormhole that didn't previously exist.

Standard cosmological models are homogeneous, so they don't have wormholes in them -- if wormholes do exist, they're just at a smaller scale, a level of granularity that we aren't considering.

Thanks. Ebony was 'senior doggie' among our three until a few weeks ago. Smartest for sure. She was almost 15 ...we really miss her. What's almost worse, my wife now talks to me instead of the dog! So I am trying to hang out in these forums and appear busy, hoping not to be noticed.

I'm sorry to hear about her death. So the icon is sort of a memorial? :-( My wife and I have been debating the extent of the resemblance between our dog and yours. We've always figured our dog, Lucy, is half schnauzer, but we don't know. Her face looks almost identical to Ebony's to me. Lucy has a white chest and paws, and a tail that curves over like a question mark. She's only 2, so I'm hoping we have many more years with her.

 

[bcrowell]

no you are playing philosopical games

You can like or dislike philosophy, but a hallmark of philosophy is that philosophers try very hard to define their terms carefully. I've defined my terms carefully, but I don't see that you have.

if this thing has no points at infinity, it is not a thing nor is it infinite.

I defined in #28 what I meant by an infinite universe. Your quoted statement is false according to the definition I gave. A simpler example is that by the definition I gave, the real number line is infinite, but it has no points at infinity.

 

[PeterDonis]

Thread closed for moderation.