How Can the Distance Between Two Points Exceed the Size of the Universe?

[LoudAmp]

I’m learning about cosmology and I’m struggling understanding the size and shape of the universe.

If the universe has a radius of approximately ~46 billion light years, then the maximum distance between any two points in the universe today is ~92 light years. It follows then, that if I am standing at Point A and Point B is ~46 billion light years away, while Point C is ~46 billion light years in the exact opposite direction of Point B, then the distance of B to C would be ~92 billion light years. However, if my friend is standing at Point C, then they would measure Point A at ~46 billion light years away and Point D in the opposite direction of Point A at ~46 billion light years away. Thus, the distance from A to D would be ~138 light years, making it longer than diameter/length of the universe. How can the distance of A to D, exceed the size of the universe?

Am I making the mistake of treating particle horizon as the radius of the universe?

 

[mal4mac]

The simplest answer is: we don't know the size and shape.

That said, current best guess is that it's infinite in size and flat in shape. So let's go with that for the moment.

That figure of 46 billion light years is the radius of the observable universe.

The distance of A to D exceeds the size of the observable universe, and that's fine. There's a lot of room in an infinite universe!

 

[PeroK]

I’m learning about cosmology and I’m struggling understanding the size and shape of the universe.

If the universe has a radius of approximately ~46 billion light years, then the maximum distance between any two points in the universe today is ~92 light years. It follows then, that if I am standing at Point A and Point B is ~46 billion light years away, while Point C is ~46 billion light years in the exact opposite direction of Point B, then the distance of B to C would be ~92 billion light years. However, if my friend is standing at Point C, then they would measure Point A at ~46 billion light years away and Point D in the opposite direction of Point A at ~46 billion light years away. Thus, the distance from A to D would be ~138 light years, making it longer than diameter/length of the universe. How can the distance of A to D, exceed the size of the universe?

Am I making the mistake of treating particle horizon as the radius of the universe?

Think of the same question on the surface of the Earth. There is a maximum distance between any two points on the Earth's surface.

 

[Bandersnatch]

Am I making the mistake of treating particle horizon as the radius of the universe?

The simplest answer is: we don't know the size and shape.

Actually, the simplest answer is "yes".

 

[mal4mac]

Think of the same question on the surface of the Earth. There is a maximum distance between any two points on the Earth's surface.

What does this have to do with a flat, infinite universe?

 

[Chronos]

As you look into the distant reaches of the universe, you see objects as they appeared in the past. Due to expansion, they are now more distant than they were when they emitted the light you now see. Finally, you see the CMB, which is a baby picture of the universe. For the layperson accustomed to rulers and such, the natural question is 'just how far away is that puppy?'. The scientist hesitates momentarily then says 'right now, about 46 billion light years'. The scientist could have quibbled and caveated a lengthy explanation of expansion, redshift and the Hubble flow, but, sensing the futility of such an effort, gave a ruler distance - despite realizing how inappropriate it is. It's like seeing a baby picture and asking 'how far away is that baby?'. The queried party might reply '46 miles' - all the while wondering what kind of question is that? The observable universe has an age, not a size or distance to some phantasmal 'edge'.

 

[mal4mac]

I think it's quite a reasonable question! It's like a ship appearing over the horizon and someone asking "How far away is the horizon, then?" It's perhaps less interesting than asking "How far away is the edge of the earth?", but it's still interesting, & perhaps useful, to know the furthest distance we can see from the shore.

It might even be useful to ask "How far is that baby?" Maybe you want to give the baby a birthday present and wondering whether to walk, drive or fly...

Anyway, jargon busting page here with nice animations of "Hubble flow", etc:

http://astronomy.swin.edu.au/cosmos/h/hubble+flow

 

[aboro]

It's like seeing a baby picture and asking 'how far away is that baby?'. The queried party might reply '46 miles' - all the while wondering what kind of question is that? The observable universe has an age, not a size or distance to some phantasmal 'edge'.

Chronos - - you have a great way of explaining difficult concepts regarding cosmology in simple terms to a layman.

 

[Chronos]

I do try to simplify things, probably too much at times.