When people talk about the current size of the observable universe

[TobyC]

Could I just quickly derail this thread and ask that frequently asked question?

When people talk about the current size of the observable universe, are they talking about how far away the furthest objects were when they emitted their light? Or how far away the furthest objects will be now?

 

[JesseM]

Could I just quickly derail this thread and ask that frequently asked question?

When people talk about the current size of the observable universe, are they talking about how far away the furthest objects were when they emitted their light? Or how far away the furthest objects will be now?

How far the furthest objects that we could potentially see (at some point in their past) are at the present cosmological time. To figure out how far they were when the light was emitted, you have to take their present distance and multiply by the "scale factor" which is a function of redshift, see here.

 

[TobyC]

How far the furthest objects that we could potentially see (at some point in their past) are at the present cosmological time. To figure out how far they were when the light was emitted, you have to take their present distance and multiply by the "scale factor" which is a function of redshift, see here.

Great thanks, I was confused by how the observable universe could be bigger than the age, but this explains it

 

[JesseM]

Great thanks, I was confused by how the observable universe could be bigger than the age, but this explains it

Well, in special relativity it wouldn't make sense for the radius of the observable universe to be more than twice the age * c, since we'd just now be seeing the light from something that was 13.7 billion light years away 13.7 billion years ago, and even if that object was moving away from us arbitrarily close to the speed of light it could not have traveled more than an additional 13.7 billion light years in that time. So if you think in those terms, a radius of 46 billion light years should be impossible! But in general relativity it is quite possible for the proper distance to a galaxy to increase faster than the speed of light due to the expansion of space, see the discussion in the third paragraph in this section of the wiki "comoving distance" article.

 

[TobyC]

Well, in special relativity it wouldn't make sense for the radius of the observable universe to be more than twice the age * c, since we'd just now be seeing the light from something that was 13.7 billion light years away 13.7 billion years ago, and even if that object was moving away from us arbitrarily close to the speed of light it could not have traveled more than an additional 13.7 billion light years in that time. So if you think in those terms, a radius of 46 billion light years should be impossible! But in general relativity it is quite possible for the proper distance to a galaxy to increase faster than the speed of light due to the expansion of space, see the discussion in the third paragraph in this section of the wiki "comoving distance" article.

Yeah I'm ok with distances increasing faster than the speed of light, I can understand how that's allowed by general relativity, it's just I still couldn't understand how the observable universe could be bigger in size than twice the age until what you said about the radius being the distance of the further objects now rather than the distance when they emitted the light. Which makes sense really, I just hadn't thought about it properly before.

Just out of interest, in an expanding universe wouldn't the observable universe still be bigger than twice the age even if the distances weren't increasing faster than the speed of light? Because the furthest object will be further away 'now' than when it emitted the light.

 

[JesseM]

Yeah I'm ok with distances increasing faster than the speed of light, I can understand how that's allowed by general relativity, it's just I still couldn't understand how the observable universe could be bigger in size than twice the age until what you said about the radius being the distance of the further objects now rather than the distance when they emitted the light.

When I said that in SR objects shouldn't be at a distance of more than twice the age, I was talking about their distance now, not the distance when they emitted the light. In SR it would be impossible for us to be seeing light from any objects whose distance now is more than twice the age.

Just out of interest, in an expanding universe wouldn't the observable universe still be bigger than twice the age even if the distances weren't increasing faster than the speed of light? Because the furthest object will be further away 'now' than when it emitted the light.

No it couldn't, that was my point. In SR, if we can see the light from an object today, then the distance when it emitted that light can't have been more than 13.7 billion light-years away in a universe only 13.7 billion years old (if it emitted light from greater than that distance, the light wouldn't have had time to reach us by today). So if it was receding at just under the speed of light, its distance today could have increased by no more than an additional 13.7 billion light years, giving a maximum distance today of 13.7 billion + 13.7 billion light years, i.e. twice the age * c.

 

[Ikoro]

it is simply how far into the past we can observe.