# Q & A: Why so far across visible universe?

Q:
the universe is estimated to be about 15 billion years old. one would assume a visible universe of roughly 30 light years across. yet it is more like 93 light years across. why is that?
- Tyler Newton (age 18)
A:

The first thing that's hard to grasp about this sort of question is that the answers are very highly dependent on your choice of coordinate systems, and the same laws of physics allow us many choices, convenient for different purposes. Here's a nice article on the coordinate system choices: Part of the problem is that if you say it's 93b l-yr across now, what you mean by "now" isn't well defined for distant objects.

Let me try to illustrate the issue using special relativistic coordinates, which are not actually part of the family of general relativistic coordinate systems but are simple enough to give you a feel for what's up. Let's say the universe is 14 b yr old. Let's approximate and say that there hasn't been acceleration since very shortly after the Big Bang. Then light getting here now from somebody who initially was moving away from us at almost c left about 7 bil yr ago, after the source got about 7 bil l-yr away from us. By "now" that same thing would be 14 bil l-yr away from us. So you'd be tempted to say we can see things that are "now"  as far apart as 28 bil l-yr. However, if by "now" you mean "14 bil yr old in its own frame" then there's a big difference. The clock in that source, moving away from us at nearly c, is running very slow, according to us. By the time it reads 14 bil yr, it's much father away from us.

In genuine coordinates, this special relativistic calculation doesn't apply. Nevertheless, when something is 14 bil yrs old in its own frame, that's much later than when its that old in the sort of frame you're tempted to use by intuition. So it's gone much farther away. Is that where it is "now"? As I said, it turns out that question isn't actually meaningful,  since "now" has no absolute definition. However, if we go with the  "same age in its own frame" definition, it does turn out to be ~46 bil ly away, just as you heard. You can see  for a fuller discussion.

Mike W.

(published on 04/28/2013)

## Follow-Up #1: size of universe

Q:
If nothing can go faster than the speed of light and the universe is 13.7 billion years old, how is it that the universe (entire, not observable) can be greater than 13.7 billion light years across?
- Ty (age 31)
Rancho Cucamonga, CA USA
A:

The law that nothing can go faster than the speed of light applies only to the local speeds. In other words, nobody can whiz past you at faster than the speed of light. The overall expansion of distances in the universe isn't limited by that law. So even for a finite universe an inflationary period can give distances expanding faster than c. Also, we have no compelling reason to think that our universe was finite to begin with. When people talk about how small it once was they're just talking about the part that's visible now.

Mike W.

(published on 01/09/2014)