# Size of the Universe is 13.7 billion light years?

## Main Question or Discussion Point

Hi.

I'm not a student of physics, so please forgive me for my ignorance. I only have a very simple question.

If the observable universe is about 93 billion light years in diameter, how could the universe have reached that size in only 13.7 billion light years? Doesn't it stand to reason that the size of the universe is only 27.4 billion light years in diameter, OR it's about 41 billion years old?

Is this a stupid question?

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Hi there, I'm a newbie too, so go easy on me.

So the Universe is 13.7 billions years old, as you said, and it has been expanding from the very moment it came into existence. If you take a point in time, relatively soon after the beginning of the Universe, say, a couple of million years, and say that the Universe was about 1000 times smaller then, than it is today, so 1 light-year then, has now been stretched to become 1000 light-years now. So the light hasn't physically travelled the 93 billion light-years to us, but the starting point of that light photon has moved that far away.

Sorry for my poor explanation, i'm only 16 so I haven't been taught anything about this, but have picked it up from various places. (Also sorry if I am entirely wrong :P)

EDIT: Just realised all the other threads on this topic, so bleh :P

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I guess others have wondered the same thing. Although, I don't much like their shaky explanations.

Chronos
Gold Member
The 93 billion light year thing is a size 'now' estimate. It is an unnecessarily confusing description of the size of the universe. The observable universe is fixed at 13.7 billion light years in all directions from earth. Most of the observable universe is currently receeding faster than the speed of light, as measured by redshift. This is possible because light from these objects reached us before they started receeding at superliminal velocities. This is generally referred to as causal contact. Light from these bodies will continue to reach us forever, it will merely become increasingly red shifted [and time dilated] until it becomes too faint to detect.

What do you mean by this:

"Most of the observable universe is currently receeding faster than the speed of light, as measured by redshift."

???

Chronos
Gold Member
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That second article makes it very clear how so much space was created in so little time. Thank you.

Here is another question:

How can astrophysicists describe the universe as infinite and expanding at the same time? If the universe is already infinitely large, how could it be expanding? Where is it expanding to? ...another infinity?

The 93 billion light year thing is a size 'now' estimate. It is an unnecessarily confusing description of the size of the universe. The observable universe is fixed at 13.7 billion light years in all directions from earth.
Aren't you confusing the light-travel time with the actual distance to the observed objects? Because of the Universe's expansion since the Big Bang light from 13.7 billion years ago would reach us from objects now 3 x 13.7 billion light-years away - BUT that light can't reach us. Firstly, it's infinitely red-shifted, and secondly there's the glow of the Big Bang itself in the way. All the opaque plasma of the era of decoupling of light and matter means the Big Bang is forever hidden from electromagnetic vision. At best we see the surface of last-scattering, when light and matter went their separate ways, and that's at a red-shift of about ~1,000, producing the Cosmic Microwave Background. It's the practical limit of vision backwards to the Big Bang.

Most of the observable universe is currently receeding faster than the speed of light, as measured by redshift. This is possible because light from these objects reached us before they started receeding at superliminal velocities. This is generally referred to as causal contact. Light from these bodies will continue to reach us forever, it will merely become increasingly red shifted [and time dilated] until it becomes too faint to detect.
Assuming the cosmic expansion keeps accelerating that is. If expansion slows, halts and reverses at some future epoch, then the distant Universe may return to view.

marcus
Gold Member
Dearly Missed
Aren't you confusing the light-travel time with the actual distance to the observed objects? Because of the Universe's expansion since the Big Bang light from 13.7 billion years ago would reach us from objects now 3 x 13.7 billion light-years away - BUT that light can't reach us. Firstly, it's infinitely red-shifted, and secondly there's the glow of the Big Bang itself in the way. All the opaque plasma of the era of decoupling of light and matter means the Big Bang is forever hidden from electromagnetic vision. At best we see the surface of last-scattering, when light and matter went their separate ways, and that's at a red-shift of about ~1,000, producing the Cosmic Microwave Background. It's the practical limit of vision backwards to the Big Bang.

Assuming the cosmic expansion keeps accelerating that is. If expansion slows, halts and reverses at some future epoch, then the distant Universe may return to view.
Graal, what you say is right on of course. According to standard cosmology, the current distance to the farthest stuff we can see is about 46 billion LY. This is the radius of the observable universe. (According to the consensus model and the way distances are normally quoted in scientific writing.)

It's evident that you realize this and know the basic definitions---the particle horizon, the (slightly smaller) distance to the surface of last scattering. You sound like a pro (that's not a question, just an observation.) Thanks for helping keep the discussion on track!

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marcus
Gold Member
Dearly Missed
Hi there, I'm a newbie too, so go easy on me.

So the Universe is 13.7 billions years old, as you said, and it has been expanding from the very moment it came into existence. If you take a point in time, relatively soon after the beginning of the Universe, say, a couple of million years, and say that the Universe was about 1000 times smaller then, than it is today, so 1 light-year then, has now been stretched to become 1000 light-years now. So the light hasn't physically travelled the 93 billion light-years to us, but the starting point of that light photon has moved that far away.

Sorry for my poor explanation, i'm only 16 so I haven't been taught anything about this, but have picked it up from various places. (Also sorry if I am entirely wrong :P)

EDIT: Just realised all the other threads on this topic, so bleh :P
Matt, that is a really clear explanation. Don't worry about there being other threads. People keep coming in with the same confusions and they benefit from a concise response like yours instead of being give a link.

You are talking about redshift z = 1000 when distances were 1000 times smaller (well, 1001, there is that z+1 convention )
You guess it refers to a time within a million years or so from expansion-start. Why not check that: google "wright calculator" and put in z = 1000.
I guess it will tell you the expansion age at z = 1000 was around 400,000 years. Less than a million actually.

OK so you say you are self-educated about cosmology. Sounds like you did a good self-ed job so far. Welcome. Now how would you respond to Beaudoin's problem. He thinks the "big bang" was like an explosion of stuff flying out into space from a central point. This is a common confusion we get constantly from newcomers. He thinks if it was stuff flying outwards it cant travel faster than c, so he thinks expansion is limited by c.

How would you respond? Even if I try, consider posting your response. It could actually be more helpful.

...If the observable universe is about 93 billion light years in diameter, how could the universe have reached that size in only 13.7 billion light years? Doesn't it stand to reason that the size of the universe is only 27.4 billion light years in diameter, OR it's about 41 billion years old?
...
Hi Beaudoin. If you mean a period of time, please be clear and say "in only 13.7 billion years..." Don't say light years, if you mean time.

Be careful to distinguish between the observable part and the whole universe. In standard cosmology the size of the observable is not the whole story.

When pop-sci media talks about the observable they are talking about the stuff that we see. The stuff we got light from already, and the space that that stuff occupies, if you can imagine space (the geometry, the distance relations) as having a kind reality.

(General) relativity says geometry is dynamic, it changes. Distances can expand and contract---and that can happen without stuff actually moving in the ordinary sense.
Changing geometry is governed by an equation first written in 1915 by Einstein, which has been checked over and over again.

So the expansion of distances is not governed by the Special (1905) relativity speed limit. That only applies when there is some matter actually traveling thru space, approaching some destination.

In General (which trumps 1905-special) there is no limit on how rapidly distances can expand. So not to worry.

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Chronos
Gold Member
Here is another question:

How can astrophysicists describe the universe as infinite and expanding at the same time? If the universe is already infinitely large, how could it be expanding? Where is it expanding to? ...another infinity?
The problem is we cannot tell the difference between a very large, or infinite universe by curvature alone. Right now the curvature tensor is too close to 1.000 to discern the difference. I guess the easy answer is it is possible for the universe to be observationally finite, but not spacially finite. That is what the math tells us. We know the observable part is finite because of the surface of last scattering [source of the CMB].

OK so you say you are self-educated about cosmology. Sounds like you did a good self-ed job so far. Welcome. Now how would you respond to Beaudoin's problem. He thinks the "big bang" was like an explosion of stuff flying out into space from a central point. This is a common confusion we get constantly from newcomers. He thinks if it was stuff flying outwards it cant travel faster than c, so he thinks expansion is limited by c.

How would you respond? Even if I try, consider posting your response. It could actually be more helpful.
Thank you Marcus

My only real attempt of a response would be to say that would be to say that no matter or "stuff" was moving any faster than the speed of light, but it was the actual dimension of space itself that was unfurling out. There was no real central point due to the fact that there was "nothing" before it, the expansion just happened everywhere.

Again, please correct me if i'm wrong, i'm only clutching at straws here

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marcus
Gold Member
Dearly Missed
... would be to say that no matter or "stuff" was moving any faster than the speed of light, but it was the actual dimension of space itself that was unfurling out. There was no real central point due to the fact that there was "nothing" before it, the expansion just happened everywhere.
...
Sounds good to me. Even though you may not yet had a calculus course or worked with simple differential equations, you might begin to expose your self to things like the Friedman equations and the Friedman metric---the distance function---which has an increasing term a(t) called the scale factor, which multiplies spatial distances.

When people say "expanding universe" that is just words and the real mathematical meaning is simply that this a(t) scalefactor is an increasing function of time. You may be aware of this already.

And the Friedman equations are simple differential equations that give you the slope of a(t), the rate it increases. So they determine the expansion history. But you need freshman calculus. You have to be comfortable with taking the first derivative and the second derivative of a real-valued function.

Still, at whatever stage you are at, you could look at the wikipedia page for "friedman equations". That's the heart of cosmology. Those equations are what the online calculators implement, so you can work with the model hands-on without having to solve equations and actually do the calculus yourself---a great blessing . Equations are to understand, not solve!
To get the calculators you google "wright cosmo calculator"
or to get morgan's you google "cosmos calculator".
I can't remember if I mentioned that to you.
Anyway it is a big help to get off from thinking in words like "expanding" and actually get your eyes and hands on the mathematical model that is behind the words.

Thanks again, I shall check out the wiki page. I think i'll leave differential equations and all that until after my exams, because i'll hopefully actually be taught them in A level Maths.

Oh, and just to clarify, I haven't self-educated as such, just read a few books and articles on what interests me. I am hoping to do Physics (possibly with astrophysics and cosmology, or nanotech) at university if I am lucky enough to have the chance. :)