How Can We See Galaxies 47 Billion Light Years Away When the Universe is Only 13 Billion Years Old?
This is my second post in the Just Science Week Challenge.
This 2003 paper in Physical Review Letters puts a lower limit on the size of the universe at no smaller than 46.5 billion light years in radius. If the universe is geometrically flat, that is.
In this video I made on the Hubble Deep Field, I mentioned this number and was immediately inundated with questions and comments from people screaming that that number could not possibly be correct. How can the universe be that big if the fastest anything can travel is the speed of light? The universe simply CAN’T be larger than the distance light travels during age of the universe, right?
Wrong.
It is true that the universe is 13.5 billion years old, and it is also true that nothing can travel faster than the speed of light. But it does NOT follow that the size of the universe is simply the distance light traveled in 13.5 billion years. You can’t stop there. Why?
Because the universe is expanding, and has been for 13.5 billion years.
Remember yesterday’s post? Everything in the entire universe is flying away from each other at a rate linearly proportional to its distance. That’s Hubble’s Law. The distance that light has to travel over time is continuously getting bigger and you MUST take that into account.
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Remember in my last post, we’ve established that the universe is expanding at roughly the Hubble Constant, and that number is a function of time. It matters WHEN you take your measurement of the redshifts of far away galaxies. Right now, the universe is expanding at about 71 km/sec/Mpc and is accelerating.
A somewhat simpler way to think of the expansion rate of the universe is that it expands at roughly the age of the universe to the 2/3 power: AgeOfUniverse^(2/3). Unfortunately, it’s not simply a plug and chug formula, since the expansion is occurring continuously, you need to apply some calculus. Here’s the formula, but I’ll go through a simple example a little later:
Illustration Credit: Ned Wright
The above integral just takes the ratio of elapsed expansion time to the age of the universe raises it to the 2/3 power and does this over the entire time the expansion is occurring.
What all of this means is that whenever you discuss the size of the universe, you need to apply a scale factor that is relevant TO THE TIME you are interested in. The issue of when is very important because the size of the universe, and the rate at which it was expanding has changed since the universe began.
So, for RIGHT NOW, the size of the universe has expanded to roughly 46.5 billion light years since the Big Bang.
Let’s break down the above integral into some smaller intervals and watch what happens. Let’s use 13 billion years as the age of the universe and let the universe expand for an average of five billion years at three different points in time: 2, 7, and 12 billion years after the Big Bang:
- At age of universe = 2 billion light years: the universe has expanded by a factor of (13/2)^2/3 = 3.48
- At age of universe = 7 billion light years: the universe has expanded by a factor of (13/7)^2/3 = 1.51
- At age of universe = 12 billion light years: the universe has expanded by a factor of (13/12)^2/3 = 1.08
So combining these scale factors over the two intervals above, the universe has expanded to a size of:
(average distance light travels over interval of interest) * (sum of all scale factors).
Plugging in the numbers (we used an elapsed time interval of 5 billion years):
(5 billion light years) * (3.48+1.51+1.08) = 30.37 billion light years.
The 5 billion light year number above is the average distance light traveled in 5 billion years so the units are in light years.
Now, this is a discreet example, taking only three points in time, but already we have a number bigger than 13 billion light years. Since the universe is expanding continuously, we actually need to do the integral above and when you do that, the answer approaches 47 or so billion light years.
Actually, this is a little misleading, the number cited in the above paper does a different analysis and I’m doing something a little different that what the authors of that paper did, so I’m trying to make a number fit that was derived using different techniques in my example above and it won’t work out that way. Still, the end results are similar and nothing is really lost by doing that.
But, ignoring the details for a minute, what I’m really trying to do here is show that the size of the universe isn’t simply the light travel time over the age of the universe. The expansion of the universe requires that you apply a scale factor as outlined above.
If the math is confusing you, just remember this: that scale factor is important. It accounts for the distance the universe has expanded over the time period you’re interested in. It doesn’t go far enough to say that the size of the universe is simply the distance light travels over the course of the age of the universe. Since the creation of time, everything has gotten farther apart, remember Hubble’s Law: everything is speeding away from everything else, all the time.
So, when the Hubble telescope took the deep field images, it provided us with the deepest views we’ve ever seen into the universe. Those galaxies were approaching the farthest edges of our cosmic home, and they weren’t 13.5 billion light years away, they were much, much farther.
UPDATE: Here’s a good graph I found on Universe-Review.ca, they have kindly given permission for me to post this.
Illustration Credit: Universe-Review.ca
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11 opinions for How Can We See Galaxies 47 Billion Light Years Away When the Universe is Only 13 Billion Years Old?
r06u3AP
Feb 12, 2007 at 8:37 pm
You have provided us with an excellent description of why the SIZE of the Universe is greater than 13.7 Glyr in radius. But the size of the Universe is NOT in dispute. The scale factor due to the expansion is WELL UNDERSTOOD (at least, I THINK that I understand it.)
But you entitle this article “How Can We SEE Galaxies 47 Billion Light Years Away When the Universe is Only 13 Billion Years Old?” and your final paragraph states:
“…the Hubble telescope … provided us with the deepest views we’ve ever SEEN … Those galaxies were approaching the farthest edges of our cosmic home, and they weren’t 13.5 billion light years away, they were much, much farther.”
I really don’t think so, Tony!
The argument is about what is “OBSERVABLE”. OF COURSE there are objects out beyond the horizon! OF
COURSE they’re greater than 13.7 Glyr away. But do we actually see them? NO! That’s why it’s an event horizon! There’s only been 13.7 Billion years worth of time for ANY electromagnetic emission from ANYTHING to travel across the Universe, regardless of the geometry and regardless of the
expansion.
Let’s see if I can simplify the problem. Let’s call the age of the Universe a “Cosmic Epoch”. Let’s further say that there are two objects, shortly after the big bang that are relatively close to each other. Now, follow what happens as the expansion pulls them apart to a distance of
2 light-epochs from each other. The expansion is nearly constant, but since more and more expanding space is being added between them, the rate at which they separate accelerates as time marches on until they each go beyond their mutual event horizon, when their velocity relative to each other exceeds the speed of light. Just prior to that point, cosmically speaking, the image of one as seen from the other is just 1 Cosmic Epoch old and is doppler shifted down far into the microwaves if not lower. It’s just like watching something fall into a black hole approaching the horizon.
So, there is obviously no way that the image of one object as seen from the other object can ever be greater than 1 epoch old; the universe has only been around that long! Which is also why you will never ever observe anything beyond the cosmic event horizon, which must >> of necessity
tony
Feb 12, 2007 at 10:26 pm
@r06u3AP:
Excellent comment. Thanks for taking the time to leave it, I really appreciate it.
I used to argue the same thing, until I read some texts and discovered that we can actually see these things from these distances.
I will admit, that this topic is stretching my writing ability, so let’s see if this helps (taken from Ned Wright):
“Another way of seeing this is to consider a photon and a galaxy 42 billion light years away from us now, 14 billion years after the Big Bang. The distance of this photon satisfies D = 3ct. If we wait for 0.1 billion years, the Universe will grow by a factor of (14.1/14)^2/3 = 1.0048, so the galaxy will be 1.0048*42 = 42.2 billion light years away. But the light will have traveled 0.1 billion light years further than the galaxy because it moves at the speed of light relative to the matter in its vicinity and will thus be at D = 42.3 billion light years, so D = 3ct is still satisfied.”
The key phrase there is: light is moving from the distant galaxy “relative to the matter in its vicinity”.
Taken from Ned Wright’s Cosmological FAQ:
http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN.
He is talking about the integral that I left above (which was also taken from his FAQ).
Does this help?
Thanks again for leaving that comment!
tony
Feb 12, 2007 at 10:31 pm
@r06u3AP:
BTW, what’s the story behind that handle? It is quite unusual, I’ve been trying to figure it out, but I think it’s an inside joke or something, I’d have to know you to get it.
r06u3AP
Feb 13, 2007 at 1:14 pm
You are very perceptive, the handle is a whimsical sort-of inside joke. The hacker-esque “R06u3AP” refers to unauthorized wireless Access Points sometimes installed by people for convenience at their workplace, unbeknownst to their boss. The trouble with doing that is that they expose the company network and everything on it to unauthorized access by others outside the facility. Hence, they are termed “rogue AP”s. As a worker in the IT biz, dealing with wireless networks and the detection of such rogue APs, I thought it made a neat handle.
BTW, I noticed that my original comment didn’t post in its entirety, I don’t know if there’s a limit or if you cut it off. In any case, I’ll attempt to post the rest of it here:
…..Which is also why you will never ever observe anything beyond the cosmic event horizon, which must >> of necessity
r06u3AP
Feb 13, 2007 at 1:15 pm
ALWAYS be 1 light-epoch away in all directions, receding from the observer at the speed of light.
To see anything more distant would require that the light from it travel backward in time! If there is any other way for EM radiation of any wavelength to have travelled for longer than 13.7 billion years in our Universe, I certainly cannot see how.
If I’m wrong, just shoot me, because the reason I’m wrong must be totally beyond my ability to comprehend.
I also have a problem with the article “Constraining the Topology of the Universe”. Now, maybe I’m just not smart enough to get my head around all the fancy math and all but I always thought that EM radiation obeyed the principle of superposition such that even if you do have patterns of the CMB sky repeating around the 2-sphere they would necessarily have to combine additively(?) with what is naturally there to begin with thus yielding an essentially random pattern with no detectable repetition anyway. But I admit, I am by no means a brilliant degreed cosmologist so I’m sure that those more learned than I would surely have thought of that all too obvious hitch and clearly knows how to extract random patterns out from, uh….., random patterns???
Huh? Oh well, like I said, just shoot me because I’m just too dumb to understand it.
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Dominic
Dec 2, 2007 at 11:14 pm
I’m just curious,if the big bang happened hurling our matter (planet) at the speed of light and then a millionth of a milisecond later there was a flash of light we would never see anything untill we slowed down to sub light speed relative to said light,so how can anyone know for sure how old any observed light really is without knowing how the universe accelerated or decelerated relative to the singularity?
James Dunn
Dec 30, 2007 at 10:09 am
I only have a trivial understanding of what is currently known about the Universe. However.
1) My problem with your supposition is that we are using a scale factor as a fudge factor.
2) The Hubble Telescope can detect energy that appears to be coming from beyond the limits of the distant galaxies it can see. So the size of the Universe is not known as yet.
3) The apparent expansion of the Universe is not as yet conclusive.
4) After the supposed Big Bang (interesting support, but still a theory), as the energy masses formed varying densities as the energies raced out into space (assuming for the moment that nothing travels faster than the speed of light, even though we now know that is not true; see “entangled pairs”) the energy bundles would dominantly be moving under the speed of light. Since mass at the speed of light supposedly is infinite mass and we would be living in fluidic space.
If the mass is escaping at a rate that continues to allow accelerating expansion, then at no time would the masses have slowed down. Unless there were multiple forces involved that acted on the masses non-linearly. As such, no simple calculation would explain the age of the Universe.
As I said, I only know a trivial amount regarding the Universe, but the supposition that the Universe is of any specific age seems to be nieve given all the variables we do not know about.
With respectful guarded interest,
James
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