Age of the observable Universe?

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1. Aug 1, 2015

G.D.

Forgive my ignorance?.. If we can see 13.8-ish billion light years away how can the universe be the same age? Matter cannot travel at the speed of light, so how are we as far away (in light years) as the universe is old?

2. Aug 1, 2015

marcus

We routinely see stuff that is now between 45 and 46 billion LY away. But we see it as it was around year 380,000 of the expansion, not as it is now.

Relativity allows distances to grow at several times the speed of light---that is not subject to the same rules as ordinary motion, stuff moving thru its surrounding space.

3. Aug 1, 2015

Bandersnatch

Hi G.D., welcome to PF!

Matter did not have to go to the edge of the observable universe before emitting its light. What we see now at the edges of observability (as marcus said, at about 46-ish billion light-years), started already some distance away from the point where we're at now. It emitted its light 13.8 billion years ago when it was about a thousand times closer than it is now (~44 million light years) and kept on moving away as its light kept on moving through the expanding space towards us. By the time the light reached us, after 13.8 billion years of travel, the object that was the source managed to recede to 46 billion light years.

The key point here is that at the time of emission of the light we observe, the stuff in the universe was already spatially separated.

4. Aug 1, 2015

G.D.

Hello and thank you both. So let me see if I've got this. The universe is 13.8 ish billion yrs old, but in that amount of time the universe has expanded to the point where our furthest viewable objects are 46 billionish light years away. Matter can't travel faster than the speed of light, but the space inbetween galaxies can expand faster. So if something is 46 billionish light years away that doesn't mean it's that old.

5. Aug 1, 2015

Bandersnatch

Just to make sure it is clear - while we can say that the farthest object we see is NOW at 46 billion ly because we can calculate how it will have receded, we still only see the light that it emitted 13.8 billion years ago, when it was much closer.

Feel free to ask if you'll have more questions. Although I have to say that this topic is the mainstay of the cosmology section of the forums, so perhaps you'll find your questions already answered in another thread.

6. Aug 1, 2015

marcus

Hi G.D. would you like to know how to calculate that 46 billion LY for yourself? It is a simple integral from early time up to present, so if you have taken (even very beginning level would do) calculus, you might not be put off by the integral and enjoy using it to get the distance to the farthest matter we can see.

there is a website called numberempire.com that does integrals for you online. it's easy to use and free. You just go there, paste or type in the function you want to integrate over some range----and put the limits (start and finish of the desired range) of integration in and press calculate.

Basically the integral is telling you how far a flash of light can travel in 13.8 billion years when it is helped by expansion. You add up all the little cdt steps the light takes multiplied by how much each step gets expanded between the time it takes the step and the present. dt is a bit of time, cdt is the original length of the step, and then there is the expansion factor S(t) and the integral adds all these little S(t)dt steps up. We use units where c=1 so we don't have to include the speed of light explicitly.

If you don't want to bother with the integral yourself, it's fine, there's also an online calculator called "Lightcone" that does all that stuff for you. I keep the link in my PF signature to have it handy.

7. Aug 1, 2015

marcus

http://www.numberempire.com/definiteintegralcalculator.php

What you put in for "function to be integrated" (I'll explain why later) is 1.3*(sinh(1.5*t))^(-2/3)
and because the variable is t you change x to t in the variable box
and for the limits you put in 0.00001 and 0.8

If you want the answer directly in billions of LY you can instead put in 17.3*1.3*(sinh(1.5*t))^(-2/3)

8. Aug 1, 2015

marcus

It may be a little confusing because I'm using a time unit which is 17.3 billion years, to make the formulas simple. On that scale the present is 0.8.
(the universe is still young, only 80% of one of its time units)
and on that scale the universe expands as sinh(1.5t)2/3

So that between time t and the present 0.8 distances get enlarged by the ratio of the two sizes:
sinh(1.5*0.8)2/3/sinh(1.5t)2/3=1.3/sinh(1.5t)2/3. It happens that the present value of that size function is 1.3 so can we put that in for the numerator.

The integral adds each dt step taken around time t, scaled up by the appropriate ratio 1.3/sinh(1.5t)2/3

Last edited: Aug 1, 2015
9. Aug 1, 2015

Chalnoth

What we see are the light rays that have been traveling for about 13.8 billion years.

10. Aug 1, 2015

Chronos

While it is true matter cannot travel that fast there is nothing to prevent empty space from expanding that fast and it carries along the matter embedded in it like a surfboard.

11. Aug 2, 2015

Stephanus

How can we determine that those things are 45 billion ly? The red shift?Doppler?
And from what I learnt in SR Forum.
Supposed V = 0.99c, so red shift is $k = \sqrt{\frac{1+V}{1-V}} = 14$ Even if its V is 0.99....99c still if we multiply it by the age of the universe it can't be farther than 13.5 billion ly.
So how can we know that this particular thing is farther than 13 billions ly?

12. Aug 2, 2015

Stephanus

Yes, matter can't travel faster than the speed of light, it's the space that is expanded.
But how we measure that the object is 46 billion lys?

13. Aug 2, 2015

Stephanus

Ahh, that's the answer. Sorry, just haven't read the incoming threads. Is it the combination of doppler shift factor and hubble law?

14. Aug 2, 2015

Chronos

Expansion of the universe is related to cosmological redshift which is an entirely different beast from doppler shift.

15. Aug 2, 2015

timmdeeg

We can measure the light emitted by the object then. From this combined with the knowledge of how the universe expands we can calculate the distance then, about 46 million lys, and the distance now, 46 billion lys; assuming that the universe expanded by a factor of 1000.

Last edited: Aug 2, 2015
16. Aug 2, 2015

Chalnoth

Special relativity doesn't work in an expanding universe, as special relativity assumes flat space-time, and the expansion is curvature in space-time.

The redshift that we see for objects far away in the universe has nothing to do with the Doppler shift. Instead, it's due to the expansion itself. When the universe doubles in size, photon wavelengths are also doubled. The CMB photons have been redshifted by a factor of approximately 1090, meaning that the universe has expanded 1090 times in each direction since the CMB was emitted.

To get the distance to the CMB, we use what is known as the first acoustic peak. In the early universe plasma, there were pressure waves. These pressure waves sort of "bunch up" at a distance called the sound horizon: the distance that the waves could have traveled since our universe began. This creates the first acoustic peak, and its distance is approximately a separation of one degree on the sky.

So if we know how old the universe was when the CMB was emitted, and can model how far the sound waves in that early plasma could have traveled, then we can use the one degree separation to estimate how far away those peaks were, and the answer is approximately 46 million light years. As the universe has expanded by a factor of about 1090 since then, the current distance to the matter that emitted that light is around 50 billion light years*.

*The different numbers in this thread come from different observations. The numbers I'm quoting here are from a combination of data including the WMAP 9-year data. I use WMAP instead of the better Planck data because the website is better-designed and it's easier to look up the numbers.

17. Aug 5, 2015

Gaz

Well that can't be true I think its safe to assume that the galaxies would have been moving around independently somewhat to ?
But I guess no one can really know how much ?

18. Aug 5, 2015

marcus

Good point! Things do have their individual motions in the local space surrounding them and that does contribute a doppler bit on top of the main distance expansion redshift.

In many situations the cosmological redshift is the main thing and the individual random motions are (as you suggest) very hard to determine---they tend to be small (a few hundred km/s) and get neglected.

But there are some nice situations where one can estimate the small contribution they make.
For example if you can resolve a spiral galaxy seen edge on. Besides the cosmological redshift due to how much the distance to the galaxy has expanded---you have the stars on one side coming towards us and the stars on the other side going away, due to rotation. That gives a doppler effect over and above the cosmological redshift so you can measure the speed of rotation.

Also clusters of galaxies have the individual random motions of the galaxies within the cluster. So there is doppler (from the RADIAL component of those motions) which is over and above the redshift due to the change in overall distance to the cluster. One can get a very rough idea, at least.

Or so I'm told : ^)
not an expert in that kind of thing.

Last edited: Aug 5, 2015
19. Aug 5, 2015

Chalnoth

I was a little bit short in that explanation, you're right. Especially within very massive clusters, the local motions can be pretty large, but not large compared to the cosmological redshift for far-away galaxies. The largest are, if I recall correctly, about 3,000 km/s, which translates to a redshift of $z = 0.01$. Most galaxies are going to have much smaller local motions (our own motion relative to the CMB is about 600km/s). Obviously for galaxies at a redshift of 1-2 or higher, this isn't going to be an issue (for the most part). Most cosmologists just ignore the local motions of galaxies entirely, and that approximation works extremely well.

As for how we know this, when astronomers are doing surveys of large numbers of galaxies, they measure the position of the galaxies by direction and redshift (since the redshift is directly measurable, while the distance is not). Galaxy clusters on such maps look as if they have been elongated along the line of sight: instead of a nearly spherical blob, clusters are long blobs oriented along the line of sight (when redshift is converted to the appropriate units to approximate distance). This fact can be used to estimate the velocities of the galaxies within the cluster.