Time and distance relative to an expanding universe

[Genx63]

As I understand it, the universe is approx. 14 billion years old. Light from the farthest observed galaxies took several million or billion years to reach us. Now my question is: If it takes for example, 500 million years for light from a certain galaxy to reach us it is 500 million light years away. So it stands to reason that the light originated 500 million light years away 500 million years ago. According to the expanding universe theory, 500 million years ago the universe was significantly smaller than today. Therefore that light was closer to us when it originated and it wouldn't take 500 million years to get here. Can someone help me wrap my ignorant mind around this? Thank you.

 

[mathman]

The light took 500 million years to get here. The galaxy would be further away.

 

[Drakkith]

We have been moving away from the light ever since it was emitted, causing it to travel further before arriving. The emitting object could have been 250 million light years away when it emitted the light, yet it took longer than 250 million years that for the light to arrive. I don't know the exact distances off the top of my head, but there are some cosmological calculators you can find on Google that will calculate this stuff for you.

 

[Spourk]

Here's a good article discussing just that:

How can we see galaxies 47 billion light years away, when the universe is only 13 billion years old?)

 

[Chalnoth]

As I understand it, the universe is approx. 14 billion years old. Light from the farthest observed galaxies took several million or billion years to reach us. Now my question is: If it takes for example, 500 million years for light from a certain galaxy to reach us it is 500 million light years away. So it stands to reason that the light originated 500 million light years away 500 million years ago. According to the expanding universe theory, 500 million years ago the universe was significantly smaller than today. Therefore that light was closer to us when it originated and it wouldn't take 500 million years to get here. Can someone help me wrap my ignorant mind around this? Thank you.

Well, this comes down to the expansion mucking things up with regard to distances. The article Spourk linked to is probably a good explanation, but I'll offer a shorter one here.

The expansion of the universe increases the distances between objects in the universe, no matter what those objects are. This even includes light rays. That is, if a light ray is emitted some 500 million light years away, then the expansion of the universe will, each second, cause more distance to be added between us and the light ray. So that in the end, over time, that light ray has to travel more than 500 million light years in order to finally reach us. How much more? Well, that depends upon how fast the universe is expanding, and that changes over time.

For example, when the CMB was emitted, our universe was expanding so fast that stuff that was, at that time, some 43 million light years away has actually had to travel a full 13.7 billion light years in order to get to us. So we're seeing bits of the CMB today that were at that time only 43 million light years away. But the universe has expanded since then, by a factor of 1090, so that the stuff that emitted that light is now a whopping 46.6 billion light years away.

This may seem counter-intuitive, but remember, the expansion has carried the light ray away from us fast enough for it to need to cross 13.7 billion light years, but that light ray has been moving towards us the entire time. The matter that light came from hasn't! So the same amount of expansion has been applied to a larger distance between us and that galaxy than us and the incoming light ray, so that it was pushed away even further.

 

[phinds]

Good explanation, Chalnoth, and I would add for the benefit of the OP, even though it may add to the initial confusion, that the particles that emitted the CMB are not only some 46 billion light years away from us at present, they are currently receding from us at about 3 times the speed of light, and will continue to move away from us faster and faster. This does not cause any speed tickets to be issued, since they are not moving IN space faster than light, they are being carried away by the expansion of the scale factor of the universe (which some people describe as "the expansion of space", a term that I now understand to be misleading).

 

[Spourk]

If I might add to what Phinds said as well, if curiosity has you,This Old But Accurate Article/FaQ explains the various ways that the speed of light IS exceeded in similar ways. In other words, nothing goes faster than light, but there are some interesting exceptions that are basically piggy backed off the movement of other objects.

Take a galaxy sized pair scissors for example...

 

[Chalnoth]

If I might add to what Phinds said as well, if curiosity has you,This Old But Accurate Article/FaQ explains the various ways that the speed of light IS exceeded in similar ways. In other words, nothing goes faster than light, but there are some interesting exceptions that are basically piggy backed off the movement of other objects.

Take a galaxy sized pair scissors for example...

One way to understand this is that in General Relativity, nothing can outrun a light ray. That is to say, nothing can go faster than a light ray along the same path the light ray takes. But an object can beat a light ray to a destination if it takes a shorter route to get there. And in curved space-time, if there is enough curvature, sometimes a massive object can get to a destination faster if it takes a much shorter route than the light ray.

There's also the point to be made that the velocity of far-away objects isn't actually well-defined: it depends entirely upon the numbers we use to describe the space-time, and it is perfectly possible to describe the exact same space-time with extremely different numbers. So if we make up a definition of velocity that seems reasonable, then there just isn't any limit on how much different velocities can differ unless they are at the same point. At one single point, the difference in velocity is well-defined, hence the previous statement that nothing can outrun a light ray.

 

[Genx63]

Thank you all for helping me understand. Whenever I can't grasp a concept it nags me until I get it so thank you

 

[alphachapmtl]

From wikipedia:

the observable universe consists of the galaxies and other matter that humans can in principle observe from Earth in the present day,
because light from those objects has had time to reach us since the beginning of the cosmological expansion
http://en.wikipedia.org/wiki/Observable_universe
...
The region visible from Earth (the observable universe) is a sphere with a radius of about 46 billion light years,
based on where the expansion of space has taken the most distant objects observed.
...
The most precise estimate of the universe's age is 13.72±0.12 billion years old,
based on observations of the cosmic microwave background radiation.
...
This expansion accounts for how Earth-bound scientists can observe the light from a galaxy 30 billion light years away, even if that light has traveled for only 13 billion years; the very space between them has expanded.
...
http://en.wikipedia.org/wiki/Universe#Size.2C_age.2C_contents.2C_structure.2C_and_laws