# Very confused about path of light from distant galaxies :-(

Hello there!

Sorry for the dumb question, but for years I have been very curious and confused about this: I just read that they discovered a galaxy 13.7 Bn light-years away -- therefore its light was emitted 13.7 Bn years ago and travelled 13.7 Bn light-years in some line.

But, 13.7 Bn years ago, the universe was only 750 M years old - so if Earth had existed by then the visible universe had a radius of at most 750 M light-years and that galaxy would be at most 750 M light years away.

So, either the light made several "loops" around (what sounds silly), or the visible universe was bigger than 750 M light-years when it was only 750 M light-years old (what also sounds silly), or that galaxy was not in the visible universe by then and now it is (what sound even sillier).

So how come its light took 13.7 Bn years to travel a distance that was at most 750 M light years? Where have these photons been all that time?

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The universe is expanding. So when the light started out the distance between galaxies was a lot less than it is when we measure it now.

phyzguy
Imagine running towards something that is getting steadily further away. Say you run at 10 miles/hr, and start running toward something that is 10 miles away. You will get there in 1 hour, right? But suppose the object is moving away from you. By the time you cover the original 10 miles, the object has moved further away, so you have to keep running to reach it. This is analogous to what is happening with light from the distant galaxies. The initial distance was much less than the distance that the light ultimately ended up traveling.

The universe is expanding. So when the light started out the distance between galaxies was a lot less than it is when we measure it now.

Precisely. So, those rays of light started to travel 13.7 Bn years ago. By that time, the galaxy was say 500 M light years away. So those rays of light had 500 M light years to travel.. should have taken 500 M years, not 13.7 Bn years....?

I imagine that there is some sort of time dilatation effect to be considered, but I can't see where, given our reference system is stationary, so when the ray of light was emitted from the galaxy's reference system, from our point of view that was just another ray of light emitted from 500 M light-years, travelling towards us at speed = c.

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Imagine running towards something that is getting steadily further away. Say you run at 10 miles/hr, and start running toward something that is 10 miles away. You will get there in 1 hour, right? But suppose the object is moving away from you. By the time you cover the original 10 miles, the object has moved further away, so you have to keep running to reach it. This is analogous to what is happening with light from the distant galaxies. The initial distance was much less than the distance that the light ultimately ended up traveling.

Right, but speed of light is absolute... so a ray of light emitted from a galaxy moving at 90% of the speed of light will still travel with speed = c, even if it will be hightly shifted to red.

fbs7 = very confused.. :-(

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A.T.
Right, but speed of light is absolute...
In expanding space this is only true locally, not across large distances. Imagine an ant walking from one end to the other on a rubber band that is being stretched.

Ah, I'm getting it now. Cannot just expand my reference frame to far away galaxies, neither to far away back in time.

Those articles are quite interesting - will be quite some time reading them. Thank you both!

D H
Staff Emeritus
Meanwhile our reference system is stationary relative to us. Therefore, a ray of light emitted when that galaxy was 500 M light-years away in our reference system should have taken 500 M years to reach us, still in our reference system.
You are implicitly assuming that the remote galaxy and ours are stationary. Ignore the expansion of space for now (but do see the last few posts). Ignore that space and time are not quite as simple as you think. Just consider the fact that that remote galaxy and ours are and were moving apart from one another. Assume that at some time when the galaxies are separated by 500 million light years and that one of the galaxies transmits a distinguishable signal toward the other. After traveling for 500 million years, that signal from that remote galaxy would have reached the distance where our galaxy was 500 million years ago. Our galaxy is no longer at that location. It has moved beyond it. Even assuming a simple universe, it would take a very, very long time for the light from that remote galaxy to reach ours if the two galaxies were receding at a constant velocity that is just a tiny bit smaller than the speed of light.

And that's for a simple, non-expanding universe. Now add in the expansion of space and you get something truly bizarre.

A.T.
Ignore the expansion of space for now ... Just consider the fact that that remote galaxy and ours are and were moving apart from one another.
Do the galaxies "move apart" if we ignore the expansion of space?

Assume that at some time when the galaxies are separated by 500 million light years and that one of the galaxies transmits a distinguishable signal toward the other. After traveling for 500 million years, that signal from that remote galaxy would have reached the distance where our galaxy was 500 million years ago. Our galaxy is no longer at that location. It has moved beyond it.
How would all that look like in the frame of "our galaxy"?

Even assuming a simple universe, it would take a very, very long time for the light from that remote galaxy to reach ours if the two galaxies were receding at a constant velocity that is just a tiny bit smaller than the speed of light.
A signal from a source receding away from me needs longer to get to me, than a signal from a source at the same distance at rest relative to me?

A signal from a source receding away from me needs longer to get to me, than a signal from a source at the same distance at rest relative to me?
In SR?
No, they take exactly the same time.

However a signal from two sources co-locating, one at rest and the other in motion relative to the receiver does not, the one in motion takes less time.

DaveC426913
Gold Member
Do the galaxies "move apart" if we ignore the expansion of space?
The fact that the galaxies are moving apart is the issue (empirical) - why they are moving apart is not the issue (theoretical). Even in a theory where the universe were not expanding, we could easily have galaxies with receding relative motion. This would still result in stretching out of the light path.

So, D_H's point is that, even in the simplest representation of the universe, we still have the effect, regardless of any theoreticals.

Even in a theory where the universe were not expanding, we could easily have galaxies with receding relative motion. This would still result in stretching out of the light path.
How?

A sees B moving away, B emits a light pulse, how does the light path gets "stretched out" as you cal it?

The fact that the galaxies are moving apart is the issue (empirical) - why they are moving apart is not the issue (theoretical).

Well I think it is clear that gallaxies are moving apart because of the growing decoherence.
Isn't space a measure of de-coherence, after all?

Only partly joking.

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A related question on this issue - and very sorry if that will sound dumb, this whole thing is mind-boggling.

When the Universe was say 1 year old, does it make sense to say that the galaxy was at say 0.5 light-years away at that moment (from Earth's point of view)? I assumed that I could because I thought the visible universe couldn't have a radius of more than 1 light-years, given it was only 1 year old.

If the light from that galaxy actually would actually take 10 B years to reach Earth as measured by the local time on Earth, then perhaps we could say that it was 10 B light-years away, even if the universe was only 1 year old?

After all, if somehow I could take a big ruler and measure the actual distance to that galaxy at that moment, from Earth's point of view, and found that it was, err, 0.5 light-years away... that wouldn't mean anything, because even if it was much closer its light would still take 10 B years to reach us.

ps: somehow I think I'm again falling into that trap of trying to extend my local reference frame to long distances (even when those distances were by then much closer)

D H
Staff Emeritus
Ignore the expansion of space for now ... Just consider the fact that that remote galaxy and ours are and were moving apart from one another.
Do the galaxies "move apart" if we ignore the expansion of space?
You completely missed the point of my post. The continuing expansion of space is not needed to explain the phenomenon asked about in the initial post. All that is needed is that the galaxies are somehow receding from one another. Imagine an alternate universe that started in a similar manner as did ours. In that alternate universe, imagine that expansion stopped after the initial inflationary period. The doesn't mean the material stopped moving; it just stopped accelerating.

In that alternative universe, galaxies would still be receding from one another and it would still take considerably longer than the initial separation distance divided by c for the light from some remote galaxy to reach our (alternative) galaxy.

All that the continued expansion of space does is to add to the confusion. For example, in our universe, the remote galaxy that we are seeing just now is "now" 65 billion light years away from ours.

phinds
Gold Member
When the Universe was say 1 year old, does it make sense to say that the galaxy was at say 0.5 light-years away at that moment (from Earth's point of view)?

You would likely find it interesting to read up on the early universe.

Up until about 400,000 years there were NO stars/planets/galaxies, etc and there CERTAINLY was no earth ... that didn't form until billions of years later.

You would likely find it interesting to read up on the early universe.

Up until about 400,000 years there were NO stars/planets/galaxies, etc and there CERTAINLY was no earth ... that didn't form until billions of years later.

I know :^)

I just wrote 1 year to stop writing big numbers, but I appreciate your call for precision. Please read 750 M years/light years instead of 1 year/light year, 500 M light years instead of 0.5 light-year, and 13.7 G years/light years instead of 10 G light-years. And by "Earth" I mean some reference system whose origin is nearby the Earth in today's Earth's time.

All that the continued expansion of space does is to add to the confusion. For example, in our universe, the remote galaxy that we are seeing just now is "now" 65 billion light years away from ours.

Wow, that's fantastic!

A.T.