Where, in the Universe, are we?

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Main Question or Discussion Point

Astronomers can see the same distance in every direction, so we have the right to regard ourselves as being at the centre of the detectably Universe.
However, experts, and to some extent logic, assure us that every other point in the Universe also has a right to see itself as being at the centre.
Does this mean that there is no point in the Universe from which it not possible to see an equal distance in every direction? If so, how could this be possible in a finite universe?
 

Answers and Replies

  • #2
Chronos
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Correct. Every observer in the universe has the illusion it resides at its center. The temporal edge of the observable universe appears to be 13.7 billion years distant in every direction. Other observers in the universe perceive the temporal edge of the universe is also equidistant. For example, were we to receive a message [sent at light speed] from scientists residing in a galaxy 3 billion years distant, they would report the temporal edge of the universe appears to be 10.7 billion years distant in every direction.
 
  • #3
marcus
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... no point in the Universe from which it not possible to see an equal distance in every direction? If so, how could this be possible in a finite universe?
Start by thinking of a 2D surface of a sphere. With no surrounding 3D space. All existence is concentrated on that 2D surface. Very large so nearly flat. With 2D creatures living on it.
All they know is the 2D space they live in (we call it 'surface' but for them it is space.)

That 2D world is finite but has no boundary. every point is equal. matter is uniformly spread, on average, all over.

Then think of the 3D analog of that. It is finite. It has no boundary. Matter is approx. evenly spread throughout. Every point is equal, and equally surrounded by approximately the same material scene, roughly the same density of stars galaxies etc.

That 3D space, finite and boundaryless, is called the hypersphere S3
It is one possible model of the space we live in.
There are others, but this is the most commonly meant when cosmologists consider a finite spatial volume universe.
 
  • #4
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Thanks Chronos & Marcus.

I had thought of the spherical analogy, but reckoned that this would work only if spacetime were sufficiently curved to result in a closed universe. As far as I can discover, this model of the Universe is not the "flavour of the month".

Chronos said:
For example, were we to receive a message [sent at light speed] from scientists residing in a galaxy 3 billion years distant, they would report the temporal edge of the universe appears to be 10.7 billion years distant in every direction.
I'm not clear on this one. At light speed, the other scientists' message would have left 3 billion years age. Are you saying that light from beyond 10.7 billion L Y away would not have reached those scientists at that point? If so, what is that based on?
 
  • #5
marcus
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Thanks Chronos & Marcus.

I had thought of the spherical analogy, but reckoned that this would work only if spacetime were sufficiently curved to result in a closed universe. As far as I can discover, this model of the Universe is not the "flavour of the month".

...
It certainly is not in disfavor. It came up in the NASA WMAP report based on the first 5 years of data from the WMAP spacecraft.
It is consistent with current measurements of the curvature of space.
Which allow either for a slight positive curvature, or zero flat infinite, or slight negative. There is a 95% confidence interval around zero curvature.

As it happens the hypersphere, with slight positive curvature, is the case they typically consider as an alternative to flat infinite. And in the WMAP report they analyzed both.
They came up with an estimate that the radius of curvature in the hypersphere case would , with 95% confidence, have to be at least 100 billion lightyears (now distance)
Or you could say the circumference would have to be at least 600 billion lightyears (now)
meaning if you could freeze the expansion process right now a signal would take 600 billion years to get back to its starting place.

We dont know finite or infinite, we dont know slightly curved or flat. Hypersphere is not "flavor of month" but it certainly is taken seriously.

These things are speculative, you have to keep your options and continue analyzing how it could be in several different alternative cases.
 
  • #6
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Thanks again, Marcus.
Just to check that my elderly, non-scientific brain cells are absorbing all this, am I right in thinking the following?

WMAP report indicates 95% chance that space is flat, but could be positive or negative curvature.

Current thinking is that positive curvature is second choice.

If there is positive curvature the resulting sphere would have a minimum circumference of 600 billion light years.

This still seems to leave the question: if space is not positively curved, would there be any point in the Universe where an observer would not be able to see the same distance in every direction? I apologise if I'm just being thick.
 
  • #7
marcus
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very nearly perfect summary, and clear question! old brain cells are good brain cells.

about the 95% confidence interval, with that much confidence, space is at least nearly flat, either perfectly or just slightly pos or neg curvature.

Now we are talking about the standard cosmology model that the pros use, not about what we KNOW. All we can do is write down a simple model that best fits the data and conforms to the general relativity law of how geometry should behave. And keep testing it with all the data we can get. We can't be sure.

And using that model the answer to your question is no, there would not be an observer like that. Unless he stayed in the basement all the time.

Or was traveling very fast so that relativistic effects made his horizon not be spherical but be oblate. He would be seeing the same horizon, the same surface of last scattering, as we do but it would appear closer in front of him. The part in front would be closer than the part off to the side, according to how he measured distance.

I tend to think of observers at rest relative to CMB and think of people like that as exceptional.

There would be no POINT where a stationary observer wouldn't see the same dist in all directions, but you could set up a state of motion where (from our point of view) he wouldn't the same distance in all directions. That is getting too technical for my taste anyway. I don't think that is what you meant. You meant a POINT that would somehow be near a boundary. In standard cosmo there is no boundary. The U is assumed boundaryless with on average an approximately uniform distribution of matter.
So no point is remarkably different from any other.

Of course living down in the basement or next door to a blackhole things could be atypical but that is not what I think you meant.
 
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Marcus, you are right, I was not thinking of someone living in a basement or near a B H, nor someone travelling at high speed (relatively, of course).
What I am still struggling with is the idea that in a finite, flat universe it might not be possible for an observer to be sufficiently close to a boundary to see a shorter distance in that direction than in the opposite direction.
 
  • #9
marcus
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Endervhar, I understand your puzzle. People naturally encounter this conceptual difficulty because the idea of "finite" intuitively makes us think "boundary".

And if a boundary existed. If there was something outside the universe, across on the other side of the boundary, or perhaps if the boundary was some impenetrable wall without anything beyond it(!) then there would be observers near the boundary whose vision would be limited in that direction.

But eventually most of us are satisfied by thinking of space as a hypersphere with a very slight (perhaps even imperceptibly small) positive curvature. Then it could be finite and also boundaryless. There is no logical reason that a finite space must have a boundary.

However you have taken this problem one step further. You are saying, if I understand, what about the FLAT case. You are asking what if space is not just nearly flat or approximately flat but is really flat, average curvature zero. Would it then have to be infinite? Or is there some way a zero-curvature space could be finite volume, and also boundaryless. (In conventional cosmology space is always boundaryless, all existence is in the universe there is no surrounding non-universe.)

Is there some way a zero-curvature boundaryless space could be finite volume? Is it even logically/mathematically possible? This is the way I interpret your question.
Please object, or correct me, if you do not like that way of putting it.

The answer is unintuitive and is Yes. It arises from the fact that cosmology is a mathematical science and that space is represented by a mathematical object called a differentiable manifold which does not have to be surrounded by any higher dimensional space. A 3D manifold does not have to live in a larger 4D surroundings. It simply has to look right in any particular neighborhood you pick, and the neighborhoods be smoothly compatible at overlaps.

This allows, for example, a square flat sheet of paper to be identified N with S and E with W so that it is effectively "glued" to form a torus, and yet it remains flat.
You just have to specify the neighborhoods at the E edge of the square AS IF they joined with the W edge.

I don't recall cosmologists talking much about the possibility that we could live in a flat, toroidal universe. A 3D analog of the 2D flat piece of paper with mathematical "gluings" or identifications to eliminate the edges.

There was a paper sometime around 2006 by Spergel Cornish and somebody else that attempted to rule this out to whatever extent they could. They couldn't completely rule out the possibility but they did find that if it was toroidal or "periodic" in any such way then it would have to be very very big or else we would have noticed the stars in one direction looking like the stars in another direction.

That kind of thing is mathematically possible. But only a few cosmologists spend time thinking about it. And of them, some devote their efforts to trying to rule it out observationally.

There are also multiverse scenarios in which our part of the universe has a boundary beyond which the laws of physics may be different. This is mostly just an unempirical form of entertainment. Pure speculation without possbility of testing. Stimulating fantasies.

In standard mainstream cosmo, where one fits model to data, the model has no boundary and if it is perfectly flat it is infinite (or there are these exotic toroidal etc possibilities) and if it is only nearly flat then it might reasonably be a hypersphere.
 
  • #10
Chronos
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Thanks Chronos & Marcus. ...

I'm not clear on this one. At light speed, the other scientists' message would have left 3 billion years age. Are you saying that light from beyond 10.7 billion L Y away would not have reached those scientists at that point? If so, what is that based on?
Correct, there was no light more ancient than 10.7 billion years available for ET to observe. It was the age of the universe from the perspective of ET. Before extrapolating this beyond reason, bear in mind the universe has been expanding all the while. Our galaxy was closer than 3 billion light years [to ET's galaxy] when the message was sent. So it would be incorrect to deduce residents of any galaxy more than half the distance to the big bang [>6.85 bly distant] could not see our galaxy because it was outside their observable universe. Rest assured our galaxy [or its progenitor] was safely inside the radius of their observable universe.
 
  • #11
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the question, 'where, in the universe, are we?' is interesting, but is irrelevant. A paradox occurs whereby we are the centre of the universe, but so is everywhere else. In fact, there is no centre to the universe, so there is no possible reference point by which to determine 'where' we are.
There is no centre of the universe because there is no edge of the universe. In a finite universe, space is curved so that if you could travel billions of light years in a straight line you would eventually finish back where you started. It is also possible that our universe is infinite. In both examples, groups of galaxies completely fill the universe and are moving apart at all points making the universe expand.
There is a common assumption that the Big Bang was an explosion that occured in empty space and that the explosion expanded into the empty space. This is wrong. Although space may have been concentrated into a single point at the Big Bang, it is equally possible that space was infinite at the Big Bang. In both scenarios the space was completely filled with matter which began to expand.
There is no centre of the expansion, the universe is simply expanding at all points. Observers in any galaxy see most of the other galaxies in the universe moving away from them.
The only answer to the question "Where did the Big Bang happen?" is that it occured everywhere in the Universe.
Space was created in the Big Bang. Our universe has no edge or boundary - there is no outside of our universe. It is possible that our universe is part of an infinity of universes, but these universes do not necessarily need a space to exist in.
It is possible that our universe is infinite and has been filled with matter everywhere since the Big Bang. But there is also nothing stopping the universe expanding faster than the speed of light. Although at any local point within the universe, nothing can travel faster than the speed of light, this is not true for the entire universe. There is no limit on how fast space can expand.
Imagine galaxies are like balls sitting on a rubber sheet which represents space. If we stretch the sheet, the balls move apart. Balls which are close together will only move apart slowly. Balls which are widely separated will seem to move apart very quickly.
People living on any one of the balls will see their own ball as stationary. They will see nearby balls moving away slowly and they will see distant balls moving away quickly. Very distant balls (beyond the horizon) can be moving away faster than the speed of light, but the people cannot see them - locally in their own part of the universe nothing is travelling faster than the speed of light.
 
  • #12
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the question, 'where, in the universe, are we?' is interesting, but is irrelevant. A paradox occurs whereby we are the centre of the universe, but so is everywhere else. In fact, there is no centre to the universe, so there is no possible reference point by which to determine 'where' we are.
There is no centre of the universe because there is no edge of the universe. In a finite universe, space is curved so that if you could travel billions of light years in a straight line you would eventually finish back where you started. It is also possible that our universe is infinite. In both examples, groups of galaxies completely fill the universe and are moving apart at all points making the universe expand.
There is a common assumption that the Big Bang was an explosion that occured in empty space and that the explosion expanded into the empty space. This is wrong. Although space may have been concentrated into a single point at the Big Bang, it is equally possible that space was infinite at the Big Bang. In both scenarios the space was completely filled with matter which began to expand.
There is no centre of the expansion, the universe is simply expanding at all points. Observers in any galaxy see most of the other galaxies in the universe moving away from them.
The only answer to the question "Where did the Big Bang happen?" is that it occured everywhere in the Universe.
Space was created in the Big Bang. Our universe has no edge or boundary - there is no outside of our universe. It is possible that our universe is part of an infinity of universes, but these universes do not necessarily need a space to exist in.
It is possible that our universe is infinite and has been filled with matter everywhere since the Big Bang. But there is also nothing stopping the universe expanding faster than the speed of light. Although at any local point within the universe, nothing can travel faster than the speed of light, this is not true for the entire universe. There is no limit on how fast space can expand.
Imagine galaxies are like balls sitting on a rubber sheet which represents space. If we stretch the sheet, the balls move apart. Balls which are close together will only move apart slowly. Balls which are widely separated will seem to move apart very quickly.
People living on any one of the balls will see their own ball as stationary. They will see nearby balls moving away slowly and they will see distant balls moving away quickly. Very distant balls (beyond the horizon) can be moving away faster than the speed of light, but the people cannot see them - locally in their own part of the universe nothing is travelling faster than the speed of light.
I disagree, and would reformulate that as: whenever you are, there you are. We're always at the temporal edge, and any observer will note the same.
To be clear: a better question is: "when in the universe are we?"
 
  • #13
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I've had some great responses so far, thanks folks. Don't relax yet, though! I shall have to find some time to digest all this, then I feel sure there will be more questions.
In the meantime, Nicodemus, I would be fascinated if you would expand your ideas a bit more. I have a particular interest in time.
 
  • #14
For example, were we to receive a message [sent at light speed] from scientists residing in a galaxy 3 billion years distant, they would report the temporal edge of the universe appears to be 10.7 billion years distant in every direction.
Doesn't the example above assume the universe is expanding at exactly the speed of light?

Doesn't it also assume the universe has expanded at exactly the speed of light for the last 3 billion years?

I thought the universe expanded faster than the speed of light during the big bang? If so, when did it slow to exactly the speed of light.

My knowledge of astronomy is very very elementary so please bear with me. Thank you.
 
  • #15
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Although it's honestly not something I know much about, it might be of interest to you to know that there is a doppler shift in the cosmic background radiation. I don't believe this tells us anything about position, but it might indicate motion or something else like proximity to a black hole. I wasn't immediately able to find any theories for an explanation.
 
  • #16
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The simpler answer, given what we know about the Universe, is "we are here".
 
  • #17
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I've had some great responses so far, thanks folks. Don't relax yet, though! I shall have to find some time to digest all this, then I feel sure there will be more questions.
In the meantime, Nicodemus, I would be fascinated if you would expand your ideas a bit more. I have a particular interest in time.
We're always at our own temporal horizon based on what light can reach us, and what cannot. Everyone in the universe should observe that they are in the center of the universe, which is meaningless really. Instead, it would be better to define your position in the universe based on time, where you everything you see represents the limits of the cosmological horizon for where and when you are.

I'm not sure that I understand the concept well enough to teach it unfortunately, so anyone else feel free to chime in, correct and set me straight.
 
  • #18
So it would be incorrect to deduce residents of any galaxy more than half the distance to the big bang [>6.85 bly distant] could not see our galaxy because it was outside their observable universe. Rest assured our galaxy [or its progenitor] was safely inside the radius of their observable universe.
Doesn't the example above assume the universe is expanding at exactly the speed of light?

Doesn't it also assume the universe has expanded at exactly the speed of light for the last 3 billion years?

I thought the universe expanded faster than the speed of light during the big bang? If so, when did it slow to exactly the speed of light.

My knowledge of astronomy is very very elementary so please bear with me. Thank you.
Chronos: Any input?
 
  • #19
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The simpler answer, given what we know about the Universe, is "we are here".
thats a little bit of a cop-out answer, and quite philosophical, unless of course you are refering to the Anthropic principle? But that isnt really relevant to the question, in my humble opinion anyway!
 
  • #20
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We're always at our own temporal horizon based on what light can reach us, and what cannot. Everyone in the universe should observe that they are in the center of the universe, which is meaningless really. Instead, it would be better to define your position in the universe based on time, where you everything you see represents the limits of the cosmological horizon for where and when you are.
Nicodemus, your thoughts are very interesting, i'd like to hear more, and hopefully come to a better understanding. Im not sure if im fully understanding the concept, but it did make me think of this example. After the universe is only 1 billion years old there are two galaxies relatively close to each other (A and B). When galaxy A emits its light galaxy B will recieve it when the universe is 14 billion years old, the pulse of light has been travelling for around 13 billion years and so the distance between the two galaxies will be around 26 billion light years. The light received by galaxy B will be around 1 billion years old and when it was about 2 billion light years away from galaxy A.
In the same way, the universe is probably far greater in size than we imagine, since there will be countless objects so far away that their light will never reach us, hence the universe is expanding faster than the speed of light.

I may have missed the point entirely, but this is what i imagine when you refer to our temporal position in the universe, rather than our spacial position, although wouldnt this have implications on space-time being inextricably linked? maybe ive missed the boat on that one too! please correct me if i am wrong!
 
  • #21
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Nicodemus, your thoughts are very interesting, i'd like to hear more, and hopefully come to a better understanding. Im not sure if im fully understanding the concept, but it did make me think of this example. After the universe is only 1 billion years old there are two galaxies relatively close to each other (A and B). When galaxy A emits its light galaxy B will recieve it when the universe is 14 billion years old, the pulse of light has been travelling for around 13 billion years and so the distance between the two galaxies will be around 26 billion light years. The light received by galaxy B will be around 1 billion years old and when it was about 2 billion light years away from galaxy A.
In the same way, the universe is probably far greater in size than we imagine, since there will be countless objects so far away that their light will never reach us, hence the universe is expanding faster than the speed of light.

I may have missed the point entirely, but this is what i imagine when you refer to our temporal position in the universe, rather than our spacial position, although wouldnt this have implications on space-time being inextricably linked? maybe ive missed the boat on that one too! please correct me if i am wrong!
I'd say you're pretty close, but I'm an amateur too so there needs to be some outside confirmation. I'd just say, I don't know that space is expanding faster than light, but when you take galactic recession velocities (your example) then ADD more space 'growing' between receding galaxies A and B, the result is that the light may never reach the other.

So, there is a very real limit to what ANYONE anywhere in the universe (whatever it it's like) can observe: beyond that we have our cosmological event horizon. Anything at/beyond that limit is as inaccessible to us, including observation, and will ALWAYS be. This is explicitly a function of the postulate that light has a constant one-way speed (in SR), and that does, as you say, link space and time inextricably (hence spacetime).

Remember, space is expanding... AND nearly everything seems to be hurtling away from nearly everything else (gross simplification on my part)... when you add that to space expanding.. and ACCELERATING that expansion, that horizon emerges.

I think the concept of various event horizon, universal homogeneity, and isotropy are things you might enjoy reading about. At the heart of the question of where we are, in the context of relativity, you have to remember that we're talking about 3+1 dimensions: 3 space, and 1 time... utterly of a piece.
 
  • #22
Chronos
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Doesn't the example above assume the universe is expanding at exactly the speed of light?

Doesn't it also assume the universe has expanded at exactly the speed of light for the last 3 billion years?

I thought the universe expanded faster than the speed of light during the big bang? If so, when did it slow to exactly the speed of light.

My knowledge of astronomy is very very elementary so please bear with me. Thank you.
The ET galaxy was about 2.7 billion light years distant when the message was sent and took 3 billion years to reach us. The ET galaxy is now about 3.4 billion light years distant, so it has merely receeded about 0.7 billion light years over the past 3 billion years - well short of light speed. Numbers courtesy of Ned Wright's cosmology calculator.
 
  • #23
Correct. Every observer in the universe has the illusion it resides at its center. The temporal edge of the observable universe appears to be 13.7 billion years distant in every direction. Other observers in the universe perceive the temporal edge of the universe is also equidistant. For example, were we to receive a message [sent at light speed] from scientists residing in a galaxy 3 billion years distant, they would report the temporal edge of the universe appears to be 10.7 billion years distant in every direction.
The ET galaxy was about 2.7 billion light years distant when the message was sent and took 3 billion years to reach us.
I thought the message was sent at the speed of light (see above example)? It would then take 2.7 billion years to reach us not 3 billion, correct?

The ET galaxy is now about 3.4 billion light years distant, so it has merely receeded about 0.7 billion light years over the past 3 billion years - well short of light speed. Numbers courtesy of Ned Wright's cosmology calculator.
I'm not sure where this fits in your original example...I think I get what you are trying to say but can't see the whole story fitting together.
 
  • #24
marcus
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The ET galaxy was about 2.7 billion light years distant when the message was sent and took 3 billion years to reach us. The ET galaxy is now about 3.4 billion light years distant, so it has merely receeded about 0.7 billion light years over the past 3 billion years - well short of light speed. Numbers courtesy of Ned Wright's cosmology calculator.
I thought the message was sent at the speed of light (see above example)? It would then take 2.7 billion years to reach us not 3 billion, correct?

...

I'm not sure where this fits in your original example...I think I get what you are trying to say but can't see the whole story fitting together.
Curious, I'm not sure what measure of distance Chronos is using and I don't know if he explained earlier in the thread that there are several possible measures. Haven't been following the thread.
Astronomers use several. Confusion can arise when you are not clear what defintion of distance is meant.

What I woud suggest you do, as a quick tutorial that might resolve some of the puzzle for you is google "wright calculator" go there and notice two or three of the distance numbers (I'll tell you which and what they mean.)

Googling "wright calculator" will get you to
http://www.astro.ucla.edu/~wright/CosmoCalc.html
Be sure that's where you are and take a look at these three numbers. They are already showing, as an example, so you don't have to do anything to get them! Here are the three numbers to focus on:

z=3
comoving radial dist = 21.07 billion light years
angular size dist = 5.27 billion light years

You can get other examples just by changing the number in the "z box" and pressing the "general" compute button. But let's simply discuss those three.

z is the redshift of the light coming in from the distant galaxy. The proportionate increase in wavelength---showing how much more the wavelengths in the light are now than when they started out. To get the total length you add one. z+1=4. The wavelengths are FOUR times their original length. Also largescale distances in the U are now four times what they were when the light left.

5.27 billion light years is what the distance to the galaxy was back THEN if you could have FROZEN THE EXPANSION PROCESS and timed a radar or light signal from here to there.
That was the instantaneous "freeze frame" distance at the moment the light left the galaxy on its way to us.

21.07 billion light years is how far the galaxy is NOW at the moment the light gets to our telescope, defined the same way---that is, imagine you could freeze the expansion process as the U is today, and time a light or radar signal. As things are today, with expansion frozen so distance won't change while you are trying to measure, a radar beep would take 21 billion years to get there.

Remember I said that wavelengths and distances have changed by a factor of FOUR while the light was in transit. (Distances, that is, if you measure this instantaneous freezeframe way technically called "proper" distance. The distances we are talking about have changed by the same factor as the wavelengths of the light, while the light was in transit.)

Well you can check that! Try multiplying 5.27 by four! You will find that the distance to the galaxy is now four times farther than it was back then when the light started out.

You can play around with the wright calculator by putting in different values for the redshift, then press the "general" button to get it to recalculate with the new data.

If anything seems puzzling or confusing, please ask more questions.

BTW don't let it bother you if largescale distances increase at rates exceeding the speed of light. General relativity allows this. It is not governed by the same rule as motion in a local frame of reference. Distance increase is affecting everything in the neighborhood of the galaxy. Nobody out there thinks they are moving. If you play around with the wright calculator some, you will discover that lots of galaxies are, or have been, receding at rates greater than c. Just compare the light travel time with the amount the distance has grown while the light was in transit.
 
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  • #25
Chronos
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2.7 billion years would be correct were it not for expansion. Keep in mind our galaxy was receeding during that 2.7 billion years, so it takes a few hundred million more years for light to make up the distance we have receeded since the message was sent.
 
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