Is Every Point in the Universe the Center?

[Endervhar]

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?

 

[Chronos]

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.

 

[marcus]

... 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.

 

[Endervhar]

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".

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?

 

[marcus]

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 don't know finite or infinite, we don't 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.

 

[Endervhar]

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.

 

[marcus]

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 black hole things could be atypical but that is not what I think you meant.

 

[Endervhar]

Marcus, you are right, I was not thinking of someone living in a basement or near a B H, nor someone traveling 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.

 

[marcus]

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.

 

[Chronos]

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.

 

[Grid9]

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 occurred 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 occurred 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 anyone 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 traveling faster than the speed of light.

 

[Nicodemus]

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 occurred 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 occurred 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 anyone 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 traveling 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?"

 

[Endervhar]

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.

 

[curiousphoton]

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.

 

[davilla]

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.

 

[Blakut]

The simpler answer, given what we know about the Universe, is "we are here".

 

[Nicodemus]

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.

 

[curiousphoton]

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?

 

[Grid9]

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 referring to the Anthropic principle? But that isn't really relevant to the question, in my humble opinion anyway!

 

[Grid9]

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. I am not sure if I am 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 receive it when the universe is 14 billion years old, the pulse of light has been traveling 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 spatial position, although wouldn't this have implications on space-time being inextricably linked? maybe I've missed the boat on that one too! please correct me if i am wrong!

 

[Nicodemus]

Nicodemus, your thoughts are very interesting, i'd like to hear more, and hopefully come to a better understanding. I am not sure if I am 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 receive it when the universe is 14 billion years old, the pulse of light has been traveling 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 spatial position, although wouldn't this have implications on space-time being inextricably linked? maybe I've 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.

 

[Chronos]

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.

 

[curiousphoton]

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.

 

[marcus]

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.

 

[Chronos]

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.

 

[marcus]

BTW Chronos, what is the redshift for the galaxy you are talking about? The redshift is the one unambiguous number so it would help me understand what you are saying if I knew that. You may have said earlier in the thread, but I didn't see it when I looked back.

 

[Chronos]

The redshift of a galaxy at a light travel time of 3 billion years is ~0.26.

 

[marcus]

The redshift of a galaxy at a light travel time of 3 billion years is ~0.26.

Good! So let's see if we can guide Curiousphoton to use wright's calculator for a redshift z = 0.26.

I know there is a "light travel time" version of the calculator but let's focus on the one most people know, that you get by googling "wright calculator".

I already discussed this with the example z = 3, which comes up automatically. Redshift 0.26 means the distances and wavelengths I was talking about are 26% longer now than they were back then when the light began its travel. So the multiplicative factor is 1.26.

We go to:
http://www.astro.ucla.edu/~wright/CosmoCalc.html
and type 0.26 in the "z box" over on the left and press "general" and it calculates

freezeframe distance back then = 2.6844 billion light years
ditto distance now when light gets here = 3.382 billion light years
light travel time 3.013 billion years

The calculator doesn't do much rounding off, so that's up to the personal taste of the user. In any case we can check that the the distance NOW is 1.26 times the distance THEN. Both distances and wavelengths are larger now by a factor of z+1 = 1.26

That's the essential thing about redshift, the main thing to come away with from this kind of introduction.

I wonder if Curiousphoton actually tried doing your example on the calcuator?

 

[curiousphoton]

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.

I see. Very interesting. Thanks for the explanation. I take it that means our universe has expanded at a rate less than the speed of light for this 2.7 billion years.

Let's say instead our universe was expanding at the speed of light during this 2.7 billion year time period. Does this mean we would never receive the message?

 

[curiousphoton]

Good! So let's see if we can guide Curiousphoton to use wright's calculator for a redshift z = 0.26.

I know there is a "light travel time" version of the calculator but let's focus on the one most people know, that you get by googling "wright calculator".

I already discussed this with the example z = 3, which comes up automatically. Redshift 0.26 means the distances and wavelengths I was talking about are 26% longer now than they were back then when the light began its travel. So the multiplicative factor is 1.26.

We go to:
http://www.astro.ucla.edu/~wright/CosmoCalc.html
and type 0.26 in the "z box" over on the left and press "general" and it calculates

freezeframe distance back then = 2.6844 billion light years
ditto distance now when light gets here = 3.382 billion light years
light travel time 3.013 billion years

The calculator doesn't do much rounding off, so that's up to the personal taste of the user. In any case we can check that the the distance NOW is 1.26 times the distance THEN. Both distances and wavelengths are larger now by a factor of z+1 = 1.26

That's the essential thing about redshift, the main thing to come away with from this kind of introduction.

I wonder if Curiousphoton actually tried doing your example on the calcuator?

Thanks for the info marcus. Admittedly , this is all new stuff to me as I did not take astronomy or cosmology classes at my university. I took many physics and mathematics courses and am trying to use these to reason my way through this information.

 

[marcus]

One way to express the Hubble law constant is that at present large distances between disconnected objects are increasing by about 1/140 of one percent per million years.

I take it that means our universe has expanded at a rate less than the speed of light for this 2.7 billion years.
...

How do you picture the U having one single definite speed of expansion that you can compare with c?

It has a percentage rate of expansion, or rather the distances have a percentage rate of expansion. That rate has changes by several orders of magnitude over the course of history (which is why there is no simple pairing between light travel time and the distance measures I mentioned.)

Because it is a percentage rate, large distances expand at a larger km/s rate than small do.
It's easy to find galaxies which we can see and have catalogued where the distance to them, according to Hubble law v = Hd is growing faster than c.

Nothing remarkable most known galaxies have redshift >1.7 and with any such galaxy the distance to it would be growing at km/s rate >c.

Thanks for the info marcus. Admittedly , this is all new stuff to me as I did not take astronomy or cosmology classes at my university. I took many physics and mathematics courses and am trying to use these to reason my way through this information.

Well my advice would be to get some hands-on experience with cosmology calculators which embody the standard model of the cosmos that the professionals use to fit the data.
Ned Wright's is a prominent example.

If you want to start reasoning, don't reason about what you get secondhand from popularizing journalists who don't (most of them) even say what they mean by distance.
Most of them actually use light travel time instead of instantaneous distance.
In other words get some real numbers to reason about.

I'm curious, Curiousphoton, did you indeed go to wright calculator and look at the
z=3 example that immediately comes on?
http://www.astro.ucla.edu/~wright/CosmoCalc.html

If you did, tell me what was your reaction? Was the format too technical-looking for you? (I know an alternative, for college freshmen, that has greatly simplified format and language---only a few output numbers and says simply what they are, no jargon. the drawback is that before each session you have to prime it by inputting 3 model parameters .27, .73, and 71 which Wright puts in for you.)
I'd kind of like to know, how did Wright's Cosmo Calculator go with you. Did you try a few different redshifts? Or was it a total blank? What impression did you come away with?

Did you notice that, in the z=3 example it opens with, the distance to the galaxy increases from around 5 to around 21, in the course of about 11 billion years?

In other words, we know thousands of redshift 3 galaxies and the distance to any such galaxy (according to standard model cosmology) increased by about 16 billion lightyears in 11 billion years it too for the light to reach us from the galaxy.

If this is puzzling, you might read the Lineweaver Scientific American article I have link to in my signature at the end of the post. That article is well illustrated and written--it has helped many people understand modern cosmology.

 

[curiousphoton]

How do you picture the U having one single definite speed of expansion that you can compare with c?

Because I only have a background in physics and I really don't know much about cosmology. I deduced it in this way: (1) the universe is expanding aka moving with some velocity. (2) Per every physics problem I've done, if moving matter has a velocity, it may be defined in such a fasion: v = 0.4c, 0.7c, 0.2c, c...etc.

That rate has changes by several orders of magnitude over the course of history (which is why there is no simple pairing between light travel time and the distance measures I mentioned.)

Because it is a percentage rate, large distances expand at a larger km/s rate than small do.
It's easy to find galaxies which we can see and have catalogued where the distance to them, according to Hubble law v = Hd is growing faster than c.

Nothing remarkable most known galaxies have redshift >1.7 and with any such galaxy the distance to it would be growing at km/s rate >c.

Now we are talking. That is very interesting. Thank you.

I'm curious, Curiousphoton, did you indeed go to wright calculator and look at the
z=3 example that immediately comes on?
http://www.astro.ucla.edu/~wright/CosmoCalc.html

If you did, tell me what was your reaction? Was the format too technical-looking for you? (I know an alternative, for college freshmen, that has greatly simplified format and language---only a few output numbers and says simply what they are, no jargon. the drawback is that before each session you have to prime it by inputting 3 model parameters .27, .73, and 71 which Wright puts in for you.)
I'd kind of like to know, how did Wright's Cosmo Calculator go with you. Did you try a few different redshifts? Or was it a total blank? What impression did you come away with?

Nope not to techanical. It is very nicely set up and looks to be geared toward high school level and up.

The variables within the Wright Calculator meant nothing to me. I'm going to have to read the tutorials because this is all new stuff to me.

Thanks for all of the info. You've been patiently helpful.

 

[Endervhar]

Thanks for all the contributions. This turned into a very interesting and informative thread.

One problem, though; I am still not sure if a perfectly flat, finite universe could exist without a boundary, and if it could, how this could be.

The consolation prize is that I think I have a better grasp of the complications involved in looking at distant things in an expanding universe.

 

[Chronos]

A perfectly flat universe is spatially infinite. A finite universe curves back upon itself. This is, however, essentially useless information. Our universe is so large it may as well be spatially infinite. The observable universe is, however, temporally finite and bounded. The temporal boundary is about 13.7 billion years in our past - the surface of last scattering [CMB]. God has a wonderful sense of humor. Every time we think we almost have it all figured out, a weird observation crashes our GUT party.

 

[Endervhar]

A perfectly flat universe is spatially infinite.

Could we be getting somewhere? Perhaps I could ask for comments on my line of thought from here.

If the Universe is flat, it is spatially infinite.
Nothing that is finite can become infinite.
If the Universe is infinite, it has always been infinite.
The Universe must have been infinite at the point of the Big Bang.
If the Universe is spatially infinite, and nothing finite can become infinite, it is also temporally infinite (eternal).
If the Universe is eternal, it must have existed before the BB.

Every time we think we almost have it all figured out...

 

[marcus]

A perfectly flat universe is spatially infinite...

Could we be getting somewhere?

Be careful. Chronos is stating a personal opinion. Not part of professional cosmology and not suppoted mathematically. So you would be starting your train of reasoning on shaky ground.

You said the one thing you didn't understand was how a flat, spatially finite, boundaryless U could exist. Do you want to try to understand that? Or is it more attractive to you to discuss your train of thought leading to the "eternal universe" conclusion?

It is up to you what we discuss.

 

[Endervhar]

Thanks marcus, warning noted.

Yes, I do want to try to understand how a flat, spatially finite, boundaryless Universe could exist. I am quite willing to accept that my train of thought might contain errors, and I would certainly rather not arrive at a conclusion based on these. Been there, done that!

 

[marcus]

EDIT: Whoah! I didn't see your post #37 while I was typing this. It looks like my post #38 here is completely unnecessary, and perhaps a bit grouchy. I will not delete it, but will try to quickly respond to what you just said in a followup to this.

Perhaps I could ask for comments on my line of thought from here.

If the Universe is flat, it is spatially infinite...
..., it must have existed before the BB.

My main comment would be that although the starting premise is unfounded and the logic is not perfect, the CONCLUSION is accepted by lots of professional cosmologists as a real possibility.

The idea has become increasingly popular with the pros in the past few years, and it dominates the research literature in a subfield of cosmology called quantum cosmology.

So your CONCLUSION ("existed before BB") is not novel or surprising. You are in good company---hundreds of experts.

They come to that conclusion by starting with the classic mainstream equation model of the U based on Einstein's GR equation (the geometric way gravity works) and quantizing the equation model of the U. Then they find that there is no "singularity" at the start of expansion. Typically, or in many cases studied, solving the equation model shows a simple bounce----a contracting collapsing U reaching a high enough density so that quantum effects dominate, gravity repels, and there is a violent rebound. Some work suggests that this bounce was favorable to inflation and may have triggered it, or ensured that the inflation episode was sufficient to make a U matching observations. Ways to test observationally, testing bounce and inflation ideas together, have been proposed. It is an active research field these days!

At this point most cosmologists would be surprised if it turned out that the U did NOT exist before BB. (This is discussed in the Einstein-online link in my sig, public outreach from a branch of the Max Planck Institute. The discussion might interest you.)

At this point you are kind of at a fork in the road. You can try to understand why so many cosmologists are working on equation models which don't develop a singularity and which yield results where the U goes back before bang, i.e. before start of expansion.

AFAICS their reasons are unrelated to your chain of reasoning and do not depend on the concept "eternity" at this point in the game.

Or, alternatively, you can ignore what the mainstream research community is doing and ask us to comment on your personal chain of reasoning.

The question is, which are you more interested in doing? I have no preference---I'm good with either but not with both at the same time, there should be some clear focus.

 

[marcus]

Responding to your post #37, which I didn't see earlier:

OK, it looks like you want to go the route of getting acquainted with this current research initiative into "before bang" models.

There is that public outreach website from the German national research establishment MPI. It has an essay called "A Tale of Two Big Bangs" which gives some of the reasoning.

The MPI (Max Planck Institute) is very big, old, reputable and mainstream. Nothing in science is sure and eventually all theories are seen to be flawed and must be improved on. But MPI is at least not some crackpot outfit. You might try their essay A Tale of Two Big Bangs.

There was a sea-change around 2005. I would ignore outreach writings from before 2006. The MPI stuff "Einstein-online" is at least recent. So you could try it.

I'm going to propose that even if you are a complete tenderfoot (slang for newcomer) you take a look at the actual current research in quantum cosmology (QC) and just be sure not to get bogged down or scared by technical detail you don't understand.

Here is the professional research literature in quantum cosmology after 2006 ordered by citation count---that means the most cited papers (usually the more important, more highly valued by other researchers) are listed first.

If you want a brief summary of any paper, just click "Abstract". If you want a complete PDF of the article you can usually get that by clicking "PDF" on the abstract summary page. Often the first and last paragraphs of a research paper are written in ordinary English. Well, sometimes they are. But the main thing is to scan the TITLES and authors to get an idea what TOPICS and who is doing research that gets cited by other research.

If you have eyeballed the listing of the, say, top 50 papers in QC, post 2005 or post 2006, then it helps me talk to you because then if I say "Abhay Ashtekar" to you it will not be some strange out of the blue incomprehensible signal. The name will ring a bell.

Somewhere on that list (not yet up near the top) there should be papers by a model-testing expert named Aurelien Barrau. He looks for ways to shoot down models by comparing with observational data, like cosmic microwave background maps which are getting constantly more precise. They bear traces of what happened in early U. He is not a theorist with a stake in anyone theory or model. He is what is called a phenomenologist (their specialty is putting models on trial).

So let's look. Spires is the Stanford database for research papers. We will use the keyword "quantum cosmology" and do a search of the professional literature post 2006.

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=dk+quantum+cosmology+and+date%3E2006&FORMAT=WWW&SEQUENCE=citecount%28d%29

Can you get this on your computer? Sometimes it takes a couple of minutes. If the Stanford search engine is busy. May also time out, but just try again.

I also want to look at the same search but post-2007. To see where the newer papers are going. There may be some trend. Or we could look post-2008

 

[marcus]

Yes! This post-2008 search gives a much clearer idea of where the field is really going.

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+DK+QUANTUM+COSMOLOGY+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%28d%29

Do have a look! You can see the testing people---the phenomenologists---recent entry into the field. They are rising in the cite-count lists as the importance of testing, and its technical feasibility, is increasingly recognized.

On this list you see a phenom paper by Julien Grain down around #27 and right after it #28 a paper by Barrau (co-authored with Grain and Mielczarek).

Now I see also that #6 and #13 are phenom papers as well. They are deriving from the bounce cosmo model feature that they can look for in the CMB (microwave background temp and polarization maps)

Don't worry about the technical details. The primary interest is how observational testing is coming to the forefront.

Also in post-2008 QC you see a lot of "spinfoam" cosmology papers in the top-cited 25 or 50. That is new. If you look at post-2006 you don't see them because older papers (which have had more time to accumulate cites) dominate the list.

The very recent stuff has not had time to build up a substantial number of cites, so we don't see it. But we see the trend.

There is already quite a contrast between the post-2006 and the post-2008 list.

When I went back, the Stanford Spires was slow, so I am going to try the German mirror site "DESY search"
http://www-library.desy.de/spires/hep/
That worked better:
http://www-library.desy.de/cgi-bin/spiface/find/hep/www?rawcmd=find+dk+quantum+cosmology+and+date+%3E+2008&FORMAT=WWW&SEQUENCE=citecount%28d%29

 

[Endervhar]

Marcus, thanks for the mass of info. I certainly wouldn't have considered your post #38 as grouchy. I post on a couple of other fora (forums?) and compared with some of the responses on those, anything I have seen on PF would be pleasant and immersed in smilies.

In spite of my being retired, time tends to be in short supply, as is my technological expertise, so wading through the links will probably take a while. My possible absence should not be taken as a sign of loss of interest.

 

[marcus]

...

In spite of my being retired, time tends to be in short supply, as is my technological expertise, so wading through the links will probably take a while. My possible absence should not be taken as a sign of loss of interest.

Since time is short, I will offer my take and spare you the trouble of sifting thru the evidence. I find that when you search the QC (quantum cosmo.) field a large portion of the models have a bounce.

I see that people quantize classic Einstein-based cosmo equations and they either solve the resulting system or they run computer simulations, i.e. solve numerically. Time and time again they get a bounce. It is what is called a robust prediction---doesn't depend on fine tuning or special cases. Bounce means that time doesn't end as you go back, dynamical evolution continues on back in time before start of expansion, no singularity.

If you look at the top 50. The fifty QC papers most cited, it is mostly LQG-based quantum cosmology. Loop quantum gravity. Its predominance is a fairly new feature of the situation.
You might expect Hawking papers, or stringtheory cosmology papers, instead of LQG.
But no, I think in the second search I linked, the most cited Hawking paper was only #50. Fortynine other papers were more cited.

If you want to check, you can look down the list of the top 50. Not all LQG papers are labeled as such, but you will often see the word "Loop" in the title, and you will see a lot of papers by Ashtekar, and by people who you see by looking at other papers have coauthored with Ashtekar. His former students, former postdocs, colleagues at PennState, etc.

Loop is the leading type of quantum cosmo that produces a bounce.

Then if you look at the most recent the post-2008 you see a lot of occurrences of the term "spin foam" in the title. Spinfoam models applied to cosmology are a new LQG development. You will see Ashtekar and his team getting into spinfoam cosmology, but also people from a different group, Rovelli's team at Marseille.

And, as I mentioned before, there is the sudden appearance of the phenom'ist people, the professional theory testers.

Basically there has been a big change in quantum cosmology. Much of it quite recent.
A lot of this involves a robust theoretical prediction which runs the model smoothly back into the past before the bang. And which so far agrees with observation as well as the classical model agrees, which is pretty well all things considered.

===============
Now you don't have to work on it. You can take my interpretation and summary on faith, and if you want you can check up. Look at the research publication data for yourself. But only if you want to. I think I've given an objective and fair report, but you should be able to check anything you feel like checking.

 

[Endervhar]

Thanks for the summary. So far I've found some nice simple stuff on MPI, and some nasty complicated stuff on Spires. Currently looking for something in between.

 

[Chronos]

Be careful. Chronos is stating a personal opinion. Not part of professional cosmology and not suppoted mathematically. So you would be starting your train of reasoning on shaky ground.

You said the one thing you didn't understand was how a flat, spatially finite, boundaryless U could exist. Do you want to try to understand that? Or is it more attractive to you to discuss your train of thought leading to the "eternal universe" conclusion?

It is up to you what we discuss.

I'm flattered, but, unworthy. I assumed this was common knowledge and failed to cite a credible source - like NASA:
http://wmap.gsfc.nasa.gov/universe/bb_concepts.html
"... Given the assumption that the matter in the universe is homogeneous and isotropic (The Cosmological Principle) it can be shown that the corresponding distortion of space-time (due to the gravitational effects of this matter) can only have one of three forms ... It can be "positively" curved like the surface of a ball and finite in extent; it can be "negatively" curved like a saddle and infinite in extent; or it can be "flat" and infinite in extent ..."

 

[marcus]

Outreach site, contains a technical error. "Universe 101" does not have footnotes to authoritative sources and is not one itself. Popularization like that often glosses over finepoints and may be re-written largely by staff or dumbed-down in the editing process.
Again, general warning, be careful with info off the internet.

 

[Chronos]

Acknowledged, marcus. In cosmology, the truth is rarely as simple as it appears in popular accounts. Another source:

arXiv:0802.2236v1
The Shape and Topology of the Universe
Authors: Jean-Pierre Luminet

page 11
“In most studies, the spatial topology is assumed to be that of the corresponding simply connected space: the hypersphere, Euclidean space or the 3D-hyperboloid, the first being finite and the other two infinite.”

Footnote: a "hypersphere" represents a closed [omega > 1] universe, "Euclideans space" is flat [omega = 1], and "3D hyperboloid" [omega < 1] represents an open universe. See excerpt from p13.

p 12
“From an astronomical point of view, it is necessary to distinguish between the “observable universe", which is the interior of a sphere centered on the observer and whose radius is that of the cosmological horizon (roughly the
radius of the last scattering surface), and the physical space. There are only three logical possiblities. First, the physical space is infinite - like for instance the simply connected Euclidean space. In this case, the observable universe is an infinitesimal patch of the full universe and, although it has long been the preferred model of many cosmologists, this is not a testable hypothesis.”

p 13
“The “concordance model" of cosmology describes the Universe as a flat infinite space in eternal expansion, accelerated under the effect of a repulsive dark energy. The data collected by the NASA satellite WMAP [11] have produced a high resolution map of the CMB which showed the seeds of galaxies and galaxy clusters and allowed to check the validity of the dynamic part of the expansion model. However, combined with other astronomical data [12], they suggest a value of the density parameter 0mega = 1:02 +/-0:02 at the 1 sigma level level. The result is marginally compatible with strictly flat space sections. Improved measurements could indeed lower the value of omega closer to the critical value 1, or even below to the hyperbolic case. Presently however, taken at their
face value, WMAP data favor a positively curved space, necessarily of finite volume since all spherical spaceforms possesses this property.”

As the author notes in this paper, a flat universe is not necessarily spatially infinite. There are any number of possible bounded [finite] 3D manifolds with flat topologies - cylinder, torus, poincare dodecahedron, etc. Signs of these other possible manifolds have been searched for, but, have not been found. The simply connected, spatially infinite model is the simplest explanation, and the one preferred by most cosmololgists.

 

[Xander756]

I've always wondered about this question myself. I don't mean to sound like an *** but there has been a lot of posts in this thread since the question was asked and without having to go back and read every single post, could someone give me a brief rundown of the discussion/answer thus far?

I'd also like to ask my own question on top of this (hoping it hasn't already been asked) but couldn't the universe be more than 13.7 billion years old and we just can't see out past that because the light hasn't reached us yet? So the observable universe goes out to 13.7 billion years but it could actually be much larger and older?

 

[Chronos]

The universe could be infinitely old, just not the part we can observe. That part is 'only' 13.7 billions years old. Light from more distant regions can never reach us. We are forever trapped by the CMB boundary. In fact, the light 'currently' emitted by many objects we presently observe will never reach us. They will not just go 'poof' and vanish, merely redshift into obscurity. Our observable universe is temporally, not spatially bounded.