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KingNor
2008-Oct-17, 05:15 PM
So I've been trying to wrap my mind around something for a little bit and I'm not exactly sure how to articulate it, but here goes:

Normally the further you look into the distance the more you see, what I mean is the whole arc second thing. The moon is close and it's small, but because it's close it appears the same size as the sun, which is big and far.

Ok? So my question is that when we look into the deep universe, we're seeing back.. billions of years, right? ..so, how does it work when we look 10 billion years back in time, we're looking at a much smaller universe?

I have weird notions that we'd be seeing an effect where objects that are small might appear huge behind closer objects which are the same size (in an overly extreme example). It's like, if a galaxy is 11billion years old, and we're seeing it 11 billion light years away and it's the same physical size as a galaxy that's only 100 light years away, what would the older distant galaxy look like? Aren't we looking into "smaller space".

How does our visual cone, penetrating into the distant, less expanded old version of our universe work?

What's hurting my mind is that we live in an expanded (big) universe that should appear to be completely surrounded by an ever smaller looking universe the farther we look away from us (and back in time). How can the big egg be inside the small egg?

How's that work?

My poor brain. :confused:

speedfreek
2008-Oct-17, 05:43 PM
So my question is that when we look into the deep universe, we're seeing back.. billions of years, right? ..so, how does it work when we look 10 billion years back in time, we're looking at a much smaller universe?

Completely correct!

I have weird notions that we'd be seeing an effect where objects that are small might appear huge behind closer objects which are the same size (in an overly extreme example). It's like, if a galaxy is 11billion years old, and we're seeing it 11 billion light years away and it's the same physical size as a galaxy that's only 100 light years away, what would the older distant galaxy look like? Aren't we looking into "smaller space".

Your notions are not weird at all, you are describing what cosmologists call the angular diameter - redshift relationship.

If we take the most extreme example, the highest redshift galaxy we have detected is a z=6.96 galaxy whose light has been travelling for nearly 12.9 billion years. That galaxy has an angular size (how large it looks) that puts it at an original distance of around 3.5 billion light-years away, when it emitted the light we are now seeing.

If we look at a "closer" galaxy, with a redshift of "only" z=1.4, the light from that galaxy has only been travelling for 9 billion years, and the galaxy has an angular size that puts it at around 5.7 billion years away when it emitted the light we now see.

The higher redshift z=6.96 galaxy is a lot dimmer but is also a lot larger than the lower redshift z=1.4 galaxy, as it was a lot closer to us when it emitted its light than the z=1.4 galaxy was.

The Distance Scale of the Universe (http://www.atlasoftheuniverse.com/redshift.html)

And for a more technical description of the angular diameter - redshift relationship:

Observational Cosmology: World Models and Classical Tests (http://www.astr.ua.edu/keel/galaxies/obscosmo.html)

PraedSt
2008-Oct-17, 05:48 PM
You know, that's a really good question...:confused:

alainprice
2008-Oct-17, 06:07 PM
If we look at a "closer" galaxy, with a redshift of "only" z=1.4, the light from that galaxy has only been travelling for 9 billion years, and the galaxy has an angular size that puts it at around 5.7 billion years away when it emitted the light we now see.

The higher redshift z=6.96 galaxy is a lot dimmer but is also a lot larger than the lower redshift z=1.4 galaxy, as it was a lot closer to us when it emitted its light than the z=1.4 galaxy was.

The Distance Scale of the Universe (http://www.atlasoftheuniverse.com/redshift.html)

And for a more technical description of the angular diameter - redshift relationship:

Observational Cosmology: World Models and Classical Tests (http://www.astr.ua.edu/keel/galaxies/obscosmo.html)

I want to repeat what is being said.

If you look back far enough, that galaxy was actually very close when the light was emitted.

Imagine the moon gives off a flash of light right now, but for some reason, it's also flying away from us. By the time we see the flash, it is as far as the sun. Guess what? The moon flash will look just as big as we are used to seeing the moon, because that's where it was when the flash occured.

Far away galaxies look a lot bigger than you would expect.

speedfreek
2008-Oct-17, 11:32 PM
To take the idea of "looking back into a tiny distance" even further, we might consider the Cosmic Microwave Background Radiation (CMBR).

The theory here is that it was around 380,000 years after the Big-Bang that the CMBR was emitted throughout the universe, and those CMBR photons were the first independent photons.

Back to the present, and we detect these CMBR photons coming in from all directions. So, assuming that all these photons travel at the same speed, the ones we currently detect must all have been emitted at approximately the same distance away, and we could represent that distance as a sphere of "emission coordinates" with us in the centre of it.

That sphere, known in cosmology as the surface of last scattering, is thought to have had a radius of only around 42 million light-years when the CMBR photons we detect were originally emitted. Any CMBR photons that were originally emitted at distances closer than 42 million light-years and were heading in this direction have already passed us by. Any CMBR photons that were originally emitted at distances larger than 42 million light-years and are heading towards us, have yet to reach us.

So we can "look" back to when our observable universe was relatively tiny - only 42 million light-years in radius. I say relatively tiny, as 42 million light-years seems like a huge distance, but to put it into context we think that the coordinate where those CMBR photons were emitted from, if it moves with the expansion of the universe, would now be over 46 billion light-years away. This is where we get the current size of the observable universe from.

So to sum up, we think the observable universe has expanded from being 42 million light-years radius when the CMBR was emitted to 46 billion light-years in radius today. We can only see back to 380,000 years after the Big-Bang and the observable universe then was tiny, when compared to the size we think it is now.

grant hutchison
2008-Oct-18, 12:20 AM
A diagram (http://www.ghutchison.pwp.blueyonder.co.uk/lookback.jpg) from Edward Harrison's Cosmology: The Science of the Universe, 2nd Edition (ISBN 0 521 66148 X), which I trust falls within the bounds of fair quotation, since all on its own it explains why Tim Thompson keeps telling you that you really should go out and buy this book. :)

Time is marked along the radial lines, space along the circumferences. Our lightcone visibly connects back into to a smaller Universe, and you can imagine that the circle around the words "big bang" marks the surface of last scattering for the cosmic microwave background radiation.

Grant Hutchison

KingNor
2008-Oct-18, 12:41 AM
I was wondering because.. in essence with enough time, it would be possible to do a hubble deep field survey that mapped an entire sphere around earth, one can imagine that sphere covered with ancient galaxies.

but since we'd have mapped a smaller "primitive" universe than the "current" expanded one we're in now, the 'image' of all those galaxies has to essentially be stretched.. right?

This sounds very mind bending, but I'm surprised I've never heard this mentioned before when talking about really distant stuff. Is it because the concept is very hard to describe and visualize so when talking publicly about this stuff, its just not brought up?

I can imagine that diagram of space, time, and light cone would be quite upsetting to a lot of people.

Cougar
2008-Oct-18, 01:03 AM
The higher redshift z=6.96 galaxy is a lot dimmer but is also a lot larger than the lower redshift z=1.4 galaxy, as it was a lot closer to us when it emitted its light than the z=1.4 galaxy was....

Great couple of posts, there, speedfreek.

...we think the observable universe has expanded from being 42 million light-years radius when the CMBR was emitted to 46 billion light-years in radius today.

That seems like a pretty high rate of expansion. But then, 13 billion years doesn't just seem like a long time...

RussT
2008-Oct-18, 01:30 AM
Completely correct!

Your notions are not weird at all, you are describing what cosmologists call the angular diameter - redshift relationship.

If we take the most extreme example, the highest redshift galaxy we have detected is a z=6.96 galaxy whose light has been travelling for nearly 12.9 billion years. That galaxy has an angular size (how large it looks) that puts it at an original distance of around 3.5 billion light-years away, when it emitted the light we are now seeing.

If we look at a "closer" galaxy, with a redshift of "only" z=1.4, the light from that galaxy has only been travelling for 9 billion years, and the galaxy has an angular size that puts it at around 5.7 billion years away when it emitted the light we now see.

The higher redshift z=6.96 galaxy is a lot dimmer but is also a lot larger than the lower redshift z=1.4 galaxy, as it was a lot closer to us when it emitted its light than the z=1.4 galaxy was.

The Distance Scale of the Universe (http://www.atlasoftheuniverse.com/redshift.html)

And for a more technical description of the angular diameter - redshift relationship:

Observational Cosmology: World Models and Classical Tests (http://www.astr.ua.edu/keel/galaxies/obscosmo.html)

Linear development of perturbations won't cut it to clump matter fast enough; there is something major here that we don't know about making galaxies.

And, I hesitate to do this here, because speedfreek has posted quite a few of these kind of 'supposed' mainstream expansion scenarios, and none of the "Pro's" have jumped in to correct any of them, BUT as soon as I show the following, that will, IMHO definitely happen...;)

And, this goes straight to the OP's...

How can the big egg be inside the small egg?

If we take the most extreme example, the highest redshift galaxy we have detected is a z=6.96 galaxy whose light has been travelling for nearly 12.9 billion years. That galaxy has an angular size (how large it looks) that puts it at an original distance of around 3.5 billion light-years away, when it emitted the light we are now seeing.
If we look at a "closer" galaxy, with a redshift of "only" z=1.4, the light from that galaxy has only been travelling for 9 billion years, and the galaxy has an angular size that puts it at around 5.7 billion years away when it emitted the light we now see.
The higher redshift z=6.96 galaxy is a lot dimmer but is also a lot larger than the lower redshift z=1.4 galaxy, as it was a lot closer to us when it emitted its light than the z=1.4 galaxy was.My Bold

This will show how disconnected from reality this whole expansion from a 'point' really is!

How did the High Z galaxy (Whether it is a Dwarf/Spiral/ or Elliptical) "Pass" the lower Z galaxy???

grant hutchison
2008-Oct-18, 02:22 AM
How did the High Z galaxy (Whether it is a Dwarf/Spiral/ or Elliptical) "Pass" the lower Z galaxy???It didn't.
You really need Edward Harrison's book, which I cited above. In fact, the diagram I offered shows what's going on in speedfreek's (entirely mainstream) description.
The high-z galaxy has always been farther away than the low-z galaxy. It emitted its light towards us during the early life of the Universe, at a time when both galaxy and light were being carried away from us faster than light by the expansion of the Universe. After a long time, when the Universe was considerably larger, and expanding more slowly, the light from the high-z galaxy (now cosmologically redshifted by the expansion of the Universe) eventually passed the closer low-z galaxy. The low-z galaxy was by that time (because of the expansion of the Universe) farther from us than the high-z galaxy was when it emitted its light. Light from high-z and low-z then continued towards us, undergoing further cosmologically redshift, until eventually they arrived simultaneously here on Earth.
So it's routine for models of the expanding Universe to produce high-redshift galaxies which have lower distances at their look-back time than do medium-redshift galaxies: the details depend on the model. The effect is visible in my earlier linked diagram (http://www.ghutchison.pwp.blueyonder.co.uk/lookback.jpg), in which the past light-cone of galaxy A begins to narrow after having achieved a maximum width. You see the same thing in the graph on the Distance Scale Of The Universe (http://www.atlasoftheuniverse.com/redshift.html) webpage. The angular diameter distance DA reaches a maximum at redshift 1.65 and then declines: we see very high-redshift galaxies closer than those at medium redshifts, and the numbers match what speedfreek has told you.

Grant Hutchison

RussT
2008-Oct-18, 05:49 AM
It didn't.
You really need Edward Harrison's book, which I cited above. In fact, the diagram I offered shows what's going on in speedfreek's (entirely mainstream) description.

Great, so you have endorsed speedfreek's (entirely mainstream) description.

The high-z galaxy has always been farther away than the low-z galaxy.

That's NOT what this said that I even Bolded

The higher redshift z=6.96 galaxy is a lot dimmer but is also a lot larger than the lower redshift z=1.4 galaxy, as it was a lot closer to us when it emitted its light than the z=1.4 galaxy was.My Bold

It emitted its light towards us during the early life of the Universe, at a time when both galaxy and light were being carried away from us faster than light by the expansion of the Universe.

UH,er, how long did "Inflation" last??? Galaxies weren't even formed yet, when there was 'supposedly' faster than light (Superluminal) expansion in the 'early universe'

Please respond to these first and then we'll get into the rest.

speedfreek
2008-Oct-18, 12:44 PM
There is always superluminal expansion at a certain distance. The surface of last scattering was receding at something around 58 times the speed of light when the CMBR was emitted (when that surface was 42 million light-years away), and it is still receding at around 3 times the speed of light now (as it is 46 billion light years away).

With metric expansion there will always be a distance where a co-moving coordinate is receding at the speed of light, and so a distance past which objects apparently recede superluminally. This distance is known as the Hubble Radius. Let me try to explain.

Let's make a model to illustrate an easy example of metric expansion.

Now to model an expanding volume with space in it, we need to assign coordinates within that space. For the moment, forget about any edges to the volume, we don't need edges, we just need coordinates in order to measure the expansion of a volume of space. Galaxies come later, so for now just imagine a 3 dimensional grid. At each grid intersection we will assign a coordinate, a point, a dot. Let's say each intersection point is 1 meter apart.

Put yourself on a point somewhere in this volume. Whatever axis you look along you see neighbouring points 1, 2, 3, 4, 5 etc meters away, receding off into the distance. Then we introduce some expansion. Let's say the volume grows to 10 times its original size in 1 second! That seems fast perhaps, but this is just a model with easy numbers. The key thing to remember is that the grid expands with the volume.

So, here we are, still sitting on our point (but it could have been any point) 1 second later. Now lets look along an axis. We see those neighbouring points are now 10, 20, 30, 40, 50 etc meters away. The volume increased to 10 times the size, and so did the distance between each intersection point on that grid.

Our nearest neighbouring point has receded from 1 to 10 meters in 1 second, so it has receded at 9 meters per second. The next point away has receded from 2 to 20 meters in 1 second, so that point receded at 18 meters per second. The fifth point has moved from 5 to 50 meters away in 1 second, so that one has receded at 45 meters per second. The further away you look, the faster a point will seem to have receded! And the view would be the same, whatever viewpoint you choose in the grid.

Remember I said the grid of points receded off into the distance.. well a point that was initially 33,000,000 meters away will have moved away to 330,000,000 meters in 1 one second, meaning that it has receded at 300,000,000 meters per second - the speed of light. Any point initially more distant than 33,000,000 meters away from another point will have receded from that point faster than the speed of light. That is the distance were an object recedes at light speed in this "little" model of expansion. If you look at a point that has receded at the speed of light, then from that point, the point you are on has receded at the speed of light.

So now we can consider the distance where an object (or a co-moving coordinate) is apparently receding at the speed of light. As the rate of expansion (or more accurately, the change in the scale factor of the background metric) was incredibly fast in the early universe, this means that the distance at which a co-moving coordinate was apparently receding at c was very close to this point in space. Imagine, if you will, that right after the Big-Bang (or inflation) distances down at the Planck length were increasing at the speed of light, but that the rate of expansion instantly decelerated from that value. Inflation itself is a special case where even down at the planck length, the distance between two co-moving coordinates was increasing superluminally.

If the expansion rate had remained constant, then so would the distance at which a co-moving coordinate was receding at c would have remained constant. But the rate of expansion decelerated over the first six billion years or so and therefore the distance at which a co-moving coordinate was apparently receding at c became larger.

After inflation the observable universe was the size of a grapefruit, but 380,000 years later it had a radius of around 42 million light years. The edge of the observable universe had, at that point, receded from what would become this point in space at many multiples of the speed of light in order to move 42 million light years in only 380,000 years, so at that point the distance where a co-moving coordinate was receding at c would have been well within that radius.

And yet, we receive photons today that were emitted from the edge of the observable universe all those years ago. We receive photons that were emitted from the "surface of last scattering", which was receding from this point in space at 58 times of the speed of light at the time those photons were emitted. They were only 42 million light years away when they were emitted, but they took 13.7 billion years to reach us, passing galaxies that had subsequently formed along the way.

The rate of expansion continued to slow, and after something over 100 million years, the earliest galaxies formed. The observable universe was something around 2 billion light years in radius at that time. We have seen dim blobs that might be these galaxies, but the oldest, dimmest, most distant galaxy we have reliable measurements for emitted its light around 800 million years after the Big-Bang, it has a redshift just under z=7 and is estimated to have been 3.5 billion light years away when it emitted its light.

Now lets look at a galaxy at redshift z=3. This (much brighter) light was emitted when the universe was 2.2 billion years old, 11.5 billion years ago when that galaxy is estimated to have been 5.3 billion light years away.

Now we move closer still to redshift z=1.4 and here is where we find the galaxies that are apparently receding at the speed of light – that is, they were receding at the speed of light when they emitted the light we are now seeing. The light we are seeing was emitted when the universe was around 4.6 billion years old, just over 9 billion years ago. These galaxies are estimated to have been 5.7 billion years away when they emitted the light we see, and what is more, they are the most distant objects we have seen in the universe! Let me say that again. Objects that are apparently receding at the speed of light are the most distant objects we have actually seen. Let me explain what I mean by this...

We use measurements of a galaxy's angular diameter (how big the object actually looks in the sky) to determine how far away they were when they emitted the light we are now seeing. This makes sense, as you always see any object at the distance it was when the light left it, regardless of whatever it does or however it moves afterwards. Anyway, that is how astronomers determine the distance a galaxy was from us when it emitted the light we are now seeing (of course, they also have to determine what the galaxy's actual or absolute size was to do this, and this is a whole other subject unto itself!).

We find that the most distant galaxies by angular size are the ones that are apparently receding at c, and yet we see light from more distant (in time) galaxies that are dimmer and more redshifted and yet those galaxies have increasing angular diameter the further we look in that direction.

Lets look at the figures (The first line is the CMBR or surface of last scattering) I took from Ned Wrights cosmology pages.

Redshift____Distance then____Time since emission
z=1089_____42 million ly_____13.7 billion years ago
z=7________3.5 billion ly_____12.8 billion years ago
z=3________5.3 billion ly_____11.5 billion years ago
z=1.4______5.7 billion ly_______9 billion years ago
z=1________5.4 billion ly______7.7 billion years ago

So you can see that if our criteria is the object that was furthest away when it emitted the light we are now seeing, then the most distant object we have seen, seen as it was when it was that distant, was a galaxy at redshift z=1.4 at 5.7 billion ly. But we have also seen objects that are a lot older, were a lot closer when they emitted the photons and are now estimated to be a lot more distant as we receive those photons, than the objects that are currently apparently receding at the speed of light!

The key thing to remember is that light never overtakes light. If you look at those figures above and also remember that we received all those photons at pretty much the same time you will find that:

Photons were emitted 3.5 billion light years away, 12.8 billion years ago. 1.3 billion years later, photons were emitted 5.3 billion light years away and if light never overtakes light then those older photons must have “been moved away by the rate of expansion” to that distance. 2.5 billion years later still, photons were emitted 5.7 billion years away and so our older photons must have moved away that far by then. And all those photons reached us at the same time, along with the CMBR which was originally emitted only 42 million light-years away.

So the light from that redshift=7 galaxy was receding from us (as it made its way towards us) from emission at 12.8 billion years ago until it passed the point where objects are apparently receding at lightspeed from us, 9 billion years ago. All light (including the CMBR) we now detect that was emitted before that time was effectively moving away from us whilst it made its way towards us until it passed that point 5.7 billion light years away that was receding at c, 9 billion years ago, and then took another 9 billion years to reach us after that through a universe where the rate of expansion was levelling out and starting to accelerate again.

There has always been superluminal expansion at a certain distance. 9 billion years ago, when that z=1.4 galaxy emitted its light, that galaxy was receding at c. The distance to the Hubble radius (where a co-moving object recedes at c), was 5.7 billion light-years at that time. Today, 9 billion years later, the Hubble radius is around 14 billion light years away.

If you cannot get hold of the book that Grant recommended, may I suggest you read through

Inflation and the Cosmic Microwave Background (http://arxiv.org/abs/astro-ph/0305179)

and

Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe (http://arxiv.org/abs/astro-ph/0310808)

Both these papers contain space-time diagrams that illustrate everything I have said above. Sorry about my layman-like "wall of post" but no doubt somebody like Grant will be able to condense what I have said into something more manageable!

grant hutchison
2008-Oct-18, 01:03 PM
The high-z galaxy has always been farther away than the low-z galaxy.

That's NOT what this said that I even Bolded

The higher redshift z=6.96 galaxy is a lot dimmer but is also a lot larger than the lower redshift z=1.4 galaxy, as it was a lot closer to us when it emitted its light than the z=1.4 galaxy was.My Bold The high z-galaxy was a lot closer to us when it emitted its light than the low-z galaxy was when it emitted its light. Speedfreek walked you through that in the two sentences before the one you chose to quote. But the high-z galaxy was always further away than the low-z galaxy at any instant of cosmic time.

The sequence goes like this:
1) 12.9 million years ago, the high-z galaxy was 3.5 billion light years away from us. At that time, the low-z galaxy lay just over a billion light years from us. The high-z galaxy emitted a photon which started travelling in our direction.
2) The Universe expanded for 3.9 billion years, carrying high-z and low-z galaxy to greater distances, faster than light. During that period, expansion was vigourous enough to expand all distances by a factor of 5.6: the high-z galaxy was now 19.6 billion light years away; the low-z galaxy 5.7 billion light years away.
3) At this time, the high-z galaxy's photon eventually managed to pass the low-z galaxy. It had struggled across the distance between the two galaxies for 3.9 billion years, as space expanded around it. By this time, it had already acquired a redshift of 5.6. The low-z galaxy now emitted a photon which accompanied the high-z photon towards Earth.
3) The Universe expanded for 9 billion years, at a slower rate: the increase in size of all distances is by only a factor of 1.4. This is the redshift factor the two photons acquire during the their journey from the low-z galaxy to Earth.
4) The photons arrive at Earth simultaneously, one with a redshift of 7, and one with a redshift of 1.4.

UH,er, how long did "Inflation" last??? Galaxies weren't even formed yet, when there was 'supposedly' faster than light (Superluminal) expansion in the 'early universe'You're confusing the inflation period (which was very short) with superluminal expansion, which is still happening now, at sufficient distances.
The reason photons have taken 12.9 billion years to reach us across the 3.5 billion years gap which originally separated us from the high-z galaxy is because galaxy and photons were being carried away from us faster than light when the photon was emitted. Although the photon propagated towards us through space at light-speed, space moved away faster than light-speed. That's how the photon ends up 5.7 billion light-years away, after travelling towards us for 3.9 billion years: it has been moved 2.2 billion light years farther away by the time it encounters the low-z galaxy.

Please respond to these first and then we'll get into the rest.No, I've a better idea. Please do some basic reading first, and then get back to us.
I'd suggest Davis and Lineweaver's Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe (http://arxiv.org/abs/astro-ph/0310808). Pay particular attention to Sections 3.2 & 3.3.

Grant Hutchison

speedfreek
2008-Oct-21, 12:16 AM
Sorry KingNor, I missed your post in the ensuing kerfuffle! :)

I was wondering because.. in essence with enough time, it would be possible to do a hubble deep field survey that mapped an entire sphere around earth, one can imagine that sphere covered with ancient galaxies.

but since we'd have mapped a smaller "primitive" universe than the "current" expanded one we're in now, the 'image' of all those galaxies has to essentially be stretched.. right?

Not really. Imagine you are at the centre the observable universe when it was only 800 million years old. There are young galaxies all around you, emitting their light in all directions. The light from the young galaxies that were 3.5 billion light-years away at that time, is the light we are receiving today, 12.9 billion years later. It's as simple as that. We see them at the distance they were.

I don't think of the image as stretched. A quick thought experiment - if light could move instantly and thus you could see the whole universe as it was at any instant, if you go back to when the universe was only 800 million years old, what would all the galaxies 3.5 billion light years away look like if you removed all the others? This is what a snapshot of the universe at a redshift of z=7 would look like, at least in terms of angular size. It looks a lot dimmer though.

You might think of them as the dim ghostly after-images of galaxies that used to be closer than the brighter but more distant galaxies we see!

This sounds very mind bending, but I'm surprised I've never heard this mentioned before when talking about really distant stuff. Is it because the concept is very hard to describe and visualize so when talking publicly about this stuff, its just not brought up?

I can imagine that diagram of space, time, and light cone would be quite upsetting to a lot of people.

I think you may be right, on both counts!