Hi everyone, I've been reading a book recently (Stephen's hawkings expanding universe, The comos explained) and there's something i cant quiet get my head around. i would go as far as to say it's been keeping me up at night trying to figure it out!

This is the Red shift and the expanding universe???

Please take time to read this as although i know what i'm on about i find it difficult to articulate my thoughts, here goes:

hmm, i'll start by saying that the universe began in an explosion, or the big bang as it's commonly known. All this matter is thought to originate from a single point which is the size of a lemon???

Because of the vast amounts of matter and energy, the universe expanded and still is, expanding, accelerating even (now this is where it gets confusing)

How is the universe accelerating, where is this energy coming from?

The red shift 'theory' states that an object moving away from us has certain bands in the light signature (not sure if that the correct terminology) that are positioned further in the red band of light, hence the red shift.

Lets take an object in the far off distant universe; this has a bigger red shift, so is thought to be moving away faster, however, this object being further away is also further back in time!

How can an object which we view in the past be moving faster away from us than an object which is closer to us (I said it would get confusing)

Surely if the universe IS expanding and accelerating then it would be objects closest to us that had more of a red shift as they’d had more time to accelerate!!!

I may be missing something here in my understanding of this but think a constant universe is more understandable. I don’t have Phd in astro physics or anything but I do have a great interest in understanding the natural world and cosmos.

I hope someone can find the time to help me out and maybe I’ll post again.

In a weeks time I’m visiting my parents in Nova Scotia and my dad had just took up astronomy as the sky’s are so clear compared to where he used to live (Newcastle upon tyne) I’m really looking forward to visiting and checking out his new scope as I’ve never used one before.

Anyway thanks for reading this and thanks for the reply, unless of course you’re as confused as me, LOL!!!!!!!

First, let us start with a clear understanding that cosmology is as confusing and complicated as you think it is, and therefore it is not possible to give you complete and definitive answers in a limited forum such as this. So, a few suggestions of placs to read up on the web:

• Ned Wright's Cosmology Tutorial (University of California, Los Angeles)
• Introduction to Cosmology (WMAP Project)
• Cosmology Tutorial (University of Wisconsin)
• Cambridge Cosmology Public Home page (University of Cambridge)

That should do for now.

And I will start by saying that this is a popular and very common misconception. The bang was not an explosion, and cannot properly be thought of as analogous to an explosion. It is an entirely different kind of thing. The "bang" happened simultaneously everywhere in the universe, at all places and all times. There is no center and there is no "edge". Or so it is if general relativity (GR) is a true representation of the physics of spacetime. If not, then scratch everything I said. All statements about the origin and early history of the universe are entirely dependent on assumptions based on a cosmological model. In this case, the model is provided by general relativity, but there are those who argue for other theories, on which to base other models.

A literal interpretation of GR requires that the universe began in a "singular" state, which is commonly misinterpreted to mean "infinitely small", but really means "undefined". The origin of the universe can be neither described nor explained in terms of classical GR. As a result, cosmology has generally not concerned itself with the question of origin, and has contented itself with describing the post-origin history of the universe.

Any theory intended to describe or explain the origin of the universe must, so far as we know, include quantum field theory. But GR, which has no quantum aspects, is the only viable theory of spacetime. So there is much work going on in attempting to "quantize" GR. String Theory & Loop Quantum Gravity are the best known, though there are other efforts underway. Only when such a theory becomes available, will anyone be able to meaningfully address the question of the origin of the universe.

Short answer: Nobody knows.
Long Answer: There is no good physical answer to this question. There are several candidate mathematical answers. The most popular answer amongst cosmologists at the moment is the "cosmological constant" (CC). Originally invented by Einstein and inserted into his equations of general relativity, in order to maintain a static universe, the CC works just as well to force the universe to expand faster than it would if it were just coasting after the bang. A physical interpretation of the CC might be quantum mechanical energy embedded in spacetime. But there are other bits & pieces in Einstein's equations where an expanding force can hide. Quintessence is a cosmological idea that expresses the accelerated expansion in terms of a force embedded in the spacetime equations of general relativity. It has an advantage over the CC in that it is not required to be constant everywhere & everywhen. But it has a disadvantage, in that its functional form is entirely unknown (and maybe unknowable), so we can use quintessence to make universes that accelerate, but then suddenly screech to a halt & contract, for no particular physical reason, but just because that's how the functional form behaves. And there are several other, similar candidates for an acelerating force.

No, but again the answer may not come too easily. The real point of expanding universe ("big bang") cosmology is that the expansion is not a motion of the galaxies through spacetime, but rather a motion of spacetime which carries the galaxies along for the ride. Think of spacetime as a flat elastic sheet, which expands by simultaneously stretching outwards in all directions from every point. As the sheet expands outward, it will carry anything sitting on it. Things that are farther away have a longer distance of stretching sheet between it & us. If the sheet expands at a constant rate, per unit length, a longer distance will then expand faster, because it has a larger number of unit lengths in it. You can see that in the units used to express a numerical value for the Hubble Constant, say about 70 km/sec/Mpc. That's 70 kilometers per second per megaparsec, a velocity (km/sec) per unit distance (Mpc). So, the farther out you get, the greater the expansion velocity. That is the way the expansion of the universe appears to us.

Now, consider the difference between what the universe is, and what the universe looks like. If we understand things more or less correctly, then as we look out at the deep sky, we look farther away in distance, and farther back in time. If the universe is expanding, then as we look farther back in time, we look at a smaller universe. But from where we sit, the universe appears to surround us as ever more distant spherical shells, which look bigger the farther we go. So, as the universe actually gets smaller, the farther awy we look, the bigger it looks from here. So we see the universe as if through a strongly distorting lens, it looks much different than it really is. That's why cosmology is more dominated by mathematics & mathematical models, than are more conventional astronomy & astrophysics.

The universe "is" what it looks like from here. After all, how can we even use the word "is" to describe something that stretches over time, from yesterday, to 10 billion years ago, all at once? This, along with the distortion of distance, makes cosmology a trying thing to talk about!

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The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell

And to Tim's rather complete response across the board, I would add this point to this particular issue. You are right that light from farther away was emitted when the universe was younger and less expanded, but what you are missing is that older light has "aged" with the rest of the universe, and in a sense has "experienced" all the old expansion, in addition to all that new accelerated expansion that the more nearby light is experiencing. Your confusion stems from thinking that the redshift is somehow "frozen in" once the light is emitted, but it's not-- it continues to redshift as the universe ages and expands. For this reason, it is best not to think of that redshift as the Doppler shift of motion of the source, but rather, think of it as a record of the sum total of all the expansion that has occurred since the emission of the light. If you think of it that way, it is obvious that older light is always more redshifted.

While above answers are spot on, I would like to add that even if we would assume that the redshifts would arise from actual motion, the objects closest to us would still exhibit lowest motions (low redshifts) even in accelerating universe. One important thing is that you are talking about motion of distant objects, but you also have to consider our own motion, because it adds to the redshift too. I'll give you one dimensional illustration of this. Here I have one dimensional universe presented in 4 moments of time (A - D), and distance between each object is accelerating so that it doubles between each moment of time (objects: 1 - 4 are galaxies, E is Earth, points represent certain distance of empty space):

Here, object 1 is most distant object from Earth, and during time Earth along some other objects are moving away from it. Notice that object 1 appears to remain still. At moment of time A, distance from all objects to their closest neighbours is one unit of space, presented by one point between each object.

You see that distance between E and 4 increases from one unit of space to two units of space between A and B moments of time so we can say that velocity of E and 4 with reference to each other is one unit of space per one moment of time (at moment of time B).

Similarily, distance between E and 3 increases from two units of space to four units of space between A and B. That means that velocity of E and 3 with reference to each other is 4 - 2 = 2 units of space per one moment of time. So, object 3 has two times higher velocity from Earth's point of view than object 4, and object 3 is twice as far from Earth as object 4. You can repeat this exercise with other objects and other moments of time in my illustration, and you see that in all cases you get higher velocities for more distant objects.

So, my answer to your question would be that even if our closest objects have had more time to accelerate than far away objects, we are also accelerating with them, so there's not much velocity difference between us and our closest objects, but there is huge velocity difference between us and far away objects because we have had time to accelerate.

The illustration can also be presented like this:

Now Earth appears to remain still, but calculated velocities work as before. We can also try to illustrate what Tim says so that objects remain still and more space "grows" between them:

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Ari, it is certainly illustrative to use simple special-relativity pictures to understand redshifts, and the above examples bring in useful insights, but don't be surprised if contradictions appear (like the one raised in the OP) if those pictures are taken too literally, because they have limited applicability in accelerated situations. For example, in the SR picture, there is actually a difference in what you will see on Earth if you compare the first set of models where the Earth was accelerating, and the second set where it is galaxy "1" that is accelerating, if you are not going to do anything special with the light as it propagates from left to right (witness the twin paradox). That's why you really do have to use general relativity, since then it doesn't matter which reference frame you choose to be "stationary". In cosmology, all galaxies share the same overall acceleration, and this is impossible to depict in a simple flat SR-like spacetime as in the above examples. It really has to have curvature, but it is easier to just use the traditional explanation that the light wavelength "expands with the space".

That's true, Ken, and I do have to emphasize that what i presented in my post above is just a though experiment that doesn't present the real situation.

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At BB+10^-43 or-45 what was the volume of "everywhere"? Is this question germane?

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?

Fair enough, there are many helpful ways of thinking of things, and each has its advantages and disadvantages.

It's not really germane, because "everywhere" is not scientifically definable. All we can do is take all the matter that we have observed (the "observable universe") and ask what volume it occupied at that time. But for many practical purposes, this is the same thing as "everywhere", it's just easy to foster misconceptions that way.

Indeed it is. I'm still trying to be sure I am comprehending what the rest of you are saying so I can deal with a most annoying burr under my collar--the quantization, if any, of space expanding that leaves the volume occupied by various masses and the volumes in which they intimately interact unaffected--neutrino, quark, electron, proton, hydrogen, me, asteroid, planet, star, galaxy, local group, cluster, supercluster, etc.,

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?

That's one of the trickiest points of all, that if all space expanded, including the space occupied by particles and bound systems, then it would be as if nothing had happened at all. The reason that something has indeed happened is the contrast between the bound systems, which don't expand, and the space between them, which does. For example, we all live in a pocket of space that has not expanded since our galaxy formed-- expansion is happening out there, not around here. I can't say I have a terribly clear handle on why this is, it may require an absolutely complete understanding of general relativity.

This sounds like the old "tired light" argument and begs the question: where does the energy lost by the light go?

It also makes me wonder why space can expand but not the space between atoms/molecules/subatomic particles? From your statement space can expand between the "ends" of a light wave which leads me to believe that if space can expand in such a small place then the entire universe expands geometrically which also includes the space within my body and my galaxy.

No, it's totally different from tired light, in that it uses general relativity, a proven system, versus inventing new physics just to satisfy a philosophical prejudice. No tired light description works. And the energy doesn't "go" anywhere, but you can think of it as a gravitational effect.

This is a very understandable confusion, but the generally given answer is that space within bound systems (like a galaxy) does not expand, and light within such a space does not redshift. The expansion, and the redshift, occurs only in the huge voids between galaxies.

Perhaps micro is expanding as well as macro. How can we tell if the expanion is tiny and our yardsticks are also expanding? If a length of a billion times a trillion = 10e21 meters is expanding at a million meters per second, then a length of a trillion meters is expanding one millmeter per second and a length of a million meters is expanding one nanometer per second = 3600 nanometers per hour. A length of 1000 meters is expanding 3.6 nanometers per hour, which is difficult to measure, even if our measuring tools are not expanding. Neil

I think the OP wanted a simpler answer than those posted. Here's my try.

The "Big Bang" as the OP understands it is like an explosion and askes how it can continue to accelerate.

Think of a volume of pressurised gas. in the apmosphere it would expand and its pressure would fall untill its pressure was the same as the apmosphere. Then it would stop expanding. The surrounding apmospheric pressure is pushing back on the pressurized volume eventualy stopping the expansion. At first the expanding gas accelerates and then it decelerates to a stop.

Now think of that expanding volume expanding in a vacuum with no apmosphere pushing back on its expansion. It will continue to expand forever and continue to accelerate forever because the pressure outside the volume wil always be less than the pressure inside even if the pressure inside is the vacuum of space inside the universe. The pressure outside has no gasses to push back and stop the expansion.

The thing is that it gets complicated here. Early after the discovery of the red shift it was assumed that the red shift is caused by the movement of distant objects away from us. It was a reasonable assumption because we could demonstrate red shift due to movement at close range experimentaly. The problem with this assumtion and the "Big Bang" description of the universe that developed at tha time gave a picture of the universe that put us nearly at the center.
This rang alarm bells right away because it was known that the history of astronomy had previosly given us an erroneous picture of the universe that had us at the center.
It also gave us a picture that the universe is vastly larger than previously imagined.

A calculation was done and it can be seen that the odds against our just happening to be randomly at the center are 1/1 to the 600th.

With such long odds astronomers and physicists started trying to figure out other pictures of the universe that explaned how we could appear to be at the center but not really be.

This is where the idea of the "expanding" universe comes in. That picture tries to explain it by the analogy to a balloon expanding with the stars and galaxies on it. When the ballon expands the galaxies get farther apart and any point on the ballon has all the other points moving away from each other and the farther points to moving faster. That is called closed finite but unbounded. It is a picture of the universe as a sphere. There is also a picture of the universe called open finite and unbounded. One of the more familiar pictures it paints is of a saddle shaped universe. It also points to an infinite number of other possible shapes.

The current dilema in astronomical physics is that there are some obvious limitations on our perception of the universe at that scale. One is that we can never know the dynamics and content of space, time and light at that scale. We can only make assumptions about it based on what we can observe at shorter scales.

Physics tries to find evidence at shorter scales that would support a conclusion to the matter but so far the evidence is too thin.

Often when questions about this are asked the answers lean towards one picture or the other rather than to point to the variety of possibilities that are still on the table and so the answers get unneccesarily complex.

In a supernova explosion the gravitational well of the former intact star is destroyed by gravitational isolation of the constituent fragments from the core and the other debris - the same is true for the big bang expansion - the expansion gravitationally isolates the galaxies.

The well is destroyed, in a supernova quickly, but also in the big bang.

When we look backwards in time through our telescopes we see that the galaxies from the beginning are isolated just as the galaxies of the present (near by) so I would contend that spacetime expansion is ineffective at redshifting the light from distant galaxies (cosmological redshift) which leaves only the velocity of the galaxies to redshift the starlight.

We know that velocity can redshift light because in viewing spiral galaxies we can discern the direction of rotation by the different amounts of redshift between the different sides: one is coming towards us and the other is moving away from us.

In the Hafele-Keating experiment it was not the relative velocity of the airplanes that caused the time dilation but rather it was the velocity of the airplanes with respect to a common 3rd point, the axis of rotation of the earth. I would contend that the same is true with the universe.

If two galaxies are moving away, in opposite directions, from the common centerpoint of the universe at 0.4c for each galaxy then the relative velocity between the two galaxies is 0.8c but since their velocity with respect to the 3rd point is equal then there is no apparent time dilation between the two galaxies - there is only time lag which is a result of the travel time of light between the two galaxies.

The atomic clocks self-adjust to these common reference systems and so red-shifting of light (a type of clocking mechanism) also self-adjusts to the common centerpoint of the universe.

In other words the redshifting of galaxies leads me to believe that our galaxy is somewhat near the center of the universe because almost all galaxies are redshifted, except a few nearby galaxies.

I think your supposition, which I have bolded above, is incorrect, so of course your conclusion is also. The Hubble Ultra-Deep Field photograph contains roughly 10,000 very distant galaxies, but the field of view of the photo is no more than one-tenth the diameter of the full moon. That's a lot of galaxies crammed into a very small "peep-hole" in space, implying that the early universe was considerably more crowded. Also, as the linked page points out, most of those distant galaxies are very different than the "majestic" spirals and ellipticals we see around us today. They're not "newborn" galaxies, but they're "toddler" galaxies.

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Everyone is entitled to his own opinion, but not his own facts.

That is an interesting point you bring out, Cougar.

In the article it states that the patch of sky represents an area with a diameter one tenth that of the moon.

The moon's diameter is 3,476 km
The average distance to the moon is 384,403 km
The distance to the 10,000 galaxies shown in the photo is roughly 12.5 billion light years.

Setting up a ratio to determine the diameter of the area shown by the photo yields:

0.1*3476 / 384403 = X / 12.5*10^12

X = 11,303,241,650 light years

Roughly 10,000 small circles (representing galaxies) will fit into a circle 100 times the diameter of the small circles and so if we divide X by 10,000 we will get an average distance between galaxies:

Average distance between galaxies in Hubble Ultra Deep Field Photo: 11,303,241,650 / 10,000 = 1,130,324 light-years

Compare this average distance between Hubble Ultra Deep Fiield galaxies to the distance to the closest galaxy to our own Milky Way galaxy: 178,647 light-years.

If I did my math correct then the galaxies in the photo are 10 times farther apart than the distance to our nearest galactic neighbor.

I don't think the gravity well was very effective at such distances and so the redshift for distant galaxies must be velocity produced.

Oops, I made a mistake. I calculated the diameter of the area observed and so to get 10,000 equally sized galaxies into this diameter I should have simply divided the diameter by 100 NOT 10,000 and so the average distance between galaxies in the photo is:

11,303,241,650 / 100 = 113,032,416 light-years!!!!!

This also does not account for volume but simplifies the calculation by putting all the galaxies shown into a single flat plane - the actual 3-D distance between galaxies would be even greater.

Wow, the farther back in time we look the farther apart the galaxies get - sort of like an explosion rather than an expansion. This would also explain why the farther away the galaxies are the faster they recede from us which gives greater redshifts - because the explosion velocities would be greatest on the outer edges of the explosion.

Double oops 'cause I used trillion with 12 zeros instead of billion with 9 zeros and so the average distance between galaxies in the Hubble Ultra Deep Field photo according to my crude calculations is:

113,032 light years.

I used 12.5 billion light years because the generally accepted age of the universe, according to the big bang theory, is 13.7 billion years and the article stated that the photo was of the time 800 million (0.8 billion) years after the big bang which the simple math yields: 13.7 - 0.8 = 12.9 billion years but then I subtracted a "safety" factor and reduced it to 12.5 billion light years.

Given that our best astronomers are not fools, I think you can rest assured that the density of observed galaxies is quite obviously increasing with distance. Or, maybe you think no one ever thought to check?

There's another factor - are lines straight?

In a GR universe, you need to specify the geometry, and when making estimates - of the kind you're attempting - you must apply the geometry so specified.

An example: what is the angular size-distance relationship, in a GR universe?

I mean, if I have a standard 'flat disc', I place such standard flat discs at equal distances (perpendicular to the line of sight), out to 12 billion ly, I measure the angle each subtends on the sky, and plot this against distance, what do I find?

In a Euclidian universe it's easy, right? The observed size is proportional to what power of the distance?

Interesting point, Nereid, does GR affect the apparent distances between the galaxies shown in the Hubble Ultra Deep Field photo?

I did some calculations based upon volume estimates and using simple cubes I calculate that the distance between galaxies is 4.64 times greater than my previous "flat" estimate which now yields: 524,648 light-years between the galaxies.

I basically just created a cube with the sides equal to the photo diameter that I calculated previously and then divided the volume value by 10,000 (the number of galaxies) which gave me a "galactic volume" which I then used to calculate the size of the sphere that fit into the cube.

If my crude calculations are in the ballpark then the universe was quite dispersed even 12.5 billion years ago.

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But then I had another thought that even if it turns out that my calculations are off by a factor of 10 or even 100 and the galaxies are much more tightly grouped than my calculations indicate then what does this new info tell us?

When I look at the photo I see separate and distinct galaxies which if the galaxies are approximately the size of our Milky Way galaxy would mean all the galaxies should be overlapping and colliding everywhere - which I do not see.

If it is true that the galaxies are much closer than my calculations then that tells me that universal expansion not only affects the space between the galaxies but that universal expansion affects the space within the galaxies because the galaxies are much smaller in the past.

This would mean that ideas like snowflakeuniverse's uniform expansion universe are quite likely and, indeed, I may be correct in my suppositions presented in my "Slowing Universe" thread ( I knew so little back then) or Peter Wilson's ideas on the universe.

If all space expands equally, there's no expansion at all, of this you may be sure. Expansion is not an absolute entity, it is a relative entity (like everything else, and certainly everything that has to do with space). What the word really means is that the space between very distant galaxies expands relative to the size of solid objects (like rulers). A ruler is just a bound object, like a galaxy, so galaxies follow what rulers are doing, not what "space" is doing.

As for your density calculation, I applaud your effort to apply common sense to what you are seeing, but you need all the facts. It will interest you to know that galaxies are not spread evenly, they come generally in clusters with huge amounts of void space between them. It is really that huge void space that is expanding, not even the galaxy clusters, since even a galaxy cluster is a bound "object". Thus the distance between galaxies in a single cluster would not be expected to increase. I don't know enough about the Hubble deep field to know if you are seeing all one cluster there, but this fact certainly goes a long way toward solving any problems you are encountering (and rest assured the calculation you are doing has been done, accounting for these important details, though I still think it is good that you would try it yourself. That's the beauty of science, it does not require authority, but it does require a lot of knowledge).

What defines a cluster - I must ask? I believe it should be the fact that the galaxies are gravitationally bound to each other.

But then even clusters can be gravitationally bound to other clusters - there is no clear demarcation between bound and unbound or is there?.

Then there is the question of cluster size or membership: how many galaxies are in the "average" cluster?

This photo also makes me wonder about the generations of star formation because "generation I" stars are supposed to burn out, explode and then the debris collapses to form "generation II" stars - these explosions should become visible as we look backward in time since such supernovas should produce quite a pronounced flash (supernovas are supposed to be so bright as to outshine their galaxy).

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One might read these latest posts and wonder what this talk of the HUDF photo has to do with redshift but, in my opinion, this current talk deals with the heart of the currently accepted redshift mechanism: cosmological redshift.

Da-da-lump! Da-da-lump! Da-da-lump! Celestial Mechanic rides to the rescue again!

Here's how the average distance of galaxies in the Hubble Ultra Deep Field should be calculated. First of all, the galaxies are not all at the same distance, certainly not at the maximum distance of 12.5 billion light-years that was adopted. Some of the galaxies are close by (maybe less than 100 million light-years), others farther away. So what we need is the volume of the square pyramid of "height" 12.5 billion light-years and base of area b which will be determined.

We are given that the field is 1/10 of the Moon's angular diameter across. Since the Moon's angular diameter is about 1/2 degree, this means that the field has a diameter of (1/20 degree)*(pi radians/180 degree) = (pi/3600) radians. This is small enough that we can ignore the difference between the sine of this angle and the angle itself (in radians), so the size of the base is (pi/3600)*h light-years across. Please put your calculators down, we're not ready for that yet.

The volume of this pyramid is (1/3)*b*h = (1/3)*(pi/3600)²*h³. If the 10,000 galaxies in the field are distributed uniformly, this means that each of them will have (1/3)*(pi/3600)²*h³/10000 = (pi²/3/3600²/10⁴)*h³ = (pi²/3/60⁴/10⁴)*h³ = (pi²/3/600⁴)*h³ = (pi²/3/600)*(h/600)³ cubic light-years of volume each. That means each galaxy fits in a cube that is (h/600)*cuberoot(pi²/1800) light-years on a side. Now get out your calculators!

I get 3.7 million light-years, a comfortable distance.

Of course the galaxies in the past were at smaller distances the farther away and back we go. But if we could see the galaxies at z=9 as they are right now, they would have the same average distance as the galaxies in our neighborhood (taking the neighborhhod to be about 100 million light-years). These galaxies would have been 1/(1+z) as far from one another, or 370,000 light-years, still a comfortable enough distance.

Da-da-lump! Da-da-lump! Da-da-lump!

"Who was that masked scientist?"

"That was the Celestial Mechanic."

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Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

Who was that masked man who saved the universe ... again?

Thanks, CM. You are indeed a galloping rescuer of rationality.
This was a rather loose claim on my part, since I really had no reference to rely on. There is little question, however, that the distance between clusters is increasing, however you view redshift. The simplest of logic then leads one to conclude that they were closer together in the past.
This has probably been covered before, but you shouldn't consider the distant, old objects as actually "moving." They are more or less stationary in space, and it is the space between here and there that is expanding. Since there is more space between here and the more distant objects, then there is more expansion happening between here and there, which gives the appearance of a greater relative velocity (and causes a greater spectral shift).

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Everyone is entitled to his own opinion, but not his own facts.

That has been answered here.

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I did a quick google search for the average distance between galaxies and, without qualifiers, I found the value: 1 Mpc (see question number 3).

Comparing this value to that calculated by Celestial Mechanic means that the average distance is pretty much the same now as it was then - I see no expansion.

In regard to CM's calculation, according to the article with the HUDF photo, the telescope was aimed at an area*** of the sky with no stars visible (either by the naked eye or telescope) and so I wonder how much of the volume calculated by CM can be subtracted since there are no objects visible out quite a ways. In other words how far out can we see via eyesight or via ground telescopes?

*** "In ground-based images, the patch of sky in which the galaxies reside (just one-tenth the diameter of the full Moon) is largely empty."