Talk:Expansion of the universe/Archive 1

Archive 1

Archive 2

Archive 3

Changes

Nice article. Hope you like the small changes made. They are as follows:

1. Group the "ant" and "raisin" models together under one top-level section, "models used to explain the expansion"
2. Move the technical paragraph (that it is a feature of certain solutions of XYZ... time-varying universe..." etc) to an "overview" section, because this really is too "heavy" fro newcomers to be hit with on line #1. Also merge in with it, the "expansion in our universe" -- together they make a really good overview section of the field
3. Add simpler replacement para's for the intro. Might not be technically 100% literally perfect at PhD level, but at lay-level they give a good idea without discouraging further reading. If any significant misinformation has been introduced please do fix it -- I can't warrant this myself, though I * think * its ok.
4. I'm still unsure about my edit to para 3 of the intro. Some review of the DIFF (before and after) would help. You can probably see what I'm trying to do, but I'm not sure if it's worked well yet.

Nice work! FT2 ^{(Talk | email)} 15:49, 16 July 2006 (UTC)

Space is observed to be Euclidean (flat)

The observable universe is flat. It may be non-Euclidean on unobserved scales, but cosmic inflation prevents us from knowing what kind of curvature the manifold happens to have. --ScienceApologist 22:43, 16 July 2006 (UTC)

Thanks :) My main concern is to communicate a complex idea to readers. If the xsimplification's inaccurate then its good someone spots it. meantime it does now seem to achieve that with your latest edit, so I'm happy on both scores.

Onwards and upwards :) FT2 ^{(Talk | email)} 23:15, 16 July 2006 (UTC)

Explanations

I've got two ways to explain this for lay-readers, to try and make the point simply.

One is this:

It is as if, without objects moving, more space is somehow being continually fitted in between them.

This captures the idea that it is not about objects moving, but about the nature of space changing. As a lay-explanation I think its a good starting point to show how very different metric expansion is and make it comprehensible.

This is fine, though we should make it clear that it isn't "space creation" but "space expansion". Space stretches, it doesn't "appear". There are subtle differences. --ScienceApologist 13:55, 17 July 2006 (UTC)

The other is this diagram (self drawn):

A fractral-like analogy. An observer at A (the left) and one and B (the right) or indeed any two observers, will see the "ground" between A and B as remaining almost flat, however on a macro scale, as one moves from top to bottom there is a gradually increasing distance for a 1-D walk between any two points.

The crucial emphasis in these two descriptions being (unlike the ant and raisins) to show that it is the metric of space that is expanding. The more common analogies, although well known, actually demonstrate normal expansion to a lay-person -- exactly what is being attempted not to be shown. I feel these are two ways to describe it for Wikipedia, that show the key idea that space itself is changing.

Like em? FT2 ^{(Talk | email)} 13:46, 17 July 2006 (UTC)

Your image could do with some tweaking. I think what you are trying to convey is local flatness which is a feature of general relativity as well as the geometry of our particular space time. What would be better would be to have a picture of a space with simple curvature (not ripples but a single curve) and an ant crawling along. Then enlarge that image to show that the ant perceives space to be flat because the curvature is macroscopic. --ScienceApologist 13:55, 17 July 2006 (UTC)

On second readthrough, I think you may actually have created an image that is based on a misconception. The expansion of space isn't due to the taxicab paradox, but rather is due to an actual expansion (think the stretching of the balloon) of space. --ScienceApologist 14:00, 17 July 2006 (UTC)

It's neither. I'm trying to think of ways to convey the idea that the sense/appearance/reality of "distance" itself is changing, even if the objects themselves separate from the metric expansion, are not. the current analogies both imply "explosion of objects into a bigger unknown, which is exactly what metric expansion isn't. That's the problem I have with it -- that is a fundamental distinction, its not expansion into emptiness, its a change in the distance/metric of existing space. Those are 2 ways I can think of to convey that idea. Can you think of a way that works for you? (and yes, "growing" is a good edit) FT2 ^{(Talk | email)} 15:16, 17 July 2006 (UTC)

Are you trying to describe how something can "expand" without "expanding into" something else? If so, I don't know that this is an idea that lends itself to visualization in a simple image. One can imagine space getting larger as a property of space while the galaxies (essentially geometrical points with no metric size) stay the same size. I really don't know what the image is supposed to convey. --ScienceApologist 15:50, 17 July 2006 (UTC)

Basically yes, and I agree that it isn't easy to visualize. But right now we're saying "Its not the same as things expanding into emptiness, so here's two analogies which exactly sound like things expanding into emptines to imagine it." That seems inconsistent and counterproductive even though they are common analogies. I'm looking for a way to explain it that starts with two objects the same distance apart but space (the "distance") between them increases even though the line still looks "straight" to both. That conjored up sonme form of fractral analogy, which in turn gave rise to the above idea.

How else could we eplain that "there is more distance between objects because of a change to 'distance' rather than because they are physically moving apart"? That's what I'm trying to convey. The above "wavey line" analogy shows this clearly -- they are further apart not because they are "Moving", but because in a subtle way the nature of 'distance' is increasing. At least if we say "Its like B, not like A" lets have an analogy that doesnt immediately present it in terms of A. Makes more sense why? FT2 ^{(Talk | email)} 17:50, 17 July 2006 (UTC)

What you are describing are distance paradoxes having to do with the limits of continuous paths. This is totally different than spacetime expanding. In some sense, the description you are making is almost like Zeno's paradox which doesn't really apply to a space that is expanding because of a fundamental property of its geometrical fabric. I understand your desire to get a better analogy, but the reason we quote those two analogies on this page is because they are used (however flawed they are) by other sources. It is our job at Wikipedia to explain the ideas of others, not to come up with our own interpretations. Please see original research for more on this subject. --ScienceApologist 17:56, 17 July 2006 (UTC)

Understood. Note that OR covers self-created discoveries, opinions, and the like. The presentation of a notable/verified idea, in a new style that makes it easy to understand, isn't OR, it's in a way one of the jobs of an encyclopedia (making the inaccessible relatively accessible). But yes, I think we see each others point. What OR says is, coming up with new theories about space and the universe is not okay. But a better or more helpful analogy to explain the existing notable theories, is okay (ISmilar to how a novel summarizing of existing material into a new article is not OR either). But yes, I think you can see my concern. We're getting there on the description but I'm not convinced we're there quite yet. For what its worth you're a good editor to have on this because you're making sure that in creating descriptions and analogies, misinformation is kept out as far as possible. Which is a Good Thing. My concern is to slip a little technically (we aren't writing for PhD level cosmologists) and convey the impression so others can understand the concept more. We're mostly there I think, but we're still slightly figuring out the remainder. FT2 ^{(Talk | email)} 20:16, 17 July 2006 (UTC)

I agree that we aren't there yet. Keep on editting. Oh, and if you come across any references (especially print) that you can use to start footnoting the article, please do so. I am going to dig out some Astro 101 texts to try to provide some, but I might not get to it for a few days. --ScienceApologist 22:32, 17 July 2006 (UTC)

Well, I've got a lay question for you. How can space, emptiness-an empty set-a vacuum, have any properties aside from the possiblity of being occupied. And how can emptiness expand? More importantly if void is expanding, what is it expanding into, non-void? A conundrum, to say the least. Is there any evidence for this? If so these phenomena could be reproduced in microcosm on earth in a lab. In addition, to me the word universe means "everything", the all inclusive set, thus how can it be expanding unless it's really not "universal," meaning provincial in some sense. Wouldn't it be more correct to say that all matter and energy within the current sphere of human perception is expanding through empty space based on a massive explosion that occured at the earliest point in time presently discernible and that there might be other sets of matter/energy in remote regions trillions of light years from here etc. Thank you.Tom Cod 15:05, 1 November 2006 (UTC)

Space can have other properties because it is properly defined by a metric and not just by the possibility of being occupied. As such, even if we lived in an empty universe, there would still be spacetime (just nothing to observe it) according to the theoretical models of general relativity. All this would be pie-in-the-sky if it were not for the enormous amount of observational confirmation (detailed, in part, in the evidence section of this article) that this model enjoys. To imagine how space can expand, picture a universe that is empty but filled with imaginary rulers that determine distances (even though there are no objects to measure the distance between). An expanding space would cause these rulers to all stretch and if there were no physical objects in the universe you wouldn't be able to tell the difference between the universe before it stretched and the universe after it stretched. The universe has gotten larger, but it hasn't expanded "into" anything, the rulers all just got stretched. There is an invariance between the universe before the expansion and after the expansion in terms of space itself, but this symmetry is broken if you add physical objects to your universe. For two physical objects in our otherwise empty universe that each sit at different intersection points for the rulers, the universe appears to be expanding even while it is an indistinguishable expansion without these objects. Let the space expand and what happens is the two objects perceive themselves as moving away from each other, even though they are fixed in your grid of space. Any way you chose to measure the physical distance between these two objects (for example, by shining a laser beam from one object, bouncing it off the other objects, and waiting for the beam to return, timing this phenomenon, and determining the distance by taking the time divided by the speed of light) will indicate that at later times the objects will be physically farther away from each other. The objects themselves are not expanding or moving through space: they're fixed. It is the space itself that is moving them apart. Thus the Big Bang is a terrible misnomer because the "explosion" in question was an "explosion" of space and not of the physical objects in the universe. --ScienceApologist 13:24, 2 November 2006 (UTC)

I'm really trying to struggle with this. When you say space is properly defined by a metric, what do you mean, as measured by units of the metric system? From this does it flow that space is contigent on human quantification. Yes, I am intrigued by the laser experiments you allude to, since they represent ostensible empirical evidence, but as a philosophical "materialist", I find the conclusions you state, to the extent I am understanding them, hard to accept. Have any of these conceptions been adopted by modern engineering, which to my mind is the embodiment of the application of classical physics. How can a void expand? C'mon. If the ruler stretches, or the clock marks time differently, then to me that represents a mechanical flaw and failure, material stresses on these objects, not a variance or indicia of some quasi-mystical property of reality. As to the staight line v. the wavy line, all that shows, as you yourself mentioned, is that there are different routes of varying lengths that can be taken between two points in a given area, which remains the same in all the examples shown. Moreover, those who state that the "universe" began with the Big Bang are negating the principle of cause and effect and seem to be asserting a variation of the theory of "spontaneous generation" disproved in biology by Pasteur. To me time and space are abstractions, like the King's Foot or pi, that cannot fundamentally be, ironically, affected by any material forces. Culturally my skepticism is further conditioned also by New Age gurus, even "intelligent design" advoctes who sieze upon and tout these conceptions as evidence of the supernatural and so forth (See the movie "What the Bleep is this"), something that raises a big red flag in mind re the rule of reason versus sophisticated feel good superstition. No, as a former mariner I know time, for example, is not defined by clocks, it's measured as an interval of the rotation of celestial bodies, but is fundamentally simply a basic intangible parameter or context of reality. A second or an inch is immutable whether on Mars a black hole, the Bowery, or wherever. The ant on a balloon can't be an analogy to the universe as there's the area above and outside the balloon, whose surface area actually is expanding due to the material cause of the introducion of air gas into it. Thus the great project of the Royal Society described in "Longitude." I'm really going to have to see some more compelling empirical evidence before I'm going to believe that matter came out of nothing in a genesis moment and that space, a vacuum, can explode any more than I'm going to believe the Biblical version as they both defy common sense. To me, Zeno's paradox says it all. I would say that space is defined a void, that extends infinitely in all directions and that time is its chronological context that similarly extends from the infinite past to the infinite future. Thus there cannot have been a beginning or can there be an end because for every moment and event there was surely one preceding it and one which will succeed it and for every distant point, however far from the last atom, there's a place farther beyond it. Thus, are you sure the Known Universe is not expanding in the sense that observable matter and energy is expanding through infinite space on the basis of the force of an ancient explosion. Isn't that what the red shift type evidence shows, the increasing velocity of matter through space? Thank you.Tom Cod 07:42, 3 November 2006 (UTC)

This isn't the place really to learn about basic physics and mathematics. It is really a talkpage about the article. I will answer your questions here on your talkpage, but please, if you have more, don't clutter up this talkpage which is ostensibly supposed to be about making the article better. --ScienceApologist 12:17, 3 November 2006 (UTC)

Introduction

Please, keep it shorter and simpler. The intro is an short introduction, for newcomers, we need to resist the temptation to make it a substantial technical "advanced readers" subarticle of its own :)

I'll revert some of it, trying to not lose any of the info, but I think honestly the previous level of detail was better. It's just gone a bit too far back towards "technical creep". Will try not to lose any valuable edits though. A couple of edits I'm thinking don't need to be in the intro include:

1. "Is the phenomenon where..." -- its still only a theoretical one, so I'm unhappy about saying its a "phenomenon" (implies confirmed) rather than a "part of our present understanding" (doesn't imply confirmed).
2. For the same reason I've changed back the minor edit to make clear that if true, expansion would be a feature of the universe (does not imply confirmed), rather than it "is" a feature (implies confirmed), and that observations "tend" to support the model (in case some are ambiguous or don't fully)
3. Last, I've reverted much of the 1st paragraph (too much complex "feel" for too little benefit, for me), and some of the edits to the 2nd (including unnecessary emphasis on this being about "metric expansion").

Hope this is okay with you. Its just slipping to the point its unhelpful, otherwise. FT2 ^{(Talk | email)} 21:41, 18 July 2006 (UTC)

Yikes! Please don't revert. Try to see what I was getting at through this diff link. I'm really just trying to make everything as clear as possible. Edits to make my wording clearer are appreciated. Any paragraphs that need to be removed to elsewhere can be. --ScienceApologist 21:50, 18 July 2006 (UTC)

I wish you would keep the first paragraph at least in the form I had it in. We need to define the phrase first before we describe it as part of "science's" understanding. --ScienceApologist 21:53, 18 July 2006 (UTC)

Not sure that's even so, really. Compare:

1. The metric expansion of space is the phenomenon where space itself expands over time. It is a key part of the current cosmological model of the universe, where the vacuum of space is described by a relativistic metric that can changes as time passes. Metric expansion explains how the universe expands in the Big Bang
2. The metric expansion of space is a key part of science's current understanding of the universe, whereby space itself is described by a metric which changes over time. It explains how the universe expands in the Big Bang model

Compare them... The 1st says "Its is the phenomenon where space expands over time. That doesnt explain much, and its slightly misleading on 2 scores: its a (speculated theoretical) hypothesis not an (observed) phenomenon, and it emphasises space expanding rather than the metric describing space expanding -- a really crucial distinction to introduce up front (especially given the title). It then goes on to talk about the vaccuum of space, where at this poiint just "space" is almost as accurate and much simpler, and says the tensor is relevatistic which again is too much detail at this point.

The 2nd says, its a part of our understanding, in which space is described by a metric that is changing, which explains how the universe expands. Much simpler. Thoughts? FT2 ^{(Talk | email)} 22:21, 18 July 2006 (UTC)

The first doesn't define the idea and the distinction between "interpretation" and "observation" is very artificial. All explanations of observations are "interpretations". Metric expansion is as much an observation as "the grass is green". --ScienceApologist 00:42, 19 July 2006 (UTC)

Not sure about the latter. Expansion is an observation. That the expansion is metric rather than some other cause (eg residual motion in a fixed-metric space) is not, as far as I understand it. To say we observer metric expansion seems wrong. We observe expansion, and we believe it is caused by metric changes rather than some other reason, but the former and latter are confirmed observation and current theory. The observation is reliable, but the theory we have to explain it is by no means certain yet, so I'm reluctant to present it as such or claim we observe metric expansion per se. We don't, if I understand it correctly. FT2 ^{(Talk | email)} 01:20, 19 July 2006 (UTC)

The expansion has to be a metric expansion because of the cosmological principle. While it is true that the principle was not tested until the 1990s, it has been tested since then and observed to be correct (See Big Bang#Theoretical underpinnings). In a universe where the cosmological principle holds (and it holds to a great degree of accuracy in our universe by observation) it is required that the expansion be isotropic and homogeneous - a metric expansion. --ScienceApologist 13:39, 19 July 2006 (UTC)

Thanks. Having read both, I still have a few concerns though:

1. Theres a lot of "assumes" and "axioms". If the evidence is stronger than that, then it looks like Cosmological Principle needs updating from Big Bang (theory+observations) to include the evidence and discussion around it.
2. It seems that the main reasoning for metric expansion is something like this: space and microwave background is strongly isotropic, which would rule out expansion from a single fixed point and would of necessity require (or imply) an expansion of a metric rather than physical kind. Is that roughly correct? Are there other possible explanations? Does this mean metric expansion is considered utterly confirmed by indirect observation, even if we can't detect it directly? (And do we have a cite from strongly credible sources saying it is effectively considered confirmed in the field?)
3. Is 10^-5 considered exceptionally strong evidence? I'm concerned both that I might not have a reliable sense of order of magnitude in judging the figure, and that many discoveries are undermined or discovered by seeming small variations in evidence later on.

These would help reassure me, I think you can see where I'm at. Its more that I would not like to assume argument from ignorance by mistake... especially since having edited that article beforehand, I have no excuse and I'd be a bit embarrassed to fall into it!! FT2 ^{(Talk | email)} 15:56, 19 July 2006 (UTC)

Comments

1. The cosmological principle was assumed for a great many years before cosmologists had the observational evidence to verify the assumption. But as the theoretical underpinnings section discusses, the cosmological principle has been tested to at the very least the 10% level and at most a level of one part in 10⁵ (depending on whether you are interested in homogeneity or isotropy).
2. The isotropy and homogeneity of space does not rule out a central point expansion, but the Copernican principle does. The observational test that verified the Copernican Principle are the observations that show the dynamics associated with metric expansion are observed to exist in the CMB spectrum and in, for example, the temperature of the CMB measured at earlier epochs. Metric expansion is considered confirmed based on direct observations and the extent to which the theoretical underpinnings of the Big Bang are confirmed. This is a pretty strong inference compared to most other inferences that go on because it is dependent on observations of the past rather than future observations. For example, how do you know that grass is not grue? You only know from inference (and it's actually a weaker inference than the inferences which are made to show metric expansion is correct).
3. It is often said that stars are blackbody radiators and to the extent that their spectra roughly follow the blackbody curve, this is correct. The CMB, on the other hand, follows a blackbody curve so closely (at 10^-5) that the error bars are thinner than 1-pt thick lines. It's the best example of a theoretical blackbody curve known in existence. So close to a blackbody that there is no thermal mechanism you have ever come across that is closer to such a spectrum.

--ScienceApologist 17:57, 19 July 2006 (UTC)

If thats the case, I've drafted an "evidence" section based on my understanding of the above. As ever, can you fix it for any misunderstandings and errors? Thanks. FT2 ^{(Talk | email)} 22:40, 19 July 2006 (UTC)

Two further quick questions on Time

Quickies for you:

1. On the one hand we describe the inflationary epoch as 10^-32 sec. on the other hand you say "inflation wasn't brief when it happened, it occurred over a time that was multiples of the age of the universe". Can you clarify this for me?
2. On a similar theme you say "It is absolutely required that space and time are not absolutes". I thought time also was variable. In some places time is treated as absolute, in others like this it sounds like a metric too. Again, can you clarify how time behaves over time, so to speak(!)

Can you discuss or explain how time behaves below, a bit, and clarify these two issues? Thanks FT2 ^{(Talk | email)} 16:03, 19 July 2006 (UTC)

Yes, as a former mariner I'm intrigued by this because I think time actually is immutable, that it is immaterial and intangible and cannot possibly be affected by material forces although the quality of what occurs during it can vary. The book "Longitude" is interesting in this regard. As a died in the wool agnostic, I am open to evidence to the contrary, however. Thank you. Tom Cod 15:25, 1 November 2006 (UTC)

Clarifications

1. Although the inflationary epoch lasted for 10^-32 seconds it started when the universe was 10^-34 seconds old. That means that it took 100 times longer for inflation to happen than the universe was in existence. Just because 10^-32 seconds is "brief" for a human doesn't mean that it is brief compared to the relevant timescales.
2. Time has not been considered to be absolute since special relativity came into the picture. After all, there are such things as time dilation which could not occur if time was an absolute. What is an absolute is spacetime.

--ScienceApologist 17:48, 19 July 2006 (UTC)

Good Article

This is a great article, however it is only sourced by 2 science magazines. If you can get better referencing, and expansion in general, it can defintely become a Good Article. --GoOdCoNtEnT 19:21, 10 August 2006 (UTC)

My view on sourcing is very different yet partly compatible. I'll repeat what I wrote elsewhere: in my very limited understanding of cosmology this article is an attempt to summarize what's pretty much agreed among interested physicists and it's therefore unnecessary to say that A comes from X and B comes from Y. If I'm right here, then I suggest that the article should get either (i) some discursive footnotes, describing roughly what in the article comes from where (in addition of course to any needed footnotes saying which more controversial assertion comes from precisely where), or (ii) descriptions in the list of references, wherein the contribution of the source to the article is briefly explained. -- Hoary 07:01, 19 August 2006 (UTC)

What a great criticism. Indeed, the article is both organic and redundant, but it is needed. There are different "levels" of articles sometimes needed (see for example introduction to special relativity and special relativity). This article is actually a more basic explanation of Big Bang. It is needed so that people are able to understand the basics of expansion before they can explore the big bang in its totality. --ScienceApologist 08:42, 19 August 2006 (UTC)

When you wrote that, I wasn't quite sure what you meant, and I'm still not sure. I notice that you've renominated the article in the meantime, but before doing this you haven't taken up either of my recommendations (or explicitly turned them down). Again, I think it would be a good idea if you either (i) added a few discursive footnotes (explaining not merely that the immediately preceding assertion came from such-and-such a place, but rather that the following content of kind A comes from W and X, and that of kind B comes from Y and Z, etc.), or (ii) added comments after each item in the lists of external links and printed works saying how the item has contributed. As it is, some of what's in the list is very surprising, notably Eddington's work, written half a century or so before what I learn (or misread) was a kind of crystallization of the notion of the metric expansion of space. -- Hoary 15:10, 20 August 2006 (UTC)

I'm not the best at doing this. I'll leave it to other editors to do this task. The Eddington reference is surprising because it is such a good explanation of the expanding universe. Realize that although it has taken decades to confirm the expanding universe, people assumed the universe was expanding (based on reasonable assumptions and the evidence at hand) since the 1930s. --ScienceApologist 20:07, 20 August 2006 (UTC)

I've taken a look at the article. In my opinion, the only thing that separates it from Good Article status is a lack of inline references. As I said on the dispute page:

I'm another reference stick-in-the-mud, often asking for them in reviewing articles. There are purposes for asking for in-line references and they have nothing to do with note stacking to make it look impressive.

The first is to give academic credit to someone who discovers a fact, compiles a statistic, creates a hypothesis, comes to a reasoned conclusion, etc. (The negative side is to avoid charges of plagiarism) My rule of thumb is that, if a statement can be found in two or more expert sources, no need for a citation. I also arbitrarily look for at least one cite per section.

The second is to help a reader find the exact source of a notion if they want to learn more. This is what I actually urge my students to use the wiki for.

The third is to help us with verification, especially where there is controversy among editors (this one may not apply to you).

The only other observation I have as a complete layman on this subject is that, while nicely written, I'm still having difficulty wrapping my brain around the subject. This would not stop my promoting it, but thought you all would like to know. --CTSWyneken^(talk) 11:23, 22 August 2006 (UTC)

• The complaint made on the dispute page about needing to have x number of references to satisfy some kind of dilettante smell test is a sheer and utter fatuity and I salute User:Hoary for his patience in making what I thought was a crystal clear explanation as to why such thinking is both ill-conceived and ridiculous. Let me make one additional point. This is supposed to be (particularly at GA level) an encyclopedic treatment of a topic and should contain enough further reading to help readers get a start on finding additional information. However, it is amateurish to cite references on points that are generally accepted principles in a particular field. That might be okay for a first year term paper of someone trying to find their scholarly feet, but readers of an encyclopedia assume that the information offers a synthetic, broad and up-to-date understanding of the field. Specific references on topics of broad consensus really need only be offered to the degree where they treat a particularly controversial aspect of the subject, or in ref. to a specific citation. Further readings need be broad enough to demonstrate (to the knowledgeable eye) that the article is able to provide the standard references that are considered first class, seminal, etc... in their field. As such, this article really ought to be reviewed by someone with deep familiarity with the topic and I ain't that someone. Excellent work though. Very informative, well written and to my untrained eye, comprehensive and hits the right level of synthesis. Eusebeus 21:51, 25 August 2006 (UTC)

Little questions

I've put some little questions into <-- SGML comments --> within the article. -- Hoary 07:01, 19 August 2006 (UTC)

Confirmation vs lack of refutation and predictive power

I'm sure physicists can happily live without advice from physics-ignorant people (that's me!) with a vague memory of some philosophy of science courses. Still, I have to point out that every crackpot 20th century theory of the psyche was able to come up with observations that confirmed what it proclaimed. A question (if I may hugely oversimplify) was of whether and how it risked empirical refutation. (Notoriously, nothing we can even imagine would show that the Freudian model is wrong, and therefore the model is scientifically worthless.) So I'm not so impressed by a lot of the "Observational evidence", at least as it is described. I am interested in the predictive power, as alluded to in the final paragraph of that section. But this is described very vaguely. What are these predictions? Did earlier theories make the wrong predictions, less accurate predictions, or no predictions at all? -- Hoary 07:13, 19 August 2006 (UTC)

I have been dealing with science for years, and this is the best question I have had asked of me about a subject. Scientists often take for granted the fact that models need to predict novel ideas before being accepted as reasonable. The metric expansion of space is a story about how science really works: hundreds of ideas promoted by hundreds of people and then one is selected of the hundreds to explain the observations made by the data-collectors in return. What happened with the expansion is space is something akin to a game of 20-questions. People asked "What kind of universe would fit this data?" an then "What kind of universe would fit that data?" until what was left was a metric expansion of space. The theory grew organically beause ideas about the rationality of science had been in the works long enough to protect scientists' extrapolations about the universe long enough for one of them to be confirmed. That's the present state of science -- and it's one that the metric expansion of space couldn't exit without. --ScienceApologist 08:39, 19 August 2006 (UTC)

You flatter my question, but on its behalf I thank you all the same. I hope my prodding here and there doesn't irritate you. Something about the contrast between this article and the vapidity of the subject-matter of many indubitably good articles sticks in my craw; I'd like to see this promoted to "Good Article" too. -- Hoary 14:34, 19 August 2006 (UTC)

On hold status for "Good article" nomination

I put the "Good article" nomination on hold on this article, because I had some concerns with factual correctness. I hope to fix these minor nits personally, with appropriate feedback from the originator & other editors to "keep it simple". I then propose that someone else review the final result. I have some concerns about verifiability of this article - the factual errors crept in in the first place due to writing from memory rather than citing sources. I'm going to commit the same mistake, probably, because all my references are too technical to be useful. But I'll leave the end decision on the fate of the article up to the final reviewer. Meanwhile I want to fix some stuff Pervect 20:49, 22 August 2006 (UTC)

• I think I'm through editing now. I will remove the hold in a few days, unless someone else does it first. I want to give others a chance to comment and/or fix errors before releasing the article to be reviewed. For instance, we've already had a silly grammatical error of mine fixed up by an anon user Pervect 07:58, 24 August 2006 (UTC)

• I've removed the hold, after a very minor additional edit. Technical issues in my mind are down to a single word defintion - is it better to use "comvoing" distance or "proper" distance, and are they really exactly the same defintion, or actually slightly different? I've put the article on hold long enough, so I'm removing the hold without this issue being totally resolved. There don't appear to be any other active editors at the current time. Pervect 20:59, 25 August 2006 (UTC)

Lorentz interval?

My technical side would really like to add a note explaning that the metric of space-time computes not ordinary distance, but the Lorentz interval.

However, I'm afraid that this might scare readers, and not otherwise add much to the article, since the Lorentz interval reduces to proper distance for spacelike paths, and proper time for timelike paths.

Thus at the moment I'm leaving well enough alone. Pervect 23:08, 22 August 2006 (UTC)

This article is terrible

At first I thought it was me, but these are clearly self-contradictions:

• From the lead section: "space itself is described by a metric which changes over time"

• From the Overview: "The metric of space appears from current observations to be Euclidean. The same cannot be said for the metric of space-time, however."

So, which is is that changes, the metric of space, or the metric of space-time? Lurk22 01:17, 17 September 2006 (UTC)

The title of the article is "Metric expansion of space" not "Metric expansion of spacetime". The metric of space changes. The metric of spacetime also changes inasmuch as the spatial part of it is expanding. The time part is, however, unaffected by the expansion. As the old saying goes "time marches on". --ScienceApologist 01:31, 17 September 2006 (UTC)

I think this is a valid criticism, but I'm not sure what the best way of fixing it is. By getting more into the physics of the Lorent interval, it would be possible to explain this point further, to explain how 4d space-time is not flat, while the 3d hypersurfaces of simultaneity are flat. But I'm not sure it is a good idea to get too deep into this issue. I have a feeling even talking about the 3d hypersufaces of simultaneity would be too complex for the level this article is at. Pervect 19:33, 17 September 2006 (UTC)

It indeed would not add anything of value. We can just rely on our weak separation of the metric into spatial and temporal parts. Even though the spacetime interval can mix these two according to the Lorentz interval, it's absolutely true that in all inertial reference frames, it is only the spatial part of the metric that will expand. I'll try to modify the lead so it is clear that while the spacetime metric is the thing that is changing over time, it is only the spatial part that is affected. This may remove the "apparent" contradiction. --ScienceApologist 22:26, 17 September 2006 (UTC)

GA Re-Review and In-line citations

Note: This article has a small number of in-line citations for an article of its size and subject content. Currently it would not pass criteria 2b.
Members of the Wikipedia:WikiProject Good articles are in the process of doing a re-review of current Good Article listings to ensure compliance with the standards of the Good Article Criteria. (Discussion of the changes and re-review can be found here). A significant change to the GA criteria is the mandatory use of some sort of in-line citation (In accordance to WP:CITE) to be used in order for an article to pass the verification and reference criteria. It is recommended that the article's editors take a look at the inclusion of in-line citations as well as how the article stacks up against the rest of the Good Article criteria. GA reviewers will give you at least a week's time from the date of this notice to work on the in-line citations before doing a full re-review and deciding if the article still merits being considered a Good Article or would need to be de-listed. If you have any questions, please don't hesitate to contact us on the Good Article project talk page or you may contact me personally. On behalf of the Good Articles Project, I want to thank you for all the time and effort that you have put into working on this article and improving the overall quality of the Wikipedia project. Agne 05:51, 26 September 2006 (UTC)

Reply to comments left on my talk page
Please read this. Very briefly, I as a (distinctly!) non-expert suggested that the ideas presented in this article are now mainstream within physics; the interested person can therefore make his or her own choice of mainstream physics book for verifying or reading more about it. The (apparently) expert editors seemed to agree. Meanwhile, the original physics research papers would be hugely too difficult for any but a minuscule percentage of WP readers; the tiny number of people who can read them would not be reading WP articles about the subject. -- Hoary 08:41, 26 September 2006 (UTC)

I have to point out some pertinent details from the main policy that has driven this. From WP:V..."The threshold for inclusion in Wikipedia is verifiability, not truth." Followed by the Section on Burden "The burden of evidence lies with the editors who have made an edit or wish an edit to remain. Editors should therefore provide references. If an article topic has no reputable, reliable, third-party sources, Wikipedia should not have an article on that topic."

Simply put, it is not the readers job to find a mainstream physics book in order to verify any particular aspect of the article. The burden lies squarely with the editors. I think especially with Math and Science articles, the need for in-line citations is even more abundant given the weight of WP:OR. We have to expect that a significant portion of this article's readership will be "non-experts" as well and they would have no way of knowing that these are mainstream with physics. The attaching of a reliable source will at least give creed to that notion. As for the sources being difficult to read, there are still the other benefits that WP:CITE list for why citing sources is simply good form.Agne 17:31, 26 September 2006 (UTC)

As a contributor to the above dispute, I concur. Please note my comments there. I would weigh in on the talk page at the GA space, but the argument is already long and any additional reflections I have would probably only add to the noise. But this article highlights the problem with having a rigid citation rule. The subject matter is arcane to uninformed readers, but to scientists, the discussion is quite elementary and fundamental. It is like requiring a citation that the sun rises in the east. I worry that the effect of applying WP:CITE blindly can lead to an amateurish presentation of subjects that will sponsor laughs from an informed reader; in other words, out of place for a serious encyclopedic project. (Don't misunderstand me though: generally, citation is hugely important.) Also, citations are not always good citations. I failed the GA nom for Marcel Proust in part b/c the works cited were woefully inadequate. Having a cite policy that reqires x or y number, however, may lead reviewers to feel that material has passed some kind of verifiability test, even when the cited sources would lead an informed reader of the subject to look askance. Eusebeus 14:41, 26 September 2006 (UTC)

The policy is not X or Y number but for the benefit of WP:V all major claims should be attached to a reliable source that verifies that claim. Simple as that. If a reviewer is blindly impressed with a number then they are simply not a good reviewer with that lacking falling on them and not the criteria. In all honestly, this is not new. It is something that the foundational wikipedia guidelines have asked for all along and in a time when Jimbo and the rest of the Wikipedia community are steering towards more quality over quantity, the GA project is moving accordingly. I don't doubt the truth of this article or that it is mainstream physics. But it has never been about truth but rather verifiability.Agne 17:31, 26 September 2006 (UTC)

The editors of this page have decided what constitutes "major claims" and have attached them to reliable sources. Therefore it appears to me that the requirements of this reviewer have been satisfied unless they can point to a specific instance of a major claim that is not attached. I find vague suggestions that there aren't enough cites to be penny-wise and pound-foolish. The number of citations doesn't indicate anything about the quality of the references or the verifiability of the article. --ScienceApologist 17:37, 26 September 2006 (UTC)

Ok, this is getting out of hand folks, (I notice SA put a warning template on Agne's talk page, I presume for trying to paste the message about GA criteria changing) there's still a GA review open on this page from before this started, can we move the conversation there? Two people arguing with each other often doesn't produce much resolution. Homestarmy 18:09, 26 September 2006 (UTC)

The review for this page is about a completely different issue which was already resolved. If you would like to open a new review (or add your new comments to the existing one) be my guest. --ScienceApologist 18:30, 26 September 2006 (UTC)

I have made a request regarding this issue here. --ScienceApologist 21:01, 26 September 2006 (UTC)'

Relating this to Gravitational Metric Expansion would clarify it

This article would be much stronger with more specific reference to the relationship between metric expansion and gravitation - specifically, the metric tensor that describes how matter expands, shrinking space over time to produce the effects of gravity. It needn't and shouldn't be mathematical or obscure, and can actually clarify the article for lay readers.

Like space, matter itself is expanding - in ways that are easier to measure with a scale than a ruler. We can verify that the earth's surface is expanding at an acceleration of g by placing an object of known mass on a scale. To observers also being pushed by the earth's surface, this motion of the surface creates an impression that inertial objects are falling toward the earth. In this sense, Newtonian gravity is a fictitious force like the centrifugal force experienced by a rider on a merry go round. The strongest clue that it's really the earth's surface accelerating outward is, all the inertial objects appear to accelerate downward at the same rate, independent of their mass or lack of it. The equivalence of gravitational and inertial mass is a fundamental observation of general relativity.

The 'real' force responsible for our weight is the outward expansion of the earth's surface. Gravity doesn't pull us; the earth's surface pushes against us where we contact it. Since every atom and object at the earth's surface is expanding at the same rate, a ruler made of atoms won't show it.

Explaining this can give readers a clearer idea of both metric expansion and gravitation, and why metric expansion may not be obvious from our point of view. Moreover, metric expansion of space helps explain how the earth can be expanding this way without colliding with say, the sun: space itself is expanding too. Thus, the two should be discussed together. --Dlevity 12:26, 19 November 2006 (UTC)

While the metric expansion of space is characterized by a single scale factor, the equivalence principle gravitational acceleration is due to curvature of the Einstein tensor and the fact that the geodesics for massive objects in a Schwarzschild-like metric head toward the singularity. These are different considerations. There is no inertial frame of reference where the surface of the Earth is "expanding". In reality, the surface of the Earth just represents a set of space-like potential barriers that are fixed at a particular observable radial coordinate from the "singularity". There isn't really any "expanding" of the Earth's surface, it's just that locally, the potential barrier prevents free-fall and is therefore, locally, equivalent to outward acceleration. --ScienceApologist 14:49, 20 November 2006 (UTC)

Actually, from the point of view of say, an inertial satellite, it travels in a straight line yet fails to increase its overall distance from the earth because of the expansion of earth's radius (along with all matter around it). You don't see this if you stay on our space-like surface; from here it looks like an invisible force is pulling the satellite into (roughly) an ellipse, the Newtonian model. In the relativistic model, "curved" spacetime means the space itself is falling in toward the earth over time as the satellite travels in a straight line through it. We can say that space is shrinking in toward the earth, or from another point of view, that the earth is expanding with respect to it. Relativistically, both views are valid, and are more accurate than the Newtonian view. --Dlevity 21:24, 20 November 2006 (UTC)

What you are describing is a coordinate (that is local) expansion as opposed to a global (metric) expansion seen in, for example, the FRW metric. It only works if you artificially fix the Schwarzschild radial coordinate. The equivalence between these two "expansions" reduces to triviality and is physically different because the spatial components of the metric are the only components which experience scaling in FRW metrics while there is also time dilation associated with being in a gravitational field. Indeed, conformal "time" solutions to FRW metrics act more like distances than times in a global sense.

To see this, note that while the Schwarzschild metric is:

$ds^{2}=-c^{2}\left(1-{\frac {2GM}{c^{2}r}}\right)dt^{2}+\left(1-{\frac {2GM}{c^{2}r}}\right)^{-1}dr^{2}+r^{2}d\Omega ^{2}$

The FRW metric is:

$ds^{2}=dt^{2}-{a(t)}^{2}\left({\frac {dr^{2}}{1-kr^{2}}}+r^{2}d\theta ^{2}+r^{2}\sin ^{2}\theta d\phi ^{2}\right)$

Finding equivalence between the two of these metrics is only possible when r=constant (a trivial solution).

--ScienceApologist 21:46, 20 November 2006 (UTC)

I wasn't suggesting that the two metrics are equivalent, nor artificially setting r to a constant. The goal is an explanation that helps the reader visualize expansion and its effects. People (including physicists) have a natural psychological resistance to believing that the inch or meter is changing size over time, globally or (perhaps even more so) locally. (This resistance caused Einstein to invent and later be embarrassed by his cosmological constant.) Visualizing space itself as shrinking and falling in a gravitational field - and seeing how the dynamic 'size' of matter and space are effected from different points of view - can be helpful. Animation showing the equipotentials moving or the planet growing, respectively, can help. For most audiences, I don't know if the equations above do it.

By the way, regarding the radius not being fixed: picture our satellite in an eccentric elliptical orbit. We should be able to describe its motion in a 'straight' line at constant velocity, through space whose dynamic curvature makes it look like the satellite slows down and travels further as it moves toward the apogee where space itself is moving slower. I haven't seen animation depicting this, and I don't think many physics students get to see a clear depiction of it. It's one of the great challenges for articles like this. --Dlevity 07:07, 21 November 2006 (UTC)

We can describe the changing nature of the metric in terms of the changing Lorentz interval, but leaving it baldly in the spatial part is a bit problematic already in the article and I'm afraid pointing out inches or meters changing in size over time will give the impression that it is just rulers that are changing and not the Lorentz interval itself. This new radial coordinate you propose will have a non-zero dr'/dt term that is different from the Schwarzschild radial coordinate, but as you can see from the Schwarzschild metric, it will also have a changing component of the metric that is time-like as well. --ScienceApologist 10:29, 21 November 2006 (UTC)

Visualizations of a Hypersphere

I've got a model for an expanding universe that allows for all the various effects to be incorporated. Universal expansion, a time of acceleration from a point and a time of acceleration back into a point.

I'm autocading the design right now.

Is there a particular format I should use for formatting the article? --Mad Morlock 19:30, 11 December 2006 (UTC)

Recent edits

Old text:

We then choose a metric which will be used to calculate the distance between nearby points in terms of the difference in the coordinates between them. In principle we can choose any one of a multitude of metrics, but in practice we choose a metric that seems to fit our purposes best. For example, local mapmaking often ignores curvature, whereas airline flights and distances are based upon a Great Circle. Since the Earth is not flat, the "distance" between two points (such as London and New York may differs depending on how it is to be measured (ie, the metric which is to be utilized). In measuring small distances on Earth, there is in theory always an effect due to curvature, but in practice the the Earth's curvature is so small as to be almost unnoticable for short distances.

This is not quite correct. We cannot arbitrarily chose different metrics. There is a physical distance between any two nearby points that is well defined. The metric calculates the distance between nearby points. Thus there is no freedom to chose the metric coefficients once we have chosen a coordinate system, only one set of metric coeffients will give the correct answer for distance.

In the example given, the distance between New York and Lodon is not strictly defined until one defines the exact curve connecting New York and London. The usual convention is to chose a 'great circle' connecting them, but one might chose a different curve.

But this choice of connecting curve does not matter to the metric coefficients, which determine the distance between nearby points. When two points are close, the curvature does not matter, and we can consider the points to be in an essentially Euclidean space.

When we go to the relativistic metric, we replace the concept of distance by the concept of Lorentz interval. This is something that should perhaps be added into the article, but I'm not sure if/how it can be done without confusing the reader. Once we have chosen the coordinate system, and once we have chosen whether the metric should represent pure distances (as on the surface of the Earth) or the Lorentz interval, we have no freedom in choosing the metric coefficients. Pervect 01:24, 12 December 2006 (UTC)

I've had a go at rewriting this section to give an example (which I think's needed) but not misinform. I'm on shakey ground here, could you (or someone) review it and clean up any misinformation I've inadvertantly added? I also added in your reference to the lorenz interval somehow. Thanks. FT2 ^{(Talk | email)} 15:26, 12 December 2006 (UTC)

Metric Expansion of Space != Inflationary Period

Hi, I love this article, because it's explained expansion to me, in a way that makes sense to me. If you take a bunch of points, and multiply their coordinates by 3.0, it doesn't matter where you set the origin, it'll all appear the same: like everything is going away from everything else, depending on the distance. I get it: theres more space between stuff. I love this article.

I have one small request: Can you somehow make it clearer that the Inflationary period at the time of the big bang is something very different than the Metric Expansion of space? That, it's a very brief time, during which the metric expansion of space happened very quickly, but that otherwise, the increase of the metric expansion of space is constant? That was something that I didn't get from the article, but learned later, from a usenet conversation. (I may be misled.) I kept getting the metric expansion of space confused with the inflationary period, and I think this page could more clearly distinguish them.

Thank you, Lion Kimbro.

LionKimbro 05:03, 21 December 2006 (UTC)

Does the last paragraph in the lead not do it for you? --ScienceApologist 05:09, 21 December 2006 (UTC)

Evidence for a Creator

It should be mentioned that the expansion of the universe is often used as evidence for a Creator in Christian and Islamic Apologetics.

Christian sources:

• http://www.creationevidence.org/scientific_evid/evidencefor/evidencefor.html
• http://www.allaboutcreation.org/scientific-evidence-supporting-creation-faq.htm
• http://www.biblicaldefense.org/Writings/scientific_case_for_creation.htm
• http://www.reasons.org/resources/apologetics/newproofs.shtml
• http://www.skeptics.com.au/journal/reviews/vs-sciencegod.htm
• http://www.time.com/time/magazine/article/0,9171,1553986-3,00.html

Islamic sources:

• http://www.albalagh.net/general/expansion_universe.shtml
• http://www.creationofuniverse.com/html/bigbang_03.html

--Jorfer 23:48, 26 January 2007 (UTC)

Doesn't belong on this page. Those sites are not reliable sources for this scientific subject. Sorry. --ScienceApologist 03:54, 29 January 2007 (UTC)

Quick opinion:

• The question of "implications of the expansion of space" is certainly a legitimate topic for an encyclopedia article on the expansion of space. There are many philosophical and other implications people draw from that knowledge, about the nature of the universe/existance. Although only worth a short section, they do have a place.

• Unfortunately that place is not this specific article. This article isn't a general article on cosmology and spatial expansion and the universe. It's a very focussed one, explaining the nature of a non-intuitive model which mathematicians and others use to examine the nature of that expansion. a small section under Big bang or such might be fair, but this is not a general article on the expanding universe. It's essentially an article on a mathematical model.

Hence I concur with the above - it simply doesn't belong on this page, any more than a section on angels would belong on a page about fluid hydrodynamics, just because the latter is used to model flight, or a section on Creation would belong on an article explaining stellar nuclear fusion heat cycles, just because the sun and its creation is referenced in various religious texts. Hope this helps. FT2 ^{(Talk | email)} 18:09, 30 January 2007 (UTC)

Problems visualising this

I tried to generate an animation to illustrate this concept, but I ran into difficulties.

My idea was to draw a couple of circles (representing bodies in space) on a square grid, where the number of grid squares represents the measured distance between them. Then I was planning on shrinking the size of the grid squares over time. This would result in an increase in the number of squares (i.e. measured distance) between the two bodies, without them visually moving apart.

This appears at first glance to be a great illustration, but it results in the measured diameter of each body increasing over time at the same rate that the separation increases.

On the assumption that the metric expansion of space does not entail the expansion of all bodies within space, the obvious solution is to decrease the size of the circles so that their diameter is constant relative to the shrinking squares. However, if you visualise what such an animation would look like, you can see that it would look an awful lot like the 'camera' was zooming out from an image of two discs that were moving apart from one another. Is this assumption wrong? Are bodies supposed to expand, or is it only the space between them that does so? If the former, then the raisin bread analogy is flawed because the raisins don't expand. Hubble's Law makes no distinction between light from stars in our galaxy and light from other galaxies, right? So what are the "raisins"?

Can anyone shed any light on this? SheffieldSteel 21:32, 1 March 2007 (UTC)

Problems visualising this may alway be. No model is prefect. I like the balloon model, to demonstrate, I will put dots on it. As the balloon is inflated-expands the dots get farther apart. The dots on the balloon are galaxies. The key is the curve of the balloon is not just space but time. We call this time-space curvature. In the expansion of universe, not just space is expanding, but time as well. The galaxies are on the surface of the 4D universe as it expands. The expansion started with the Big Bang 13.7 billion years ago, when all space, time and matter came into existence. As the universe expands the time-space curvature is less. In the early universe time-space curvature was greater and the galaxies closer to each other. Telecine Guy 08:32, 12 March 2007 (UTC)

Olbers's Paradox

I was hoping to find some mention of Olbers's Paradox in this article. — Loadmaster 22:32, 23 July 2007 (UTC)

Local Expansion?

What is the rate of this metric expansion? Does it increase the distances in our solar system over time? If so, doesn't it affect the length of a year? Does mass remain constant with this metric expansion of space?Landroo 05:23, 27 July 2007 (UTC)

The metric expanion of space only occurs measurably over cosmological scales. There is no solar system influence. Nondistinguished 18:32, 3 September 2007 (UTC)

Unclear use of "distance", and numerous assaults on common sense

In the Overview, the article explains in a somewhat roundabout and indirect, but understandable way how a metric of distance can be constructed and applied to a coordinate space. This is good.

However, the part that says "The metric of space appears from current observations to be Euclidean, on a large scale. The same cannot be said for the metric of space-time, however. The non-Euclidean nature of space-time manifests itself by the fact that the distance between points with constant coordinates grows with time, rather than remaining constant." is, I think, confusing. It's not clear what "distance" is growing with time. Is it "just some obscure mathematical construct" (bear with me, I'm trying to see this from a complete layman's perspective, which isn't difficult because I almost am one), or is it the "real distance" between the two points? How is this distance, the distance that grows with time, measured? In other words, what is the metric of the universe (the one that is expanding)?

Later, the article goes on to say "In spaces that expand, the metric changes with time in a way that causes distances to appear larger at later times" -- this seems to imply that they aren't "really" larger, they just "appear" to be larger. I realize that this is very difficult to explain at this basic level, but since this seems to be what the article is attempting to do (which I think is a good idea), maybe you could try harder. The reader has to let go of the everyday concept of distance to avoid confusion; see below.

A simplified description of the metric should, I think, appear earlier in the article.

Another issue giving rise to confusion is the common-sense argument that as everything we observe is in space, right, then a hypothetical tape measure we could measure distances with would also be in space; hence, if space were to expand, then the tape measure would expand with it, and we'd still be reading the same distance. The statement "the metric itself changed exponentially, causing space to change from smaller than an atom to around 100 million light years across" seems, approached from a common-sense perspective, to imply that there is some unchanging "super-space" "outside our space", and that during the early life of our universe, our space, measured on a tape measure in this "super-space", was smaller than the size of an atom across, but then suddenly expanded, again measured on the tape measure "outside", to a size of 100 million light years. The "size of the atom" would then, apparently, be the size an atom is now, measured on this absolute tape measure; since, if space is expanding, the space inside an atom is also expanding, making the atoms bigger, surely? But, since our non-absolute tape measures are also likewise expanding, we're none the wiser, right?

This apparent implication should, I think, be addressed to remove confusion. Maybe explain that distances can be shown to have increased because light is taking longer to traverse them, and also why this doesn't mean that light slowed down, or that time speeded up (which, superficially, would both appear to be plausible explanations of light taking longer to cross a fixed distance).

I think the "Measuring distances" section should be expanded to serve as an introductory-level description of the problem and solution of measuring "long" distances. As it is, anyone familiar with the subject matter will probably understand it, but a layman, even armed with a fair understanding of mathematics, will probably not. The construction of the comoving distance metric seems arbitrary, and its physical meaning is unclear. I'm not sure how it could be explained in an intuitive way. Also, it's unclear whether it is in fact the, or only the, comoving distance that is increasing as space expands, or whether the other possible distance measures alluded to are also affected, and what the physical meaning of this is.

The figure caption only adds to the confusion as it says "The Hubble constant can change in the past ..." -- "you what?", my internal semantic parser thinks. :) How can a constant change? And how can it change in the past, yet in the present tense? Don't you mean "it can/may have changed" or "it could/might have changed"? Also, how can it change dependent on the observed value of density parameters? Surely, it doesn't matter whether we observe them or not?

The Copernican Principle as cited seems to contradict (again, based on common sense) what the article says earlier about the early universe having the size of an atom - surely, that atom-sized structure had a well-defined center, and well-defined boundaries? Where did these go, if they aren't around anymore? And if space is expanding, it is "expanding away" from the original center of that atom-sized structure, right? That is, there "must be" a well-defined center of the universe -- in fact, if the amount of matter is finite, it is even possible to define it as, say, the center of mass of all matter, right? And if expansion is symmetric, then this point is really the center of the universe, right? Wow, awesome! Can we put up a sign? :)

About "Ant on a balloon": the analogy is good, but there is an unaddressed issue related to the "everything is in space" argument above. The problem is that the ant is not itself in the "plane" of the balloon surface, but on it and is thus not itself directly affected by the balloon growing (maybe it has to shuffle its legs around a bit to keep them close to each other :). If the ant were in the fabric of the balloon (as we, observers of the universe, are in the fabric of said universe), then it would expand just as the balloon expands, and, depending on how it measures the distance between two points (e.g. by counting the number of steps required to reach B from A), it wouldn't necessarily detect a change in distance.

The raisin bread model does talk about the problem of the expanding ruler (or tape measure) a bit, but I think it's too little, too late. The concept of being "bound", and how and why it affects expansion, should be introduced earlier. Also, since gravity has an infinite range (although its effects approach zero as distance from the mass approaches infinity), all objects in the universe are "bound", aren't they? The distance between any two objects is finite, hence they exert a finite gravitational force on each other, right? OK, it's not called a force in relativity, but still, they both curve spacetime to a finite degree around the other object, making them "bound", right?

Modern science is a series of assaults on common sense: the Earth is not flat even though it appears to be; the Sun doesn't revolve around it even though it appears to; etc. I think it's important to explain why the assertions that apparently violate common sense are still true, and how common sense is mistaken/misled.

--195.56.53.118 23:47, 2 August 2007 (UTC)

Writing tip: few read past the first paragraph.

Anyway, to answer a point raised if space is expanding, the space inside an atom is also expanding, making the atoms bigger, surely? -- well no, actually, the size of the atom is defined by various physical constants and we can measure the size of atoms by bouncing light back and forth. So as space expands the size of an atom remains the same. Article should probably say this. --Michael C. Price ^talk 00:13, 3 August 2007 (UTC)

I know that the atoms don't increase in size; my point is that this is what everyday logic, or common sense, seems to suggest, which is why the article should, as you now also point out, explain that this is not the case.

About only reading the first paragraph: what would a good way to raise all these points have been? Add a separate discussion item for each? --195.56.53.118 08:45, 3 August 2007 (UTC)

I think a lot of confusion arises from the failure of the article to explain that the constancy of the speed of light provides a means of measuring distance -- probably the only easy, objective way of measuring it. Once that is established then it becomes easier to explain why atoms aren't expanding along with the universe (which is a common sense notion, I agree).

Always a problem being brief enough to maintain attention, but verbose enough to provide enough details -- no easy answers there, I'm afraid. I do think that most of your points revolve around how do we measure distance -- once that is established then the rest sort of falls into place. --Michael C. Price ^talk 09:24, 3 August 2007 (UTC)

I agree with 195.56.53.118. Galaxies are moving apart from each other so co-moving co-ordinates are chosen as a convenience. Other co-ordinate systems could be used to cover the manifold, eg. lots of different systems in describing black holes. Just because the co-ordinates are moving doesn't mean space is. What does it mean that space is expanding? It doesn't mean that objects can't move closer together. It doesn't make atoms get any larger. I can't see that it means anything, for example, how could you tell the difference between stationary objects in expanding space and stationary space with objects moving apart? Please tell me where I'm wrong and be as technical as you like. I see Ned Wright's cosmology tutorial seems to agree with me.Neodymion 04:53, 3 September 2007 (UTC)

It seems to me that with expanding space a Hubble horizon will form (since there is no upper limit, including c, to the recession velocity), whilst with objects moving through stationary space that no horizon will form (i.e. we can always see them all, albeit redshifted), since their recession velocity is now limited by c. --Michael C. Price ^talk 08:24, 3 September 2007 (UTC)

According to the source I linked: It seems that we can't see the ones that haven't had time for their light to reach us yet. As to their velocity being limited by c, it is, but in the same way as SR, where adding velocities by Lorentz boosting always gives an answer less than or equal to c. Thanks for answering my question, though, at least I don't feel like I'm completely missing something now.Neodymion 12:50, 3 September 2007 (UTC)

I agree with the points you made, but they don't affect the horizon business, which is still the critical difference. Interesting link, BTW. --Michael C. Price ^talk 14:13, 3 September 2007 (UTC)

On further reading I agree with you about the horizon thing. OK, so space is expanding. What's causing it? The cosmological constant? Neodymion 14:03, 4 September 2007 (UTC)

In a way, yes. Space was blown apart in the big bang by cosmic inflation, and we are living in its aftermath. The cosmological constant is a very slow form of inflation, and seems to be the dominant factor nowadays.--Michael C. Price ^talk 14:55, 4 September 2007 (UTC)

Current theory is that dark energy is driving the cosmic expansion. The cosmological constant is simply a measure of the expansion rate, not its cause. — Loadmaster 15:04, 4 September 2007 (UTC)

I believe the latest measurements are favouring dark energy as a cosmological constant (that is just an intrinsic parameter in the Einstein field equations). Either way the cosmological constant is not a measure of the expansion: either it's causing it, or it doesn't exist. --Michael C. Price ^talk 16:38, 4 September 2007 (UTC)