Talk:Milne model

[| First Draft]
This article appears to describe mainly User:JDoolin's personal views on the model and its comparative merit. It contains first-person references, assumptions on what constitutes a "good" theory, analyses of current theoretic problems that Milne may or may not have made himself, just as a few examples. I suppose this model is a fine subject for an article, but it needs to be revised according to WP:NPOV and WP:NOR. Gazpacho 21:00, 16 August 2006 (UTC)

Thank you for not subjecting the article to immediate deletion! I would like to request help on section 3. Self-Consistent Properties of the Standard Cosmological Model. i.e. Expert Needed! As I am not neutral, it really is not fair for me to define a viewpoint which I think is incorrect, even if I am simply repeating what I have heard, from people who I consider experts. Verify that these are the Standard Cosmological Model, and that my reasoning is accurate. I will continue cleaning up what I can of the neutrality issues. I don't think I will be able to render it completely neutral.

JDoolin 23:26, 16 August 2006 (UTC)


 * Just do what you can. Whether reasoning is accurate isn't really the relevant question. For example, I don't think any of the claims made at Nazi UFOs is reasonable, but as long as they're attributed to the people who made them and cited, that doesn't matter. Given the choice between saying what you can trace to sources and saying everything you want to say, the former is usually a better option. Gazpacho 23:48, 16 August 2006 (UTC)

Cleanup
Whatever alse may be a problem with this article, it doesn't conform to encyclopedic style. See our style guide or just look at some good articles for a comparison. --Pjacobi 08:32, 25 August 2006 (UTC)

Reference
Please give your sources for this comparison. See WP:V, WP:RS, WP:NOR. This articles needs sources doing the comparison between the two models. Doing the comparison yourself, is in violation of WP:NOR. --Pjacobi 08:37, 25 August 2006 (UTC)

Cleanup beginning
Milne's universe is simply the empty universe. I applaud the work of the amateur who began this article, but I'm afraid much of what he or she wrote will have to go as original research. Milne's model is as described in the first two sections. The next two sections, while mostly superficially correct, are pretty much unneeded and redundant. --ScienceApologist 23:00, 29 August 2006 (UTC)

Factual Dispute
I notice that you haven't actually placed Relativity, Gravitation, and World Structure in your list of sources. I think that a few of the tings that you've said are quite misrepresentative. You bring up the homogeneity issue which you've completely misrepresented. You misrepresent the background of finite intensity You misrepresent that Milne's Model fits into the FLRW metric. It does not. You appear to be quoting other critiques of the work, without sourcing them, which are all flawed.

I suggest a revert to an earlier version of the article, where your issues are addressed somewhere near the top. I have no objection to having the historical objections being presented. JDoolin 23:56, 29 August 2006 (UTC)


 * All my edits are accurate. State the objections explicitly so we can deal with them. --ScienceApologist 00:11, 30 August 2006 (UTC)


 * Inasmuch as the Milne Model represents a singular solution to the Einstein Equations, it can be seen as a special case of the Friedmann equations. However, it is true that there are other singular solutions that can be found which are not the Milne Model. It is not true that the Milne Model "does not" fit into the FLRW metric. --ScienceApologist 00:20, 30 August 2006 (UTC)


 * You've changed it since I last looked, and I feel that you are making it more fair. Thanks.  There are still a few more issues that I feel should be analyzed, but I'll address them directly in the next few days.  I can see now that Milne's Model is compatible with the "static space" idea, and can address the concepts through the assumption that all motion in Milne's model is Peculiar Motion.  So I withdraw that criticism.  I think I have presented Milne's Homogeneity argument through the equations I've just added, so this might be cleared up if you don't dispute what I'm saying.


 * The background of finite intensity, though, I feel is a clear prediction of the Cosmic Background Radiation which has been observed, where you (and Peebles) seem to maintain that it is a prediction of some more complicated phenomenon which has not been observed. I admit that you are in very good company, but I still think this matter deserves to be disputed. JDoolin 14:44, 30 August 2006 (UTC)


 * I have tweaked the time-evolution of density section to be more summative. I'm not exactly sure what this supposed to illustrate other than the "shape" of the Milne distribution, but that's fine to include here.


 * I'm going to have to see a citation for the "finite intensity background" being the same as a cosmic microwave background with a temperature of 2.7 K and the precise inhomogeneities observed by WMAP. From my understanding of the Milne Universe, he was proposing instead an observed backlog of physical material at the "edge" of the universe which would be observable in some unspecified manner. In order for this to be correct, Milne has to get around Olber's paradox (since the stars would be piled up one on the other, ever line of sight would end up on a star and the sky would be as bright as the stars reduced by the redshift K-correction) and would have to explain the isotropy/homogeneity of the background which his model explicitly rejects. --ScienceApologist 18:04, 30 August 2006 (UTC)


 * To my knowledge he did not specify a temperature. Milne's model did not reject that a two dimensional inner surface of the sphere should be homogeneous.  He simply rejected that the density of the universe along any axis was homogeneous.  The density equation if expressed as a function of r, if r=sqrt(x^2+y^2+z^2) is only a function of r and t.  He predicted that the density would tend to infinity as r -> ct, and his major concern was to prove that the intensity would be finite instead of infinite.  And yes, the reason for him wanting to prove this was get around Olber's paradox.  I don't have the book with me right now, but if I recall correctly, it was in the appendix.


 * As far as the "observed backlog of physical material" goes, I'm not sure what that could even mean.

The backlog of physical material is the infinite density as r -> ct. --ScienceApologist 11:45, 31 August 2006 (UTC)

The claim that all motion within Milne's model is peculiar needs some citation. As one solves the Einstein (Friedmann) equations this gives rise to a scale factor that is linear in time and could (as far as I know) result in redshift by expansion of space. --User:Virtakuono April 26th 2009

Problem with the density function

 * $$n dx dy dz = \frac{B t dx dy dz}{c^3

\left(t-\frac{x^2+y^2+z^2}{c^2}\right)}$$


 * where $$n$$ is the density and
 * $$B$$ is a constant equal to the density at the very center of the sphere at t=1.

This doesn't make sense unitarily. Time t=1 is a meaningless statement unless you've scaled time to be 0 ab initio and 1 today. Even if this was done, the formula still doesn't conform to the rules of dimensional analysis unless:

1/(c^3-c x^2)

is unitless which it clearly is not. Therefore I have removed the function outright until the mathematics can be fixed.

--ScienceApologist 11:53, 31 August 2006 (UTC)

correction
I mis-copied it.


 * $$n dx dy dz = \frac{B t dx dy dz}{c^3

\left(t^2-\frac{x^2+y^2+z^2}{c^2}\right)^2}$$

I will look at it later today and make sure this is right and whether I defined $$B$$ correctly. I think you have the right idea--if you want to use B as the current local density, then it is approximately right if you scale time to be 0 ab initio and 1 today. You're locking down the density, then defining the time scale. I was thinking in terms of locking down the time-scale first and defining the density as it was at t=1 second. In any case, it was hardly helpful either way without the correct equation.

Very sorry about that. JDoolin 10:28, 1 September 2006 (UTC)

If $$c$$ is expressed in $$\frac{meters}{second}$$ and n is in $$\frac{particles} {meter^3}$$, then B is in particles. B is roughly the number of particles that were contained in a cubic meter of space containing the center of the sphere at time t=1 second. JDoolin 18:29, 1 September 2006 (UTC)


 * The time scaling has to be done via a coordinate shift. This needs to be specified because it doesn't make any sense to simply refer to t=1. And since the ab initio t=0 is not easily specified according to Milne, there has got to be a better way to define this. As it is, the mathematical explanation is inconsistent or at the very least incomplete. --ScienceApologist 14:50, 2 September 2006 (UTC)

Removing dispute tag
It looks that we have come to an article which everyone can agree upon is a neutral description of this noteworthy model. Therefore, I'm removing the factual dispute tag. That does not mean, of course, that editors must cease editting. I'd like to congratulate User:JDoolin on his patience and reasonability when writing this article. I think we really have a good one developing. --ScienceApologist 14:26, 1 September 2006 (UTC)

I agree that we are approaching some consensus. I still have a few things to change around, but they may be more semantic than factual. JDoolin 18:30, 1 September 2006 (UTC)

Putting dispute tag back.
Apparently I was wrong about approaching a consensus. I should point out that I was the one who put the dispute tag there in the first place. As you are not adding anything to the article but just removing my explanations, I will now put it back. JDoolin 02:53, 2 September 2006 (UTC)


 * If you keep putting in mathematically inconsistent formulae, original research, or redundant explanations that don't conform to Summary style, then I will continue to press for improvement. As it is, your last contribution was nothing but those three. --ScienceApologist 13:28, 2 September 2006 (UTC)


 * I apologize if I did not make it clear that all 17 properties I listed were enumerated in the book and cannot be taken for original research. I have also taken some care to check that the equation is correct now, and whether or not your opinion is that it is mathematically inconsistent, it must appear in the final version of the article, as it is the model.  Also, if you are to claim what Milne's model did and did not predict, or that you have made some kind of analysis of it through the FLRW metric, I also regard that as original research on your part, and as far as I can tell, you have not actually seen the book. The italicized comments in the text where I pointed out that evidence had disputed Milne's model were my own, and I will remove them from the article and place them in the discussion page. As for whether or not these explanations are redundant, I think that the explanations from the book Milne wrote should remain, and the explanations which are from another source should be either removed or categorized under "arguments against the Milne Model"JDoolin 23:28, 2 September 2006 (UTC)
 * On the other hand, perhaps I can go back to my original strategy of taking it point-by-point. I should be correcting what I see is wrong, rather than just trying to express it in the Talk section.  JDoolin 23:50, 2 September 2006 (UTC)
 * I realize that what I was angry about was more limitations I was putting on myself rather than anything you specifically did. I was trying to only quote verifiable sources while it seemed to me that you were pretty much putting down anything you wanted.  I was not addressing some of the issues I had because I thought it would be better to present a complete description from the book which was verifiably not original research.  I found the perfect description in section 112 of RGWS, and presented it.  When you removed it, I thought you immediately saw it's merit and it's potential to collapse your current theory, so you rushed to cover it up immediately.  I saw your rush to remove what I consider to be useful, informative, and relevant information as being a symptom of whatever has prevented this rather simple and self-evident theory from being seen by the public for the last 70 years.  Now I realize that you think I'm just making things up.  Now I realize that it is just too long and too technical to use in this forum.  But I still hop you realize that I'm not making any of this up.  For reference I present the information again, here on the talk page.

List of properties of the Milne Density Distribution
Milne gives the following equation where

"$$n$$ is the spatial particle density for $$t$$ large" and   and "$$B$$ is an arbitrary positive constant."


 * $$n dx dy dz = \frac{B t dx dy dz}{c^3

\left(t^2-\frac{x^2+y^2+z^2}{c^2}\right)^2}$$ This is derived as equation (9), in section 91 of Relativity, Gravitation, and World Structure, and repeated in a summary in section 112 as equation (36). In section 94, Milne proves that this distribution is Lorentz Invariant

In section 112, "Properties of the 'hydrodynamic' or simple kinematic system," Milne lists these seventeen properities of the system. (Except for 14-16, these are exact quotes.)


 * 1) "The system is described in the same way by the same formula (36) by any observer situated on any particle of the system, using his own coordinates, in flat space constructed out of his own clock measures."
 * 2) "The system is spherically symmetrical round any particle of the system, in the experience of the observer attached to that particle."
 * 3) "The particle-density is locally homogeneous near any given particle-observer O of the system, in O's reckoning. Departures from homogeneity are of the second order in r/ct."
 * 4) "The particle density, in the reckoning of any particle-observer O, at any given epoch t, increases outwards."
 * 5) "Near O, at any fixed distance, the particle-density decreases at a rate inversely proportional to the cube of the time."
 * 6) "The system is contained at any epoch t within a finite expanding sphere centred round any particle-observer O, of radius r=ct where t is the age of the system in O's reckoning. The radius of this sphere increases with the speed of light."
 * 7) "As the distance r tends to ct, i.e. for points nearer and nearer the expanding light-sphere, the particle-density tends to infinity."
 * 8) "The total number of particles in the system is infinite."
 * 9) "The members of the system form at any epoch t in the experience of any particle-observer O an open set of points of which every point of the expanding sphere r=ct is a limiting point. Every particle of the system is completely surrounded by other particles. No particle stands on the 'edge' of the system."
 * 10) "Every particle of the system is in uniform radial motion outward from any arbitrary particle O of the system, and the acceleration of every particle in the system is zero. But the acceleration of a freely projected particle, other than the given particles, is not zero."
 * 11) "The domain occupied by the system, though finite in volume, has all the properties of infinite space, since its boundary is for all time entirely inaccessible by any hypothetical observer travelling with a speed not exceeding the speed of light."
 * 12) "The velocities of different particles at any one epoch are proportional to the distances of the particles from any assigned particle taken as origin, and tend to the velocity of light as the distance tends to ct."
 * 13) "If the particles are supposed to be luminous, then the luminosity near the expanding boundary approaches zero, since the particles are receding with nearly the speed of light (see Note 7)"
 * 14) describes the phenomenon of desynchronization
 * 15) gives the relativistic doppler shift equation
 * 16) says that the age of the universe at any given event is indefinite, the system has "no definite age or radius at any assigned event, the age t and radius ct depending on the epoch assigned to the event, which depends in turn on the observer making the assignment."
 * 17) "A particle-observer O at the moment of experiencing an event E2 at himself is at a much later stage of his own experience, reckoned in his own time-scale, than P is in his (P's) time-scale at the event E1 at P which O is then observing."

Many of these points are redundant to the article already and some are almost meaningless to include in a general summary. Also, I removed the editorializing that represented the last few edits to this page. I am willing to discuss the removal of any of these edits, so if User:JDoolin has questions, please ask them here. --ScienceApologist 12:26, 5 September 2006 (UTC)

Why would you say that the Milne model is an empty universe? JDoolin 14:27, 27 September 2006 (UTC)

Because GR is Minkowski space when there is no curvature. One way to get this to happen is when the stress-energy tensor is zero: thus the universe is "empty" of mass-energy. --ScienceApologist 17:58, 27 September 2006 (UTC)

Perhaps you mean SR (not GR) is Minkowski space when there is no curvature. In any case, I think you should not try to say that Milne "assumed" an empty universe, unless you can find a quote of his where he did so. Everything I've read indicates he believed there were an infinite number of nebulae and particles, and at no point did he make the case that these were massless or energyless.

If Bob's model were that the universe were made of iced tea, would you put on the wikipedia page for Bob's model that Bob's model was the Friedmann metric? No, you'd say Bob thinks the universe is made of iced tea. People could judge for themselves whether Bob's model was accurate. Why don't you let it be said what Milne's model is? JDoolin 20:55, 29 September 2006 (UTC)


 * The article does not state that Milne assumed an empty universe. It said he derived an empty universe. Milne wasn't aware of the implications of GR when he derived his model. Later he would invent the cosmological principle as a foundational idea behind the Big Bang. The Milne model is a model that is described by a Minkowski metric, and because an empty universe follows the Minkowski metric, the empty universe is a Milne universe by definition. It may not have been what Milne intended, but he couldn't have intended it because he didn't know about general relativity when he developed the model. --ScienceApologist 21:05, 29 September 2006 (UTC)

Noncompliant
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—The preceding unsigned comment was added by ClairSamoht (talk • contribs) 23:33, 28 September 2006.

New "light cone" image
We have prepared a new "light cone" image. The intention was to imply the correct scale of space-time relative to the observer. Interstellar light-years vs years scales seemed appropriate. If you have any comments please post them at the Graphics Lab entry. Dhatfield (talk) 22:42, 28 June 2008 (UTC)

Correction needed
There ist a fundamental flaw in this article. The Milne metric ist not the Minkowski metric. In order to make any sensible definition of a scale factor, you have to make sure that space is isotropic and homogeneous. This is achieved by a coordinate transform, see eg.. The scale factor is then not constant, but increases linearly with time. Ich42 (talk) 13:10, 2 December 2008 (UTC)
 * It depends on which coordinates you adopt. You can recast Milne's universe into Minkowski metric as long as you assume an explosion associated with the objects that are expanding outwards. This casting is, of course, unphysical in light of the unifying features of general relativity, but it's what Milne was going for. ScienceApologist (talk) 15:08, 4 August 2010 (UTC)

Specific space-time coordinate of the big bang
In Milne's Model, the event of the Big Bang has a specific space-time coordinate, and thus it is subject to the laws of Special Relativity.

This statement was removed as inaccurate. However, Milne's model can be seen here: (File:Milne_Model.jpg) to be expanding from a specific event in space-time. So the statement is accurate. In any case, to discuss Milne's model without mention of the faster-than-light particles that he presents, seems to me to be MORE inaccurate a presentation.

For that matter, though "Milne, Relativity, Gravitation and World Structure, Oxford University Press, 1935" is listed as a source for the article, I don't think this article actually contains much of ANYTHING from that book.

Most of the material appears to come from secondary sources, which DO NOT present Milne's model accurately, or fairly. —Preceding unsigned comment added by JDoolin (talk • contribs) 21:01, 4 May 2010 (UTC)
 * Nothing in the page scan (which I turned into a link as displaying a fair use image here is not allowed) supports the assertion that the big bang or any event has a specific coordinate. In fact, that idea is completely counter to relativity. The second part of the sentence, "thus it is subject to the laws of Special Relativity", is at best irrelevant. All we can generally say is that special relativity applies locally at any event. This article starts out by mentioning that Milne's cosmology is a special relativistic model, and the erroneous section I deleted added nothing useful to that description. I realize you have particular points of view about Milne's model that are contrary to all the reliable secondary sources so far presented, but all that means is that your opinions don't belong in the article. There are other venues where unsupported personal opinion and original research are welcome. A central tenet of this encyclopedia is that content is supposed to be mainly based on reliable, secondary sources. Tim Shuba (talk) 17:21, 5 May 2010 (UTC)

Two Facts Issues and one Semantics Issue
(1) The article currently states that “Unless the universe modeled has zero density, Milne's proposal does not follow the predictions of general relativity for the curvature of space caused by global matter distribution”  I think this is an incorrect statement.

The standard model assumes that the amount of matter in the observable universe is finite. Hence, there is a gravitational asymmetry at every point in the universe as everything is pulled toward the center. This creates an environment where space-time must expand, or the mass would quickly collapse on itself.

However Milne determined that the density of the universe is infinite at t=0, and in the expanding sphere, r = c*t. Here, contrary to the standard model, the amount of matter in the observable universe is infinite. Because of the symmetry of the bulk of this matter, there is no gravitational asymmetry, and no need for space-time to expand to prevent it from collapsing. (JDoolin (talk) 13:32, 30 July 2010 (UTC))
 * I don't have Milne's original paper on me, but if this is true it manifestly violates flux conservation associated with fields inside a uniformly charged sphere. The argument that Einstein struggled with is not actually that everything is pulled toward "a center". The argument is actually that a static universe is unstable. ScienceApologist (talk) 15:05, 4 August 2010 (UTC)

(2) Also the article currently states that “in particular (Milne's Model” makes no prediction of the cosmic microwave background radiation . . .”  While Milne of course never uses the words “cosmic microwave background radiation” and in fact, should not have any idea whether such a thing would still be visible, it should be noted that Milne's model is fully compatible with the CMBR.

The article later states: “Edward Arthur Milne predicted a kind of event horizon through the use of this model: "The particles near the boundary tend towards invisibility as seen by the central observer, and fade into a continuous background of finite intensity." The horizon arises naturally from length contraction seen in special relativity which is a consequence of the speed of light upper bound for physical objects. In Milne's universe, the velocities of objects asymptotically approach this upper bound while the distance to these objects approaches the speed of light multiplied by the time since the event of the initial explosion of material. Beyond this distance, objects do not lie in the observable part of the Milne universe.”

The only difference between Milne's CMBR and the CMBR of the standard model is that the standard model says the apparent reduction in temperature (3000 K to 2.73 K) is caused by stretching of space, while in Milne's Model the redshift would be due to the time dilation caused by recession velocity. It may well not have occurred to him that the natural source of this light would be hydrogen in its recombination stage—but that's a matter of particle physics—not cosmology. (JDoolin (talk) 13:32, 30 July 2010 (UTC))
 * What you are referencing is so-called "integrated starlight" which is not uniform enough to account for the CMB. ScienceApologist (talk) 15:05, 4 August 2010 (UTC)

(3) There is possibly a confusion about "the observable part of the Milne Universe" In the standard model, objects can "pop in" to the observable universe, as the speed of light overtakes the stretching of space. In Milne's model, all of the matter is there, from the initial event (t=0, r=0) Everything is causally connected to that single event from the beginning, so every bit of the infinite amount of matter is in the observable part of the universe. (JDoolin (talk) 13:32, 30 July 2010 (UTC))


 * This may be a technical difference without distinction. The horizon in the Milne universe comes from the explosion itself. ScienceApologist (talk) 15:05, 4 August 2010 (UTC)

Dispute Tag
Due to a conversation I was just having with George Dishman at https://www.researchgate.net/post/Is_the_use_of_relativity_of_simultaneity_in_standard_cosmology_appropriate I just now went and put the dispute tag back into the article about the Milne model today. ScienceApologist removed the dispute tag and the "List of properties of the Milne Density Distribution" at the same time. It won't do any good to put the dispute tag back in, of course, because, George, you may feel free to go back in there and remove the dispute tag, and let everybody know that I'm vandalizing Wikipedia. It's the sort of behavior I've come to expect from defenders of the FLRW metrics. Since you're required to have "good faith" in the other editors to participate at Wikipedia, and I became convinced that ScienceApologist was a liar, I could no longer participate without breaking the rules.

Now seeing that some time ago, ScienceApologist was banned for trolling, I think it should be noted that he removed the dispute tag and the LIST OF PROPERTIES OF THE MILNE DENSITY DISTRIBUTION at the same time. At that time, the tag that says "Protected by the relativity task force" and several threats to access to ban me from Wikipedia, and the use of my account were also made. I did not see it worthwhile to respond to any of ScienceApologists other comments, because they are irrelevant. — Preceding unsigned comment added by JDoolin (talk • contribs) 13:56, 16 May 2018 (UTC)

This link can take you straight to the page of Relativity Gravitation and World Structure where the properties are listed: https://archive.org/stream/RelativityGravitationAndWorldStructure/Milne-RelativityGravitationAndWorldStructure#page/n119/mode/2up/search/'hydrodynamic'+or+simple+kinematic+system JDoolin (talk) 20:46, 16 May 2018 (UTC)

Am J Phys article
I am not a specialist in this field but I recently read this article:

Therein the Milne model is described as a low-density expanding universe, and, as "flat Minkowski spacetime of special relativity expressed in nonstandard coordinates", with the footnote:
 * This fact is an occasional source of confusion, because a low-density universe is an open universe, in which space, as opposed to spacetime, has negative curvature. What matters in the present context is the spacetime curvature, that is, the deviation of the overall spacetime metric from that of special relativity, not the spatial curvature. The latter describes the geometry of a “slice” through the spacetime at constant time in a particular coordinate system.

Upon reading this I thought the Milne model would be a very interesting pedagogical tool (like Rindler coordinates) and wanted to look up the Milne model. I found this wikipedia article, which has been tag bombed and seems a bit muddled and short on references. Perhaps this Am J Phys article could be helpful. --Nanite (talk) 21:10, 14 May 2021 (UTC)