Talk:Cosmological principle

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"When viewed on a large enough scale"Edit

So, if it turns out not be, the scale at which we're viewing it simply isn't large enough? This is a semantic problem with the word 'enough'. Anything will X when you do enough Y, and if it doesn't X, that only means you need to Y more. Is there no formal definition which avoids this problem?

Some explanation could help, but it seems to be referring to the largest scale possible, which would be the entirety of the universe. Starting at the largest value possible narrows it down to at least a maximum, which can then be tested against the statement. Regardless of if it holds true for any smaller frame of reference, it only needs to apply to the most extreme case.
Perhaps there should be some added explanation below the quote to explain this?

TittilateMyTasteBuds (talk) 10:09, 15 February 2020 (UTC)

Should this sentence be moved to Criticism?Edit

However, the European Space Agency has concluded, based on data from the Planck Mission showing hemispheric bias in 2 respects: one with respect to average temperature, the second with respect to larger variations in the degree of perturbations. i.e. temperature fluctuations, i.e. densities, that these anisotropies are, in fact, statistically significant and can no longer be ignored .[8]

--Logical Gentleman (talk) 05:06, 30 July 2016 (UTC)

Support for thisEdit

What observations and axioms support this. Hackwrench 18:08, 1 November 2005 (UTC)

My understanding, and perhaps someone can correct/expand as needed, is that the cosmological principle is itself taken as an axiom, but there is experimental evidence as well. The best evidence for isotropy is the [cmb] which is isotropic to one part in 10,000. I think for homogeneity, we can look at other galaxies/clusters and see that the physics there appears to be the same, and galaxies on average are the same. Threepounds 06:54, 26 November 2005 (UTC)

This is true and there is more to it. The distribution of matter (galaxies and clusters) , dark matter, dark energy all seem homogeneous and isotropic. In fact, we can put some limit on the inhomogeneity and anisotropy of the universe on the large scales and we find out that it is agreeing very well with the cosmological principle. But we cannot ignore the tiny possibility that the cosmological principle is not 100% true, but we might never detect the slight variations. There is also a lot of theoretical arguments in favor of the cosmological principle. I don't want to go into the details but let's say that it is very hard to invent a successful model of our universe in which the cosmological principle is not respected. Basically, all work on cosmology (with FRW cosmological models at least) uses equations which were derived assuming the cosmological principle. So I'd say there is very good support in favor of the Cosmological Principle. (F.G. - McGill - Physics) —Preceding unsigned comment added by (talk) 15:50, 18 November 2007

i've deleted the section on "inhomogeneities" because it misinterprets the substance of the specific paper cited (which i've read): for example, in the concluding paragraph, the authors speculate about the implications of their findings for areas of the universe outside their observational sample and offer "tilt" as a pervasive structural feature of the universe *as a whole*, a claim which requires the cosmological principle to assert! the two points that were omitted or misappreciated in the earlier version of this wikipedia article are that (1) the cosmological principle is in one respect a *distributional* assumption about structure (isotropy) and a *validity* assumption about observational location (homgeneity); and (2) the cosmological principle is not violated by any gross anomaly, such as a "really big hole", unless this constitutes evidence of something novel or inexplicable in terms of smaller similar structures or known physical laws. perhaps the problem that is missed by previous writers is that the cosmological principle is a double edged sword, serving as a presumption that we can extend known physical laws to all phenomena, and as a "null hypothesis" that highlights events we *cannot* explain as the points deserving more intensive inquiry -- inquiry based on the working assumption that the events are explicable in terms of known physical laws. Macevoy (talk) 16:28, 8 January 2010 (UTC)

This vs. AnthropicEdit

OK, I'll bite: Under what logic does the Cosmological principle disprove the Anthropic principle? Do sources exist for such claims? ----Jasonuhl 21:26, 13 October 2005 (UTC)

I agree that this needs to be expanded. I think more needs to be said or this part removed. It seems to be that the Cosmological principle is a statement about averages over cosmological distances (as the article indicates) while humanity exists on an entirely negligible length-scale. It is not obvious to me how the two should be compared or where a contradiction exists. Threepounds 06:42, 26 November 2005 (UTC)

I've removed this sentence. The link between this and the Anthropic principle seems tenuous at best, and a claim that one disproves the other without any attempt at explanation adds nothing but confusion. ----Jasonuhl 23:42, 21 February 2006 (UTC)

Milne's Formalization of the Cosmological PrincipleEdit

I found a link in Timeline of cosmology that said Milne "formalized" this cosmological principle. While I agree that he did, I don't think that the gist of his argument is well presented here. For instance, Milne did not like the idea of a finite universe, nor did he like the idea of expanding space.

Milne says in Relativity, Gravitation, and World Structure "I am well aware that some mathematicians believe that such difficulties are at once swept awy if we use the concept of 'curved space.' I have examined such attempts at explanation with the greatest care, and I have found that in all cases the proposed explanations break down at some point. Two-dimensional analogies with hypothetical inhabitants on the surface of a sphere fail as soon as we recall that a survey of the astronomical universe is made by taking a photograph with a telescope and camera, and that, for a telescope of arbitrarily large light-gathering power, either the number of nebulae that can be counted is finite and therefore contains one faintest and so presumably most distant member, or it is infinite, in which case either the same nebula is photographed as an infinite number of separate spots or the total number of actual nebulae in existence is infinite. The latter will be our eventual conclusion. Here I am only concerned to argue that the phrase 'curvature of space' used in connexion with astronomical photographs merely involves a mist of mysticism. Such photographs can always be interpreted in flat space, and then the assumption of a finite number of density-maxima inevitably leads to some kind of accessible edge of the universe."

In this book, at least, Milne eventually concluded that the universe was not finite in terms of number of nebulae. He did not conclude that space was curved. JDoolin 16:27, 27 August 2006 (UTC)

I never read that book but I wanted to point out one thing. If you assume no big bang and an eternal universe, then you can assume that a large enough telescope could possibly measure an infinite number of nebulae. But if there is a big bang, then you cannot see further than the light travel-time since the big bang so you will always get a finite number of nebulae no matter how big your telescope is. This explanation had a name I cannot recall and was figured out long ago. Anyway, I guess this was already obvious and that this book is contemplating the possiblity of no big-bang. —Preceding unsigned comment added by (talk) 15:57, 18 November 2007

I guess you mean Olbers' paradox. You don't even need a large telescope because the number of galaxies increases with distance as fast as the light dims. Cosmo0 (talk) 22:56, 18 November 2007 (UTC)

Sorry I forgot I had posted to this discussion. Milne's model is a model with a big bang which actually is a Big Bang. An infinite amount of matter exploding from a point, the majority of which expands outward at the speed of light. The shrapnel in the middle forms the galaxies of the observable universe. The expanding surface is a time-dilated shell we would see the inner part of and call the CMBR. You can actually see further than the speed of light times the age of the universe in such an environment, if you take into account acceleration and Lorentz Transformations, changing reference frames etc. The Milne Model is an infinite mass model. Not, contrary to popular belief, a zero mass model. (JDoolin (talk) 01:21, 1 August 2010 (UTC))

In layman's termsEdit

Guys, this doesn't read at all well for someone not well versed in cosmology/physics. I imagine it is quite complex but is it possible to be expresed in more simple terms, or at least to explain the concept a little better? Some parts of it read almost like the article was created with the intention of being as obscure as possible. :-) Diliff | (Talk) (Contribs) 23:47, 21 August 2007 (UTC)

  • Words like "homogeneous" and "isotropic" probably must stay. ;) ◙◙◙ I M Kmarinas86 U O 2¢ ◙◙◙ 18:22, 24 August 2007 (UTC)
Unforunately, Diliff, many articles are obscuranist like this. I've added a line to the intro that, hopefully, makes things a little clearer.--Michael C. Price talk 18:27, 24 August 2007 (UTC)

"The universerve is the same everywhere" does not make anything clearer. It just states you assume the reader to be an imbicil. 12:06, 6 September 2007 (UTC)

I agree (well, imbecile is taking it a bit far). That's what the links to the articles on homogeneity and isotropy are for. Cosmo0 10:27, 23 September 2007 (UTC)

i agree with the initial complaint. i've edited the lede to clarify the essential point of the cosmological principle; the previous version fetishized homogeneity and isotropy into incomprehensibility. i've also deleted the section "a different view", since the issues of extrapolation it describes are not at issue in the cosmological principle (which is a principle of interpretation of evidence, not a principle of knowing what we can't see), and because the two sources cited in that section are both textbooks in the social sciences, not in astonomy or cosmology.Macevoy (talk) 19:08, 9 January 2010 (UTC)

Merge from Perfect Cosmological PrincipleEdit

I propose that Perfect Cosmological Principle should be merged into this article as a new section, since it's a simple extension of the subject discussed here and there's not much more to add to the other article that wouldn't be repeating this article. Cosmo0 21:20, 22 September 2007 (UTC)

Opposed. These are radically different concepts. --Michael C. Price talk 07:54, 23 September 2007 (UTC)
In what sense are they radically different? The perfect principle is just an extension of the other (the dictionary of astronomy on my bookshelf defines it as precisely that). Everything that can be said about the cosmological principle also applies to the perfect cosmological principle. Cosmo0 10:24, 23 September 2007 (UTC)
One is compatible with big bag, the other only with a steady-state cosmogony. That's pretty different.--Michael C. Price talk 13:22, 23 September 2007 (UTC)
True, although you could argue that even that isn't a big difference compared to the basic assumption of spatial homogeneity & isotropy. Anyway, I'm not dead set on this merger - I was just going through the astronomy stubs and I didn't think that the perfect CP article was likely to progress much beyond a stub without significant repetition of this one. But if you can think of some ideas to expand it then that's great. I suggest we leave it a week or two to give others a chance to comment and if there's no consensus in favour of merging (or the consensus is against) I'll remove the tags. Cosmo0 13:33, 23 September 2007 (UTC)

These two concepts should not be merged or confused. The Cosmological Principle is what we commonly refer to and is consistent with the standard model of cosmology (big bang, inflation, dark energy, etc...). The Perfect Cosmological Principle is a weird concept which contradicts this standard model. For instance, there cannot be a big bang if the universe never changes in time. The Perfect Cosmological Principle is somewhat along the lines of Einstein's original view of a static universe. Even if some strange theories might be able to fit in the Perfect Cosmological Principle, it remains an unproved principle unlike the Cosmological Principle which seems to apply very well to our universe. I hope it is now clear that these two concepts should not be merged together and it should even be emphasized that they are very different. I hope this helps. Sorry this is my first post on Wikipedia so I don't know the format and stuff. ( F.G. - McGill - Physics )—Preceding unsigned comment added by (talk) 15:40, 18 November 2007

The fact that one is consistent with observations and the other manifestly inconsistent doesn't make them "very different" as principles. Both are rooted in a much more basic principle, often called the principle of mediocrity: that we do not occupy a special place in the Universe. The fact that the perfect cosmological principle is almost certainly an incorrect application of that principle is why I don't think it deserves its own page.
The concensus appears to be against me so I'll withdraw my suggestion and remove the tags.
Cosmo0 (talk) 23:06, 18 November 2007 (UTC)

"smooth (i.e.: not fractal)"Edit

I don't get it. An isotropic fractal is an oxymoron then, or am I missing something? (it's not unlikely that I am) --Extremophile 19:25, 8 October 2007 (UTC)

I'm no expert, but as I understand it, fractal means that something looks the same viewed at different scales - it doesn't say anything about how it appears when viewed from different directions, so I imagine an isotropic fractal is possible. But a fractal that is smooth on large scales but not on small scales isn't, by definition. Cosmo0 21:18, 8 October 2007 (UTC)

Is the cosmological principle still true?Edit

There is a big hole in the sky! Although you can't see it with the naked eye it actually covers almost 3 degrees of the sky, and to put that into perspective the full Moon covers about half a degree! Until recently no-one was sure how big or far away this void was but the latest calculations suggest it is 900 million light-years across and 8,000 million light-years away. So can we still say the universe is homogeneous and isotropic? Is the Big bang theory still true?

24 November 2007

IN AUGUST, radio astronomers announced that they had found an enormous hole in the universe. Nearly a billion light years across, the void lies in the constellation Eridanus and has far fewer stars, gas and galaxies than usual. It is bigger than anyone imagined possible and is beyond the present understanding of cosmology. What could cause such a gaping hole?

— Preceding unsigned comment added by (talk) 06:39, 30 November 2007

See here for the details of the story. Structures on many scales have been discovered before (e.g. the Great Wall and the Sloan Great Wall); their existence doesn't invalidate the cosmological principle, which only requires the universe to be asymptotically homogeneous on very large scales. This particular result is interesting because it is judged to be very unlikely in the standard cosmology (although it's difficult and dangerous to draw statistical inferences from a sample of one) and because it explains a previously unexplained feature in the cosmic microwave background. Cosmo0 (talk) 09:30, 30 November 2007 (UTC)

What do you mean by aymtotically homogeneous? How big must the hole be before we can abandon the idea that the universe is homogeneous and isotropic? —Preceding unsigned comment added by (talk) 02:10, 3 December 2007 (UTC)

I already did.Kmarinas86 (talk) 18:18, 5 December 2007 (UTC)
If it's asympotically homogeneous, all that would really mean is that if the hole is bigger, then it must be farther away. That's the same as a fractal.Kmarinas86 (talk) 18:23, 5 December 2007 (UTC)

Huge misconceptions are being bandied about here!

The cosmological principle is completely unscientific. That doesn't mean it's wrong or useless, but it's an assumption based on weak circumstantial evidence. Not only is the cosmological principle unscientific, but it's impossible to give enough evidence for it to remove reasonable doubt about it. This is because "large scale" has no upper bound in definition: if the universe is larger than the observable universe, good luck "proving" anything about the unobservable parts of the universe. Even if the universe ends up smaller than the observable universe, the principle is too vague to "prove."

As for this specific scientific development, many voids and superfilaments (strings of superclusters of galaxies) have been found before. It's not as if scientists are suddenly "baffled" at this just because the press imagine they are. The superstructure of the universe is little understood, but for example CDM theory doesn't do a bad job at explaining it. (talk) 02:02, 30 September 2008 (UTC)

DECEMBER 2013- A new bigger structure was discovered, namely the Hercules-Corona Borealis Great Wall. It's 10 billion light-years across. Can this structure challenge the cosmological principle? ==Johndric Valdez (talk) 02:17, 20 December 2013 (UTC)==

Looks like this one is on its way outEdit

Peculiar velocities of clusters of galaxies can be measured by studying the fluctuations in the cosmic microwave background (CMB) generated by the scattering of the microwave photons by the hot X-ray emitting gas inside clusters. While for individual clusters such measurements result in large errors, a large statistical sample of clusters allows one to study cumulative quantities dominated by the overall bulk flow of the sample with the statistical errors integrating down. We present results from such a measurement using the largest all-sky X-ray cluster catalog combined to date and the 3-year WMAP CMB data. We find a strong and coherent bulk flow on scales out to at least > 300 h-1 Mpc, the limit of our catalog. This flow is difficult to explain by gravitational evolution within the framework of the concordance LCDM model and may be indicative of the tilt exerted across the entire current horizon by far-away pre-inflationary inhomogeneities. -- Kashlinsky, A., et al. (2008) "A measurement of large-scale peculiar velocities of clusters of galaxies: results and cosmological implications." Astrophysical Journal Letters (Science Daily,

Spring Back (talk) 05:25, 24 September 2008 (UTC)

History missingEdit

The article should present how the principle emerged into cosmological physics, including opposition and criticism. __meco (talk) 10:58, 2 May 2010 (UTC)

Needs updates from Planck DataEdit

as described here

and discussed in 2008 here

basically the Planck data has confirmed the CMB anisotropy first seen in the WMAP data, but now in very fine detail. There is an axis to the Universe, and in one direction the contrast of background temperature variations is higher than in the other direction. It's very close to the ecliptic.

This data throws a wrench in the Cosmological principle. the " uniformity of conclusions drawn from observation" is not the same, and we know it now. Far in one direction the Universe is different than far in the other direction. signed: jmdugan (talk) 02:52, 25 March 2013 (UTC)

I added the Planck results using well researched and accepted references, and tied it back to the WMAP and COBE results. Copi et. al., and others were waiting for confirmation or denial of the correlations from Planck, and confirmation is what they got. Wyattmj (talk) 16:01, 10 April 2013 (UTC)

Karl Popper CriticismEdit

The criticism seems a bit disingenuous since the cosmological principle is just an assumption not something that has ever been considered a fact. Is the opinions of Popper really relevant in an article about cosmology? (talk) 16:32, 27 February 2014 (UTC)

The entire study of the Big Bang was based on the assumption that the cosmological principle is true. If the cosmological principle had never been adopted, cosmology would be open to a greater diversity of explanations, and that would have been a great thing for science.siNkarma86—Expert Sectioneer of Wikipedia
86 = 19+9+14 + karma = 19+9+14 + talk
03:47, 23 March 2014 (UTC)
What Popper didn't seem to get (based on what this article is saying) is that the 'comsmological principle' isn't 'adopted' in a strict sense (it's not considered an undisputable fact or axiom) it's simply a commonly made assumption. No-one is being prevented from making different assumptions, cosmology is wide open to any explanation that agrees with experimental data. (talk) 04:00, 31 March 2014 (UTC)
"No-one is being prevented from making different assumptions, cosmology is wide open to any explanation that agrees with experimental data." In theory, what you say is correct, but in practice, it's not. The Big Bang theory is presented in almost a monopolistic way. For every cosmologist that rejects the cosmological principle there is perhaps 100 cosmologists whose work requires that it's true.siNkarma86—Expert Sectioneer of Wikipedia
86 = 19+9+14 + karma = 19+9+14 + talk
22:22, 31 March 2014 (UTC)
But that is true for every theory: they are derived from a bunch of assumptions. If experimental results agree with what the theory is predicting people tend to think the assumptions are correct, That doesn't mean the assumptions are dogma. The fact that people aren't as open-minded as we might like has more to do with human psychology. (talk) 11:18, 2 April 2014 (UTC)
True that. As per usual, Popper was scoring a cheap point that really amounted to nothing. The academic-sociological background to this is that many folk still smart from the fact that our modern knowledge of the universe shows us up as "nothing special" and hence this pretend-deep sort of criticism plays very well. Add to that the fact that academic philosophers not are not only ignorant of science these days, but also immensely proud of it, I predict that this kind of stupid will have legs and legs and legs. 2A01:CB0C:CD:D800:4DCF:8A84:9B04:97AC (talk) 12:33, 20 April 2019 (UTC)

3.26 ly/pc x 6,500 Mpc = 21.2 Gly. Article says 11.1 Gly. See article on "parsec". — Preceding unsigned comment added by (talk) 23:03, 27 October 2014 (UTC)

incorrect material in leadEdit

There is some material in the lead that is both incorrect and out of place:

"The second implicit qualification is that "looks the same" does not mean physical structures necessarily, but the effects of physical laws in observable phenomena."

This is followed by a discussion about upper limits on variations in the fine structure constant. This is just plain wrong. The cosmological principle certainly *does* refer to physical structure. What the author of this material is talking about is referred to as local position invariance (LPI), which is closely related to the equivalence principle. There is nothing inherently cosmological about LPI; it can be tested on both laboratory scales and cosmological scales. You can have LPI without the cosmological principle. I'm going to remove this incorrect material from the lead.-- (talk) 23:29, 10 May 2015 (UTC)

De facto homogeneityEdit

The Universe is expanding at a superluminal rate if we compare afar regions. This superluminal mean distance will shrink to point expansion everywhere, the omni-singularity or Big Bang. Big Bang is default space at the ultimate apex of decohesion, thus there is no need to transform any quantum information so that will get homogeneous. There is only one form of "default space", and it always explodes Big Bang way. Homogeneity is derived via superlumic defaulting spacetime (apex of decohesion fills the gaps expansion created because absolute decohesion among the universal components is not allowed). — Preceding unsigned comment added by 2A02:587:410E:8300:5C60:852E:2E99:DF75 (talk) 02:57, 24 February 2016 (UTC)

Homogeneity vs isotropyEdit

The article has quotes like:

... 'Viewed on a sufficiently large scale, the properties of the universe are the same for all observers.' ... the part of the universe which we can see is a fair sample ... the universe is knowable and is playing fair with scientists ... the same physical laws apply throughout ... the cosmological principle [means that] the universe looks the same whoever and wherever you are ...

That sound like just homogeneity though, doesn't it.

The explanation of isotropy given is:

Isotropy means that the same observational evidence is available by looking in any direction in the universe ("the same physical laws apply throughout").

How do we get there from 'the same physical laws apply throughout'? That's not the obvious reading of that phrase. -- (talk) 12:23, 27 September 2016 (UTC)

It's talking about the laws of physics, specifically conservation. Taking the entire universe as a control mass, no matter from where it's measured, it will have a constant value. Similarly, if the momentum of the universe as a whole (traveling through the void beyond), it would have the same vector if the same coordinate system is used. Which really would equal zero if one assumes there is no void and the universe is infite or non-expanding.

In other words, the flux or change in any of the universes physical properties is equal to zero. TittilateMyTasteBuds (talk) 09:57, 15 February 2020 (UTC)

Understanding of a Cited PaperEdit

This is written under the criticism heading: "In September 2016, however, studies of the expansion of the Universe that have used data taken by the Planck mission show it to be highly isotropical, reinforcing the cosmological principle."

However my understanding of the referenced paper was that if homogeneity is assumed, the we can say that the universe is very likley (121,000:1) expanding in an isotropic way. — Preceding unsigned comment added by Dextrion (talkcontribs) 19:57, 30 October 2016 (UTC)

Contradiction on Planck dataEdit

There are 2 paragraphs here about the results of the Planck mission that seem to contradict:

″Data from the Planck Mission shows hemispheric bias in 2 respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). Therefore the European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies are, in fact, statistically significant and can no longer be ignored.[12]"
- Added 16 May 2015 (Note: You can find this using WikiBlame)

I read this as: The Planck data showed lots of anisotropies that cannot be ignored, suggesting a potential rethink regarding the Cosmological constant.

"In September 2016, however, studies of the expansion of the Universe that have used data taken by the Planck mission show it to be highly isotropical, reinforcing the cosmological principle[17]"
- Added 13 September 2016

I read this as: The Planck data showed lots of isotropy, so there's no need to rethink the Cosmological constant.

The second paragraph starts with "however", implying that it contradicts, but supersedes, the points presented just before it about large observed structures. Yet I don't understand how these things are related. If there are these large structures, how come the Planck mission didn't pick them up as well? Perhaps the Planck mission was measuring a different thing. In that case, why should the Planck data override the existence of these structures?

It sounds like the second sentence is just given as a convenient conclusion to tie up the loose ends introduced by the "Inconsistencies" section.

Perhaps the paragraphs can be brought together, using something like "The Planck data showed mostly a lot of uniformity, though it did find some discrepancies". Spur (talk) 20:11, 24 May 2017 (UTC)

Add to section "Inconsistencies": indications of spatial variations of the fine-structure constant and the rate of the expansion of the UniverseEdit

Please add information on these two papers (or their subjects along with information on related papers) to section "Inconsistencies":

Here is what I added to the article 2020 in science:

Also see Fine-structure constant#Is the fine-structure constant actually constant?

--Prototyperspective (talk) 14:24, 23 May 2020 (UTC)

  1. ^ "Rethinking cosmology: Universe expansion may not be uniform (Update)". Retrieved 15 May 2020.
  2. ^ Migkas, K.; Schellenberger, G.; Reiprich, T. H.; Pacaud, F.; Ramos-Ceja, M. E.; Lovisari, L. (8 April 2020). "Probing cosmic isotropy with a new X-ray galaxy cluster sample through the LX–T scaling relation". Astronomy & Astrophysics. 636: A15. arXiv:2004.03305. Bibcode:2020A&A...636A..15M. doi:10.1051/0004-6361/201936602. ISSN 0004-6361. Retrieved 15 May 2020.
  3. ^ "The laws of physics may break down at the edge of the universe". Futurism. Retrieved 17 May 2020.
  4. ^ "New findings suggest laws of nature 'downright weird,' not as constant as previously thought". Retrieved 17 May 2020.
  5. ^ Field, David (28 April 2020). "New Tests Suggest a Fundamental Constant of Physics Isn't The Same Across The Universe". Retrieved 29 April 2020.
  6. ^ Wilczynska, Michael R.; Webb, John K.; Bainbridge, Matthew; Barrow, John D.; Bosman, Sarah E. I.; Carswell, Robert F.; Dąbrowski, Mariusz P.; Dumont, Vincent; Lee, Chung-Chi; Leite, Ana Catarina; Leszczyńska, Katarzyna; Liske, Jochen; Marosek, Konrad; Martins, Carlos J. A. P.; Milaković, Dinko; Molaro, Paolo; Pasquini, Luca (1 April 2020). "Four direct measurements of the fine-structure constant 13 billion years ago". Science Advances. 6 (17): eaay9672. doi:10.1126/sciadv.aay9672. ISSN 2375-2548. Retrieved 17 May 2020.
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