Talk:Three-torus model of the universe

Should be deleted
Peebles 1980 gives the customary definition of putting the Universe on a 3-torus to make sure that Fourier representations are well-defined. So Zeldovich and Starobinsky weren't doing anything new or special. They did plenty of other stuff. 72.130.124.148 (talk) 03:58, 26 August 2020 (UTC)

No information
This article offers no meaningful information regarding anything. — Preceding unsigned comment added by 86.11.230.77 (talk) 15:46, 6 August 2020 (UTC)

i strongly disagree. this article eruditely and concisely enlightens the reader as to what a completely opaque and gobsmackingly superficial wikipedia article looks like. Drollere (talk) 05:41, 4 August 2021 (UTC)

Errors in this article
This article confuses the two-dimensional torus with the three-dimensional torus, and makes some extraordinary and unsourced claims about the Big Bang theory and cosmic inflation. This article seems to based on a misunderstanding of this popular science article from the New York Times. Is there anything that can be salvaged from this mess ? I think the underltying ideas are much more clearly and succintly described in the shape of the Universe article. Gandalf61 (talk) 16:40, 6 February 2011 (UTC)
 * 1) "The doughnut theory of the universe describes the shape of the universe to be similar to that of a doughnut" - in what way can the shape of the universe possibly be similar to a dougnut ? My best guess is that this sentence is trying to say that the universe may have the topology of a three-dimensional torus - but describing this as a "doughnut" is very misleading.
 * 2) "The structure of a torus allows for two ways to perform a loop in the torus: a loop around the outer edge and a loop around the tube of the torus" - this now appears to be talking about a two-dimensional torus. Even then, it is wrong - there are an infinite number of ways to "perform a loop" on a torus, even if you only count loops which cannot be continuously deformed into one another. In other words, the fundamental group of a torus is infinite.
 * 3) "The doughnut theory’s finite, torus shaped universe is a complete contradiction to the infinitely expanding Big Bang inflation theory" - okay, let's assume this means a 3-torus again. Exactly how does that contradict the Big Bang theory or cosmic inflation (two separate theories, by the way) ? No source is given for this claim.
 * 4) "If a toroidal universe existed, there would be two perpendicular ways to travel in a straight path and perform a complete loop around the universe" - now it seems to have switched back to talking about a two-dimensional torus. In a 3-torus, you can find three perpendicular paths that "perform a complete loop" - and there are infinitely many choices of such triple paths.
 * 5) "Equations of a Torus" - this section describes a two-dimensional torus, so no idea how this is relevant to the topology of our three-dimensional universe.
 * 6) "A finite, torus shaped universe is a strict contradiction of the inflation theory’s infinitely expanding universe" - another repetition of this unsourced claim.


 * Okay, I am going to try to salvage something from this mess of an article by removing erroneous and irrelevant material. Seems like a slightly better approach than taking it to AfD, but I am open to arguments to the contrary. Gandalf61 (talk) 14:31, 10 February 2011 (UTC)

Simpsons Reference
In one Simpsons episode Homer talks to Stephen Hawking about his idea of a donut-shaped universe.

Possible movement of the Torus Universe

 * "The history & shape of the universe which is usually accepted is known as the big bang theory, however this theory best describes the formation & behaviour of solar systems. When the big bang theory is used to describe the history & shape of the universe it is often flawed as it is best suited to describing the formation & behaviour of solar systems.
 * http://www.youtube.com/watch?v=EKtevjrZOGs
 * The torus model of the universe describes how solar systems, galaxies & the universe functions, it is a model of the universe. The balls are galaxies, notice when the galaxies approach the line of decreasing into the vortex of singularity at the centre of the universe torus, well this is like approaching death, better known as the black hole, here matter transmutates, energy is destroyed & then created here, for just as the centre of galaxies have a black hole, so does the centre of the torus universe also have a black hole.
 * Therefore it is possible for humanity to escape extinction by always solar system hopping & galaxy hopping in spacecraft, for as a solar system or galaxy approach the line of decreasing into the vortex of singularity at the centre of our torus universe, otherwise known as the black hole of the universe, spacecraft can thus jump to the nearest solar system or galaxy towards the expanding line closer to the outer reachs of our torus universe. Planets, moons, asteroids & meteors & some other intergalactic debris thus become desirable material to mine, process, possibly compress & finally used as the building material for sophisticated spacecraft which serve as habitats for humanity."

What the ...

The article is completely incomprehensible
The article is completely incomprehensible, I mean, at least to a mathematician, I suppose to a physicist, too. It goes on and on saying that probes and explorers support the model, can anyone explain in which way, for God's sake? 78.15.173.67 (talk) 00:33, 5 August 2015 (UTC)

Removing distracting text
I'm removing the following text from the article, as it seems to just be a long-winded digression about COBE and WMAP, which may inform current theories, but not a theory that was created before their existence. I'm hoping that this will re-focus attention on the three-torus model, instead of peripheral concerns. My feeling is that this text may be more useful in the COBE and WMAP articles, if it's not already there. I'm sure these somehow support the three-torus theory, but the section I left mentions COBE and WMAP, and could be easily extended to explain how these data support the model more directly. 75.139.254.117 (talk) 19:29, 2 April 2017 (UTC)

Cosmic Background Explorer (COBE)
The Cosmic Background Explorer was an explorer satellite launched in 1989 by NASA that used a Far Infrared Absolute Spectrometer (FIRAS) to measure the radiation of the universe. Led by researchers John C. Mather and George Smoot, COBE was able to obtain precise readings of radiation frequencies across the universe. With data on the universe’s radiation distribution, Mather and Smoot discovered small discrepancies in temperature fluctuation known as anisotropies throughout the universe. The finding of anisotropies led Mather and Smoot to conclude the universe consists of regions of varying densities. In the early stages of the universe, these denser regions of the cosmos were responsible for attracting the matter that ultimately became galaxies and solar systems. In “Microwave Background Anisotropy in a Toroidal Universe” by Daniel Stevens, Douglas Scott, and Joseph Silk of University of California Berkeley, the cosmologists proposed the isotropic universe suggests a complicated geometric structure. The researchers argued the density fluctuations reported by COBE proved “multiply connected universes are possible, [and] the simplest [and most probable multiply connected universe] is the three-dimensional torus.” Additionally, the journal concludes a torus shaped universe is compatible with COBE data if the diameter of the torus' tube is at least 80% greater than the torus’ horizontal diameter. Thus, COBE provided researchers with the first concrete evidence for a torus-shaped universe. COBE was eventually decommissioned by NASA on December 23, 1993.

Wilkinson Microwave Anisotropy Probe (WMAP)
The Wilkinson Microwave Anisotropy Probe (WMAP) was launched in 2001 as NASA’s second explorer satellite intended to map the precise distribution of CMB across the universe. Improving on the design of COBE, WMAP was able to represent an extremely accurate, fine resolution map of the CMB. Analysis by Max Tegmark, Angélica de Oliveira-Costa, and Andrew J. S. Hamilton of University of Colorado provided fresh evidence supporting a torus-shaped universe. After eliminating the radiation from stars and our own galaxy, the CMB of the universe appears more concentrated (intense) across one plane of the universe than all others. This concentration of CMB forms a straight line in the universe and may indicate a compact, finite universe.

Tegmark proposes his explanation, to his co-written study, that the universe is finite - the amount of radiation in one area is limited to and thus indicative of the size of the area in that direction. Where radiation exceeds its quota for the size of the plane seen, the universe has overflowed in that direction creating a plane in other directions. The perpendicular to the direction of the plane may thereby have created an invisible loop of a torus. Therefore, Tegmark suggests a torus geometry is the most probable shape consistent with his analysis of WMAP CMB maps.

Rename
Can this article be renamed to the shorter Three-torus model? Is "of the universe" in any way canonical? 47.32.217.164 (talk) 20:53, 9 May 2017 (UTC)

Rename to "3-torus..."
I think this article should be renamed to "3-torus model of the universe". I came here expecting some strange theory involving three toruses, not an ordinary 3-torus. 93.139.85.181 (talk) 21:52, 17 November 2017 (UTC)