User:J kay831/Donut Theory

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Doughnut Theory of the Universe The doughnut theory of the universe describes the shape of the universe to be similar to that of a doughnut. The technical name for the geometric shape of a doughnut is a torus. 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. Therefore, a doughnut shaped universe would allow for two ways to travel in a seemingly straight path and end up at the starting point. The geometry of a torus may also be described algebraically.
The foundation for the doughnut theory started with Bell Lab’s discovery of cosmic microwave background (CMB). With the information provided from the study of CMB, Dr. Alexi Starobinski conceived the doughnut theory of the universe along with his mentor, Dr. Yakov B. Zeldovich, in 1984 from the Landau Institute in Moscow. [1] With the study of CMB as the best source for information on the universe’s geometry, NASA launched two explorer satellites, the Cosmic Background Explorer (COBE) in 1989 and the Wilkinson Microwave Anisotropy Probe (WMAP) in 2001, to map CMB. The information from these satellites led many cosmologists to believe the universe is shaped like a torus.
Despite evidence supporting a finite, torus shaped universe, contradicting theories provide opposing evidence to the doughnut theory. Although neither theory is proven, the

inflation theory
is the most popular and threatening theory to the doughnut theory. The doughnut theory’s finite, torus shaped universe is a complete contradiction to the infinitely expanding Big Bang inflation theory.

The Geometry of The Universe

Overview

A torus

While visualizing the universe in the structure of a doughnut is an easy and general way to understand the doughnut theory, the technical name for a doughnut-like structure is a

linear until the journeyers arrived where they started. Thus, the loop is still completed despite the lack of connectivity between the inner and outer edges of the flat torus. [4]

The torus consists of two circles in which one may theoretically loop around the universe

Equations of a Torus

To understand the mathematical expressions of a torus certain variables must be defined:

  • α is the radius of the cylinder that makes up the tube of the torus
  • β is the radius from the center of the torus to the center of the tube
  • x is the x-coordinate on the Cartesian coordinate system with X = 0 on the direction of the torus
    axis of symmetry
  • y is the y-coordinate on the Cartesian coordinate system with Y = 0 on the direction of the torus axis of symmetry
  • z is the
    z-coordinate
    on the Cartesian coordinate system with Z = 0 on the direction of the torus axis of symmetry
  • ν is the angular parameter variation that represents time

1) The surface equation in

Cartesian coordinates
is

(β − (x^2 + y^2)^(1/2))^2 + z2 = α2

2) The parametric equations are

x = cosφ(β + αcosν)
y = sinφ (β + αcosν)
z = αsinν


3) The Riemannian metric equation is

ds2 = (β + αcosν)2 dφ2 + α2dν2

4) The position of a point on the torus surface is specified in

spherical coordinates
by

x = Rsinθcosφ
y = Rsinθsinφ
z = Rcosφ


5) From (2) and (4)

R2 − 2Rβsinθ + β2 − α2 = 0 [5]

Supporting Evidence

Dr. Alexi Starobinski first proposed the doughnut theory of the universe along with his mentor, Dr. Yakov B. Zeldovich in 1984 from the Landau Institute in Moscow; however, the basis for his theory began much earlier than 1984. The foundation for any knowledge of the shape of the universe began in the mid-1960s with the discovery of cosmic microwave background (CMB) by Bell Labs. Greater understanding of the universe's CMB provided greater understanding of the universe's geometry; therefore, in a quest for cosmic understanding, NASA supported two explorer satellites, the Cosmic Background Explorer (COBE) in 1989 and the Wilkinson Microwave Anisotropy Probe (WMAP) in 2001, which have gathered more information on CMB.

Cosmic Microwave Background (CMB)

isotropic radiation or black body. Dicke and Peebles proved that the near perfect black body of the CMB meant the universe began much denser and hotter than it is today.[3] Despite Dicke and Peebles contributions to humanity’s understanding of the universe, they were unable to obtain a concrete understanding of the shape of the universe. Rather, the cosmologists' research allowed Dr. Alexei Starobinski to devise the doughnut theory. With the knowledge provided from the greater understanding of CMB, Dr. Starobinski believed the most probable shape of the cosmos that complied with known rules of the universe resembled that of a doughnut. ” [1]

Cosmic Background Explorer (COBE)

The

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 [8]. Thus, COBE provided researchers with the first concrete evidence of the doughnut theory. COBE was eventually decommissioned by NASA on December 23, 1993. [7]

Wilkinson Microwave Anisotropy Probe (WMAP)

WMAP cosmic microwave background map

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 universe’s CMB. [9] Such accuracy of WMAP’s CMB charts provided cosmologists with new data to analyze. The analysis of WMAP data in “A high resolution foreground cleaned CMB map from WMAP” by Max Tegmark, Ange ́lica de Oliveira-Costa, and Andrew J. S. Hamilton of University of Colorado provides further evidence of a doughnut shaped universe. The research team discovered that if the WMAP CMB map is analyzed while eliminating the radiation from stars and our own galaxy, the CMB of the universe appears more concentrated in one direction than the other. This concentration of CMB forms a straight line in the universe, which is believed to be characteristic of a compact, finite universe. Tegmark proposes that if his data does prove the universe is finite, then the amount of radiation in one area would be limited to size of the area in that direction. If the radiation exceeded the size of that area, the universe would overflow in that direction creating a plane in other directions. The perpendicular to the direction of the plane would create the loop of the doughnut, or torus. Therefore, Tegmark suggests a torus geometry is the most probable shape consistent to his analysis of WMAP CMB maps. [1][10]

Opposing Evidence

The most significant opposing argument to the doughnut theory is evidence supporting the more popular

CMB, no monopoles have been found. The inflation theory states monopoles may have existed before inflation expansion, but inflation expansion decreased the density of these monopoles to undetectable levels. [11]
Thus, the convincing evidence supporting the Big Bang inflation theory is the greatest threat to the validity of the doughnut theory.

References

  1. ^ a b c Overbeye, Dennis. New York Times 11 March 2003: Web. 16 January 2011. “Universe as Doughnut: New Data, New Debate”
  2. ^ a b Halpern, Paul. Cosmos. 6 September 2007. Web. 16 January 2011.“Is the universe a doughnut?”
  3. ^ a b Halpern, Paul. Hoboken, NJ: John Wiley and Sons, Inc., 2007. Web. 29 Jan. 2011. "What’s Science Ever Done For Us?”
  4. ^ Kostyuk, Victor. math.cornell.edu. Cornell University. Web. 1 Feb. 2011. “Flat Life”
  5. ^ Murdzek, R. Romanian Journal of Physics. 27 April 2006. Web 16 January 2011. “Cyclic Universes From Torus Geometry”
  6. ^ Scott, Douglas. Martin White. Astro.ubc.ca. 10 Feb. 2000. Web. 1 Feb. 2011. “The Cosmic Microwave Background”
  7. ^ a b Smoot, George. Encyclopedia of Astronomy and Astrophysics. Brunel Road, UK: Institute of Physics Publishing, 2001. Web 28 Jan. 2011. “Cosmic Background Explorer: COBE”
  8. ^ Stevens, Daniel. Douglas, Scott. Joseph, Silk. Phys. Rev. Lett. 71 (1993): Web. January 24 2011. “Microwave Background Anisotropy in a Toroidal Universe”
  9. ^ Griswold, Britt. Edward J. Wollack. nasa.gov. NASA, 29 Oct. 2010 Web. 2 Feb. 2011. “Wilkinson Microwave Anisotropy Probe”
  10. ^ Tegmark, M., A. de Oliveira-Costa, & A. J. S. Hamilton, 2003. Physical Review D. “A high resolution foreground cleaned CMB map from WMAP”.
  11. ^ Griswold, Britt. Edward J. Wollack. nasa.gov. NASA, 6 April. 2010 Web. 2 Feb. 2011. “What is the Inflation Theory?”

External links

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