Six-dimensional space

In mathematics the sixth dimension is the six-dimensional Euclidean space generated by considering all real 6-tuples as 6-vectors in this space. As such it has the properties of all Euclidian spaces, so it it linear, has a metric and a full set of vector operations.

It is the lowest dimension that is not normally interpreted as a model for the universe. Three-dimensional space is the space we live in, the fourth dimension can be interpreted as spacetime a model for the universe used in special relativity, while the fifth dimension can be used to to model the curvature of spacetime as required in general relativity.

Geometry

6-polytope

Main article: 6-polytope

A polytope in six dimensions is called a 6-polytope. The most studied are the regular polytopes, of which there are only three in six dimensions.

Regular polytopes in six dimensions

• 
  6-simplex
• 
  6-cube
• 
  6-orthoplex

5-sphere

The 5-sphere or hypersphere in six dimensions is the five dimensional surface equidistant from a point, e.g. the origin. It has symbol S⁵, with formal definition for the 5-sphere with radius r of

$S^{5}=\left\{x\in \mathbb {R} ^{6}:\|x\|=r\right\}.$

The volume of the space bounded by this 5-sphere is

$V_{6}={\frac {\pi ^{3}r^{6}}{6}}$

which is 5.16771 × r⁶, or 0.0807 of the 6-cube that contains the 6-sphere.

Examples of common theories

Time: Your point in time and space

This suggests that time itself represents three dimensions - present, forward(or future) and past. Giving us six dimensions if you add that to the normal x, y, z.

Reality: Your point in time, reality and space from the perspective of the observer

This suggests that scale, time, and a reality (or multiverse) index should apply. Giving us x,y,z, the point in time, the quantum reality index (see also Many-worlds interpretation) and overall scale you are observing at. Basically Time(Reality(scale(x,y,z))). In this context in addition to normal x, y, z, time could be considered like x, reality like y, and scale like z. Giving us 6 dimensions.

S²: Two spheres framework for a six-dimensional universe

This is a more complex theory that in simple terms suggests a six dimensional manifold created by combining two spherical dimensions. This is the most well known 6 dimension theory in science circles, it was originally published in 1989.

Theological: The 6th dimension is part of a 15-dimension universe

Some theological beliefs exist on the number of dimensions, one suggests that the Sixth Dimension exists, and is the universe where the physical matter that makes up our soul exists. This exists as part of a larger 15 dimension universe.

Electromagnetic universe

The electromagnetic field (E,B) has six dimensions. In metaphysical naturalism this six-dimensional world may be enough to describe phenomena. The electromagnetic field tensor shows the six parameters as well as other mathematical descriptions of the electromagnetic field. The dynamics of this 6-space are given by the electromagnetic wave equation, and the geometric flexibility with coordinate transformations is given by the six-parameter Lorentz group.

Notes

Sixth dimension discussions are less common than fifth dimension and eleventh dimension theories popularized in science at the moment by mathematicians in quantum physics under quantum mechanics, string theory, and quantum gravity. This is possibly due in part to stigma of time travel becoming a popular topic in science fiction, or simply that research has not needed to move in that direction lately.

The Theories above are examples only, many others exist. Judgments on them are not intended to be within the scope of this article.

References and external links

• Science Journal: Il Nuovo Cimento A (Vol 103, No. 12, December 1990, page 1729) A Six-Dimensional Universe (S²) By J. Rayski, and J. M. Rayski Institute of Physics, Jagellonian University, Cracow, Poland 29/11/1989 Article available here
• Starman:C=T/sD The six dimensional universe
• Keylontic Science Theology: Structure of our universe (Theology related to Melchizedek)
• Sepp Hasslberger on the Universe

See also

• Fourth dimension
• Fifth dimension
• Calabi-Yau manifold
• Little string theory
• Eleventh dimension

External links

• the theory of everything?
• Extradimensional theories of the universe as opera
• example of 6 dimensional Calabi Yau

References in popular culture

• Ace Lightning TV show and Video game
• Star Trek Includes many plots containing dimensional and temporal paradoxes

Sources

• Science Journal: Il Nuovo Cimento A (Vol 103, No. 12, December 1990, page 1729) A Six-Dimensional Universe By J. Rayski, and J. M. Rayski Institute of Physics, Jagellonian University, Cracow, Poland 29/11/1989
• http://www.springerlink.com/content/5457k6t82511vl41/
• http://www.sciforums.com/showthread.php?p=1831954
• http://www.azuritepress.com/New%20Comers/structure_of_universe.html
• http://www.daviddarling.info/encyclopedia/C/Calabi-Yau_space.html
• http://science.howstuffworks.com/theory-of-everything.htm/printable