> ;=:M bjbj== %.WWl$,8$BPmoooooo$0 PfNmm<KmD(o $d4]m0em Notes from internet sources on KuluzaKlein Theory
HYPERLINK "http://www.matterantimatter.com/kaluzaklein_theory.htm" http://www.matterantimatter.com/kaluzaklein_theory.htm
Modern KaluzaKlein Theory
The HYPERLINK "http://astro.uwaterloo.ca/~wesson/home.html"Modern KaluzaKlein Theory unifies Maxwell's Theory of Electromagnetic and Einstein's Theory of General Relativity & Gravity. The theory provides the scientific and technical basis for modeling galaxies, solar systems, and spacecraft for traveling to the stars.
In 1919, HYPERLINK "http://wwwgroups.dcs.stand.ac.uk/~history/Mathematicians/Kaluza.html"Theodor Kaluza unified Maxwell's Electromagnetism and Einstein's Theory of General Relativity & Gravity by adding a fifth dimension. The idea came from Hermann HYPERLINK "http://wwwgroups.dcs.standrews.ac.uk/~history/Mathematicians/Minkowski.html"Minkowski who had successfully used the fourth dimension to solve the "spacetime continuum." In 1921, Kaluza published his theory, with Albert Einstein's encouragement. Kaluza's Theory became the framework for HYPERLINK "http://www.glenbrook.k12.il.us/gbssci/phys/class/relativity/reltoc.html"Einstein's Theory on General Relativity.
In 1926, Oskar Klein applied Kaluza's Theory to quantum theory, which is used in modern string theory. Over the past seventy years, scientists have had a difficulty correlating the KaluzaKlein Theory to physical reality. They have modified the assumptions, evaluated compactified, and used extra dimensions. The String & Super String Theories, which have resulted, do not giving acceptable solutions to the physical world.
In 1998, HYPERLINK "http://xxx.lanl.gov/abs/grqc/9805018"Overduin & Wesson successfully demonstrated that the fifth dimension would solve the HYPERLINK "spacetimematter.htm"SpaceTimeMatter Continuum by eliminated the cylindrical assumption from KaluzaKlein Theory. In Wesson's book, "SpaceTimeMatter, Modern KaluzaKlein Theory," there are numerous examples that correlate Modern KaluzaKlein Theory to the physical reality including general relativity and elementary particle physics.
People will be able to visualize the possible solutions of the "SpaceTimeMatter Continuum" that would enable them to travel to the stars within this century.
HYPERLINK "http://astro.uwaterloo.ca/~wesson/home.html" http://astro.uwaterloo.ca/~wesson/home.html
We are a loosely bound group of physicists and astronomers with a common interest in pursuing HYPERLINK "http://en.wikipedia.org/wiki/Einstein"Einstein's dream: the unification of what he called the "lowgrade wood" of matter and energy with the "fine marble" of geometry. Our approach follows one originally due to HYPERLINK "http://en.wikipedia.org/wiki/KaluzaKlein"Kaluza and Klein, but with important differences. Like Kaluza, we write down Einstein's field equations in more than four spacetime dimensions, with no explicit higherdimensional source terms. Unlike Klein and many others since, we avoid overly restrictive assumptions about the scale or topology of the extra coordinates. Dimensional reduction then leaves us with the usual field equations of gravity in four dimensions, plus extra terms. We identify these extra terms with matter and energy in the fourdimensional world.
HYPERLINK "http://arkadiuszjadczyk.org/papers/kk.htm" http://arkadiuszjadczyk.org/papers/kk.htm
RIEMANNIAN GEOMETRY, FIBER BUNDLES, KALUZAKLEIN THEORIES AND ALL THAT..... HYPERLINK "http://www.daviddarling.info/encyclopedia/K/KaluzaKlein_theory.html" http://www.daviddarling.info/encyclopedia/K/KaluzaKlein_theory.html
KaluzaKlein theory
A model that seeks to unite classical HYPERLINK "../G/gravity.html"gravity and HYPERLINK "../E/electromagnetism.html"electromagnetism by resorting to HYPERLINK "../H/higher_dimensions.html"higher dimensions. In 1919 the German mathematician Theodor Kaluza (18851954) pointed out that if HYPERLINK "../G/genrel.html"general relativity theory is extended to a fivedimensional HYPERLINK "../S/spacetime.html"spacetime, the equations can be separated out into ordinary fourdimensional gravitation plus an extra set, which is equivalent to Maxwell's equations for the electromagnetic field, plus an extra field known as the dilaton. Thus electromagnetism is explained as a manifestation of HYPERLINK "../C/curvature.html"curvature in a HYPERLINK "../F/fourth_dimension.html"fourth dimension of physical HYPERLINK "../S/space.html"space, in the same way that gravitation is explained in Einstein's theory as a manifestation of curvature in the first three.In 1926 the Swedish physicist Oskar Klein (18941977) proposed that the reason the extra spatial dimension goes unseen is that it is compact curled up like a ball with a fantastically small radius. In the 1980s and 1990s, KaluzaKlein theory experienced a big revival and can now be seen as a precursor of HYPERLINK "../S/stringtheory.html"string theory.
HYPERLINK "../S/space_and_time.html"SPACE AND TIME HYPERLINK "../P/particle_physics_entries.html"PARTICLE PHYSICS HYPERLINK "../C/cosmology_entries.html"COSMOLOGY HYPERLINK "../M/mathematics_entries.html"MATHEMATICS
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