Open Questions: Higher Dimensions of Spacetime

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See also: Supersymmetry -- Superstring theory


Kaluza-Klein theories




Quantum gravity

Modified general relativity

Experimental investigation

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The notion that there may be dimensions of space beyond the three that are apparent in everyday experience has exerted a powerful fascination on popular (and scientific) imagination for over a century.

It probably began with mathematicians like G. F. B. Riemann in the 1860s who first explored geometries that are alternatives to the 3-dimensional Euclidean geometry that had been studied since the Greeks, more than two millennia ago. The trend gathered considerable momentum from Einstein's special theory of relativity (1905) and general theory of relativity (1915), in which spacetime was conceived as a 4-dimensional geometry with a decidedly non-Euclidean metric. (Einstein was heavily indebted to Riemann for the proper mathematics with which to develop his theories.)

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Why 10 dimensions
Article from Wikipedia.
Extra Dimensions, Quantum Gravity, and Superstrings
Slides from a talk by Sean Carroll at an October 2001 conference on cosmology.
Brane new world
June 28, 2001 news feature article in Nature about the "brane-world" proposal of Arkani-Hamed, Dimopoulos, and Davali.
Testing the gravitational inverse-square law
April 2005 article form Physics World, by Eric Adelberger, Blayne Heckel and C D Hoyle. "If the universe contains more than three spatial dimensions, as many physicists believe, our current laws of gravity should break down at small distances."
The hunt for new dimensions
February 2001 news article from PhysicsWeb. "For decades physicists have toyed with the idea that the universe may contain extra dimensions beyond the familiar four dimensions of space and time. This idea has been proposed to account for the exceptional weakness of gravity. But remarkably, nobody has measured the strength of gravity on scales much less than a centimetre - and that is exactly where theorists believe the extra dimensions could be hiding. Now Eric Adelberger and co-workers at the University of Washington in the US have measured for the first time the gravitational attraction between objects just 0.2 mm apart - and concluded that any new dimensions must be concealed on even smaller scales."
The search for extra dimensions
November 2000 article from Physics World, by Steven Abel and John March-Russell. "The idea that the universe is trapped on a membrane in some high-dimensional space-time may explain why gravity is so weak, and could be tested at high-energy particle accelerators."
Extra dimensions round the corner?
Summary of a June 1999 article in Physics World.
(De)Constructing Dimensions
April 2001 technical paper by Nima Arkani-Hamad, Andrew G. Cohen, and Howard Georgi. "We construct renormalizable, asymptotically free, four dimensional gauge theories that dynamically generate a fifth dimension."

Recommended references: Magazine/journal articles

Large Extra Dimensions: A New Arena for Particle Physics
Nima Arkani-Hamed; Savas Dimopoulos; Georgi Dvali
Physics Today, February 2002, pp. 35-40
In the "desert picture" of the unification of fundamental forces, there is an enormous range of energies in which no essentially new physics occurs. This situation gives rise to the hierarchy problem, among other things. A new proposal suggests that all forces, including gravity, can be unified at a much lower energy, with the extreme weakness of gravity being explained by the existence of "large" extra dimensions of spacetime.
The Universe's Unseen Dimensions
Nima Arkani-Hamed; Savas Dimopoulos; Georgi Dvali
Scientific American, August 2000, pp. 62-69
Although superstring theories have stimulated consideration of physics in more than three spatial dimensions, it now seems that such extra dimensions could be much larger than supposed. The observable universe could line on a 3-dimensional membrane in a higher-dimensional space, which might help clear up several current important puzzles such as the comparative weakness of gravity and the nature of "dark matter".
Hunting for Higher Dimensions
Peter Weiss
Science News, February 19, 2000, pp. 122-124
Various extensions to the standard model, including unified threories and string theories, imply that space has 6 or 7 additional dimensions which occur in a "compactified" form. This means that the additional dimensions would have extents far too small to be detectable. Newer considerations suggest the extents might not necessarily be so small that they couldn't be observed with current technology.
The Hidden Dimensions of Spacetime
Daniel Z. Freedman; Peter van Nieuwenhuizen
Scientific American, March 1985, pp. 74-81
Shortly after Einstein's general theory of relativity was published, Theodor Kaluza and Oskar Klein discovered how forces other than gravity might arise by extending Einstein's equation to higher dimensions. Several distinct modern theories utilize higher dimensions to unify the four known forces.

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