F-theory
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A branch of String Theory known as F-theory, developed by Cumrun Vafa, creates mathematical descriptions involving a second temporal or time variable. One of the first physicists to suggest such a thing was Andrei Sakharov in the 1980s [1].
The new vacua described as F-theory were discovered by Vafa, and it also allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi-Yau four-folds. The letter "F" stands for "Father" much like the "M" in M-theory is often taken to stand for "Mother".
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[edit] Compactifications
F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus. By doing so, we obtain type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the two-dimensional torus.
More generally, one can compactify F-theory on an elliptically fibered manifold (elliptic fibration), i.e. a fiber bundle whose fiber is a two-dimensional torus (also called an elliptic curve). For example, a subclass of the K3 manifolds is elliptically fibered, and F-theory on a K3 manifold is dual to heterotic string theory on a two-torus. (Eight dimensions are large.)
[edit] Multiple dimensions
In mathematical physics, a framework of equations is often put forward to model the physical universe. In some sense, a dimension simply means that a mathematical variable exists in some equation, allowing the use of certain mathematical tools. The physical implications of multiple dimensions are theoretical, at best; it is not always clear what real meaning these extra dimensions actually have[1]. Many branches of F-theory involve multiple temporal (time) dimensions.
Ascribing real, physical existence to multi-dimensional universes is largely a fringe idea and is not widely accepted amongst the scientific community because of lack of experimental support. Also, Ed Witten has argued that the second time dimension is only a mathematical fiction used to simplify calculations [1].
Max Tegmark has written a paper arguing that life cannot exist in a universe with more than one macroscopic temporal dimension, because differential equations would not be hyperbolic in such a universe, rendering prediction of "future" states impossible; also, he argues that matter would be highly unstable, tending to scatter across the extra time dimensions. [2] For this reason, Chris Hull has proposed that the extra time dimensions are compactified, much as are the extra space dimensions used in more conventional string theories; he has also argued that string theoretic duality can change the signature of spacetime, thereby converting space dimensions into time dimensions or vice versa. Itzhak Bars has proposed another hypothesis; he argues that each time dimension could have become associated with a separate array of space dimensions, with only one associated with our own "universe" [1].
[edit] Prior Theories
A second temporal dimension is also seen in Penrose's Twistor theory, which is mainly of historical interest.
[edit] References
- Bars, Itzhak (1997, March 7). "Theories with two times".
- Hull, C. M. (1999, November 11). "Duality and strings, space, and time".
- ^ a b c d Siegfried, Tom (2002). ["http://darwin.nap.edu/books/0309084075/html/235.html" "Strange Matters: Undiscovered Ideas at the Frontiers of Space and Time (chapter 10)"]. Washington DC: Joseph Henry Press. ISBN 0-309-08407-5. page 235.
- ^ Tegmark, M. (1997, April 4). "On the dimensionality of spacetime".
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