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Concept
Multiple time dimensions
Summary
The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy. Similar ideas appear in folklore and fantasy literature.
Speculative theories with more than one time dimension have been explored in physics. The additional dimensions may be similar to conventional time, compactified like the additional spatial dimensions in string theory, or components of a complex time (sometimes referred to as kime).
Itzhak Bars has proposed models of a two-time physics, noting in 2001 that "The 2T-physics approach
in d + 2 dimensions offers a highly symmetric and unified version of the phenomena described by 1T-physics in d dimensions."
F-theory, a branch of modern string theory, describes a 12-dimensional spacetime having two dimensions of time, giving it the metric signature (10,2).
The existence of a well-posed initial value problem for the ultrahyperbolic equation (a wave equation in more than one time dimension) demonstrates that initial data on a mixed (spacelike and timelike) hypersurface, obeying a particular nonlocal constraint, evolves deterministically in the remaining time dimension.
Like other complex number variables, complex time is two-dimensional, comprising one real time dimension and one imaginary time dimension, changing time from a real number line into a complex plane. Introducing it into Minkowski spacetime allows a generalization of Kaluza–Klein theory.
Max Tegmark has argued that, if there is more than one time dimension, then the behavior of physical systems could not be predicted reliably from knowledge of the relevant partial differential equations. In such a universe, intelligent life capable of manipulating technology could not emerge. Moreover protons and electrons would be unstable and could decay into particles having greater mass than themselves. (This is not a problem if the particles have a sufficiently low temperature.)
Multiple time dimensions appear to allow the breaking or re-ordering of cause-and-effect in the flow of any one dimension of time.
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