Multiple time dimensions
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.
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.
Multiple time dimensions appear to allow the breaking or re-ordering of cause-and-effect in the flow of any one dimension of time. This and conceptual difficulties with multiple physical time dimensions have been raised in modern analytic philosophy.
As a solution to the problem of the subjective passage of time, J. W. Dunne proposed an infinite hierarchy of time dimensions, inhabited by a similar hierarchy of levels of consciousness. Dunne suggested that, in the context of a "block" spacetime as modelled by General Relativity, a second dimension of time was needed in order to measure the speed of one's progress along one's own timeline. This in turn required a level of the conscious self existing at the second level of time. But the same arguments then applied to this new level, requiring a third level, and so on in an infinite regress. At the end of the regress was a "superlative general observer" who existed in eternity. He published his theory in relation to precognitive dreams in his 1927 book An Experiment with Time and went on to explore its relevance to contemporary physics in The Serial Universe (1934). His infinite regress was criticised as logically flawed and unnecessary, although writers such as J. B. Priestley acknowledged the possibility of his second time dimension. John G Bennett in his book 'Dramatic Universe' (1956) described three dimensions of time: Ordinary Time, Eternity and Hyparxis.
Multiple independent timeframes, in which time passes at different rates, have long been a feature of fairy tales. Fantasy writers such as inklings J. R. R. Tolkien and C. S. Lewis have made use of these and other multiple time dimensions, such as those proposed by Dunne, in some of their most famous stories. Tolkien borrowed them for Lórien time in The Lord of the Rings. Lewis adopted them for his Chronicles of Narnia.
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