Because relativity showed time as one dimension of space-time and string theory predicts extra space dimensions, a natural question would be whether string theory also predicts (or at least allows for) extra time dimensions.
According to physicist Itzhak Bars, this may actually be the case, in a field he calls two-time physics. Though still a marginal approach to string theory, understanding this potential extra dimension of time could lead to amazing insights into the nature of time.
With one time dimension, you have the arrow of time, but with two time dimensions, things become less clear. Given two points along a single time dimension, there’s only one path between them. With two time dimensions, two points can potentially be connected by a number of different paths, some of which could loop back on themselves, creating a route into the past.
Most physicists have never looked into this possibility, for the simple fact that (in addition to making no logical sense) it wreaks havoc with the mathematical equations. Time dimensions have a negative sign, and if you incorporate even more of them you can end up with negative probabilities of something happening, which is physically meaningless.
However, Itzhak Bars of the University of Southern California in Los Angeles discovered in 1995 that M-theory allowed for the addition of an extra dimension — as long as that extra dimension was timelike.
To get this to make any sense, he had to apply another type of gauge symmetry, which placed a constraint on the way objects could move. As he explored the equations, he realized that this gauge symmetry only worked if there were two extra dimensions — one extra time dimension and one extra space dimension.
Two-time relativity has four space dimensions and two time dimensions, for a total of six dimensions. Two-time M-theory, on the other hand, ends up with 13 total dimensions — 11 space dimensions and two time dimensions.
The gauge symmetry that Bars introduced provided exactly the constraint he needed to eliminate time travel and negative probabilities from his theory. With his gauge symmetry in place, the world with six (or 13) dimensions should behave exactly like the world with four (or 11) dimensions.