Is time one-dimensional?

Pseudo-Riemannian geometry permits one to define a geometry with an arbitrary number of spatial dimensions and an arbitrary number of temporal dimensions. The pair (n,m) specifying the number n of spatial dimensions, and the number m of temporal dimensions, is called the signature of the geometry. General Relativity plunders the mathematical resources provided by pseudo-Riemannian geometry, and suggests, in particular, that our universe has a Lorentzian geometry, a geometry of signature (n,1). Hence, if our universe is Lorentzian, then there is only one dimension of time.

However, The Daily Telegraph's Roger Highfield, and this week's New Scientist, both report on Itzhak Bars's suggestion that time may have two dimensions. If true, this requires a modification to what philosophers call the 'endurantist' notion of the persistence of an object through time. The endurantist position holds that the object which possesses a property at one time, is the same whole object which does or does not possess that property at another time. If the specification of a particular time requires the specification of two time coordinates, then the properties of an object could vary as one time coordinate is held fixed, but the other is varied. Is this the same 'whole' object which is varying or not?

There is an alternative to endurantism, dubbed the 'perdurantist' view, which holds that an object has temporal parts, and different temporal parts can possess different properties. On the perdurantist view, the persistence of an object through time is analogous to the extension of an object in space, and the different temporal parts can possess different properties just as much as the different spatial parts of an object can possess different properties. Introducing a second time dimension poses no problems, then, to perdurantism. An object's temporal extension simply extends into more than one temporal dimension.