What if spacetime had two time dimensions?

[ChrisVer]

I am pretty sure this question must have been asked before... However I was always wondering, what would a theory be like if we allowed to have two time-dimensions (so I think a SO(2,3) symmetry). In general this would allow time-rotations / rotations of the arrow of time, so I guess the light cones could also connect casually disconnected events.
What problems would that cause?
I am also asking because even at the extra dim cases (although this is a little off the SR/GR topic) we choose the extra dimensions -the ones we compactify- to be spatial ones, and not time...

 

[jedishrfu]

Rather than get caught up in discussions of non-mainstream science I refer you to wikipedia and the article:

http://en.wikipedia.org/wiki/Multiple_time_dimensions

which discusses your question with references to other sources of information.

 

[robphy]

Closed timelike curves arise, for instance.

 

[ChrisVer]

The wiki left me with the idea that it's a considerate theory...

Itzhak Bars's work on "two-time physics", inspired by the SO(10,2) symmetry of the extended supersymmetry structure of M-theory, is the most recent and systematic development of the concept (see also F-theory).

At least makes me think of that.
However I am not trying to get into non-mainstream science talk and stuff...rather understanding what's the problems arising from it...