How Does Physics Behave in 2+2 Dimensional Spacetimes?

[Intrastellar]

Does anyone know of any resources studying these spacetimes and how physics looks like in them ? Writing 2+2 never gets you any good results on google.

 

[robphy]

These google searches may help. (In addition to google, try https://scholar.google.com/ )
signature 2+2 spacetime
multidimensional time

One problem with two timelike directions is the presence of closed timelike curves.
Possibly interesting reference that came up:
Why 3+1 metric rather than 4+0 or 2+2? H van Dam, Y. Jack Ng (Physics Letters B, 2001)
https://doi.org/10.1016/S0370-2693(01)01140-6

 

[stevendaryl]

These google searches may help. (In addition to google, try https://scholar.google.com/ )
signature 2+2 spacetime
multidimensional time

One problem with two timelike directions is the presence of closed timelike curves.
Possibly interesting reference that came up:
Why 3+1 metric rather than 4+0 or 2+2? H van Dam, Y. Jack Ng (Physics Letters B, 2001)
https://doi.org/10.1016/S0370-2693(01)01140-6

It's kind of a strange argument to claim that something must be true, because otherwise, things would be very boring. Maybe that, together with the Anthropic Principle (in boring universes, there are no people to wonder what the laws of physics are)?

 

[rkyeun]

Greg Egan is a science fiction writer who spends his mathematics prowess describing such worlds. The book "Dichronauts" investigates a fictional world in such a universe. His webpage with the mathematics and descriptions provides more detail than the book does.

 

[PAllen]

Well, one use for signatures other than (1,n) is that the generalizations of Nash embedding theorems to pseudoriemannian manifolds requires an (m,M) flat manifold in general, where m > 1, and M > n, to embed the arbitrary (1,n) manifold (for isometric smooth embedding).

 

[Ben Niehoff]

Mathematicians call this "neutral signature" and you can find loads of math papers on the subject. You are not going to find much physics, though, as physics doesn't make much sense with more than one time direction.

 

[JAYJACOBUS]

From what I have read space time is time like or space like. Is there a unique variable, st, for space time and how is it measured by itself?

 

[PeterDonis]

@JAYJACOBUS , welcome to PF!

From what I have read

Where? Please give a specific reference.

space time is time like or space like

This is not correct. In fact it doesn't even make sense. Particular vectors at a particular event in spacetime can be timelike or spacelike (or null), but not spacetime itself.