# B What would a universe with two time dimensions be like?

1. Jun 15, 2016

### Jupiter60

Just what would a universe be like if it had two time dimensions?

2. Jun 15, 2016

### Paul Colby

How would you generalize equations of motion? What would the action principle look like?

3. Jun 15, 2016

### OmCheeto

hmmm....
I've heard about something called "spooky at a distance".
I do not understand it at all, but from what I've heard, it seems to violate "my" notion of our one dimension of time.
Perhaps we already have two time dimensions.

hmmmm.... Perhaps this thread belongs in the sci-fi section.

4. Jun 16, 2016

### JorisL

The idea of two time directions is sometimes used in string theory/supergravity.
A paper by Itzhak Bars http://de.arxiv.org/abs/hep-th/9809034
And more recent results can be found at INSPIRE

I'm not sure how interesting it is but it does exist (in 12 dimensions or more)

5. Jun 17, 2016

### arivero

For the sake of discussion, I would like to see how it works with two macroscopic time dimensions and flat space, with minkowsky product coming from the matrix diag(1,1,1,-1,-1).

6. Jun 17, 2016

### JorisL

I have absolutely no idea, I encountered a mention of it in a master thesis (and some articles I believe).
Maybe some day I'll find the time to check it out.

7. Jun 17, 2016

### Staff: Mentor

Where's the problem is a macroscopic diag(1,1,1,-1,-1) world?

8. Jun 17, 2016

### JorisL

Nothing from a mathematical point of view, I figure the physics would look quite different.

A guess would be that consistency of dimensional reductions can do some weird things.
I'm only a little aware of the consistency of those procedures so I have to look into it on Monday since the document that might give me a hint whether more time directions mess things up is in my dorm room.

9. Jun 17, 2016

### arivero

For a classical non-relativistic particle, it seems that instead of conditions in two extremes [a,b] in the time-line we should impose them in a circle of the time-"plane".

10. Jun 17, 2016

### Staff: Mentor

Even if we get the geometry somehow explained, what about entropy?

11. Jun 18, 2016

### Markus Hanke

From a purely mathematical point of view, having an additional time dimension would fundamentally change the form of the general wave equation, turning it into what I believe is called an "ultra-hyperbolic equation" ( correct me on this if I'm wrong ). The question then becomes how the solutions to this equation behave under a given set of initial values - for example, in a theory of electromagnetism in (3+2) dimensions, do we still get a nice, well behaved wave solution, or do we get something that evolves chaotically ? Or worse still, would we be faced with a situation where no general solution even exists ?

I am not qualified to answer any of this ( not having studied this type of PDE ), but I would also be interested to hear what the mathematicians here have to say on this. My intuition tells me that things won't work out nicely if you add an extra ( macroscopic ) time dimension, but I may well be wrong. And then of course there is the option of having the extra dimension compactified.

12. Jun 18, 2016

### Fervent Freyja

Two different universes.

13. Jun 18, 2016

### nikkkom

Well, for one you'd have trivially easily occurring closed timelike curves.

14. Jun 20, 2016

### Demystifier

The Cauchy problem is not well posed for such spacetime signatures. See e.g.
http://arxiv.org/abs/gr-qc/9702052
http://arxiv.org/abs/gr-qc/9901045

15. Jun 20, 2016

### Markus Hanke

16. Jun 20, 2016

### arivero

We could try some list of priviledged D = d + t combinations. To start with, let me note the classical signatures to have susy and other stuff related to division algebras:
R: d - t = 1
C: d - t = 2 This is our spacetime, 3-1=2
H: d - t = 4
O: d - t = 8. I think this is the 9-1 = 8 of string theory and perhaps the 10 - 2 mentioned by JorisL above
I am not sure if there is some mod8 periodicity here or the list just stops at 8.

17. Jun 22, 2016

### Qcontinuum

18. Jun 23, 2016

### Qcontinuum

For the more interested in 2 k, 4 n as 6 dimensional model you should look at Itzhak Bars work. He has interesting stringy ideas. Gravitational constant looks normal for observer but is a "shadow" of a dilaton field. He worked on many examples with many interpretations and seems to get a consistent framework for a working theory.
Here one impressing work as you see the mathematical beauty in it.
http://arxiv.org/abs/0804.1585

19. Jun 23, 2016

### haushofer

Isn't that related to the fact that AdS-space can be described as being embedded in Minkowski spacetime with two timelike directions? (the AdS group is SO(D-2,2) )

20. Jun 24, 2016

### JorisL

Seems like a good starting point to look at.
Maybe if I can find some time in the next couple of weeks I'll look into it.

This seems like the idea that underlies the arxiv-notes I linked.
I'm not well-versed in the terminology of a "target space" so I'm not sure this would lead to the AdS group?
Neither what $d$ means in this context, from the abstract it follows that $D$ is the number of spacetime dimensions.