How Does Physics Behave in 2+2 Dimensional Spacetimes?

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In summary, the conversation discusses the concept of spacetimes with multiple dimensions of time and how physics is affected in such scenarios. It is mentioned that one problem with two timelike directions is the existence of closed timelike curves. The conversation also references a study on why 3+1 metric is preferred over 4+0 or 2+2. It is noted that mathematicians have studied the concept of neutral signature in detail, but there is not much research on its implications in physics. Finally, the conversation touches upon the idea of spacetime being timelike or spacelike, clarifying that only specific vectors can be categorized as such, not spacetime itself.
  • #1
Intrastellar
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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.
 
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  • #2
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
 
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  • #3
robphy said:
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)?
 
  • #4
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.
 
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  • #5
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).
 
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  • #6
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.
 
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  • #7
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?
 
  • #8
@JAYJACOBUS , welcome to PF!

JAYJACOBUS said:
From what I have read

Where? Please give a specific reference.

JAYJACOBUS said:
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.
 

1. What is a 2+2 dimensional spacetime?

A 2+2 dimensional spacetime is a mathematical model used to describe the physical universe in which there are two dimensions of space and two dimensions of time. This means that an event or object can be located using four coordinates - two for space and two for time.

2. How does a 2+2 dimensional spacetime differ from our everyday experience of three dimensions of space?

In our everyday experience, we are only able to perceive and interact with three dimensions of space. However, in a 2+2 dimensional spacetime, there are two additional dimensions of space that we cannot perceive. These extra dimensions are thought to be "curled" or "compactified," meaning they are too small for us to detect.

3. What is the significance of 2+2 dimensions in physics?

The concept of 2+2 dimensional spacetimes is important in theoretical physics, particularly in string theory and supergravity. These theories aim to unify the fundamental forces of nature and suggest that the universe may have more than three dimensions. The inclusion of two additional dimensions in these theories allows for more elegant mathematical descriptions of physical phenomena.

4. Can a 2+2 dimensional spacetime be visualized?

No, a 2+2 dimensional spacetime cannot be visualized in the same way that we can visualize three dimensions. Our brains are not equipped to imagine or visualize dimensions beyond what we experience in our everyday lives. However, mathematicians and physicists use complex mathematical equations and models to understand and describe 2+2 dimensional spacetimes.

5. How does the concept of time work in a 2+2 dimensional spacetime?

In a 2+2 dimensional spacetime, time is treated as a fourth dimension, similar to space. This means that time is also relative and can be affected by gravity and the speed of an object. However, the concept of time in a 2+2 dimensional spacetime is still a topic of ongoing research and debate among physicists.

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