How Does Physics Behave in 2+2 Dimensional Spacetimes?

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Discussion Overview

The discussion centers on the exploration of 2+2 dimensional spacetimes, including their physical implications and the challenges associated with them. Participants seek resources and references related to the study of these spacetimes, touching on theoretical and conceptual aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants inquire about resources for studying 2+2 dimensional spacetimes, noting difficulties in finding relevant information online.
  • One participant mentions the potential issue of closed timelike curves arising from having two timelike directions, referencing a paper that discusses the preference for a 3+1 metric over other signatures.
  • Another participant critiques the argument that certain physical conditions must hold to avoid a "boring" universe, suggesting a connection to the Anthropic Principle.
  • A participant highlights the work of science fiction writer Greg Egan, who explores such spacetimes in his book "Dichronauts," indicating that his mathematical descriptions provide insights into these concepts.
  • One participant discusses the generalizations of Nash embedding theorems to pseudoriemannian manifolds, emphasizing the requirements for embedding arbitrary manifolds.
  • Another participant notes that while there is a wealth of mathematical literature on "neutral signature," there is a scarcity of physics-related discussions due to the complexities introduced by multiple time directions.
  • A question is raised about the nature of spacetime variables and their measurement, leading to a correction regarding the classification of vectors in spacetime.

Areas of Agreement / Disagreement

Participants express differing views on the implications of multiple timelike directions and the nature of spacetime itself. There is no consensus on the physical viability of 2+2 dimensional spacetimes or the interpretation of spacetime variables.

Contextual Notes

Some claims about the nature of spacetime and the implications of multiple time dimensions remain unresolved, with participants providing varying interpretations and references without reaching a definitive conclusion.

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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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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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)?
 
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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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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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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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?
 
@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.
 

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