Relativity in 2 spatial dimensions

In summary, the general theory of relativity can be applied in a universe with only 2 spatial and 1 time dimension, but the lower dimensionality limits the curvature tensor and the existence of spacetime curvature at finite distances from massive objects. However, there are still some interesting analogies and differences in this "toy model" of GR.
  • #1
cam875
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do all of the equations and postulates of the general theory of relativity apply in a universe with only 2 spatial and one time instead of 3 spatial and one time.
 
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  • #2
One could try to play with "toy models" of GR with lower spacetime dimensionality.
However, the lower dimensionality severely reduces the number of independent components of the curvature tensor.
 
  • #3
will if there is only 2 spatial dimensions than all the matter warping space will also be 2 dimensions so would the tensor be the same and all of the equations applying to 3d matter in 3d space be the same.
 
  • #4
Here's a pretty detailed discussion of the analogue of GR in a universe with 2 spatial dimensions:

http://gregegan.customer.netspace.net.au/SCIENCE/GR2plus1/GR2plus1.html

Basically, it seems you can't actually have spacetime curvature at any finite distance from a massive object in 2D, although you can have point particles which have the property that when you travel around them the angle is less than 360, like traveling around the tip of a cone (which is also a surface that's flat everywhere in differential geometry terms, since you can 'unroll' it into a flat surface with a pie-shaped wedge cut out, see http://www.allendesigns.com/AreaofCone/AreaofCone.htm [Broken]). There's a somewhat less technical discussion here:

http://www.theory.caltech.edu/people/patricia/ttif.html [Broken]

(see especially the section on 'What is the spacetime geometry?')
 
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1. What is the main concept of relativity in 2 spatial dimensions?

The main concept of relativity in 2 spatial dimensions is that the laws of physics remain the same for observers in different frames of reference, even if those frames are moving at a constant velocity relative to each other. This means that there is no absolute frame of reference and all motion is relative.

2. How does relativity in 2 spatial dimensions differ from the theory of general relativity?

Relativity in 2 spatial dimensions is a simplified version of the theory of general relativity, which applies to 3-dimensional space. In 2 dimensions, there are fewer variables and the math is simpler, making it easier to visualize and understand the principles of relativity.

3. What is the significance of 2 spatial dimensions in the theory of relativity?

2 spatial dimensions are used in relativity as a way to simplify complex calculations and better understand the principles of relativity. It allows scientists to focus on the fundamental concepts of relativity without getting bogged down in the complexities of 3-dimensional space.

4. Can relativity in 2 spatial dimensions be applied to real-world scenarios?

While 2 spatial dimensions may seem abstract, the principles of relativity in 2 dimensions can be applied to real-world scenarios. For example, it can help explain the behavior of particles in a 2-dimensional plane or the effects of gravity on objects in a 2-dimensional space.

5. How has the study of relativity in 2 spatial dimensions contributed to our understanding of the universe?

The study of relativity in 2 spatial dimensions has provided valuable insights into the fundamental principles of relativity and has helped scientists better understand the behavior of matter and energy in our universe. It has also paved the way for advancements in technology, such as GPS navigation, that rely on the principles of relativity to function accurately.

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