Could you say that GR is a theory of four or five dimensions?

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Discussion Overview

The discussion revolves around the dimensionality of General Relativity (GR) and whether it can be considered a theory of four or five dimensions. Participants explore the implications of curvature in space and how it relates to the number of dimensions in GR, comparing it to Special Relativity.

Discussion Character

  • Exploratory
  • Debate/contested

Main Points Raised

  • Some participants assert that GR is fundamentally a four-dimensional theory, comprising three spatial dimensions and one time dimension.
  • Others propose that an additional dimension could be introduced to account for the curvature of space, although it is unclear if this should be considered a separate dimension.
  • One participant suggests that the curvature of objects in three-dimensional space can be fully described using the four dimensions of spacetime in GR, implying that no additional dimension is necessary.
  • There is a discussion about whether energy (E) could be considered a dimension, with some arguing that it alters perceptions of distance, while others maintain that it does not qualify as a dimension in the traditional sense.
  • The energy-momentum tensor's role in GR is mentioned, with a distinction made between its function in describing gravity and the definition of a dimension.

Areas of Agreement / Disagreement

Participants generally agree that GR is a four-dimensional theory, but there is contention regarding the introduction of a fifth dimension related to curvature and the role of energy. The discussion remains unresolved with multiple competing views.

Contextual Notes

Participants express varying assumptions about the definitions of dimensions and the implications of curvature in GR. The discussion reflects differing interpretations of how energy relates to dimensionality.

zheng89120
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I don't really know much about GR, but I was just wondering about this theoretical question. I am asking this, because I think Special Relativity is a theory of four dimensions, and wasn't sure how many dimensions GR involved.
 
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Four. Why would it be 5?
 
Because, since space is "curved" in GR, I thought may be an addition dimension could be introduced to describe the curvature of space, but perhaps that is not counted as another dimension.
 
Four: x, y, z, and t. What's the 5th dimension?
 
zheng89120 said:
Because, since space is "curved" in GR, I thought may be an addition dimension could be introduced to describe the curvature of space, but perhaps that is not counted as another dimension.

Essentially it's all integrals with 4 elements, what makes it GRey is that the volume element changes with position in space-time
 
elfmotat said:
Four: x, y, z, and t. What's the 5th dimension?

E?
 
zheng89120 said:
Because, since space is "curved" in GR, I thought may be an addition dimension could be introduced to describe the curvature of space, but perhaps that is not counted as another dimension.

The 4 dimensions do describe the curvature of the space-time. For example, let's say you have a can of soda or a ball or something in the 3-dimensional world we're accustomed to. You can fully describe the curvature of those objects by using those 3 dimensions. A 4th dimension need not be introduced in this example.

Same idea with GR, except you now are dealing with a 3+1 dimensional spacetime instead of the 3 dimensional Euclidean space of the soda can/ball example.

TimeContinuum said:
E?

If E = energy, why would E be a dimension? It doesn't measure space-time displacements.
 
Pengwuino said:
If E = energy, why would E be a dimension? It doesn't measure space-time displacements.

Sure it does. E alters our perception of distance.
 
TimeContinuum said:
Sure it does. E alters our perception of distance.

The energy-momentum tensor in GR tells gravity, as many put it, how to curve, but that certainly does not mean it is qualified to be a dimension. A dimension has very specific meaning.
 
  • #10
TimeContinuum said:
Pengwuino said:
If E = energy, why would E be a dimension? It doesn't measure space-time displacements.
Sure it does.
OK, given an inertially moving rocket in flat spacetime where, from the rocket's perspective, would the 1 J hyperplane be located?
 

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