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

[zheng89120]

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.

 

[Pengwuino]

Four. Why would it be 5?

 

[zheng89120]

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.

 

[elfmotat]

Four: x, y, z, and t. What's the 5th dimension?

 

[maverick_starstrider]

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

 

[TimeContinuum]

Four: x, y, z, and t. What's the 5th dimension?

E?

 

[Pengwuino]

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.

E?

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

 

[TimeContinuum]

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.

 

[Pengwuino]

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.

 

[Dale]

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?