Acceleration Tensor - Rotating Frame

[PrinceOfDarkness]

If a coordinate system is rotating, that is time 't' is not independent, then does the acceleration transform as rank 1 tensor?

I thought that it wouldn't because when time is changing, so acceleration will change in a more complicated way than a rank 1 tensor. Perhaps as a rank 2 tensor.

This Q is really troubling me. There are two groups in my class, one saying it still transforms as a rank 1 tensor, the other saying it doesn't transform as a rank 1 tensor. Some even say that acceleration never transforms like a rank 1 tensor. I wonder how! I think it transforms like a rank 1 tensor if it goes fixed rotation, but 'rotating' coordinate system will mean that transformation is more complicated.

 

[dextercioby]

Rotations (with presumably fixed angular velocity) are examples of (restricted) Lorentz transformations. If you know how the acceleration behaves when being subject to a (restricted) Lorentz transformation, then everything would be fine, wouldn't you say...?

Daniel.

 

[pervect]

If a coordinate system is rotating, that is time 't' is not independent, then does the acceleration transform as rank 1 tensor?

You need to be a bit more specific here. The 4-acceleration is a geometric object, so it transforms as a tensor.

A rotating coordinate system will require a metric that is not Minkowskian, so you start getting into GR rather than SR.

The rotating coordinate system will be ill-behaved when r*w = c, some of the metric coefficients go to zero (or was it infinity? I'd have to double check - but I know they are not well-behaved).

 

[Hurkyl]

A rotating coordinate system will require a metric that is not Minkowskian, so you start getting into GR rather than SR.

No, you're merely getting into differential geometry.