On 2/28/2019 4:07 AM, [email protected] wrote:
On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote: On 2/27/2019 4:58 PM, [email protected] <javascript:> wrote:*Are you assuming uniqueness to tensors; that only tensors can produce covariance in 4-space? Is that established or a mathematical speculation? TIA, AG *That's looking at it the wrong way around. Anything that transforms as an object in space, must be representable by tensors. The informal definition of a tensor is something that transforms like an object, i.e. in three space it's something that has a location and an orientation and three extensions. Something that doesn't transform as a tensor under coordinate system changes is something that depends on the arbitrary choice of coordinate system and so cannot be a fundamental physical object. Brent1) Is it correct to say that tensors in E's field equations can be represented as 4x4 matrices which have different representations depending on the coordinate system being used, but represent the same object?
That's right as far as it goes. Tensors can be of any order. The curvature tensor is 4x4x4x4.
2) In SR we use the LT to transform from one*non-accelerating* frame to another. In GR, what is the transformation for going from one *accelerating* frame to another?
The Lorentz transform, but only in a local patch. Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
