On 2/28/2019 4:07 AM, agrayson2...@gmail.com wrote:
On Wednesday, February 27, 2019 at 8:10:16 PM UTC-7, Brent wrote:
On 2/27/2019 4:58 PM, agrays...@gmail.com <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.
Brent
1) 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
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