On Friday, March 1, 2019 at 10:14:02 PM UTC-7, [email protected] wrote: > > > > On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: >> >> >> >> 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] 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. >> > > *That's what I thought you would say. But how does this advance Einstein's > presumed project of finding how the laws of physics are invariant for > accelerating frames? How did it morph into a theory of gravity? TIA, AG * >
*Or suppose, using GR, that two frames are NOT within the same local patch. If we can't use the LT, how can we transform from one frame to the other? TIA, AG * *Or suppose we have two arbitrary accelerating frames, again NOT within the same local patch, is it true that Maxwell's Equations are covariant under some transformation, and what is that transformation? TIA, AG* > >> 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.
