On Wednesday, March 6, 2019 at 1:03:16 AM UTC-7, Brent wrote: > > > > On 3/5/2019 10:02 PM, agrays...@gmail.com <javascript:> wrote: > > > > On Saturday, March 2, 2019 at 2:29:50 AM UTC-7, agrays...@gmail.com > wrote: >> >> >> >> On Friday, March 1, 2019 at 10:14:02 PM UTC-7, agray...@gmail.com wrote: >>> >>> >>> >>> On Thursday, February 28, 2019 at 12:09:27 PM UTC-7, Brent wrote: >>>> >>>> >>>> >>>> On 2/28/2019 4:07 AM, agrays...@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 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* >> > > > *I think I can simplify my issue here, if indeed there is an issue: did > Einstein, or anyone, ever prove what I will call the General Principle of > Relativity, namely that the laws of physics are invariant for accelerating > frames? If the answer is affirmative, is there a transformation equation > for Maxwell's Equations which leaves them unchanged for arbitrary > accelerating frames? TIA, AG * > > > Your question isn't clear. If you're simply asking about the equations > describing physics* as expressed* in an accelerating (e.g. rotating) > reference frame, that's pretty trivial. You write the equations in > whatever reference frame is convenient (usually an inertial one) and then > transform the coordinates to the accelerated frame coordinates. But if > you're asking about what equations describe some physical system while it > is being accelerated as compared to it not being accelerated, that's more > complicated. >
*Thanks, but I wasn't referring to either of those cases; rather, the case of transforming from one accelerating frame to another accelerating frame, and whether the laws of physics are invariant. Here the "laws" could be ME or Mechanics. It seem as if GR is a special case for gravity, but I was asking whether invariance, or covariance, has been generally established. Also, if the LT works locally in GR, how do we transform between non-local frames? TIA, AG* > Maxwell's equations apply to the description of the EM field of an > accelerating charged particle and show that the particle loses energy to an > EM wave, but how the particle interacts with it's own field when > accelerated produces unrealistic results which were superceded by quantum > field theory. Bill Unruh showed that the accelerated system interacts with > the vacuum as though the vacuum is hot. > > 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
