On Monday, September 30, 2024 at 1:41:16 PM UTC-6 John Clark wrote:
On Mon, Sep 30, 2024 at 3:14 AM Alan Grayson <agrays...@gmail.com> wrote: *> there's a subtle but important difference between coordinate transformations, and frame of reference transformations* *That's very true. A rank 1 Tensor (a.k.a. * *a vector) is not necessarily invariant under changes in the coordinate system, instead it transforms in a **specific, consistent way**. For example angular momentum is not invariant under coordinate* *translations, but that’s OK because it's a feature of the physical situation and is not a sign of inconsistency. Changing the origin alters the angular momentum calculation* but t*his is physically consistent because angular momentum is inherently tied to the reference point. There is no such thing as absolute angular momentum; it depends on where you measure it from.* *So strictly speaking angular momentum is not a tensor it's a pseudo-tensor, or if you prefer a pseudo-vector because it has most of the properties of a tensor but not all of them. A true tensor remains unchanged under parity inversion (the letter O looks the same in a mirror) but a pseudo tensor does not (the letter L does not look the same in a mirror).* *Interesting. TY. My conclusion, in part, is that the LT and the GT are not coordinate transformations, and therefore we can't assume that ME will be invariant under those transformations, simply because ME are written in tensor form. But the original question more or less remains; namely, why are ME invariant under the former transformation, but not the latter? AG* John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/98dfd8a6-7c32-4378-a594-0aabd1c5e6d0n%40googlegroups.com.
