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 <[email protected]> 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.* *With further consideration, I think angular momentum would be invariant under a coordinate transformation because where you measure AM from, the reference point, won't change in a CT, since points don't move; they just get new labels. AG * *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).* 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/dfa3156b-2d49-4753-8ca9-14c337de1a83n%40googlegroups.com.
