On Mon, Sep 30, 2024 at 11:14 PM Alan Grayson <[email protected]> wrote:
*>> 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* > *The proximate cause is that velocities in Lorentz Transformations and in our physical world do not combine linearly like they do with Galilean Transformations. The ultimate cause nobody knows and there may not even be an ultimate cause. Nobody knows that either.* John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> nny -- 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/CAJPayv3gdye5t7s--b4-MYxRXHdm-aZ9hMeBcn8Dm892P7CJWA%40mail.gmail.com.
