🎬the physical density is invariant as a geometric object but its coordinate representation changes

The demo illustrates that a tensor density transforms with an extra Jacobian factor under coordinate changes, unlike a true scalar. While the physical density remains unchanged, its coordinate representation varies to ensure that integrals (like total mass) are invariant—demonstrating the essential property of tensor densities in geometry and physics.

Verification of Tensor Density Operations | Proof and Derivationviadean on Notion