Is Mass a Tensor?

Question

I have heard that mass is a tensor in some applications of physics?
How true is this and how do we visualise mass as a tensor?

Answer 1

Typically, mass is a scalar. But when looking at neutrino masses (or for that matter, quark masses), there is a matrix that corresponds to how masses enter into the Lagrangian. In that sitation, it could be appropriate to talk about a mass tensor. It turns out that the matrix is not diagonal which underlies the reason why different neutrino types can convert into each other (neutrino oscillations).

Answer 2

There is an inertia tensor ( I ) associated with a rigid distributed mass that relates the angular momentum vector J to the angular velocity vector W. J=I*W, where * is the matrix multiplication operator. It's analogous to momentum =mass X velocity for lineear motion. Is that what you're thinking of?

Answer 3

This means that mass is a linear quanity. Linear meaning it is only in in one direction down. I used to think of a string holding a mass in tension like I would imagine a "tensor". The string would be the opposing force to the force of gravity or the mass of the object.