Is there a Financial Conservation Standard for the Indvidual?

Why is there no differential equation for the conservation of angular momentum?

• I'm looking at it from a fluid mechanics point of view. We have standard PDE's for continuity, momentum (eg, Navier Stokes for newtonian fluids), energy and species conservation, which are usually solved numerically in CFD codes to find the flow field, temperature profile, etc. However, even though angular momentum is conserved in all systems not subjected to an external torque, a standard PDE for the conservation of angular momentum in an infinitesimal element doesn't exist and i'm not sure why.

• Answer:

  It exists, the divergence of the angular momentum tensor is zero. The angular momentum tensor is usually (for a good convention) related to the stress energy tensor as follows: Sανβ=xαTνβ−xβTναSανβ=xαTνβ−xβTνα S_{\alpha\nu\beta} = x_{\alpha} T_{\nu\beta} - x_{\beta} T_{\nu\alpha} This can always be arranged when you have a Poincare invariant local system using the Balinfante construction, and it is also clear from an argument Feynman gives in "The Character of Physical Law", relating rotations to translations. It's something that was worked out in the 1910s. Then the conservation law for angular momentum is a differential identity: ∂μSμαβ=0∂μSαβμ=0 \partial_{\mu} S^\mu_{\alpha \beta} = 0 But it is a consequence of the conservation of momentum (the zero divergence of the stress-energy tensor) plus the symmetry of the stress tensor. The statement of the conservation of angular momentum is usually stated in terms of the choice of a symmetrical stress-energy tensor.