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About the conservation

by Jhenrique
Tags: conservation
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Jun12-14, 07:06 PM
P: 686
The navier stokes equations are based in 4 presuppositions, the conservation of mass, of energy, of linear momentum and of angular momentum. Also, the KCL too is based in other conservation, the of charge. So I thought: must there is a general conservation that implies all the other particular conservations... this general conservation must be the conservation of the amount of substance (or, in terms more generals, the conservation of every particle that is possible to quantify).
If the amount of substance is conserved, so this implies that the charge and the mass too is, if the mass is conserved so the energy too is, if the energy is conserved so the momentum too is.

What you think about?
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Jun12-14, 07:23 PM
P: 17,330
If you want to unify the conservation laws it is probably better to think in terms of the symmetries that generate the conservation laws. Energy and linear momentum are conserved due to spatial and temporal translation symmetries, and angular momentum is conserved due to rotational symmetries. So all of those conserved quantities are due to Poincare symmetry. Mass conservation isn't a separate thing from energy and momentum conservation, so you can add that to the list.

Charge, on the other hand, is conserved due to gauge invariance, so that seems to be a separate symmetry.

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