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Rasalhague

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*A First Course in General Relativity*, Bernard Schutz introduces the idea of a fluid element, a different one assigned to each point in a fluid.

When he talks, in section 4.5, about the 3-volume of a fluid element, is this 3-volume defined with respect to the MCRF (Momentarily Comoving Reference Frame)?

Is Schutz's MCRF (1) a chart, or (2) a field of orthonormal basis vectors for the tangent spaces at every point in the fluid, or (3) an orthonormal basis for the tangent space at a particular point?

Is it possible to have two fluids in Minkowski space, each of which occupy a cube of the same 3-volume in some common Lorentz chart (spacetime coordinates alanogous to Cartesian coordinates) - so that there's a bijection between points in one fluid and points in the other - yet every fluid

*element*of one fluid has twice the 3-volume of the corresponding fluid element of the other fluid? I'm guessing yes, although I'm not sure what it means physically for an object defined at each point to have a volume, since a point has no extent, whereas volume does have extent.

Is the 3-volume of a fluid element something one could observe experimentally? Or is it a description one imposes arbitrarily on the fluid, then observes how these arbitrarily imposed 3-volmes

*change*with changes in pressure, energy density, number of particles etc.?