Hey guys, I am new here and hope to be able to contribute with some of the discussions in Relativity. I will start my participation with a conceptual question that arised during my studies and has been boggling me since then.(adsbygoogle = window.adsbygoogle || []).push({});

I have been studying Relativity using the book "A First Course in General Relativity" by B. F. Shcutz. Right now I am reading Chapter 4 onPerfect Fluids in Special Relativity, more specifically I am studying the section that introduces the stress-energy tensor, [itex]T^{\alpha\beta}[/itex], and its properties. The author makes an important remark before starting the more detailed discussion about the fluid elements, he says and I quote:

Afterwards, the author starts analizing the spatial components of the general stress-energy tensor. I reproduce below that part of the text: Let us in particular look at it in the MCRF (Momentarily Comoving Reference Frame), where there is no bulk flow of the fluid element, and no spatial momentum in the particles.

Having that in mind, the problem I've been facing is related to the bolded sentece above: "Since force equals the rate of change of momentum (by Newton's law, which is valid here, since we are in the MCRF where velocities are zero) (...)"The spatial componentsof the stress-energy tensor, [itex]T^{ij}[/itex]. By definition, [itex]T^{ij}[/itex] is the flux of [itex]i[/itex] momentum across the [itex]j[/itex] surface. Consider (Fig. 4.6) two adjacent fluid

http://img703.imageshack.us/img703/6631/89280364.png [Broken]

elements, represented as cubes, having the common interface [itex]\ell[/itex]. In general, they exert forces on each other. Shown in the diagram is the force [itex]F[/itex] exerted byAonВ(Вof course exerts an equal and opposite force onA). Since force equals the rate of change of momentum(by Newton's law, which is valid here, since we are in the MCRF where velocities are zero),Ais pouring momentum intoВat the rate [itex]F[/itex] per unit time. Of course,Вmay or may not acquire a new velocity as a result of this new momentum it acquires; this depends upon how much momentum is put intoВby its other neighbors. ObviouslyB's motion is the resultant of all the forces. Nevertheless, each force adds momentum toB. There is therefore a flow of momentum across [itex]\ell[/itex] fromAtoВat the rate [itex]F[/itex]. If [itex]\ell[/itex] has area [itex]\zeta[/itex], then the flux of momentum across [itex]\ell[/itex] is [itex]F/\zeta[/itex]. If if is a surface of constant [itex]x^{j}[/itex], then [itex]T^{ij}[/itex] for fluid elementAis [itex]F^{i}/\zeta[/itex].

So here comes what has been bothering me: Since there is no bulk motion and no spatial momentum on the particles, how is it possible to use Newton's law in this argument since the MCRF sees no motion at all - and consequently no acceleration - in that fluid element? Also, going deeper into the problem, is it possible to ascertain that Newton's Laws are always valid from the point of view of a MCRF?

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# Validity of Newton's Laws on a MCRF

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