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The 4-current is a 4-vector.

- #3

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So it is an invariant? I was under the impression that the four vector referred to the four momentum and the four current was apart of the energy tensor and measured fluxes and therefore densities as well. The four T^ob components of the energy tensor form an invariant?The 4-current is a 4-vector.

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What "four-current" are you referring to? Do you have a reference?I was under the impression that the four vector referred to the four momentum and the four current was apart of the energy tensor and measured fluxes and therefore densities as well.

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The four current of momentum.What "four-current" are you referring to? Do you have a reference?

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Please provide the reference Peter asked for.The four current of momentum.

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I've seen this in textbooks before but here is Professor Susskind talking about the momentum current. The four components of the fourth component. The T^oa components it stops at about 1:38:50Please provide the reference Peter asked for.

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Momentum current is not the same thing as 4-current. What is typically intended when you just say "4-current" without further specification is the electromagnetic 4-current ##J^\mu = (\rho,\vec j)##, where ##\rho## is the charge density and ##\vec j## the (spatial) current density, whichI've seen this in textbooks before but here is Professor Susskind talking about the momentum current. The four components of the fourth component.

The components of the stress energy tensor do not transform like the components of a 4-vector because they are the components of a second rank tensor. Of course, as pointed out in the previous post, each index by itself transforms in the appropriate manner and the stress energy tensor itself is an invariant object. However, your time direction is not invariant under Lorentz transformations and therefore (in general) ##T'^{0\nu} \neq \Lambda^\nu_{\phantom\nu\mu} T^{0\mu}##.

- #10

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The divergence of ##T^{0\nu}## is an invariant though, correct?. Maybe I'm confusing concepts but I thought the collection of the four components that make up ##T^{0\nu}## represents measured energy flux across all surfaces, and therefore an invariant.Momentum current is not the same thing as 4-current. What is typically intended when you just say "4-current" without further specification is the electromagnetic 4-current ##J^\mu = (\rho,\vec j)##, where ##\rho## is the charge density and ##\vec j## the (spatial) current density, whichisa 4-vector.

The components of the stress energy tensor do not transform like the components of a 4-vector because they are the components of a second rank tensor. Of course, as pointed out in the previous post, each index by itself transforms in the appropriate manner and the stress energy tensor itself is an invariant object. However, your time direction is not invariant under Lorentz transformations and therefore (in general) ##T'^{0\nu} \neq \Lambda^\nu_{\phantom\nu\mu} T^{0\mu}##.

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- #13

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Kappa could be considered an outside four vector acting on some dust cloud type of matter described by the energy tensor?

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- #16

haushofer

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Well, to be pedantic: if it supposed to be vector components under general coordinate transformations, the partial derivative should be a covariant one :P

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Sure, but I thought we discuss SR in Minkowski coordinates and keep the things simple first ;-).

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