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The dimension of the stress-energy-momentum tensor is similar to that of pressure, according to wikipedia.

The stress-energy-momentum tensor $T_{μν}$ is defined as $μ$ momentum in a spacetime box of volume $ν$. So, its dimension must be similar to that of momentum per unit volume.

Where am I wrong?

Qmechanic
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1 Answers1

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The stress-energy tensor has units of energy density. Indeed as we usually write it the $\mathrm{T}_{00}$ elements is just the energy density i.e. joules per cubic metre.

You are quite correct that the other three diagonal elements $\mathrm{T}_{11}$, $\mathrm{T}_{22}$ and $\mathrm{T}_{33}$ behave like a pressure. For more on this see Intuitive understanding of the elements in the stress-energy tensor. However pressure and energy density have the same dimensions. Pressure is force/area. Multiply the top and bottom by distance and you have force $\times$ distance/volume, and force $\times$ distance is work i.e. energy.

The other elements are a momentum flux i.e. a momentum density times a velocity. Again if you work through the dimensions you'll find this has the same dimensions as an energy density.

John Rennie
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