Page:The Meaning of Relativity - Albert Einstein (1922).djvu/66

$\left.{\begin{aligned}p_{xx}&=&&-\mathbf {h} _{x}\mathbf {h} _{x}+{\frac {1}{2}}(\mathbf {h} _{x}^{2}+\mathbf {h} _{y}^{2}+\mathbf {h} _{z}^{2})\\&&&-\mathbf {e} _{x}\mathbf {e} _{y}+{\frac {1}{2}}(\mathbf {e} _{x}^{2}+\mathbf {e} _{y}^{2}+\mathbf {e} _{z}^{2})\\&&&&p_{xy}=&-\mathbf {h} _{x}\mathbf {h} _{y}\;\;p_{xz}=&-\mathbf {h} _{x}\mathbf {h} _{z}\\&&&&&-\mathbf {e} _{x}\mathbf {e} _{y}&-\mathbf {e} _{x}\mathbf {e} _{y}\\&&&\vdots \\b_{x}&=&&\mathbf {s} _{x}=\mathbf {e} _{y}\mathbf {h} _{z}-\mathbf {e} _{z}\mathbf {h} _{y}\\&&&\vdots \\\eta &=&&+{\frac {1}{2}}(\mathbf {e} _{x}^{2}+\mathbf {e} _{y}^{2}+\mathbf {e} _{z}^{2}+\mathbf {h} _{x}^{2}+\mathbf {h} _{y}^{2}+\mathbf {h} _{z}^{2})\end{aligned}}\right\}$

(48a)

We conclude from (48) that the energy tensor of the electromagnetic field is symmetrical; with this is connected the fact that the momentum per unit volume and the flow of energy are equal to each other (relation between energy and inertia).

We therefore conclude from these considerations that the energy per unit volume has the character of a tensor. This has been proved directly only for an electromagnetic field, although we may claim universal validity for it. Maxwell's equations determine the electromagnetic field when the distribution of electric charges and currents is known. But we do not know the laws which govern the currents and charges. We do know, indeed, that electricity consists of elementary particles (electrons, positive nuclei), but from a theoretical point of view we cannot comprehend this. We do not know the energy factors which determine the distribution of electricity in particles of definite size and charge, and all attempts to complete the theory in this direction have failed. If then we can build upon Maxwell's equations in general, the