The Principle of Relativity

by Albert Einstein; H. Minkowski

| ψ₁ ψ₂ ψ₃ |

Since in this case, Φ₁ = w₄ F₁₄ = e_n (the electric force)

ψ₁ = -iw₄ f₂₃ = m_x (the magnetic force)

we have (Ω) = | e_x e_y e_z |

| m_x m_y m_z |

[M. N. S.]

Note 16.
The electric-rest force. (Page 37.)

The four-vector φ = wF which is called by Minkowski the electric-rest-force (elektrische Ruh-Kraft) is very closely connected to Lorentz’s Ponderomotive force, or the force acting on a moving charge. If ρ is the density of charge, we have, when ε = 1, μ = 1, i.e., for free space

ρ₀φ₁ = ρ₀[w₁ F₁₁ w₂ F₁₂ + w₃ F₁₃ + w₄ F₁₄]

= ρ₀/(√(1 - V²/c²)) [d_x + 1/c (v₂ h₃ - v₃ h₂)]