Annus MirabilisEinstein in 1905
Reading preferences

Reading preferences

Keep every explanation and worked example on the page. Nothing moves or plays by itself, and the larger instruments load only when you ask.

Line length
Type size
Contrast
Paragraph spacing

special relativity

The equation explained

1V{uxϱ+∂X∂t}=∂N∂y−∂M∂z,1V∂L∂t=∂Y∂z−∂Z∂y,1V{uyϱ+∂Y∂t}=∂L∂z−∂N∂x,1V∂M∂t=∂Z∂x−∂X∂z,1V{uzϱ+∂Z∂t}=∂M∂x−∂L∂y,1V∂N∂t=∂X∂y−∂Y∂x,\begin{aligned} \frac{1}{V} \left\{ u_x \varrho + \frac{\partial X}{\partial t} \right\} &= \frac{\partial N}{\partial y} - \frac{\partial M}{\partial z} , &\qquad \frac{1}{V} \frac{\partial L}{\partial t} &= \frac{\partial Y}{\partial z} - \frac{\partial Z}{\partial y} , \\ \frac{1}{V} \left\{ u_y \varrho + \frac{\partial Y}{\partial t} \right\} &= \frac{\partial L}{\partial z} - \frac{\partial N}{\partial x} , &\qquad \frac{1}{V} \frac{\partial M}{\partial t} &= \frac{\partial Z}{\partial x} - \frac{\partial X}{\partial z} , \\ \frac{1}{V} \left\{ u_z \varrho + \frac{\partial Z}{\partial t} \right\} &= \frac{\partial M}{\partial x} - \frac{\partial L}{\partial y} , &\qquad \frac{1}{V} \frac{\partial N}{\partial t} &= \frac{\partial X}{\partial y} - \frac{\partial Y}{\partial x} , \end{aligned}
In wordsIn the stationary system, the current carried by moving electricity of density, together with the rate at which the electric force changes with the time, divided by the velocity of light, equals how the magnetic force circulates across the coordinates; the equations for the change of the magnetic force are those of empty space.OverviewThe Maxwell-Hertz equations of § 6 with the currents of moving electricity added: where electricity moves, it drives the magnetic force as a changing electric force does.Full explanationThese are the equations of § 6 with one new term in each row of the left column: uxϱu_x \varrho, the current carried by electricity of density ϱ4π\frac{\varrho}{4 \pi} moving with velocity (ux,uy,uz)(u_x, u_y, u_z). The paper defines ϱ\varrho in the next display as the divergence of the electric force, which is 4π4 \pi times the density of electricity in its units. The right column, for the change of the magnetic force, has no current and is unchanged. The paper adds that if the electric masses are imagined bound invariably to small rigid bodies, ions or electrons, these equations are the electromagnetic foundation of Lorentz's electrodynamics and optics of moving bodies. The question of § 9 is whether that foundation agrees with the principle of relativity.Every step1V∂X∂t=∂N∂y−∂M∂z\frac{1}{V} \frac{\partial X}{\partial t} = \frac{\partial N}{\partial y} - \frac{\partial M}{\partial z}The first row of § 6, for empty space: a changing electric force goes with a circulating magnetic force.1V{uxϱ+∂X∂t}=∂N∂y−∂M∂z\frac{1}{V} \left\{ u_x \varrho + \frac{\partial X}{\partial t} \right\} = \frac{\partial N}{\partial y} - \frac{\partial M}{\partial z}With electricity present and moving, its current uxϱu_x \varrho joins the change of the electric force as a source of the circulating magnetic force. The other two rows add uyϱu_y \varrho and uzϱu_z \varrho.1V∂L∂t=∂Y∂z−∂Z∂y\frac{1}{V} \frac{\partial L}{\partial t} = \frac{\partial Y}{\partial z} - \frac{\partial Z}{\partial y}The equations for the magnetic force are those of empty space: there is no magnetic current.Also

Read it in the paper