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

Zur Elektrodynamik bewegter Körper

Special relativity: from clock operations to electrodynamics

[p. 916]§ 9. Transformation der Maxwell-Hertzschen Gleichungen mit Berücksichtigung der Konvektionsströme.

§ 9.§ 9Transformationtransformationderof theMaxwell-HertzschenMaxwell-HertzGleichungenequationsmitwith considerationBerücksichtigung↳derofKonvektionsströme.convection currents
[p. 916]
Wirwegehenstart fromaus↳von↳dentheGleichungen:equationswobeiwherediethe4π4\pi-fache-foldDichtedensityderofElektrizitätelectricityundand(ux,uy,uz)(u_x, u_y, u_z)dentheGeschwindigkeitsvektorvelocity vectorderofElektrizitätelectricitybedeutet.denotes
[p. 916]
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}
Explain this equation
Denktif one imaginesman↳sich↳dietheelektrischenelectricMassenmassesunveränderlichinvariablyantokleine,smallstarrerigidKörperbodies(Ionen,ionsElektronen)electronsgebunden,boundsothensindarediesetheseGleichungenequationsdietheelektromagnetischeelectromagneticGrundlagefoundationderofLorentzschenLorentz'sElektrodynamikelectrodynamicsundandOptikopticsbewegterof movingKörper.bodies
[pp. 916–917]
Transformiertif one transformsman↳diesetheseGleichungen,equationswelchewhichimin theSystemsystemKKgeltenmay hold[supposition]mögen,↳[supposition]mitwith the helpHilfe↳derof theTransformationsgleichungentransformation equationsvonof§ 3§ 3undand§ 6§ 6auftodastheSystemsystemkk,sothenerhältobtainsmanonedietheGleichungen:equationswobeiwhere
List the reasoning words in this sentence (1)
  1. gelten mögen (may hold) · [konjunktiv-i]: gelten mögen, Konjunktiv I in form: the equations are taken to hold in K, an assumption, as the Maxwell-Hertz equations were in § 6
[p. 916]
1V{uξϱ′+∂X′∂τ}=∂N′∂η−∂M′∂ζ,∂L′∂τ=∂Y′∂ζ−∂Z′∂η,1V{uηϱ′+∂Y′∂τ}=∂L′∂ζ−∂N′∂ξ,∂M′∂τ=∂Z′∂ξ−∂X′∂ζ,1V{uζϱ′+∂Z′∂τ}=∂M′∂ξ−∂L′∂η,∂N′∂τ=∂X′∂η−∂Y′∂ξ,\begin{aligned} \frac{1}{V} \left\{ u_\xi \varrho' + \frac{\partial X'}{\partial \tau} \right\} &= \frac{\partial N'}{\partial \eta} - \frac{\partial M'}{\partial \zeta} , &\qquad \frac{\partial L'}{\partial \tau} &= \frac{\partial Y'}{\partial \zeta} - \frac{\partial Z'}{\partial \eta} , \\ \frac{1}{V} \left\{ u_\eta \varrho' + \frac{\partial Y'}{\partial \tau} \right\} &= \frac{\partial L'}{\partial \zeta} - \frac{\partial N'}{\partial \xi} , &\qquad \frac{\partial M'}{\partial \tau} &= \frac{\partial Z'}{\partial \xi} - \frac{\partial X'}{\partial \zeta} , \\ \frac{1}{V} \left\{ u_\zeta \varrho' + \frac{\partial Z'}{\partial \tau} \right\} &= \frac{\partial M'}{\partial \xi} - \frac{\partial L'}{\partial \eta} , &\qquad \frac{\partial N'}{\partial \tau} &= \frac{\partial X'}{\partial \eta} - \frac{\partial Y'}{\partial \xi} , \end{aligned}
Explain this equation
So printed. Read: (1/V) dL'/dτ = dY'/dζ - dZ'/dη , (1/V) dM'/dτ = dZ'/dξ - dX'/dζ , (1/V) dN'/dτ = dX'/dη - dY'/dξ. In the transformed system of section 9, the three right-hand equations (the magnetic ones) are printed without the factor 1/V before the time derivative. The record in the correction log
[p. 916]
ux−v1−uxvV2=uξ,uyβ(1−uxvV2)=uη,ϱ′=∂X′∂ξ+∂Y′∂η+∂Z′∂ζ=β(1−vuxV2)ϱ.uzβ(1−uxvV2)=uζ.\begin{aligned} \frac{u_x - v}{1 - \frac{u_x v}{V^2}} &= u_\xi , \\ \frac{u_y}{\beta \left( 1 - \frac{u_x v}{V^2} \right)} &= u_\eta , &\qquad \varrho' = \frac{\partial X'}{\partial \xi} + \frac{\partial Y'}{\partial \eta} + \frac{\partial Z'}{\partial \zeta} = \beta \left( 1 - \frac{v u_x}{V^2} \right) \varrho . \\ \frac{u_z}{\beta \left( 1 - \frac{u_x v}{V^2} \right)} &= u_\zeta . \end{aligned}
Explain this equation
Dasince—wieasausfromdemtheAdditionstheoremaddition theoremderofGeschwindigkeitenvelocities(§ 5)§ 5folgtfollows—dertheVektorvector(uξ,uη,uζ)(u_\xi, u_\eta, u_\zeta)nichtsnothinganderesotheristisalsthandietheGeschwindigkeitvelocityderof theelektrischenelectricMassenmassesimin theSystemsystemkkgemessen,measuredsothenistisdamittherebygezeigt,showndaßthatunteron the basis ofZugrundelegung↳unsererof ourkinematischenkinematicalPrinzipienprinciplesdietheelektrodynamischeelectrodynamicGrundlagefoundationderofLorentzschenLorentz'sTheorietheoryderof theElektrodynamikelectrodynamicsbewegterof movingKörperbodiesdemto theRelativitätsprinzipprinciple of relativityentspricht.is in accordance with
[p. 917]
Eslet it be remarked[supposition]möge↳[supposition]nochalsokurzbrieflybemerkt↳[supposition]werden,↳[supposition]daßthatausfromdentheentwickeltendevelopedGleichungenequationsleichteasilyderthefolgendefollowingwichtigeimportantSatztheoremgefolgertdeducedwerdenbekann:canBewegtif ... movessich↳einanelektrischelectricallygeladenerchargedKörperbodybeliebigin any manneriminRaumespaceundandändertif ... changessich↳hierbeiin the processseineitsLadungchargenicht,notvonfromeinemamitwithdemtheKörperbodybewegtenmovingKoordinatensystemcoordinate systemaus↳betrachtet,regardedsothenbleibtremainsseineitsLadungchargeauchalso—vonfromdemthe„ruhenden“stationarySystemsystemKKaus↳betrachtetregarded—konstant.constant
List the reasoning words in this sentence (1)
  1. Es möge bemerkt werden (let it be remarked) · [konjunktiv-i]: Konjunktiv I of mögen: es möge ... bemerkt werden, ‘let it be remarked’, an aside