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Theoretical Physics · Treatise
On the Electrodynamics of Moving Bodies
by Einstein · The Mapper of Spacetime · Modern Physics, 1879-1955
A ten-part paper that rebuilds space, time, electrodynamics, and motion from two postulates.
- Brutal
- ~35 min read
- 2 chapter guides
- Public domain
Start reading · Read the § 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former guide free
Before the text
Editor's Prelude
A Magnet, a Wire, and a Crisis
A moving magnet and a moving conductor can produce the same current, yet the customary theory gives them different explanations. Einstein opens with that asymmetry. His question is physical and precise: why should a difference in the observer's motion demand a difference in the laws?
His answer begins with rods, clocks, and light signals. A clock can date an event beside it; comparing distant events requires a rule for synchronizing clocks. Once that rule is explicit, simultaneity ceases to be something all observers must share. The two postulates—identical physical laws for systems in uniform relative motion, and a constant speed of light independent of the emitter's motion—put familiar measurements of length and time under pressure.
The paper moves from these measurements to the transformation of co-ordinates and velocities, then applies the same relations to electric and magnetic fields. The magnet-and-conductor puzzle returns as a test of the new account. Light's frequency, energy, and pressure, and the motion of an electron, become further tests of what those postulates can sustain.
The final treatment assumes a slowly accelerated electron and neglects radiation in calculating its kinetic energy. Einstein also warns that the longitudinal and transverse masses he gives depend on how force and acceleration are defined. His closing pages turn these results into predictions that experiment could test.
The opening pages
The Two Postulates
It is known that Maxwell's electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighbourhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighbourhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.
Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies. The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.
Chapter guides · 2
§ 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former
One Event, Two Sets of Measurements
The transformation changes space and time together while preserving the speed of light.
One event in two systems
Einstein gives each system its own measuring rods and synchronized clocks. The same event has a position and time in each system. He seeks equations connecting those measurements. Because he takes space and time to be uniform, the equations are linear: the coordinates enter without higher powers.
Light keeps the same speed
Applying the synchronization rule gives the time relation. Einstein then uses light rays to find the spatial relations. A spherical light wave remains spherical and travels at c, the speed of light, in either system. This shows that his two postulates can hold together.
The scale factor is one
A possible scale factor remains. Reversing the relative motion and comparing a rod moving at right angles to its length fix that factor at one. Einstein calls the relative speed v and uses beta for 1 divided by the square root of (1 minus v squared divided by c squared). In the final equations, the moving x-coordinate is beta times (x minus v t), and its time is beta times (t minus v x divided by c squared). The two sideways coordinates stay unchanged.
II. Electrodynamical Part
Electric and Magnetic Forces
Changing the observer’s motion changes how electric and magnetic forces are described.
Questions readers ask
- How long does it take to read On the Electrodynamics of Moving Bodies?
- About 35 min in total.
- How difficult is On the Electrodynamics of Moving Bodies?
- Brutal. A short treatise; about 35 minutes of reading.
- Which translation is this?
- The W. Perrett and G. B. Jeffery translation from the German, first published in 1905. The text follows The Principle of Relativity (London: Methuen, 1923): W. Perrett and G. B. Jeffery's translation of On the Electrodynamics of Moving Bodies, in John Walker's Fourmilab electronic edition (1999).
- Can I read On the Electrodynamics of Moving Bodies for free?
- On the Electrodynamics of Moving Bodies is part of Nexus Premium, so reading it needs an account and a Premium subscription. The opening above and one chapter guide on this page are free to read.
- How many chapter guides are there?
- 2 chapter guides, written by the Nexus editors. One opens in full here; the rest show their opening line.
About Einstein
Albert Einstein was a theoretical physicist whose work transformed modern physics. Nexus stages him through the popular Relativity, the shorter Sidelights addresses, and the harder Princeton lectures in The Meaning of Relativity.
“What changes when space and time are not absolute backgrounds?”
Einstein changed physics and public imagination alike, making modern science a challenge to common sense as well as a technical revolution.
Source text: public domain. Chapter guides: original Nexus writing. On the Electrodynamics of Moving Bodies is part of The Nexus Archive, guided Quests through the great works.