Annus MirabilisEinstein in 1905
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Read · Special relativity: from clock operations to electrodynamics · Results

§1 · operational simultaneity

Clocks, rods and light first, then electricity and magnetism: follow the relativity paper through its introduction and all ten sections, including the later ones most retellings skip.

The paper's results

Pages 894, 895

Synchronous clocks and the time of a distant event

Two clocks at rest at A and B run synchronously, by definition, when a ray of light that leaves A at tAt_A, is reflected at B at tBt_B and returns to A at tA′t'_A takes as long out as back, tB−tA=tA′−tBt_B-t_A=t'_A-t_B; the time of an event is then the reading of such a clock at its place, and the quantity 2AB‾/(tA′−tA)2\overline{AB}/(t'_A-t_A) is set, in accordance with experience, to be a universal constant, the speed of light in empty space.

As printed

Die letztere Zeit kann nun definiert werden, indem man durch Definition festsetzt, daß die „Zeit“, welche das Licht braucht, um von AA nach BB zu gelangen, gleich ist der „Zeit“, welche es braucht, um von BB nach AA zu gelangen. Es gehe nämlich ein Lichtstrahl zur „AA-Zeit“ tAt_A von AA nach BB ab, werde zur „BB-Zeit“ tBt_B in BB gegen AA zu reflektiert und gelange zur „AA-Zeit“ tA′t'_A nach AA zurück. Die beiden Uhren laufen definitionsgemäß synchron, wenn

Die „Zeit“ eines Ereignisses ist die mit dem Ereignis gleichzeitige Angabe einer am Orte des Ereignisses befindlichen, ruhenden Uhr, welche mit einer bestimmten, ruhenden Uhr, und zwar für alle Zeitbestimmungen mit der nämlichen Uhr, synchron läuft.

Wir setzen noch der Erfahrung gemäß fest, daß die Größe eine universelle Konstante (die Lichtgeschwindigkeit im leeren Raume) sei.

Wesentlich ist, daß wir die Zeit mittels im ruhenden System ruhender Uhren definiert haben; wir nennen die eben definierte Zeit wegen dieser Zugehörigkeit zum ruhenden System „die Zeit des ruhenden Systems“.

Text on page 894 of the German source, § 1, paragraph 7 · Display on page 894 of the German source, § 1, display 1 · Text on page 894 of the German source, § 1, paragraph 9 · Text on page 894 of the German source, § 1, paragraph 10 · Display on page 894 of the German source, § 1, display 2 · Text on pages 894–895 of the German source, § 1, paragraph 11

In modern notation

tB−tA=tA,return−tBt_B - t_A = t_{A,\mathrm{return}} - t_B
tB=tA+tA,return2t_B = \frac{t_A + t_{A,\mathrm{return}}}{2}

Shown in modern letters; Einstein's are in §1 of the German source face.

  • Premise: The paper assumes that the definition can be applied without contradiction to any number of points: if the clock at B is synchronous with the clock at A, then A's is synchronous with B's, and two clocks synchronous with a third are synchronous with each other.
  • Premise: Two different things are laid down. The equality of the two travel times is a definition; that the round-trip quantity is a universal constant is stipulated in accordance with experience.
  • A comparison, not a premise: Whether the equal-times rule is a free choice was argued later, beginning with Reichenbach in 1928, and the question is still debated. The paper calls it a definition.

Decoder

tAt_A, tBt_B, tA′t'_A
The departure of the ray from A, read on A's clock; its reflection at B, read on B's clock; and its return to A, read on A's clock.
AB‾\overline{AB}
The distance between A and B.
VV
The speed of light in empty space, printed V; today it is written c.
"durch Definition"
By definition, letter-spaced in the print: that light takes as long from A to B as from B to A is stipulated, and nothing in the procedure measures it.
"die Zeit des ruhenden Systems"
The time of the stationary system: the paper stresses that the time so defined belongs to clocks at rest in that system.

Try it

SR-01: A signal leaves A at 0 s and returns at 10 s: what must B's clock read at the moment of reflection? Choose the preset “Emission at 0, reception at 10 (reflection assigned 5)” there.

SR-01: Light goes 10 light-seconds out and back: what does 2AB‾/(tA′−tA)2\overline{AB}/(t'_A-t_A) come to? Choose the preset “Round trip over 10 light-seconds (speed = c)” there.

SR-01: Clocks at B and at C are each synchronous with the clock at A: are they synchronous with each other? Choose the preset “Three mutually resting stations (A, B, C): transitivity” there.

Where this stops: A round trip read on one clock cannot measure the two one-way times separately. Setting clocks does not move them or change their rates. Read the argument

Common wrong turns

Argument
A definition, with an assumption that it is consistent and a stipulation from experience
Model
A definition for clocks at rest in one system
Evidence
A definition, not evidence; the constancy of the round-trip speed is taken from experience
History
In 1900 Poincaré had described observers moving through the ether who set their clocks by exchanging light signals and so obtain Lorentz's local time, to first order; here the procedure defines the time of the stationary system

§1 · operational simultaneity

Time at a distant clock is an operation

To set a distant clock, send light to it and back, and give the moment of reflection the time halfway between sending and receiving. That rule defines the time of a distant event; it is not the moment its image arrives.

Read the argument