Discover · A route you could take
One current, two stories.
Which one is the moving one?
It starts with a magnet, a coil of wire and a needle that moves, all of it ordinary in 1904, and asks why the textbook needs two different explanations for one reading. Following that question through means giving up the idea that “at the same time” needs no definition.
A route you could take, not a transcript of Einstein’s private thoughts. Every step can be read without running anything.
01 / Start where the paper starts
A magnet, a coil, and a needle that moves
Hold a coil of wire still and push a magnet into it: the needle deflects. Now hold the magnet still and move the coil over it instead, at the same relative speed: the needle deflects by the same amount. Every measurement you can make on the two arrangements agrees.
The accepted theory of 1904 does not describe them the same way. In the first case the moving magnet is said to produce an electric field in the space around it, and that field drives the current. In the second the field around the magnet is said to be unchanging, and the current arises instead because the wire is moving through it. Two mechanisms, two descriptions, one needle that cannot tell them apart.
02 / Decide whether that bothers you
An asymmetry in the telling, not in the measuring
This is not a crisis. Nothing is predicted wrongly. The two accounts agree on every number, and a physicist who shrugs and uses whichever is convenient will never be caught out by an experiment.
What is odd is that the theory distinguishes two situations that no measurement distinguishes. To tell the stories apart you have to say which object is really moving, and the only thing that could settle that is motion relative to the medium light travels in. Attempts to detect that motion had been made, with increasing care, and had found nothing.
How much the null results are worth here
Less than the usual telling suggests, and the route does not lean on them. They say that one route to distinguishing the two cases did not work, not that no route could. The paper refers to failed attempts to detect motion relative to the light medium in general terms, and nothing in it says which experiment mattered to its author; the shelf card says the same.
03 / Make a prediction
Can you keep both of these at once?
Here are two statements. First: the laws of physics look the same to anyone moving steadily, so there is no experiment that reveals who is really at rest. Second: light travels through empty space at a definite speed that does not depend on how fast its source was moving when it left.
Before reading on, decide whether they are compatible. If I am gliding past you at half the speed of light and we both watch the same flash, the ordinary way of adding speeds says we must get different answers for how fast it travels. Either one of the two statements is wrong, or something in the ordinary way of adding speeds is.
Why the third option is easy to miss
Adding speeds is not a law anybody tested. It follows from something more basic that has never needed defending: that you and I agree on what time it is, so we agree on how long the flash took, and we already agree on how far it went. That agreement is the assumption in the room, and it is invisible precisely because nothing has ever asked for it.
04 / Find the assumption
What does it take to say two distant things happened at once?
Stop and ask what the claim even means. Two events at the same place happening together is something you can see. Two events far apart happening together is not: you have to compare two clocks, and to compare them you have to have set them, and to set them you have to send something between them that takes time to arrive.
So “at the same time” for distant events is not something you observe. It is something you establish, by a procedure you choose. Write the procedure down and the consequence follows at once: two observers moving relative to each other, each setting their clocks by the same rule, do not end up agreeing about which distant events are simultaneous. Neither has made a mistake.
05 / Build the map
The move
Now the work is mechanical, and this is the step that the story usually skips. Take the two statements from step 3 as given, take the clock-setting procedure from step 4, and ask what relation must hold between one observer’s coordinates and the other’s. Add that space and time are the same everywhere and in every direction, and the answer is forced: only one set of relations keeps both principles and reduces to the familiar one at everyday speeds.
Work it through rather than read it. The result is often presented as a formula handed down; here it is built from a measurement procedure you can carry out, and nothing enters it beyond the two principles, the clock-setting rule, and that sameness of space and time.
06 / Read off the consequences
Moving clocks, moving rods, and added speeds
A clock moving past you reads less elapsed time than yours between the same two events. A rod moving past you measures shorter along its direction of travel. And speeds no longer add the way they used to, which is the answer to the puzzle in step 3: the flash comes out at the same speed for both of us. Neither measurement is wrong; we disagree about the times and distances that go into it.
What the moving clock reading means
The claim is about what the clock itself reads when it arrives, compared with what your clocks read, both measured in the ordinary way. A camera is a separate question: what it records also involves how long the light took to reach it, and that contribution can be calculated on its own. Keeping the two apart is the whole of the distinction.
First the clock, as a formula.
Your clocks advance by t while a clock moving past you at speed v runs between two of its own ticks. What does the moving clock read? Write it using t, v and c, the speed of light.
Answers are compared for t from 1 to 100, v from 1 × 107 to 2.9 × 108 and c from 2.99 × 108 to 3 × 108.
Show a worked explanation
The moving clock reads less than yours by the factor √(1 − v²/c²), so it reads t·√(1 − v²/c²), which you can write t*sqrt(1-v^2/c^2) or t*sqrt(1-(v/c)^2). At v = 0.6c the factor is √0.64 = 0.8: the moving clock reads 8 seconds while yours read 10. The paper writes V for the speed of light, so its form is t·√(1 − (v/V)²). Dividing by the factor instead, t/√(1 − v²/c²), gives the time your clocks show while the moving clock reads t, which is the same fact seen from the other side.
Then the rod, on numbers.
Measured this way, a moving rod is shorter along its direction of travel by the factor √(1 − v²/c²), where v is its speed and c the speed of light, which the paper writes V. A rod 1 m long when it is at rest moves past you along its own length at 0.6 of the speed of light. You mark where its two ends are at the same moment, by your own clocks, and measure the distance between the marks. How long is it? Give it in metres or centimetres.
Show a worked explanation
With v/c = 0.6, v²/c² = 0.36, and √(1 − 0.36) = √0.64 = 0.8. The rod you measure is 0.8 × 1 m = 0.8 m, or 80 cm. Across its direction of travel nothing changes, and a ruler riding with the rod still reads 1 m: the 0.8 m belongs to your way of marking both ends at once.
An answer within 1 percent is the same answer, so 0.8 m and 80 cm agree.
07 / Meet the serious rival
Lorentz gets the same formulas, and is not refuted
Keep the light medium. Say that a body moving through it genuinely contracts, and that a clock moving through it genuinely runs slow, and that what a moving observer calls time is a bookkeeping device rather than the real thing. Work it through and you reach the same equations, and every experiment above comes out the same way.
This route does not tell you that account is wrong, and it would be dishonest to. Within the scope of these measurements the two are equivalent, and no experiment listed here separates them. What differs is the bookkeeping: one account posits a medium nobody can detect and then adds contraction and local time as properties of motion through it; the other takes the two principles of step 3 and gets the same relations with nothing else assumed.
What would it take to prefer one?
Economy, which is a reason and not a proof, and reach: the same kinematics applies to any law whatever, not only to electromagnetism, which is what makes the fourth paper of 1905 possible three months later. A reader who finds the ether account tidier is not making an error that this page can correct with a measurement.
08 / Check it against the world
What had already been measured
Light in moving water is dragged along, but only partly, by a fraction measured in 1851 and awkward for the theories of its day. The new way of adding speeds gives that fraction with nothing added. A star’s apparent position shifts through the year by an amount known since 1729, and the same transformation gives the shift and the accompanying change of frequency together, from one relation rather than two.
The 1904 shelf
Nothing here is imported from later. The most interesting card is Lorentz’s, which is on the shelf as a live alternative rather than as a foil.
This list is a reconstruction aid assembled for learning, not a documentary history of what Einstein read.
Published 1687Time passes at the same rate everywhere and two events either happen at once or they do not, whoever is asking.
Available by the end of 1904
Time passes at the same rate everywhere and two events either happen at once or they do not, whoever is asking.
Historical context
Available in the published scientific literature or public proceedings prior to 1905.
Available by
Published 1687
What the paper itself cites or asserts
Not yet recorded for this card.
Where this site uses it
Primary evidence and sources
- Philosophiae Naturalis Principia Mathematica Scholium to the Definitions (1687)
Source verification pending library scan inspection.
Published 1729A star's apparent position shifts through the year by an amount set by the Earth's speed and the speed of light.
Available by the end of 1904
A star's apparent position shifts through the year by an amount set by the Earth's speed and the speed of light.
Historical context
Available in the published scientific literature or public proceedings prior to 1905.
Available by
Published 1729
What the paper itself cites or asserts
Not yet recorded for this card.
Where this site uses it
Primary evidence and sources
- A Letter giving an Account of a new discovered Motion of the Fix'd Stars Phil. Trans. R. Soc. 35, 637 (1729)
Source verification pending library scan inspection.
Published 1851Light travelling through moving water is carried along by it, but only partly, by a measured fraction rather than fully.
Available by the end of 1904
Light travelling through moving water is carried along by it, but only partly, by a measured fraction rather than fully.
Historical context
Available in the published scientific literature or public proceedings prior to 1905.
Available by
Published 1851
What the paper itself cites or asserts
Not yet recorded for this card.
Where this site uses it
Primary evidence and sources
- Sur les hypothèses relatives à l'éther lumineux Comptes Rendus 33, 349 (1851)
Source verification pending library scan inspection.
Published 1873One set of equations governs electricity, magnetism and light, and fixes the speed at which an electromagnetic wave travels.
Available by the end of 1904
One set of equations governs electricity, magnetism and light, and fixes the speed at which an electromagnetic wave travels.
Historical context
Available in the published scientific literature or public proceedings prior to 1905.
Available by
Published 1873
What the paper itself cites or asserts
Not yet recorded for this card.
Where this site uses it
Primary evidence and sources
- A Treatise on Electricity and Magnetism Oxford: Clarendon Press (1873)
Source verification pending library scan inspection.
Published 1887A careful attempt to detect the Earth's motion through the light medium found no effect of the size expected.
Available by the end of 1904
A careful attempt to detect the Earth's motion through the light medium found no effect of the size expected.
Historical context
Available in the published scientific literature or public proceedings prior to 1905.
Available by
Published 1887
What the paper itself cites or asserts
Not yet recorded for this card.
Where this site uses it
Primary evidence and sources
- On the Relative Motion of the Earth and the Luminiferous Ether Am. J. Sci. (3) 34, 333 (1887)
Source verification pending library scan inspection.
Published 1904Keep the ether, let moving bodies contract and let moving clocks keep a local time, and the equations reproduce the null results exactly.
Available by the end of 1904
Keep the ether, let moving bodies contract and let moving clocks keep a local time, and the equations reproduce the null results exactly.
Historical context
Available in the published scientific literature or public proceedings prior to 1905.
Available by
Published 1904
What the paper itself cites or asserts
Not yet recorded for this card.
Where this site uses it
Primary evidence and sources
- Electromagnetic phenomena in a system moving with any velocity less than that of light Proc. R. Acad. Amsterdam 6, 809 (1904)
Source verification pending library scan inspection.
Presented 1904The laws of physics should be the same for an observer at rest and one in uniform motion, stated as a general principle to be met rather than a result to be derived.
Available by the end of 1904
The laws of physics should be the same for an observer at rest and one in uniform motion, stated as a general principle to be met rather than a result to be derived.
Historical context
Available in the published scientific literature or public proceedings prior to 1905.
Available by
Presented 1904
What the paper itself cites or asserts
Not yet recorded for this card.
Where this site uses it
Primary evidence and sources
- L'état actuel et l'avenir de la physique mathématique Address at St Louis, 24 September 1904 (1904)
Source verification pending library scan inspection.
The dates on these cards come from standard bibliographies. No one here has checked them against the volumes, and the shelf marks each card as awaiting verification.
Where this enters the paper
The paper is thirty-one pages in two parts. The magnet and the coil are its opening paragraph, the clock-setting procedure is section 1, simultaneity is section 2, the construction is section 3, clocks and rods are section 4, velocity addition is section 5, and the electrodynamic half from section 6 onwards carries the field transformations, Doppler and aberration, and the dynamics of the electron.