Postulates of Special Relativity

Einstein's 1905 paper does not open with trains, clocks, or the Michelson–Morley experiment. It opens with this course. "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." His exhibit: a magnet and a conductor in relative motion. Move the conductor past the magnet, and the theory says a magnetic force $q\mathbf{v}\times\mathbf{B}$ drives the current. Move the magnet past the conductor — the same relative motion — and the theory tells a completely different story: a curling electric field, induced by the changing $\mathbf{B}$ , drives the current. Two mechanisms, two ontologies... and one identical, indistinguishable current. The physics depends only on relative motion; the explanation depends on an absolute state of rest that no experiment can find. That asymmetry of description, not any failed experiment, is what Einstein declared intolerable. The paper's title is the announcement of jurisdiction: "On the Electrodynamics of Moving Bodies." Relativity was born as a chapter of this subject — the resolution of a tension that had been sitting inside Maxwell's equations since 1865, where a wave speed $c=1/\sqrt{\mu_0\varepsilon_0}$ appears built from vacuum constants, with no mention of any frame it is a speed relative to. This article states Einstein's two postulates, runs his magnet-and-conductor asymmetry quantitatively, demonstrates exactly how Galilean kinematics breaks the electromagnetic wave equation, and prices the experimental verdicts. The kinematic consequences — the transformation itself, the geometry — are the next two articles; the payoff for this track, kept in view throughout, is that $\mathbf{E}$ and $\mathbf{B}$ will turn out to be one object seen from two chairs, and the magnet-conductor "asymmetry" will dissolve into a single frame-indifferent tensor.

Key takeaways

Postulate I (relativity): the laws of physics — including electrodynamics — take the same form in every inertial frame; no experiment detects uniform motion from inside.
Postulate II (light): the speed of light in vacuum is the same value $c$ in every inertial frame, regardless of the motion of source or observer.
Einstein's actual motivation was electrodynamic: the magnet–conductor asymmetry, where one physical phenomenon (an induced current) receives two unrelated explanations ( $q\mathbf{v}\times\mathbf{B}$ force vs. induced $\mathbf{E}$ ) depending on which object is called "moving."
Maxwell's equations force the issue: they predict a frame-free wave speed $c=1/\sqrt{\mu_0\varepsilon_0}$ , and the wave equation is demonstrably not form-invariant under Galilean transformations — either a preferred ether frame exists, or Galilean kinematics is wrong. Experiment (Michelson–Morley: fringe shift $<3\%$ of the ether prediction) killed the ether.
The postulates keep Maxwell and discard Galileo: simultaneity, time intervals, and lengths become frame-dependent (theorems, not assumptions — derived in the companion mechanics treatment and the next article).
Verified daily: muons reaching the ground ( $\gamma\approx9$ stretches 660 m of naive range to 6 km), GPS clocks ( $-7.2\ \mu$ s/day kinematic shift), and every collider's kinematics.
Key idea: the principle of relativity plus the frame-free $c$ hiding inside Maxwell's equations — two postulates that rescue electrodynamics whole, at the price of rebuilding space and time.

The core insight

Two axioms — same physics in every inertial frame, and a universal light speed $c$ — uniquely determine how space and time intervals transform, and they make Maxwell's electrodynamics the prototype of a relativistically covariant theory.

Where this lives today

The postulates are now metrology. Since 1983 the meter is defined by fixing $c=299\,792\,458$ m/s exactly — the second postulate promoted from discovery to definition, so that "testing the constancy of $c$ " today means testing the isotropy and frame-independence of spacetime structure: modern Michelson–Morley descendants (cryogenic optical resonators compared over years) bound direction-dependence of light propagation at the $10^{-18}$ level, and the Lorentz-violation parameter tables of the Standard-Model Extension catalogue hundreds of null results across every particle sector. Postulate I gets its own precision program: any interior experiment detecting absolute rest — from electron dipole-moment searches to clock-comparison experiments riding Earth's orbit — would falsify it, and none has. For this track, the postulates are the working foundation of everything ahead. The next two articles build the transformation they force and the geometry that houses it; then the electrodynamic harvest begins — fields transforming into each other (the magnet-conductor asymmetry dissolved by calculation), magnetism derived as the relativistic shadow of electrostatics, and Maxwell's equations rewritten in a form where their frame-indifference is visible at a glance, $\partial_\mu F^{\mu\nu}=\mu_0J^\nu$ . The historical loop will then be closed: the theory that motivated relativity turns out to be the first theory already written in relativity's native language, and the asymmetries of Einstein's opening paragraph become, in the field tensor, typographically impossible.

Origins · 1 minAlbert Einstein and how this was discovered

Albert Einstein

1879–1955 · Bern patent office, 1905 — who read the asymmetry as the message

The Einstein of the 1905 relativity paper was a 26-year-old patent examiner (technical expert, third class) who had failed to get any academic post, working through physics in evening discussions with the "Olympia Academy" — two friends and whatever books they could afford. "Zur Elektrodynamik bewegter Körper," received by Annalen der Physik on June 30, 1905, cites no literature, thanks only his friend Michele Besso, and opens not with the Michelson–Morley experiment (which Einstein later said played only an indirect role for him) but with the magnet and the conductor — a theorist's irritation at redundant explanation. The relativity paper was the third of that year's four (light quanta in March, Brownian motion in May, relativity in June, $E=mc^2$ as an afterthought in September). The distinctive move, visible already in the opening paragraph, was epistemological: treat the impossibility of detecting absolute motion not as a conspiracy requiring mechanism (contraction hypotheses, ether dynamics — Lorentz's and Poincaré's route, technically adjacent but philosophically opposite) but as a principle from which to deduce. Kinematics first, mechanism never. It is the same reflex that later produced the equivalence principle from a falling elevator — and the reason this course, a century on, still opens its relativity chapter with his magnet.

History

1632

— Galileo's ship: no interior experiment detects uniform motion — the relativity principle, for mechanics

1865

— Maxwell's equations predict waves at 1/√(μ₀ε₀): a frame-free speed appears inside physics

1887

— Michelson and Morley find no ether drift at 1/40 of the predicted signal

1889

— FitzGerald (then Lorentz, 1892) proposes contraction to rescue the ether

1904

— Lorentz's full transformation equations; Poincaré names the relativity principle and polishes the group

1905

— Einstein's "On the Electrodynamics of Moving Bodies": two postulates, no ether, kinematics rebuilt

1938

— Ives and Stilwell measure transverse Doppler time dilation directly

1983

— the meter redefined by fixing c exactly: Postulate II becomes the unit system

2017

— GW170817: light and gravitational waves arrive together across 130 million years — one invariant speed, two messengers

The physical picture

Hold the magnet-and-conductor scene in mind as this track's founding thought experiment. A bar magnet and a wire loop, approaching each other at speed $v$ . Sit on the magnet: the loop's charges sweep through your static $\mathbf{B}$ , feel $q\mathbf{v}\times\mathbf{B}$ , and a current flows — pure magnetostatics plus the Lorentz force, no electric field anywhere. Sit on the loop: nothing in the loop moves, so no magnetic force acts on anything; instead the approaching magnet makes $\mathbf{B}(t)$ at the loop change, Faraday's law demands a curling $\mathbf{E}$ , and that drives the current — pure induction, with the electric field doing all the work. The ammeter, which sits in both stories, reads the same number. Nature delivers one phenomenon; the pre-1905 theory delivers two explanations sorted by a question — which one is really moving? — that nature refuses to answer. The second thread is quantitative and older. Maxwell's equations in vacuum combine into a wave equation whose speed is $1/\sqrt{\mu_0\varepsilon_0}=2.998\times10^8$ m/s — constants of the vacuum, measurable with capacitors and coils on a bench, no astronomy involved. A speed relative to what? Nineteenth-century physics answered: relative to the luminiferous ether, the medium whose oscillations light was supposed to be — making Maxwell's equations valid only in the ether's rest frame, and the Earth's motion through it detectable as a direction-dependent light speed. The alternative reading, Einstein's, takes the equations at their word: the speed is frame-free because it is the same in every frame — and then kinematics itself, not electrodynamics, must bend.

Figure

Einstein's opening exhibit — one current, two stories, and the asymmetry that is in the theory rather than the phenomena

What the postulates then do is brutal and minimal. Postulate I extends Galileo's ship — no interior experiment detects uniform motion — from mechanics to all physics, electrodynamics included, thereby outlawing the ether frame by decree. Postulate II keeps the one feature of Maxwell that Galilean kinematics cannot digest: the frame-free $c$ . Together they are almost inconsistent — a speed the same in every frame flatly contradicts velocities adding — and the escape hatch is the only piece of furniture nobody had thought movable: the universality of time. Simultaneity, duration, length all become frame-dependent, by amounts governed by $\gamma=1/\sqrt{1-v^2/c^2}$ ; the detailed kinematic consequences are theorems built in the companion mechanics treatment (light clocks, rod measurements, the twin bookkeeping) and in the next article's transformation. Here the point is logical order: electrodynamics forced the postulates; kinematics paid the bill.

The math: the asymmetry, and the broken wave equation

First, Maxwell's own contribution to the postulates — the frame-free speed. In vacuum the curl equations combine (the calculation owned by the electromagnetic-waves chapter, recalled here in one line) into

\nabla^2\mathbf{E}=\mu_0\varepsilon_0\,\frac{\partial^2\mathbf{E}}{\partial t^2},\qquad c=\frac{1}{\sqrt{\mu_0\varepsilon_0}}=2.998\times10^8\ \text{m/s}. \qquad (1)

where: $\mu_0$ and $\varepsilon_0$ are properties of the vacuum, measured in tabletop electrostatics and magnetostatics. Equation (1) mentions no source velocity, no observer, no frame — and that silence is the crisis. Either the equation secretly holds only in one privileged frame (the ether reading), or it holds in all frames and $c$ is universal (the Einstein reading). The two derivations below sharpen each horn of the dilemma.

Derivation AThe magnet and the conductor, computed in both frames

The goal is Einstein's opening exhibit with numbers: a conducting rod of length $L$ sliding at speed $v$ along rails through a uniform field $\mathbf{B}$ (the cleanest laboratory version of the magnet–conductor scene), analyzed in the frame of the magnet and in the frame of the rod — two disjoint mechanisms, one EMF. The strategy: compute the driving force per unit charge in each frame using only pre-relativistic electrodynamics (Lorentz force; Faraday's law), exhibit the agreement, and then state precisely what is scandalous about it. Watch what each frame must deny: the magnet frame has no electric field at all; the rod frame has no magnetic force at all.

Step 1. Magnet frame (rod moves at $v$ ). Every mobile charge in the rod is carried through $\mathbf{B}$ at velocity $v$ ; the magnetic force per unit charge is $|\mathbf{v}\times\mathbf{B}|=vB$ directed along the rod. The EMF — work per unit charge around the circuit — is

\mathcal{E}=\int(\mathbf{v}\times\mathbf{B})\cdot d\boldsymbol\ell=vBL.

With $v=2$ m/s, $B=0.5$ T, $L=0.3$ m: $\mathcal{E}=0.30$ V. Mechanism: magnetic force on moving charges. Electric field in this frame: exactly zero.

Step 2. Rod frame (magnet moves at $-v$ ). The rod's charges are at rest — a magnetic field can exert no force on them whatever its strength. But the magnet's approach makes the flux through the circuit change at rate $d\Phi/dt=-BLv$ , and Faraday's law supplies a genuine electric field along the rod, $E=vB$ , with EMF

\mathcal{E}=\oint\mathbf{E}\cdot d\boldsymbol\ell=vBL=0.30\ \text{V}.

Mechanism: induced electric field on static charges. Magnetic force in this frame: exactly zero.

Step 3. State the scandal with precision. The observable — 0.30 V, and the current it drives — is identical, and depends only on the relative velocity $v$ . But the theory's causal account flips between "magnetic force, no E field" and "electric field, no magnetic force" according to which object is declared at rest — a distinction with no experimental content. Pre-1905 electrodynamics is thus empirically relativistic in this experiment while being structurally wedded to absolute rest. Einstein's judgment: a theory whose explanations distinguish frames that its predictions cannot is carrying redundant scaffolding.

Step 4. Read the resolution forward. The agreement is no accident, and the postulates convert it from embarrassment to necessity: if no experiment can distinguish the frames (Postulate I), the two descriptions must be two coordinate views of one object. The field that is pure $\mathbf{B}$ in the magnet frame has, viewed from the rod frame, an electric component $E'=vB$ (at this order — the exact transformation with its $\gamma$ arrives in Transformation of Electric and Magnetic Fields): the induced field of Step 2 is the magnetic field of Step 1, transformed. One phenomenon, one object, two shadows. Verified: both routes give $\mathcal{E}=vBL$ exactly (this equality is standard — Griffiths §7.1 and the Faraday-law article's flux rule); the field-transformation reading matches Griffiths §12.3.1's Ex. 12.14 logic and Purcell's Ch. 5 program.

Go deeper · Derivation B · 2 minGalilean kinematics breaks the electromagnetic wave equation

Derivation BGalilean kinematics breaks the electromagnetic wave equation

The goal is the dilemma's other horn, made quantitative: the wave equation (1) is not form-invariant under a Galilean transformation — so pre-Einstein kinematics and Maxwell's electrodynamics cannot both be exactly right. The strategy: transform the 1-D wave operator to a frame moving at $v$ using the Galilean rules $x'=x-vt$ , $t'=t$ , via the chain rule; exhibit the surviving cross term; read off the physical meaning (wave speeds $c\pm v$ ) and the historical stakes. This two-line calculation is the entire ether program in miniature — and the target the Lorentz transformation is engineered, in the next article, to hit.

Step 1. The chain rule under $x'=x-vt$ , $t'=t$ . For any function $f(x',t')$ :

\frac{\partial}{\partial x}=\frac{\partial}{\partial x'},\qquad \frac{\partial}{\partial t}=\frac{\partial}{\partial t'}-v\frac{\partial}{\partial x'}.

Why the time derivative picks up the extra piece: at fixed $x$ , advancing $t$ also slides the moving-frame coordinate $x'=x-vt$ backward — the derivative must account for the drift.

Step 2. Transform the wave operator. Substituting into $\partial_x^2-\tfrac{1}{c^2}\partial_t^2$ :

\frac{\partial^2}{\partial x^2}-\frac{1}{c^2}\frac{\partial^2}{\partial t^2} =\left(1-\frac{v^2}{c^2}\right)\frac{\partial^2}{\partial x'^2}+\frac{2v}{c^2}\frac{\partial^2}{\partial x'\partial t'}-\frac{1}{c^2}\frac{\partial^2}{\partial t'^2}.

The operator has changed form: a cross term $\partial_{x'}\partial_{t'}$ has appeared, and the spatial term is rescaled. No relabeling of constants restores the original shape.

Step 3. Read the broken equation physically. Its plane-wave solutions travel at $c-v$ and $-(c+v)$ in the primed frame — exactly the Galilean velocity addition an ether theory expects: light has speed $c$ in the ether, and an observer moving through the ether measures direction-dependent speeds. Maxwell's equations, married to Galilean kinematics, thus hold in one frame only, and the Earth's laboratory — orbiting at $30$ km/s — should detect its ether drift at the part-in- $10^4$ level in velocity, part-in- $10^8$ in the round-trip timing that interferometers measure.

Step 4. Confront the experiment. Michelson and Morley (1887) compared round-trip light times along perpendicular arms ( $L\approx11$ m effective), rotating the apparatus to swap roles: the ether prediction is a fringe shift $\Delta N\approx2(L/\lambda)(v^2/c^2)=0.40$ fringes for $\lambda=550$ nm — forty times their sensitivity of $\sim0.01$ . Observed: no shift, at any season, ever (modern optical-resonator descendants of the experiment bound the anisotropy at the $10^{-18}$ level). The dilemma resolves by elimination: Maxwell's equations are exactly right in every frame, the wave operator must be invariant under the true transformation between frames — and Step 2 shows Galileo's is not it. Finding the linear transformation that does leave the operator invariant is precisely the next article's opening derivation. Verified: the transformed operator matches the standard demonstration (e.g. Zangwill §22.2, French Ch. 2); fringe-shift arithmetic $2L v^2/\lambda c^2=0.40$ recomputed for this edition; the $c\pm v$ characteristics follow by factoring the Step-2 operator.

The two postulates, stated at last, and read as instructions:

\textbf{I.}\ \text{The laws of physics take the same form in every inertial frame.}\qquad \textbf{II.}\ \text{Light in vacuum moves at }c\text{ in every inertial frame.} \qquad (2)

where: Postulate I is Galileo's principle promoted to all of physics — its content here being specifically that Maxwell's equations, asymmetry-free, hold for the magnet's frame and the conductor's frame alike. Postulate II is (1) taken at face value, universalized: it is the only reading of the frame-free $c$ consistent with I once the ether is gone. Note what is not postulated: no time dilation, no length contraction, no relativity of simultaneity — every kinematic surprise is a theorem downstream of (2), with the light-clock and rod constructions living in the companion mechanics article and the unique transformation they force arriving next. And note the price paid willingly: velocity addition $u'=u+v$ , "obvious" for twenty-two centuries, is sacrificed — replaced by a law (derived next article) with the fixed point $c$ .

Figure

The logic of 1905 — Maxwell's frame-free c meets the relativity principle, and Galileo is the piece that gives way

Limiting cases

case	result	meaning
$v/c\to0$	Galilean physics recovered; $\gamma=1+\tfrac12v^2/c^2+\cdots$	Newton is the slow-motion chapter of relativity
Earth-orbit speeds, $v/c\sim10^{-4}$	effects at $v^2/c^2\sim10^{-8}$	why interferometry (Michelson) was needed, and why daily life never noticed
magnet–conductor at $O(v/c)$	$E'=vB$ appears in the moving frame	the induced field is the transformed magnetic field — asymmetry dissolved
$u=c$ in velocity addition	$u'=c$ for any boost	Postulate II enforced as a fixed point of the (next article's) addition law
massive particle, $v\to c$	$\gamma\to\infty$ : unreachable	$c$ is a limit speed, not just light's speed
Postulate I alone	Galilean AND Lorentz kinematics both allowed	the invariant speed is an independent input — II selects between them
accelerated frames / gravity	postulates silent	inertial frames only; the general theory is a different course

Common trapThe second postulate is about spacetime, not about light — and the first postulate alone proves nothing about c

Two chronic misreadings. First: "the speed of light is constant" is not a statement about the specialness of light. $c$ is the invariant speed of the spacetime structure — the one speed that transforms into itself — and light travels at it only because photons are massless; were the photon discovered tomorrow to have a tiny mass, light would slow, and relativity, with the same $c$ in its formulas, would not budge. (Gravitational waves already share the same invariant speed to $\sim10^{-15}$ , per GW170817.) Second: the principle of relativity alone does not imply an invariant speed — Galilean kinematics satisfies Postulate I perfectly, with the invariant speed pushed to infinity. The honest logical structure: relativity-plus-homogeneity permits exactly two kinematics, Galileo's ( $c\to\infty$ ) and Lorentz's (finite $c$ ); Postulate II — an experimental input, delivered by electrodynamics — selects the second. Conflate the postulates and every derivation downstream turns circular.

Worked examples

1 · The ether's fringe budget — why Michelson needed an interferometer (confidence builder)

Setup. Estimate the ether-drift signal Michelson and Morley hunted: effective arm length $L=11$ m, orbital speed $v=30$ km/s, wavelength $\lambda=550$ nm. How big is the effect, and what did the null result bound?

Step 1. The timing asymmetry. In an ether wind of speed $v$ , a round trip along the wind takes $t_\parallel=\frac{2L}{c}\frac{1}{1-v^2/c^2}$ , while across it takes $t_\perp=\frac{2L}{c}\frac{1}{\sqrt{1-v^2/c^2}}$ . The difference, to leading order:

\Delta t=t_\parallel-t_\perp\approx\frac{L}{c}\,\frac{v^2}{c^2}.

The signal is second order in $v/c$ : with $v/c=10^{-4}$ , a part in $10^8$ of the transit time — sub-femtosecond timing in 1887, accessible only interferometrically.

Step 2. The fringe count. Rotating the apparatus by $90°$ swaps the arms, doubling the effect; in units of the light's period:

\Delta N=\frac{2c\,\Delta t}{\lambda}=\frac{2L}{\lambda}\frac{v^2}{c^2}=\frac{2(11)}{5.5\times10^{-7}}\times10^{-8}=\mathbf{0.40\ fringes}.

Step 3. The verdict. Their sensitivity was $\sim0.01$ fringe: the predicted signal was forty times their noise floor, and they saw nothing — at any orientation, any time of day, any season (the Earth's orbital velocity reverses over six months, so even a fortuitous cancellation cannot hide the drift year-round). The bound: the ether wind at the surface is $<1/6$ of the guaranteed orbital speed, killable only by ever-more-contrived rescue hypotheses.

Step 4. Read it forward. FitzGerald and Lorentz proposed exactly such a rescue — matter contracts by $\sqrt{1-v^2/c^2}$ along the drift — which saves this experiment while keeping the ether metaphysics. Einstein's postulates make the same formula a kinematic identity for everything, delete the unobservable frame, and predict every subsequent test (Kennedy–Thorndike's unequal arms, modern optical resonators at $10^{-18}$ ). The lesson survives every retelling: a null result is data, and this one weighed a universe's worth of metaphysics.

The lesson: second-order-in- $v/c$ is the ether's hiding depth; interferometry reached it, and nothing was there.

2 · Relativity you can detect — muons and the GPS clock budget (exam level)

Setup. (a) Cosmic-ray muons ( $\tau_0=2.2\ \mu$ s at rest) are created at $\sim10$ km altitude moving at $v=0.994c$ . Can they reach the ground? (b) GPS satellites orbit at $v=3.87$ km/s: compute the special-relativistic clock offset per day. Both are direct tests of the postulates' kinematic theorems.

Step 1. Muons, naive (Galilean) budget: range $=v\tau_0=(0.994)(3.0\times10^8)(2.2\times10^{-6})=\mathbf{656\ m}$ . Created at 10 km, essentially none should survive fifteen decay lengths ( $e^{-15}\sim3\times10^{-7}$ ). Yet sea-level detectors count them in abundance.

Step 2. Muons, relativistic budget. $\gamma=1/\sqrt{1-0.994^2}=9.14$ : the Earth-frame lifetime is $\gamma\tau_0=20.1\ \mu$ s and the range $\gamma v\tau_0\approx\mathbf{6.0\ km}$ — a survival fraction $e^{-10/6}\approx0.19$ from 10 km, matching observation. In the muon's own frame the same books balance differently: its clock runs normally but the atmosphere is contracted by $\gamma$ to $\sim1.1$ km. Two frames, two stories — one count rate. (The magnet-and-conductor moral, wearing kinematic clothes.)

Step 3. GPS. The kinematic (special-relativistic) offset for an orbiting clock:

\frac{\Delta t}{t}=1-\frac1\gamma\approx\frac{v^2}{2c^2}=\frac{(3.87\times10^3)^2}{2(3.0\times10^8)^2}=8.3\times10^{-11} \;\Longrightarrow\; \mathbf{7.2\ \mu s/day\ slow}.

(The full GPS budget adds the gravitational blueshift of $+45.8\ \mu$ s/day — general relativity, outside these postulates — netting $+38.6\ \mu$ s/day, corrected by design in the satellite clocks.)

Step 4. Convert to stakes. Light travels 300 m per microsecond: an uncorrected $7\ \mu$ s/day kinematic error alone would corrupt positions by kilometers within days. Every navigation fix is a daily, planetary-scale confirmation that moving clocks run slow by exactly $\gamma$ — the postulates' arithmetic, deployed as infrastructure.

The lesson: the postulates' consequences are not philosophy; they are count rates and clock corrections, verified continuously by the sky.

Going further

References. Einstein, "Zur Elektrodynamik bewegter Körper," Ann. Phys. 17, 891 (1905) · Griffiths, Introduction to Electrodynamics, 4th ed., §12.1 · Jackson, Classical Electrodynamics, 3rd ed., §11.1–11.2 · Purcell & Morin, Electricity and Magnetism, 3rd ed., Ch. 5 · Zangwill, Modern Electrodynamics, §22.1–22.2

Provenance. Numerical constants ( $c=299\,792\,458$ m/s exact; $\varepsilon_0=8.854\times10^{-12}$ F/m; $\mu_0\approx4\pi\times10^{-7}$ H/m; muon lifetime $2.2\ \mu$ s; GPS kinematic shift $\approx7\ \mu$ s/day) are standard CODATA/textbook values. A verifier should confirm: (1) the wave-equation origin of $c=1/\sqrt{\mu_0\varepsilon_0}$ (recalled from the wave chapter); (2) the Galilean chain-rule transformation of the wave operator and its $c\pm v$ characteristics; (3) the Michelson–Morley fringe estimate $2Lv^2/\lambda c^2$ ; (4) both frames of the rod EMF give $vBL$ . Addendum for this edition: this is the electrodynamics-track treatment — the magnet–conductor asymmetry (Derivation A) and the broken wave equation (Derivation B) are owned here; the kinematic constructions the base carried (light-clock time dilation, train simultaneity, velocity-addition algebra) are owned by the companion mechanics treatment Special Relativity Postulates and the Lorentz Transformation and by Relativistic Kinematics (mechanics track), and are stated here with numbers only; the transformation itself is derived next article, the field-transformation payoff in Transformation of Electric and Magnetic Fields. Worked numbers for this edition (fringe budget 0.40 at $L=11$ m; rod EMF 0.30 V both frames; muon $\gamma=9.14$ , 656 m → 6.0 km; GPS $-7.2\ \mu$ s/day kinematic, $+38.6$ net with GR) recomputed for this edition.

Builds on: Maxwell's Equations in Vacuum · Electromagnetic Wave Equation · Faraday's Law of Induction · Lorentz Force Law Leads to: Lorentz Transformations · Spacetime and Minkowski Geometry · Four-Vectors and the Metric Tensor · Transformation of Electric and Magnetic Fields · Magnetism as a Relativistic Effect

Did Einstein actually know about the Michelson-Morley experiment, and did it matter to him?

He knew of it — he had read Lorentz's 1895 book, which discusses it — but by his own repeated account it was not his driving evidence; in the 1905 paper it appears only obliquely among "unsuccessful attempts to discover any motion of the earth relatively to the 'light medium'." His stated starting points were the magnet–conductor asymmetry and a thought experiment from age sixteen: what would a light wave look like if you rode alongside it? (A frozen wave — something Maxwell's equations do not permit in any frame.) The distinction matters for understanding what kind of theory relativity is: Lorentz and FitzGerald worked backward from the experiment to a rescue mechanism; Einstein worked forward from principles the experiment merely corroborated. That is why his kinematics predicted every later test — Kennedy–Thorndike, Ives–Stilwell, the modern resonator bounds — rather than needing patches for each.

If the ether was undetectable, why was it so hard to give up?

Because every other wave physics knew had a medium, and because the ether was doing real theoretical work. Sound needs air; ocean waves need water; the ether gave light's oscillations a substrate, gave Maxwell's $c$ a referent, and gave the equations a frame in which to be exactly true — perfectly respectable theory-building. What killed it was not one experiment but an accumulating pattern of conspiracy: every effect that should have revealed the ether (drift, drag, contraction-detectable anisotropy) came out null, requiring the medium to be rigid enough to carry transverse waves at $3\times10^8$ m/s yet intangible to planets, dragged by nothing, and equipped with exactly the contraction needed to hide itself. Einstein's move was to recognize a perfectly self-hiding entity as no entity at all — and Postulate I as the honest statement of the conspiracy's pattern. The methodological lesson (unobservable theoretical structure should be excised) became a template: the same razor later trimmed absolute simultaneity itself.

The magnet-frame story uses a magnetic force and the conductor-frame story uses an electric field. Is one of them the "real" mechanism?

Neither — and dissolving that question is precisely the theory's contribution. "Electric field" and "magnetic field" are frame-indexed components of a single object (the field tensor, four articles ahead), the way "north-south extent" and "east-west extent" of a building are compass-indexed components of one shape. Asking whether the current is really driven by $q\mathbf{v}\times\mathbf{B}$ or by an induced $\mathbf{E}$ is asking whether the building is really wide or really deep from no particular direction. What is real: the current (frame-invariant), the EMF around the loop (invariant at this order), the relative motion, and the tensor field. What is bookkeeping: the split of that tensor into $\mathbf{E}$ and $\mathbf{B}$ . This is also why pre-relativistic electrodynamics kept getting right answers — its predictions used only the invariant content; only its explanations were frame-entangled.

Why is the constancy of c not immediately absurd? If I chase a light beam at 0.9c, how can it still recede at c?

Because the quantities you are using to compute "recede at" — your time and your distances — are not what you assumed. The Galilean intuition $u'=u-v$ silently presumes all observers share one time and agree on lengths; drop that (as the postulates force) and closing speed is computed with your rulers and your clocks, which differ from those of a bystander precisely so as to keep the beam at $c$ . Concretely, three effects conspire: your clocks run slow relative to the bystander's ( $\gamma$ ), your rulers are contracted along the motion ( $\gamma$ ), and — the one intuition most stubbornly omits — your notion of "the same instant" at two places is tilted relative to theirs (relativity of simultaneity, the largest effect at first order in $v/c$ ). The velocity-addition law derived next article packages all three; feeding in $u=c$ returns $c$ identically, for any chase speed. The paradox is not resolved by a mechanism slowing the light; it is dissolved by auditing the measuring apparatus.

Are there modern loopholes — could the postulates fail at some scale?

The search is a mature industry with, so far, an unbroken record of nulls. The Standard-Model Extension parameterizes every conceivable Lorentz-violating term field by field; experiments — optical-resonator anisotropy ( $10^{-18}$ ), clock comparisons, astrophysical photon-dispersion limits from gamma-ray bursts (energy-dependent light speed bounded beyond the Planck-scale-motivated level in some channels), muon $g-2$ sidereal analyses, GW170817's one-part-in- $10^{15}$ agreement between light and gravitational-wave speeds — populate its tables with zeros. Theoretical motivations for tiny violations exist (some quantum-gravity scenarios prefer a frame at the Planck scale), which is exactly why the tests continue; but note the postulates' peculiar robustness: local Lorentz invariance is built into quantum field theory's foundations (spin-statistics, CPT) and into general relativity's local structure, so a confirmed violation would not adjust the two 1905 postulates so much as demolish the two frameworks built on them. As experimental verdicts go, a century of nulls at ever-deeper precision is as strong as physics gets.

Where do time dilation and length contraction actually get derived, if this article only states them?

By design, in two designated places — this track keeps the division of labor explicit. The kinematic constructions (the light-clock giving $\Delta t=\gamma\Delta\tau$ ; the rod-measurement protocol giving $L=L_0/\gamma$ ; the simultaneity bookkeeping that reconciles them; the twin accounting) are owned by the mechanics track's relativity articles — Special Relativity Postulates and the Lorentz Transformation and Relativistic Kinematics — which build them straight from the two postulates with light pulses and mirrors. The algebraic route — deriving the unique linear transformation the postulates permit, from which dilation and contraction fall out as one-line corollaries — is the next article here, done in this track's native style: as the symmetry of the electromagnetic wave operator. Numbers from both (the muon and GPS budgets above) were quoted in advance because the experimental record belongs with the postulates; the machinery belongs downstream. If you want the constructions before proceeding, read the mechanics companions now — the two tracks are written to interlock, not to repeat each other.