The Constancy of the Speed of Light

"The speed of light is the same for everybody" is the sentence that carries all of special relativity, and it does far more work than it looks. Unpacked, it is not one claim but three, logically independent: the speed of a light pulse does not depend on the motion of its source, on the frame in which you measure it, or on the direction it travels. Any one could have been false while the other two held, and each has its own experiment and its own modern bound. Electromagnetism and the Failure of Galilean Invariance left the crisis open: Maxwell's equations carry a fixed speed and cannot survive a Galilean boost, and the nineteenth century's escape was to grant them one preferred frame — the ether — and go hunting for the wind. This article does not settle the crisis. It does something more basic: it says precisely what is being claimed when someone says $c$ is constant, and how hard each part has been tested. The answer is: brutally hard, with a punchline that deserves to be quantitative. Turn the modern isotropy limit around and ask how fast an ether wind is still allowed to blow through the laboratory. Rotating optical resonators bound the two-way anisotropy at $|\Delta c/c| \lesssim 10^{-17}$ , and inverting that gives a maximum permitted wind of about one and a third metres per second — a walking pace. Meanwhile the Earth orbits the Sun at $29.8\ \mathrm{km/s}$ , and the whole Solar System tears through the cosmic microwave background at $370\ \mathrm{km/s}$ . Any surviving ether would have to be nailed to the bench to within a stroll, while the bench does 370 kilometres a second.

Key takeaways

" $c$ is constant" is three claims, not one: independent of the SOURCE's motion, independent of the OBSERVER's frame, independent of DIRECTION. They are logically independent, and each is separately tested.
Isotropy is what The Michelson–Morley Experiment bounds. Whether $c$ depends on the laboratory's speed is a different question, and it took Kennedy and Thorndike's unequal-arm interferometer (1932) to ask it. Source-independence needs a moving source — which is why the decisive evidence came from the sky.
The two-way anisotropy an ether wind would produce is second order, $|\Delta c/c| = \beta^2/2$ with $\beta \equiv v/c$ : that is $4.9\times10^{-9}$ for Earth's orbit and $7.6\times10^{-7}$ for the CMB-frame motion, against a measured bound of $\lesssim10^{-18}$ . Invert it: $|\Delta c/c| \lesssim 10^{-17} \Rightarrow \beta \lesssim 4.5\times10^{-9} \Rightarrow v_{\text{ether}} < 1.3\ \mathrm{m/s}$ , and $0.42\ \mathrm{m/s}$ at the sharpest bound. Slower than you walk.
Since 1983 $c$ is defined, exactly $299\,792\,458\ \mathrm{m/s}$ , and the metre is derived from it. You can no longer measure $c$ : an experiment that seems to is measuring the metre.
Key idea: constancy is not one fact but three, each independently established — and the combined verdict is that a preferred frame for light, if it exists at all, must be at rest with respect to your bench to within a metre per second, while that bench does 370 km/s through the universe.

The core insight

Say "the speed of light is constant" and you have made three separate promises: no dependence on the source, no dependence on the observer, no dependence on the direction. None of the three implies the others, so each must be tested on its own — and each has been, to fantastic precision. The isotropy bound is the sharpest, and reading it backwards gives the sentence that ends the ether: the fastest ether wind still consistent with experiment is slower than a walk.

Where this lives today

The isotropy hunt never stopped; it changed apparatus. Michelson's mercury-floated sandstone slab has become a pair of perpendicular optical cavities machined from cryogenic sapphire, held near absolute zero and rotated continuously on an air bearing while their resonant frequencies are compared. Any direction-dependence of $c$ would appear as a beat note locked to the turntable and to the Earth's motion. None ever has — which is how the bound reached $10^{-18}$ , and how the maximum permitted ether wind fell below half a metre per second. The defined $c$ has meanwhile become infrastructure. Every satellite navigation fix is a light-travel time converted to a distance with the exact $c$ ; every optical frequency comb ties length to time through it; and gravitational-wave detectors measure arm-length differences of $10^{-18}\ \mathrm{m}$ by counting the phase of light that, by definition, travels at exactly $299\,792\,458\ \mathrm{m/s}$ .

The physical picture

The claim sounds like a single fact, so it is worth seeing how easily it splits. Imagine a torch bolted to a rocket. Does the light leave faster because the rocket is moving? That is the source question, and a theory in which light is thrown from the lamp like a bullet answers yes. Now fly past that beam yourself. Do you measure it going slower? That is the observer question, and Galilean kinematics answers yes. Finally, fire the beam north instead of east: same speed? That is the isotropy question, and any ether wind answers no.

Figure

The three claims that "c is constant" actually makes, each with the experiment that closes it. They are logically independent — any one could have failed while the other two held.

Now the number that ends the argument. An ether wind of speed $v$ makes the two-way speed of light depend on direction by $|\Delta c/c| = \beta^2/2$ — the second-order result that The Michelson–Morley Experiment owns and that made the 1887 hunt so difficult. Modern rotating cryogenic resonators have pushed the bound on that anisotropy down to $10^{-18}$ . Run the relation backwards and it tells you the fastest ether wind still permitted.

Figure

PUNCHLINE — the two-way anisotropy an ether wind WOULD produce, for the two speeds the laboratory really has, against the anisotropy actually measured. Invert the bound: the fastest ether wind still allowed is 1.3 m/s — a walking pace, while the bench does 370 km/s.

That box is the whole ether question, closed. The medium is not merely undetected: it is required to sit still, to within a stroll, in a laboratory flung through the cosmos at a quarter of a million times that speed. No physical medium behaves like that. What is left is the simpler statement — there is no preferred frame for light, and $c$ is just $c$ .

The core equations

Start with what an ether would do. A laboratory moving at $v$ through a preferred frame would measure a one-way speed varying with the angle $\theta$ to its motion — a first-order effect, and by optical standards an enormous one. Ether Drift and the Absolute Rest Frame derives it, and shows why it is out of reach: a one-way speed needs clocks already synchronised at both ends of the path, and synchronising them needs the one-way speed of light.

c_{\text{one-way}}(\theta) \approx c - v\cos\theta, \qquad \frac{|\Delta c|}{c} \sim \beta = 9.94\times10^{-5} \qquad (1)

where: $\theta$ — angle between the light's direction and the laboratory's motion; $\beta \equiv v/c$ , here Earth's orbital $29.8\ \mathrm{km/s}$ . Physical reading: one part in ten thousand, and first order — which sounds easy, and is in fact unmeasurable without a prior convention about simultaneity (The Conventionality of Simultaneity). Send the light out and bring it back and the first-order terms cancel: you lose fighting the wind exactly as much as you gain running with it, to leading order. The Michelson–Morley Experiment owns the result — its arms give two-way speeds $c_\parallel = c(1-\beta^2)$ and $c_\perp = c\sqrt{1-\beta^2}$ — and what survives is second order.

\frac{|\Delta c|}{c}\bigg|_{\text{two-way}} = \frac{c_\perp - c_\parallel}{c} = \frac{\beta^{2}}{2} + O(\beta^{4}) \qquad (2)

where: $c_\parallel, c_\perp$ — two-way speeds along and across the motion. Physical reading: this is the only anisotropy a closed-path experiment can see, and it is the square of the one-way effect. Earth's orbit gives $4.9\times10^{-9}$ ; the Solar System's $370\ \mathrm{km/s}$ motion against the cosmic microwave background gives $7.6\times10^{-7}$ . Equation (2) runs backwards, and that is the point: a measured upper bound on the anisotropy becomes an upper bound on the laboratory's speed through any preferred frame — through a square root, generous to the experiment and merciless to the ether.

v_{\text{max}} = c\sqrt{2\left|\frac{\Delta c}{c}\right|_{\text{max}}} \qquad (3)

where: $v_{\text{max}}$ — the fastest ether wind still consistent with the data. Physical reading: at the resonator bound $10^{-17}$ this is $1.3\ \mathrm{m/s}$ ; at the sharpest published bound, $10^{-18}$ , it is $0.42\ \mathrm{m/s}$ . Both are slower than a person walking, and both are absurd for a medium that the Earth is supposed to be ploughing through at $29.8\ \mathrm{km/s}$ .

What constancy actually asserts

Derivation AWhat constancy claims, and how fast an ether is still allowed to blow

It is tempting to think Michelson and Morley settled the whole question in 1887, and that everything since has been decoration. They did not. This card does two things: it proves — rather than asserts — that "the speed of light is constant" splits into claims which can fail separately, so that a null result in one leaves the others wide open; and it then takes the sharpest of those claims and squeezes it for a single number, the fastest ether wind experiment still permits.

Step 1. Write the most general small deviation. Let a laboratory move at speed $V$ through some hypothetical preferred frame, and let the two-way speed it measures at angle $\theta$ to that motion be $c(\theta, V) = c_0(1 + aB^2 + bB^2\cos^2\theta)$ , with $B \equiv V/c_0$ . Why this form: a two-way speed must be even in $V$ (reversing the wind cannot change a there-and-back time) and even in $\cos\theta$ (a round trip does not care which end you start from). Relativity is $a = b = 0$ .

Step 2. Ask what Michelson–Morley measures. It compares perpendicular arms and rotates, so its observable is $c(0,V) - c(\pi/2,V) = c_0\,b\,B^2$ . It contains $b$ and nothing else. Why: rotation changes $\theta$ and nothing else, so an experiment built on rotation is blind by construction to any effect that is the same in every direction.

Step 3. Now set $b = 0$ and keep $a \neq 0$ : a speed of light that depends on the laboratory's speed but not on direction. The orientation average is $\langle c\rangle_\theta = c_0(1 + aB^2 + \tfrac12 bB^2)$ , so the Michelson–Morley signal vanishes exactly while $\langle c\rangle_\theta$ still varies with $V$ . Such a universe passes 1887 perfectly and is still not relativity. Isotropy does not imply frame-independence — which is why Kennedy and Thorndike (1932) built an interferometer with deliberately unequal arms, whose fringes depend on the round-trip time itself and therefore bound $a$ . Why unequal arms: with equal arms the round-trip time cancels out of the fringe pattern, and the instrument can only report the difference between directions — which is $b$ .

Step 4. Notice what is nowhere in $c(\theta,V)$ : the velocity of the source — in both experiments the lamp is bolted to the bench. Source-independence is a third, separate claim, and testing it demands a source in violent motion: a star in a binary orbit, or a pion decaying in flight. Why it matters: that is why the decisive evidence came from astronomy and particle physics rather than an optics bench (Emission Theories and Their Refutation).

Step 5. Now the ledger, and the squeeze. The one-way anisotropy an ether would produce is first order, $\beta = 9.94\times10^{-5}$ for Earth's orbit — but unreachable, since timing a one-way trip needs two clocks that already agree. The two-way anisotropy is second order: The Michelson–Morley Experiment owns the result $c_\parallel = c(1-\beta^2)$ , $c_\perp = c\sqrt{1-\beta^2}$ , so $|\Delta c/c| = \beta^2/2 = 4.9\times10^{-9}$ . Invert it: $v_{\text{max}} = c\sqrt{2\,|\Delta c/c|_{\text{max}}}$ . Why the square root is worth noticing: it is generous to the experimenter — a hundredfold better bound buys only a tenfold tighter speed limit — and the limits it yields are still absurd.

Step 6. Put the numbers in. At the resonator bound $10^{-17}$ : $\beta \lesssim 4.5\times10^{-9}$ , so $v_{\text{max}} = \mathbf{1.3\ m/s}$ . At the sharpest bound, $10^{-18}$ : $\mathbf{0.42\ m/s}$ . Against that, Earth's orbit is $29.8\ \mathrm{km/s}$ — $2.2\times10^{4}$ times faster — and the Solar System's motion against the cosmic microwave background is $370\ \mathrm{km/s}$ , or $2.8\times10^{5}$ times. Why this ends the ether rather than merely embarrassing it: a medium filling space would have to co-move with a bench doing $370\ \mathrm{km/s}$ , to within a walking pace, while the Earth spins and orbits and swings it through every direction in the sky. The preferred frame is not hiding. It is absent. *Verified in verify_aq-sr-constancy-speed-of-light.py: the Michelson–Morley observable reduces to $c_0bB^2$ and the orientation average to $c_0(1 + aB^2 + bB^2/2)$ , so with $b = 0$ the first is identically zero while the second still varies with $B$ ; the series $(c_\perp - c_\parallel)/c = \beta^2/2 - \beta^4/8 + \cdots$ has no linear term; and the inversions give $1.34\ \mathrm{m/s}$ and $0.424\ \mathrm{m/s}$ , with ratios $2.2\times10^{4}$ and $2.8\times10^{5}$ .*

Go deeper · Derivation B · 2 minWhy you can no longer measure the speed of light

Derivation BWhy you can no longer measure the speed of light

One fact quietly changes what all of the above means, and most popular accounts get it wrong. Since 1983 the speed of light is not a measured quantity but a defined one — exactly $299\,792\,458\ \mathrm{m/s}$ — and the metre is built out of it. This card follows what that does to the logic, including why an experiment that appears to measure $c$ is now measuring something else.

Step 1. State the definition. The metre is the distance light travels in vacuum in $1/299\,792\,458$ of a second; the second is defined independently, by the caesium hyperfine transition. Why that ordering: time is by far the best-measured quantity in physics, so the SI fixes the second, fixes $c$ by decree, and lets length be derived — trading a hard length measurement for an easy time measurement.

Step 2. Draw the consequence. Time a light pulse over a "known" length, and that length was itself realised by timing light: your experiment returns $299\,792\,458\ \mathrm{m/s}$ by construction. Why this is not viciously circular: the experiment still does real work — it calibrates your metre, and tests whether light in your apparatus behaves as the definition assumes. It simply is not measuring $c$ .

Step 3. Check the closure this forces on electromagnetism. Maxwell's Equations in Vacuum gives $c = 1/\sqrt{\mu_0\varepsilon_0}$ , so fixing $c$ ties the two constants together: $\mu_0\varepsilon_0c^2 = 1$ . With current values $\mu_0\varepsilon_0c^2 - 1 = -4.4\times10^{-14}$ — zero, to the precision the constants are known. Why not exactly zero on the page: since the 2019 SI revision $\mu_0$ is itself measured, tied to the fine-structure constant, so the closure now holds to experimental accuracy. Before 2019, $\mu_0$ was exact and so was the identity.

Step 4. Note what has not been defined away — and what genuinely remains conventional. Fixing $c$ is a choice of units: it cannot make an ether wind vanish, and a rotating resonator would still register a beat note if the two-way speed depended on orientation. But every experiment quoted here is a two-way measurement, and the one-way speed cannot be measured without first stipulating how to synchronise two separated clocks — a stipulation no experiment forces. Why to flag it rather than bury it: readers usually meet "the one-way speed of light is unmeasurable" as a debunking of relativity. It is not. It is a statement about coordinates, and The Conventionality of Simultaneity owns it. *Verified numerically in verify_aq-sr-constancy-speed-of-light.py: the SI closure $\mu_0\varepsilon_0c^2 - 1 = -4.4\times10^{-14}$ ; $1/\sqrt{\mu_0\varepsilon_0} = 2.99792\times10^{8}\ \mathrm{m/s}$ , matching the exact SI $c$ to two parts in $10^{14}$ ; and Michelson's 1926 Mt Wilson value, high by $1.2\times10^{-5}$ .*

Limiting cases

Case	Result	Meaning
Galilean limit $c \to \infty$	$\beta \to 0$ , anisotropy $\to 0$	with infinitely fast light there is no wind to find, and no constancy to assert; the whole question probes the finiteness of $c$
One-way vs two-way	$\beta$ vs $\beta^2/2$ — a factor $2/\beta = 2\times10^{4}$	the huge effect is unmeasurable; the tiny one is what every experiment actually reports
Light in a medium, index $n$	phase speed $c/n$ ; water gives $2.25\times10^{8}\ \mathrm{m/s}$	constancy is a claim about the vacuum speed only. Particles routinely outrun light in a medium — that is Cherenkov radiation

Worked examples

1 · How fast is the ether still allowed to blow?

The best rotating optical resonators bound the two-way anisotropy of the speed of light at $|\Delta c/c| \lesssim 10^{-17}$ . Turn that into a speed limit on the laboratory's motion through any preferred frame, and compare it with the speeds the laboratory is known to have.

Step 1. Take the relation an ether wind implies, $|\Delta c/c| = \beta^2/2$ , and invert it: $\beta = \sqrt{2\,|\Delta c/c|} = \sqrt{2\times10^{-17}} = 4.5\times10^{-9}$ .

Step 2. Convert to a speed: $v_{\text{max}} = \beta c = 4.5\times10^{-9} \times 2.998\times10^{8}\ \mathrm{m/s} = \mathbf{1.3\ m/s}$ . At the sharpest published bound, $|\Delta c/c| \lesssim 10^{-18}$ , the same arithmetic gives $\mathbf{0.42\ m/s}$ .

Step 3. Now the comparison, which is where the argument stops being technical. The Earth orbits the Sun at $29.8\ \mathrm{km/s}$ — that is $\mathbf{2.2\times10^{4}}$ times the fastest wind still allowed. And the CMB dipole shows the whole Solar System moving at $370\ \mathrm{km/s}$ with respect to the microwave background — $\mathbf{2.8\times10^{5}}$ times faster.

Step 4. Read it as a sentence. For an ether to survive, it must co-move with your optical bench to better than a walking pace — while that bench is carried through the universe at $370\ \mathrm{km/s}$ , and while the Earth spins and orbits and drags it through every direction in the sky over a year. This is not a medium that is hard to detect. It is a medium that does not exist.

2 · Light as a conversion factor

Because $c$ is now exact, it is no longer a measurement — it is a unit conversion between time and distance. Learning the conversion in your bones is the most useful practical consequence of this entire article.

Step 1. The engineer's constant. In one nanosecond light travels $c \times 10^{-9}\ \mathrm{s} = \mathbf{29.98\ cm}$ — very nearly a foot. Grace Hopper famously handed out wires cut to exactly this length, so that programmers would stop wondering why signals take time to cross a circuit board. Inverted: one metre of vacuum costs $\mathbf{3.336\ ns}$ of delay, which is why a signal crossing a $30\ \mathrm{cm}$ board cannot arrive sooner than a nanosecond after it left.

Step 2. Scale it up. The Moon is $3.844\times10^{8}\ \mathrm{m}$ away — $\mathbf{1.282\ light-seconds}$ . A laser pulse fired at the Apollo retroreflectors returns after $\mathbf{2.564\ s}$ , and that round trip, timed by a single clock, is precisely how the distance is known.

Step 3. Notice what Step 2 quietly demonstrates. The Moon's distance is a two-way measurement, so it is convention-free, and no synchronised pair of clocks appears anywhere in it. That is why the 1983 SI could safely build the metre out of exactly this procedure: every clean length in modern metrology is a round-trip light time. No coincidence — it is the deepest practical consequence of constancy.

Physics of the portrait

The speed of light is the only quantity in physics that has been, in turn, believed infinite, measured astronomically, measured terrestrially, elevated to a postulate, and finally defined — each step a demotion of its status as a fact about the world and a promotion of its status as a piece of the world's architecture.

Origins · 2 minSpeed of Light and how this was discovered

Speed of Light

1676–1983 · from Rømer's eclipses to the defined metre

For most of the history of physics the speed of light was a number to be found. Descartes argued it was infinite; Galileo tried and failed to catch it with lanterns on hilltops. In 1676 Ole Rømer, working on the eclipses of Jupiter's moon Io, showed it was finite: the eclipses ran late when Earth was far from Jupiter and early when it was near, the discrepancy being the extra light-travel time. Rømer gave a time, not a speed — light takes some twenty-odd minutes to cross the diameter of Earth's orbit — and it was Christiaan Huygens who turned it into a number, in the Traité de la Lumière. The distinction is worth preserving: the credit is routinely misassigned. Then the value was ground down: Bradley's aberration (1728), Fizeau's toothed wheel (1849), Foucault's rotating mirror (1862), and Michelson's decades of ever-finer work, ending at Mount Wilson in 1926 with $299\,796\ \mathrm{km/s}$ — high by twelve parts in a million. In 1905 Einstein changed the kind of thing $c$ is, promoting its constancy from a measured regularity to a postulate of special relativity. In 1983 the transformation completed: the metre was redefined from $c$ , which became exact by definition. Three centuries of measurement ended not in a final digit but in a decision. The speed of light is now the exchange rate between time and space, and the thing we measure instead is the metre.

History

1676

— Rømer, from the eclipses of Io, shows that light takes time to cross space; he reports a light-crossing time, not a speed.

1690

— Huygens, in the Traité de la Lumière, converts Rømer's timing into an actual value for the speed.

1849

— Fizeau times light over a terrestrial baseline with a toothed wheel: 3.15 × 10⁸ m/s.

1862

— Foucault's rotating mirror: 2.98 × 10⁸ m/s.

1887

— Michelson and Morley find no orientation-dependence of the two-way speed.

1905

— Einstein elevates the constancy of c from a measured regularity to a postulate.

1926

— Michelson, at Mount Wilson, measures 299 796 km/s — high by 1.2 × 10⁻⁵.

1932

— Kennedy and Thorndike test whether c depends on the laboratory's velocity, not merely its orientation.

1983

— the metre is redefined from c, which becomes exactly 299 792 458 m/s. The speed of light stops being measurable.

Going further

Texts. Taylor & Wheeler, Spacetime Physics, 2nd ed., Ch. 1 · Rindler, Introduction to Special Relativity, 2nd ed., §1 · Mansouri & Sexl, Gen. Rel. Grav. 8 (1977) 497 · Kennedy & Thorndike, Phys. Rev. 42 (1932) 400.

Provenance. The three-claim decomposition and the toy law $c(\theta,V) = c_0(1 + aB^2 + bB^2\cos^2\theta)$ follow the standard Robertson / Mansouri–Sexl test-theory framing; the proof that Michelson–Morley bounds only $b$ while Kennedy–Thorndike bounds $a$ is carried out symbolically here. The relation $|\Delta c/c| = \beta^2/2$ is recalled from The Michelson–Morley Experiment, not re-derived. Every number is recomputed in verify_aq-sr-constancy-speed-of-light.py from the band anchors $c = 2.998\times10^{8}\ \mathrm{m/s}$ (exact SI $299\,792\,458$ ), $\varepsilon_0 = 8.8541878128\times10^{-12}$ , $\mu_0 = 1.25663706212\times10^{-6}$ , $v_\oplus = 29.8\ \mathrm{km/s}$ , $v_{\text{CMB}} = 370\ \mathrm{km/s}$ , Earth–Moon $3.844\times10^{8}\ \mathrm{m}$ . Two corrections to the source brief are logged in the verifier's footer: Michelson–Morley is the isotropy test, not the frame test (that is Kennedy–Thorndike, 1932); and the ether-wind bound must be inverted from $|\Delta c/c| = \beta^2/2$ , giving $1.3$ and $0.42\ \mathrm{m/s}$ , not $0.95$ and $0.30$ .

Builds on. Electromagnetism and the Failure of Galilean Invariance · The Michelson–Morley Experiment · Ether Drift and the Absolute Rest Frame · The Principle of Relativity. Leads to. Einstein's Two Postulates · Emission Theories and Their Refutation · The Conventionality of Simultaneity.

If c is defined, isn't its constancy true by definition — and therefore empty?

No, and this is the most common confusion in the subject. Fixing $c$ is a choice of units: it says how many metres are in a light-second. It says nothing about whether light goes at the same speed in every direction, or for every observer, or from every source. Those remain hard empirical questions, and a rotating resonator would still register a beat note if the two-way speed depended on orientation. What 1983 changed is which quantity absorbs the experimental error: it used to be $c$ , and now it is the metre. The physics of constancy is untouched.

Doesn't the "one-way speed of light is unmeasurable" argument destroy all of this?

It does not, though it is a genuine and subtle point. Every result quoted here is a two-way measurement — light out and back, timed by a single clock, no synchronisation needed. Two-way speeds are convention-free and thoroughly measured. The one-way speed is different: to time a one-way trip you must first agree what "at the same time" means at two separated places, and that agreement is a stipulation, not a discovery. The isotropy of the one-way speed is therefore partly conventional — a claim about coordinates, not a crack in relativity. The Conventionality of Simultaneity does that argument properly.

Michelson and Morley found nothing in 1887. Why did anyone need Kennedy and Thorndike?

Because rotating an apparatus can only tell you whether $c$ depends on direction. Suppose light were slower in every direction alike whenever the laboratory moved faster — perfectly isotropic, but frame-dependent. Michelson and Morley's equal-arm instrument would report exactly zero, forever, and the theory would still be wrong. Kennedy and Thorndike's fix was to make the arms deliberately unequal, so the fringe pattern depends on the round-trip time itself rather than only on the difference between two arms, and then to watch it as the Earth's velocity swung through the year. The two experiments together bound both parameters; neither does alone.

Where does the 370 km/s figure come from, and doesn't it re-establish a preferred frame?

It comes from the dipole anisotropy of the cosmic microwave background: the microwave sky is measurably hotter in one direction and cooler in the opposite, exactly as a Doppler shift would make it if we were moving at about $370\ \mathrm{km/s}$ relative to the frame in which the radiation is isotropic. That frame is real and useful — but it is picked out by matter and radiation, not by the laws. Light still travels at $c$ in every direction in every inertial frame, and no local experiment detects our motion with respect to the CMB. A cosmic rest frame is not an ether: the ether was supposed to change the physics, and this does not.

Rømer measured the speed of light in 1676 — why does the history here say he did not?

Because what Rømer reported was a time, not a speed: light takes roughly twenty-two minutes to cross the diameter of Earth's orbit, deduced from the eclipses of Io running late when Earth is far from Jupiter. Turning that into metres per second needs the size of Earth's orbit, poorly known in 1676, and Rømer did not take that step in print. Christiaan Huygens did, in the Traité de la Lumière. Rømer's achievement is the greater one — he established that the speed is finite, against Descartes — and it deserves to be stated accurately rather than inflated.

Nothing can travel faster than light — is that the same claim as constancy?

No, and keeping them apart matters. Constancy is the claim that light's vacuum speed is the same for every inertial observer, in every direction, from every source. That $c$ is also a universal speed limit is a consequence, drawn later from the structure the postulates force on spacetime — it is not part of the postulate, and Einstein's Two Postulates is careful not to assume it. The distinction is not pedantry: it is why relativity forbids accelerating a massive body through $c$ while cheerfully permitting shadows, phase velocities, and the apparent motion of astrophysical jets to exceed it.