Cosmology That ClicksBonus 2 · what measuring is, at its root

Episode 1's "the speed of light can't be measured," now from the side of history — why did humanity "fix" it?

Why We "Fixed"
the Speed of Light In 1983, humanity declared the speed of light's value "settled." Never to be re-measured.
That was not progress but, in a sense, "giving up" — because there was no longer anything to compare it against.

Tools you'll need: division, and just the idea of "comparing" speed = distance ÷ time

In Episode 1 we said "even if light slows, you can't measure it, because the ruler itself is defined by the speed of light." This time, the flip side — why did we make the speed of light the definition of the ruler in the first place? This is actually the story of the moment humanity decided "we'll stop measuring the speed of light independently." It's told as a pinnacle of progress, but seen another way, it's a slightly poignant situation: with no standard left to compare against, there was no choice but to fix it. A bonus episode about the root of what it means to measure.

01"Measuring" is always "comparing"

Speed is \(\text{distance}\div\text{time}\). To measure the speed of light, measure the time light takes to travel some distance. What matters here — measuring distance needs a "length standard" (a ruler), and measuring time needs a "time standard" (a clock). Measurement is always the act of comparing against some other standard.

What measurement really is

To "measure" the speed of light \(c = \dfrac{\text{distance}}{\text{time}}\) = to compare it against two "rulers," a length standard and a time standard. With no standard, you can't produce a number at all.

So the value of the speed of light has always been determined relative to a "length standard" and a "time standard." Change the standard and the number changes. Here lies the seed of this episode.

02The standard gradually moves toward light itself

Line up the history of the "length standard" humanity has used, and you notice something: the standard steadily moves toward the properties of light itself.

~1799Based on the size of the Earth. One meter defined as "one ten-millionth of the distance from the North Pole to the equator."

1889Based on a platinum-iridium metal bar (the prototype meter). "The length of this bar is one meter." Kept as a physical object.

1960Based on the wavelength of light emitted by the krypton-86 atom. "1,650,763.73 wavelengths of that light make one meter." The standard became "the wavelength of light."

1983At last, based on the speed of light itself. "The distance light travels in 1/299792458 of a second is one meter." The length standard became "the speed of light."

Metal bar → wavelength of light → speed of light. The length standard steadily drew toward light. The reason is simple: light is far more precise than a metal bar and reproducible identically anywhere in the world. A metal bar expands and contracts with temperature, and can be stolen or scratched. The properties of light are the same everywhere in the universe — so it's believed.

Why "time" took the lead role The deciding factor was that time can be measured most precisely. Atomic clocks are orders of magnitude more accurate than length rulers (better than 10-digit precision with cesium atoms). So making length from "accurate time × speed of light" is more precise than measuring length directly. The 1983 definition, you might say, put length "piggyback" on the most accurate time standard.

031983 — there was no longer anything to compare against

In the 1970s, measurements of the speed of light grew ever more precise, until the precision hit a ceiling set by "the precision of the length standard itself (krypton's wavelength of light)." That is, try to measure the speed of light more accurately and the thing you compare against, the "length ruler," is too blurry to allow it. You can't measure anything finer than the ruler's own markings.

Here humanity faced a choice. There were two roads —

Two roads

Road A: keep the speed of light a "measured quantity"

Keep a separate length standard and measure the speed of light against it. But — capped by the standard's precision. No further progress.

Road B: make the speed of light the "standard"

Define the speed of light's value as "settled (299792458 m/s)," and instead build length from the speed of light. This way, the precision of time becomes the precision of length, and the ceiling disappears.

Road B was chosen. In 1983, the speed of light became "no longer a measured quantity, but a decided value." The value 299792458 was chosen to match the best measurement up to then — so nothing physical changed; the roles swapped. The speed of light, which had been "the measured," moved to "the measurer (the standard)."

The heart of this episode — fixing is also "giving up"

The speed of light was fixed because there was no longer "another ruler" more precise than, and independent of, the speed of light. With something to compare against, "measuring" could have continued. With nothing left, there was no choice but to "declare this the standard" — put positively, a bold decision; put honestly, a choice one "had no choice but to fix," forced by the disappearance of anything to compare against.

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04So "the speed of light doesn't change" is half a "convention"

Here's the conclusion that links back to Episode 1. "The speed of light doesn't change" is often said. But since 1983, part of that is a "convention" rather than a law of physics. The speed of light staying at \(299792458\) is not because the universe behaves that way, but because we decided it "doesn't move" and build length to match. Since the ruler is made from the speed of light, measuring the speed of light with the ruler always comes out exactly \(299792458\) — this is not a discovery but a consequence of the definition.

So how can physics ask "has the speed of light changed"? As we saw in Episodes 2 and 6 — the only way is to look at the unit-free ratio, the fine-structure constant \(\alpha\). Because \(\alpha\) is a pure number depending on no ruler, you can still ask "did it really change" even with the standard fixed. What humanity let go of in 1983 was "measuring \(c\)," not "measuring \(\alpha\)." A quantity that lost anything to compare against (\(c\)) can only be fixed; only a quantity that needs nothing to compare against (\(\alpha\)) can go on being measured.

Linking voice (the series' backbone) Episode 1 ("\(c\) can't be measured even if it slows"), Episode 2 ("only the unit-free \(\alpha\) can be measured"), Episode 6 ("even \(\alpha\) runs with how finely you look") — this episode is the foundation of all of them. Quantities with units (\(c\), lengths, energies) have values set by the standard you compare against, and fixing the standard turns them into a "definition." Only the unit-free ratio (\(\alpha\)) is independent of the standard and can ask about the universe itself. Absolute values can't be measured; only ratios can — 1983 was the historical case study of what this series has said all along.

The honest line (kept light)

Saying "fixing is a convention" doesn't mean it was decided carelessly. The value \(299792458\) was chosen to match the best prior measurement precisely, preserving continuity of units. Also, the physical content "the speed of light is invariant, independent of standards" (special relativity's claim that the vacuum speed of light is the same for every observer) continues to be verified by experiment, separately from the definition. This episode is about the single point that "the numerical value \(299792458\) is a definition," not that relativity itself is a convention.

Wrap-upA number that loses anything to compare against becomes a standard

To measure is to compare. For a long time the speed of light was measured by comparing against standards of length and time. The standard steadily drew toward light itself, and by the 1970s hit a ceiling: "the precision of the speed of light = the precision of the length standard." The thing to compare against caught up to the speed of light and could no longer overtake it. So in 1983, humanity moved the speed of light from "measured quantity" to "standard" — had no choice but to fix it.

Ever since, "the speed of light is invariant at \(299792458\)" has been half physics, half convention. The window to ask whether the universe has really changed remains only in the unit-free ratio \(\alpha\). An absolute value, with nothing to compare against, can only be fixed. What can go on being measured is only the ratio — this was the deepest root of the series' backbone.

This is Bonus 2 of "Cosmology That Clicks," a reading piece for curious high-schoolers and undergraduates. The history of the meter's definition (the ~1799 Earth basis, the 1889 prototype meter, the 1960 krypton-86 wavelength, the 1983 speed-of-light definition), and the fact that in 1983 (the 17th CGPM) the speed of light was fixed at 299792458 m/s, moving from a "measured quantity" to a "defining constant," are historical facts. The value was chosen to match the best measurement of the time, preserving continuity of units. The invariance of the speed of light in special relativity continues to be verified experimentally, independently of the definition. — To print, use your browser's Print → Save as PDF.