Certificates of authenticity had been engraved on heavy Japanese paper by the Parisian society printer Stern. Each of these certificates had a formulaic rubric that gave the properties of the body it accompanied: platinum-iridium cylinder No. 39, for example, had the notation “46.402mL 1kg -0.118mg,” which is decoded as meaning the cylinder had a volume of 46.402 milliliters and was lighter than 1 kilogram by 0.118 milligrams. Certificates for the meters were a little more complicated: for instance, one of the meter bars was noted as being “1m + 6μ.0 + 8μ.664T + 0μ.00100T2,” which meant that at 0 degrees Celsius it was 6 micrometers longer than 1 meter, and at a 1 degree Celsius its length would be greater by a little more than 8.665 micrometers.
Three urns stood on a dais in the room, and officials had put into each paper slips bearing the numbers of the remaining standards—they were to be distributed among the member states by lottery. And so, in midafternoon of that warm autumn Saturday, the world lined up as if bidding for the distribution of sporting season tickets. Officials called out the countries’ names, in alphabetical order, in French. Allemagne was first, Suisse last. The draw took an hour. When it was all over the United States had received Kilograms 4 and 20, and Meters 21 and 27.* Britain had acquired Meter 16 and Kilogram 18; Japan (which by this time had signed the 1875 treaty),† Meter 22 and Kilogram 6.
By the end of the day, so the delegates set off from Paris with their invaluable bounties—all packed away in boxes (the kilograms removed from their cloches for travel), and with all the bills paid. They were not insubstantial: the cost of a platinum-iridium meter was 10,151 francs; the kilogram a comparative steal at 3,105 francs. Within days or weeks (the Japanese took theirs back by ship) the new standards were safely in the metrology institutes that were by now being established in capitals all around the world. They were all kept safe and sound—though none so safe and sound as the International Prototypes, M and K, which were now to be taken to the basement and plunged into sempiternal darkness, incomparable, accurate, and fantastically precise. In safes nearby were six so-called témoins—witness bars, which would be regularly compared against the masters. These too would remain exact and perpetually inviolate.
Except, not exactly. Not so fast. The overseers of metrology’s fundamentals had been charged with the task of eternal vigilance, of always looking for still better standards than these. And in time they did indeed find one.
THE FIRST CLUES that there might be a better system had come some years before, in 1870, long before these platinum talismans were being wrought into their final definitive shapes and sizes. The Scots physicist James Clerk Maxwell, at the British Association for the Advancement of Science annual meeting in Liverpool, had made a speech that threw a wrench into everything that had been done. His words still ring in the ears of metrologists around the world. He reminded his listeners that modern measuring had begun with the survey and then the resurvey of the French meridian, and the derivation of the metric units from the results:
Yet, after all, the dimensions of our Earth and its time of rotation, though, relatively to our present means of comparison, [are] very permanent, [they] are not so by physical necessity. The Earth might contract by cooling, or it might be enlarged by a layer of meteorites falling on it, or its rate of revolution might slowly slacken, and yet it would continue to be as much a planet as before. But a molecule, say, of hydrogen, if either its mass or its time of vibration were to be altered in the least, would no longer be a molecule of hydrogen.
If, then, we wish to obtain standards of length, time and mass which shall be absolutely permanent, we must seek them not in the dimensions, or the motion, or the mass of our planet, but in the wavelength, the period of vibration, and the absolute mass of these imperishable and unalterable and perfectly similar molecules.
What Maxwell had done was challenge the scientific basis for all systems of measurement up to that moment. It had long been self-evident that a system based on the dimensions of the human body—thumbs, arms, stride, and so forth—was essentially unreliable, subjective, variable, and useless. Now Maxwell was suggesting that standards previously assumed reliable, like fractions of a quadrant of the Earth’s meridian, or the swing of a pendulum or the length of a day, were not necessarily usefully constant either. The only true constants in nature, he declared, were to be found on a fundamental, atomic level.
And by this time scientific progress was providing windows into that atom, revealing structures and properties hitherto undreamed of. These very structures and properties that were by their very nature truly and eternally unvarying, Maxwell was saying, should next be employed as standards against which all else should be measured. To do otherwise was simply illogical. Fundamental nature possessed the finest standards—the only standards, in fact—so why not employ them?
It was the wavelength of light that was the atomic fundamental first used to try to define the standard measure of length, the meter. Light, after all, is a visible form of radiation caused by the excitation of atoms—excitation that causes their electrons to jump down from one energy state to another. Different atoms produce light ranging over different spectrums, with different wavelengths and colors, and so produce different and identifiable lines on a spectrometer.
It took a further hundred years to convince the international community of the wisdom of linking length to light and its wavelength. To the graybeards who then ran the world, abandoning the certitudes of Earth for the behavior of light was akin to believing that the continents could move—a simply preposterous idea. But just as in 1965, when the theory of plate tectonics was first advanced and continental drift was suddenly seen as obvious, a reality hidden in plain sight, so it became as much the same in metrology as it had been for geology: the notion of using atoms and the wavelength of the light they can emit as a standard for measuring everything snapped into place in a sudden moment of rational realization.
It was a late nineteenth-century Massachusetts genius named Charles Sanders Peirce who had that first moment, who first tied the two together. Few men of his generation can have been more brilliant—or more infuriatingly, insanely troublesome. He was many things—a mathematician, a philosopher, a surveyor, a logician, a philanderer of heroic proportions, and a man crippled with pain (a facial nerve problem), with mental illnesses (severe bipolar disorder most probably), and with a profound inability to keep his temper in check. On the plus side of the ledger: he could stand before a blackboard and write a mathematical theory on it with his right hand on the right side and, simultaneously, write its solution with his left hand on the left. On the minus side: he was once sued by his cook for hitting her with a brick. He drank. He took laudanum. He was much married, and was pathologically unfaithful.
But it was Peirce who in 1877 first took a pure and brilliant source of incandescent yellow sodium light, and tried as hard as he might to measure—in meters, thereby establishing the dimensional link between light and length—the black spectral line it produced when run through a diffraction grating, a kind of high-precision prism. It was one of the numberless misfortunes of his seventy-five years that this experiment never quite succeeded—there were problems with the expansion of the glass of the grating, problems with the thermometers used to measure the temperature of the glass. But he nevertheless published a short paper in the American Journal of Science, and by doing so laid historical claim to being the first to try. Had he succeeded his name would be on the lips of all. As it was he died obscurely in 1914, and in abject poverty, having to beg stale bread from the local bakery. He is long forgotten, except by a very few who agree with such as Bertrand Russell, who called Peirce “the greatest American thinker, ever.”
By 1927, after much badgering by scientists who were convinced by Maxwell’s argument that this was the best approach to setting an inviolable standard, so the world’s weights and measures community came, if somewhat grumpily, to an agreement. They first accepted, formally, that one particular element’s wavelength had thus been calculat
ed, and in fractions of a meter—a very small number. Further, they then agreed that by multiplication, the meter could be defined as a certain number of those wavelengths—by comparison a very big number, and to at least seven decimal places. Multiply the one by the other and one gets, essentially, one meter.
The element in question was cadmium—a bluish, silvery, and quite poisonous zinc-like metal that was used for a while (with nickel) in batteries and to corrosion-proof steel and now is used to make (with tellurium) solar panels. It emits a very pure red light when heated, and from its spectral line the wavelength could be determined—so accurately that the International Astronomical Union used its wavelength to define a new and very tiny unit of length, the Ångstrom—one ten-billionth of a meter, 10−10m.
The wavelength of cadmium’s red line was measured and defined as 6,438.46963 Ångstroms. Twenty years later, with the weights and measures officials in Paris now accepting both the principle and the choice of cadmium (although making its red-line wavelength slightly fuzzier by losing the final number 3, rendering it as 6,438.4696Å), the meter could have been very easily defined by simple arithmetic as 1,553,164 of those wavelengths. (Multiplying the first figure by the second gives 1.000, essentially.)
But—and in the tortuous history of the meter, this is hardly surprising—cadmium then turned out to be not quite good enough. Its spectral line, when examined closely, was found not to be as fine and pure as had been thought—the samples of cadmium were probably mixtures of different isotopes of the metal, spoiling the hoped-for coherence of the emitted light. And so it happens that the meter never was formally defined in terms of cadmium. Much else was, but not the sacrosanct meter. The platinum-iridium bar clung on gamely through all the various meetings of the weights and measures committees, surviving all the siren-like temptations of other radiations—until finally, in 1960, there came agreement.
The world settled on krypton. This inert gas, which was only discovered in trace amounts in the air in 1898, is perhaps best known as the most commonly used gas in neon signs, which are seldom filled with neon at all. More important, in this long quest to define the meter in terms of wavelength, krypton has a spectral signature with extremely sharp emission lines. Krypton-86 is one of the six stable isotopes that occur naturally,* and on October 14, 1960, the International Committee on Weights and Measures decided, nearly unanimously, that this gas, with its formidable coherence and with the exactly known wavelength of its emissions of reddish-orange radiation (6,057.80211Å) would be the ideal candidate to do for the meter what cadmium had done for the Ångstrom.
And so, with the delegates observing that the meter was still not defined with “sufficient precision for the needs of today’s metrology,” it was agreed that henceforward the meter would be defined as “the length equal to 1,650,763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton-86 atom.”
And with that simple declarative sentence so the old one-meter platinum bar was pronounced, essentially, useless. It had lived since 1889 as the ultimate standard for all length measurement: Ludwig Wittgenstein had once observed, with confusing but accurate drollery, “There is one thing of which one can say neither that it is one meter long, nor that it is not one meter long, and that is the standard meter in Paris.” No longer, for from October 14, 1960, onward, there was no standard meter remaining in Paris, nor anywhere else. This measurement had left the physical world and entered the absolutism and indifference of the universe.
MUCH ELSE BESIDES went on at the 1960 conference, which is held every four peacetime years, and usually in Paris, which on this occasion was perhaps the seminal event in metrology since the invention of the science. Most memorably, the 1960 event saw the formal launch of the present-day International System of Units, known generally by SI, initials derived from the French Système International d’Unités. Most of the world now knows, accepts, recognizes, and uses the SI—with its seven units: of length (the much-aforementioned meter); of time (the second); of electric current (the ampere); of temperature (the kelvin);* of light intensity (the candela); of the amount of a substance (the mole); and of mass (the kilogram). Six of these units are now defined in terms of natural phenomena—generally, of radiation and the behavior of or the number of atoms.
So much else came out of the meeting: the base units; the derived units—like the hertz, the volt, the farad, ohm, lumen, becquerel, henry, coulomb; the authorized prefixes for big and small—at the upper end the deca, kilo, giga, tera, exa, zetta, and yotta (this last being 1024) and at the lower deci, milli, nano, pico, femto, zepto, and yocto (this, to preserve metrologic symmetry, denoting the phenomenally tiny 10−24).
But what did not come out of the meeting was anything definite to relieve the condition of the other old standard, Le Grand K. The delegates—who had created an entirely new measurement system, after all—left Paris that late October, leaving behind them, condemned to remain locked up in a dark cellar under its triple crowns of glass, the melancholy standard mass of the kilogram, moping, miserable, a relic of an earlier century. It would take almost another sixty years for them to find a replacement, and for the highly polished solid metal cylinder, about as tall and wide as a Zippo lighter, about the size of a golf ball, to be relieved of its responsibilities of being the mass against which all the world’s kilograms could and would be measured: in late 2018, it is to be removed from under its well-guarded basement cloche and placed in a museum—a relic of former times, of more ancient technologies.
And since the kilogram’s replacement was to occur so much later than that of the meter, so it enjoyed the benefits of metrology’s even newer technological evolution. For it was to become related to a unit that had long been overlooked as the key to all others—and that is the unit of time, the second.
IT HAS TO do with the notion of frequency, which is after all the inverse of time—it is the number of occurrences of something per second. And frequency is now mentioned in no fewer than six of today’s seven foundational units of measurement.* Frequency is just about everywhere.
Three examples will suffice.
The candela, the unit that suggests the brightness of a source of light, would seem at first blush to have absolutely nothing to do with time. But it has: the international community now defines the candela as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 cycles per second and that has a radiant intensity in that direction of 1/683 watt per steradian. Light is here officially related to the second. It is officially linked to the concept of time.
The length of the meter, to select another of the seven units as an example, is now also defined in terms of the second—it is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. Length, henceforward (or since 1983, when it was so defined), is thus also related to time. A relationship that is agreed to by all.
And the much-vaunted kilogram, until lately defined as the carefully milled platinum cylinder in Paris, will soon reappear, defined this time in terms of the speed of light—and connected to it by way of the famous Planck constant, which, without going into the details of the thing, is a number, 6.62607004 × 10−34 m2 × kg/s, that, as the symbols imply, is also firmly linked to frequency, and thus to the second. Mass is thus defined in terms of time. The whole world now agrees it should be so: that time underpins everything.
Just as Galileo had so presciently realized when he gazed up at the lantern in Pisa. Just as Wilkins had later proposed, and the Prince of Talleyrand seconded. All are connected by time.
AND YET—JUST what is time?
“If no one asks me,” Saint Augustine is said to have remarked, “I know what it is. If I wish to explain it to him who asks, I do not know.” Time moves, we know that. But how does it move? What is its moving, exactly? And why does it only move forward, in one direction? And so far as time is concerned, what does direction mea
n, exactly? Can one be any more precise than simply to say, as Einstein once did, that time is what clocks measure?
All such questions are suddenly especially pertinent.
HOW WE ARRANGE—and how in history we have arranged—the accumulations of time is a matter of choice. On the matters of minutes and hours and days most generally agree*—after all, the sun’s rising and setting have long dictated the nature of time, creating a top-down arrangement that was made for the convenience of human society, and allowed for the notion, even as recently as the 1950s when the second, at the bottom of this top-down arrangement, was defined as 1/86,400th of the passage of a single day.
Beyond days—up into the other human constructs known in English as weeks and months and years—the arrangements became wildly different according to the vagaries of religion and custom and the caprices of personalities. But it is the considered aim of modern metrologists, when dealing with matters concerning the basic unit, the second, that all of the units should agree, exactly. So far as larger units of time are concerned, all are free to do as they wish. But the second itself is sacrosanct.
Until 1967 the second was very much linked to a natural phenomenon—as the fraction of the length of the day, at the top of the top-down pyramid—by way of a sundial or by a seconds pendulum, which ticked away the duration of a day at intervals that were determined by the length of the pendulum itself. It was easy enough—if time consuming—to adjust the length of a pendulum until it ticked away at the rate of 1/86,400 of the period between two sun-at-zenith moments we call noon. Easier still to apply the equation from schooldays, of T=2π√lg where l is the length of the pendulum, g is the acceleration of gravity, and T is the time taken by each beat of the pendulum.
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