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Throughout history we have used units of measure that were defined by arbitrary standards; things that were conveniently around when whichever government needed something measured. “How much tax does Bob pay?” “How about charge by his farm?” “Uh, OK? how big is it?” “About twice as big as John’s” “So charge him for two Jonny-acres then. Next!”

They never translated well; not to other countries, and often not between intellectuals.

Now we do have units of measure, like the second, which have been defined based on absolute constants in the universe. Certain discoveries and technologies made this possible. Regardless when we did finally set absolute values of measure; when did we obtain the technology needed to create one?

I think the most important one here is probably the second. But I also think that any other absolute unit could have been used to derive the others, so any absolute measurement would be accepted.

The problem is that I need to back up my alternate history, and need to know what the earliest possible point for this advancement would be.

In my understanding it would likely be 1902 when the Curies found the half-life of radium, which is universally constant. Was there an earlier opportunity?

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  • $\begingroup$ Constants and absolute measures are discovered, not created, and we just assign our arbitrary markers to them. For instance, mass is an absolute measurement, it's a property of matter and responds to the force of gravity, and we just decided to call it mass. $\endgroup$
    – Halfthawed
    Feb 18, 2022 at 22:05
  • $\begingroup$ I think this is the same thing I am saying. We cannot make an absolute measure before discovering an absolute constant. So I think you are saying the earliest time we could have created an absolute measure would be at the first discovery of a universal constant. Close? $\endgroup$
    – Vogon Poet
    Feb 18, 2022 at 22:21
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    $\begingroup$ The Curies could not measure the half life of radium sufficiently accurately to serve as the definition of the second. We still cannot, one hundred years later. $\endgroup$
    – AlexP
    Feb 19, 2022 at 0:03
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    $\begingroup$ @AlexP indeed, it is always an approximation. I can add science uses Cesium nowadays, that's a shorter interval, to be precise: the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom This yields a more accurate meter. Actually the meter is based on the definition of a second, as 9,192,631,770 Cesium transitions.. and then, one meter is the distance the light will travel in vacuum in a time interval of 1/299,792,458 of a second. en.wikipedia.org/wiki/Caesium_standard $\endgroup$
    – Goodies
    Feb 19, 2022 at 0:29
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    $\begingroup$ @hyde essentially. A unit of measure that work everywhere in the universe. By definition, it is not derived in any part from an arbitrary definitions. The distance between two scratches on a bar is arbitrary, and that was how the meter was defined. The time it takes Earth to go around the sun - a year - is arbitrary and only useful to us (Why not Mars or the Moon? Just because). The temperature that water boils and freezes is arbitrary (why water? Just because). Absolute units stand by themselves and can be found anywhere without needing access to the standard artefact. $\endgroup$
    – Vogon Poet
    Feb 19, 2022 at 16:03

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Basically, it all depends on the precision of measurement, and what you can measure more precisely. In the end, you need to find absolute definitions for a unit of time, a unit of length, a unit of mass, a unit of temperature, a unit of electic current (or any other electromagnetic unit, really), and, optionally, a unit of the amount of substance (but you can do without).

Historically, James Clerk Maxwell noticed back in 1873 that the unit of time and the unit of length could be absolutely defined in terms of the electromagnetic radiation of some specified spectral line of some specified element. But they could not really do it in the 1870s; they didn't yet know about isotopes, and even if they had known they had no practical means to separate them; and anyway, the measurement instruments were not up to the task.

(As a side note, dimensional analysis was not even a thing before the 19th century. People had a very fuzzy notion of what a fundamental unit of measurement even was.)

  • Take the second.

    Originally, the second was defined so that a mean solar day (the time from noon to noon averaged over a year) was 24 hours × 60 minutes × 60 seconds = 86,400 seconds. This was good enough for millennia.

    Then, in the 19th century, astronomers realized that the mean solar day was getting longer and longer, as the rotation of the Earth is slowed down by dissipative forces created by the tides due to the sun and the moon. This effect was measured quite accurately by the end of the 19th century. In 1952, the official definition of a second was changed, so that it became 1/86,400 of a solar day calculated with respect to a well-defined epoch. (It was 1/86,400 of the mean solar day calculated for 1st of January 1900.)

    Then in the 1950s, atomic clocks became a thing, and it was very quickly seen that they could keep time with much better accuracy then any other method, either astronomical or electronic. The second received its absolute definition in 1962: "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom".

    Note that the successive redefinitions did not change the magnitude of a second. They were made so that the new definition fell within the measurement precision of the old definition; that is the entire point: the enable more accurate measurements without invalidating previous measurements.

    The point being that an absolute definition of the second was needed and useful only when we found a way to measure time significantly more precisely than what astronomy could give us. In real history, this happened in the 1940s, when electronic clocks (based on the vibration of quartz crystals) beat astronomy for short durations, a few days; astronomy was still better for long durations. But in the 1950s we developed atomic clocks, and those were hands down more accurate than astronomy over both short and long durations.

    So that we had no choice. We had to replace the astronomical definition of a second because we could measure time more precisely than astronomers could.

    In a fictional world, with an alternative timeline, it all depends on when the fictional world develops atomic clocks; as soon as they come into existence, an absolute definition of the unit of time is mandatory.

  • Take the meter.

    For a very long time, the most accurate measurement of length was a physical measurement of some precious artifact. No absolute definition of the foot or the meter was needed or useful.

    This began to change in the late 19th century, when interferometry allowed extremely precise measurements of small distances. We still could not measure large-ish distances more precisely than we could measure the distance between two scratches on a metal rod kept somewhere near Paris, but we were getting there.

    The length of the distance between the two scratches on the metal rod started to be measured by interferometric means in the 1920s; the consensus was slow to emerge (and the CGPM, General Conference on Weights and Measures, the international body with supervises the International System of Units, meets only once every five years); but in 1960 the meter was officially defined as "1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum", acknowledging the obvious fact that for about half a century interferometric methods were more accurate than the scratches on the metal bar.

    And finally, in the 1970s it became clear that we could measure time much more precisely than we could measure length. Since the speed of light in a vacuum is a universal constant, it was obvious that we could get a more precise definition of the meter just by fixing its value to a convenient number. And that's what the CGPM did in 1983: the speed of light in a vacuum was decreed to be exactly 299,792,458 meters per second, which instantly gave a more precise definition of the meter.

    Note that the successive redefinition did not change the length of a meter: it is still equal to the distance between the two scratches on the bar of metal kept near Paris, to the precision of the scratches. But now we have a much more precise definition, so that we can measure the difference between the distance between the scratches on the far side and the near side of the metal bar. The new definition is independed of any bar of metal, and can be reproduced by any suitably well-equipped metrological laboratory in the world.

  • Take the kilogram.

    This was stubborn.

    It was hard to devise a reproducible method for the reconstruction of the mass of the chunk of metal kept near Paris.

    That it was needed had become obvious in the early 20th century: there are several such metal chunks in the vaults near Paris, all supposedly identical, and yet their masses were measurably different, and the differences increased over time.

    The breakthrough came in 1975, when Bryan Kibble, working at the British National Physical Laboratory, devised a method of measuring the weight of an object extremely accurately by measuring the electric current and voltage needed to produce a compensating force; this is called a watt balance or a Kibble balance. The Kibble balance enabled the measurement of the Planck constant with more than nine significant digits of precision, and this enabled the CGPM to construct an absolute definition of the kilogram by specifying a suitable exact value for the Planck constant.

    Nowadays, the Plack constant is exactly 6.62607015×10−34 J⋅s, by decree; this gives an absolute definition of the kilogram, because 1 J = 1 kg⋅m2⋅s−2, and the meter and the second alredy have absolute definitions.

    Note that the 2019 redefinition of the kilogram did not change the mass of a kilogram; the chunks of metal in the vaults near Paris are still about one kilogram each, to the limit of precision of their manufacture and to the limit of precision to which their masses could be measured when they were made. But the new definition is independed of any chunk of metal, and can be reproduced by any suitably well-equipped metrological laboratory in the world.

  • And, mutatis mutandis, more or less the same for the ampere and the kelvin.

  • The point being that today we have absolute definitions for all the fundamental units of measurement, independent of any artifact. Historically, the earliest we could have obtained them was:

    • For the meter, the late 1920s. That it took until 1960 for the scientific and technological community to ackowledge the obvious is understandable; humanity had some more important things to do in the 1940s, and the 1950s were not a period suitable for international coordination.

    • For the second, the 1940s or 1950s. The absolute definition came quite quickly once atomic clocks became widespread. Again, anything atomic was not really subject of international cooperation in the 1950s, so the CGPM had to wait till 1962 to make it official.

    • For the kilogram, there was simply no way to make an absolute definition till the late 1980s, and during the 1990s and 2000s the CGPM explored different methods, trying to see which gave the best precision. Overall, the 2019 absolute definition came within no more than 10 or 20 years of the earliest possible moment.

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  • $\begingroup$ Great post BTW but didn’t Anders Ångström publish a complete table of wavelengths for the solar spectrum in 1868? Is a wavelength constant in the universe? (Of course you have to define the deflection of it through whatever lens and medium; but isn’t every line of light a unique and universal wavelength? $\endgroup$
    – Vogon Poet
    Feb 19, 2022 at 1:00
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    $\begingroup$ @VogonPoet: Ångström's wavelengths were measured with respect to what he thought was an accurate standard meter, but wasn't. His wavelengths were only accurate to about 3 or 4 significant digits; not his fault, that was the state of metrology in his time. The CGPM tentatively adopted in 1927 a practical absolute definition of the meter based on the wavelength of the red line in the spectrum of cadmium, based on measurements made by Michelson and Benoît in the 1890s. Then came the hot war, and then the cold war, and in the end it wasn't until 1960 that the meter got its abolute definition. $\endgroup$
    – AlexP
    Feb 19, 2022 at 1:15
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    $\begingroup$ That’s the way the cards laid down, but think of this. What if in alt history, we decided to make the meter 10$^{30}$ wavelength of the $n$th line of light with 32° refraction in a spectrometer? Wouldn’t that have been an absolute measure? Or do wavelength-to-refraction indices vary? $\endgroup$
    – Vogon Poet
    Feb 19, 2022 at 1:38
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    $\begingroup$ @VogonPoet: (I assume that the numbers are arbitrary and you don't really mean them.) The purpose of the definitions of units of measurement is to enable metrological laboratories to recreate the standards accurately. So, how accurately can we control the optical properties of glass, such as the index of refraction? That is, if a laboratory in Minneapolis and another one in Murmask attempt to make a piece of optical glass with the exact same index of refraction, how closely will they actually match each other? Answer: not very; the best they can hope is to come within 1/10,000 of each other. $\endgroup$
    – AlexP
    Feb 19, 2022 at 3:10
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    $\begingroup$ @VogonPoet: The definitions of units of measurement must be accurately reproducible. That is their purpose. Otherwise the fancy definitions are not any better than just accepting that a meter is the distance between two scratches on a metal bar in a vault near Paris. (And note that reproducing a piece of optical glass so that the index of refraction is within 1/10,000 of the target is with all modern manufacturing technology. They would have had no hope of doiing better than 1/100 back in the 1790s.) $\endgroup$
    – AlexP
    Feb 19, 2022 at 3:11
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It could have happened any time there was a sufficiently scientific-minded government, and in fact may have happened several times.

The current meter, on which the whole metric system is based, was invented in 1793, so clearly being able to measure atomic decay is not a requirement. It was created as "one ten-millionth of the distance from the equator to the North Pole along a great circle" so it required being able to measure the diameter of the earth, which clearly took at least 18th century technology. While it is now measured as a certain number of light-microseconds, it was established without being able to measure that.

However, it was not necessary to wait until the 18th century. Any phenominon or object that could be precisely measured could be turned into a unit of absolute measure, and in fact was. The Persian Empire had a system of measurements based on the size of their coinage, which itself was precisely determined at state-run mints. The Chinese empire had an extensive and coherent system of weights and measures created in the 3rd century BC.

While none of these ancient systems of measurements would have had the precision of modern systems, due to limitations of instrumentation, they were as "absolute" as the meter was in 1793. Earlier systems defined their measurements against an arbitrary object kept by the government rather than an atomic measurement -- as did the metric system until relatively recently. No doubt civilizations of the 23rd century will consider our current cesium atom vibration measurements inaccurate and quaint.

The key here is to have a strong central government that cares about weights and measures, and decides to dispense with a reference object, rather than any kind of technological advancement.

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    $\begingroup$ Except that they measured it wrong, and in fact they could not measure it correctly, and in fact each and every meridian has a different length. In real history, the inaccuracy of the meridian definition of the meter was recognized very early. Before the first absolute definition of the meter, which came in 1960, a meter was by definition the distance between two fine scratches on a metal bar kept in a vault near Paris. $\endgroup$
    – AlexP
    Feb 19, 2022 at 0:21
  • $\begingroup$ Sure, and materially we measure time by listening to WWVB rather than running our own atomic clocks. $\endgroup$
    – FuzzyChef
    Feb 19, 2022 at 0:29
  • $\begingroup$ I am absolutely certain that the metrological bureaus of the various nations actually do use atomic clocks. (And here in Europe it's the German DCF77 time service.) $\endgroup$
    – AlexP
    Feb 19, 2022 at 0:34
  • $\begingroup$ Isn’t a Persian coin an arbitrary object kept by the government? $\endgroup$
    – Vogon Poet
    Feb 19, 2022 at 0:40
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    $\begingroup$ In other words, it is all about politics. That means 'never going to happen'. $\endgroup$ Feb 19, 2022 at 21:12
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I would argue that MOST currently used units of measure are arbitrary. The second, the meter, the gram, are ALL units of measure that pre-date any 'universal standard', and thus any attempt to 'standardize' them amounts to a 'round peg in a square hole'. They are so 'un-unitary' in physics that trying to tag them to some unitary physical constant inevitably results in decimals, and decimals by their very nature are imprecise. Even repeating decimals lead to ambiguity. Take Pi, for instance. Taking it to one more decimal place changes the 'accuracy' of anything it is used to measure.

It seems to me that the only two 'absolute universal standard units of measure' are the planck constant, and the unit of electrical charge- the coulomb - which is based on a precise non-decimal integer number of electrons. But even the planck constant has been basterdized by science. instead if calling it the 'universal unit', we have 'defined' it in terms of pre-existing units. Once you define it as some very small 'decimal-to-the-gadzillionth-power' of an existing arbitrary unit it becomes a completely arbitrary unit. How do you precisely 'chop up' an existing unit to fit? You end up with 'but if you take it a few decimals further, the measurement is no longer accurate'.

The ONLY standardized absolute unit of measurement would be something that is a unitary equivalent of some universal constant.

Our artificial concept of temperature is an example. Yes, one can define the 'zero' point as 'absolutely no movement', but how do you determine the intervals? By taking some arbitrary other temperature, and dividing the 'range' into discrete intervals? What is that arbitrary other temperature that would be agreed to by every other alien culture? Yes, you could define it as the unit-difference created by a specific atom increasing the vibration rate by an arbitrary amount in a given time, but then it becomes a derived unit.

The only way that an 'absolute universal standard of a unit of measurement' would be possible is for physics to give us a credible unitary standard 'constant', such as the planck constant for distance, or unit of charge for electricity, for all such measurable quantums. And then science would have to agree to give up all the existing pre-defined arbitrary units, and start calling that the 'unitary basic unit'. That is a matter of convention, of communicating the concept, and of accepting the concept. In other words, politics. Is THAT ever going to happen? It hasn't happened yet. Maybe some time in the far distant future.

It is a good argument for the necessity in physics for a non-arbitrary minimum unit of 'difference for time' as there is for a 'minimum unit of difference in distance'. How can physics keep 'time' constant throughout all of physics if there is not a minimum non-divisible unit? Somehow, physics knows EXACTLY what the 'division of time' is, throughout our known universe, and applies it accordingly to all other derived units. How can that be possible, without there being a minimum difference that defines the 'non-arbitrary unitary-ness' of the quantum? There are some people, and organisms, that have been conjectured to be 'in tune' with this unit of time, being able to precisely determine the passage of time internally without any outside metric. It seems that nature, as I have said in a previous answer, uses basic 'non-arbitrary units of measure' for everything it does, without them being 'defined'. They just are. It is up to human physics to 'discover' them, as we have in electricity and distance.

Until then, we are stuck with the fields of physics and biology having their own non-arbitrary universal fundamental units of measurement, known only to nature, and not 'arbitrarily defined' by us. After all, 'gravity' seems to be able to base itself on some 'non-arbitrary basic unit of measurement' of time and mass, without having to worry about exactly what that 'non-arbitrary universal unit of measurement' is.

In point of fact, the above argument is one I have seen used in forming the position that in physics, there HAS to be some 'universal minimum unit of difference' for every measurable quantum that forms the basis for physical constants, otherwise how could physics ever hold these constants 'constant'?

We just aren't there yet.

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Cavendish Experiment - possible around 2500 years ago.

The constant of gravity, G, was pretty successfully measured back in 1798, and it's a constant. You can use that to determine mass, which is an absolute measurement, so there you are. It requires some advanced carpentry skills and fine metal working, so a civilization like the Vikings (circa 800 C.E.) could have pulled it off. Or the Romans (500 B.C.E), for that matter.

It would also have required an insane amount of calculations, which the Vikings could not have done, but there were some very brilliant ancient philosophers who might have been able to pull it off. For all we know, they might have and we've lost the record of them doing that. They were dealing with atomic theory around 300 B.C.E, so it's plausible.

P.S. - yes, you wouldn't have it exactly, but you'd have to within a few experimental digits, and honestly, when it comes to practicality, that's good enough.

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    $\begingroup$ But doesn’t calculating G require a defined unit of time? If the second is arbitrary, the unit of gravitational acceleration is arbitrary. No? $\endgroup$
    – Vogon Poet
    Feb 18, 2022 at 22:23
  • $\begingroup$ No. G is a constant. Saying something isn't a constant because you're interacting with it using something relative makes your criteria impossible. Time, because of relativity, is always relative. $\endgroup$
    – Halfthawed
    Feb 18, 2022 at 22:39
  • $\begingroup$ I don’t think absolute units of measure are impossible, honestly. I agree that G is a constant (although it calculates different depending on the method you use), but a constant itself is not a unit of measure. It is the basis for one. No? How would you measure anything at all with a G? Is a car = 17 G? You see? $\endgroup$
    – Vogon Poet
    Feb 18, 2022 at 22:53
  • $\begingroup$ You use it to measure mass. Which I said in my answer. And radium's half-life isn't absolute, by the way, it's linked to time, which means radium under an acceleration of, say, 0.001% c has a different half-life than radium which doesn't. Just saying. Mass doesn't change. $\endgroup$
    – Halfthawed
    Feb 18, 2022 at 22:57
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    $\begingroup$ It’s a good post but i’m trying to see how we would have created an absolute unit of measure with G. $\endgroup$
    – Vogon Poet
    Feb 18, 2022 at 23:02
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A squirrel can run along the top of a fence, jump in the air, and catch a branch. The thing is, before the squirrel even jumps, it looks at where it is going to land, and almost always lands there. The speed maybe different, the distance changes, and the weight of the squirrel is not constant. Yet the mind of the squirrel can almost instantly use all of these factors in a calculation.

In fact, three different squirrels in a row, with different weights and speeds, following each other, can jump from different spots and hit exactly the same spot.

Yet squirrels do not have math, formulas, equations, constants, or equivalent basic units of measurement, all of the things that one would expect would be needed to achieve such a feat. Certainly, an engineer would need all of these things to do the calculations.

Obviously, there is something about the animal (and human) mind that allows different individuals to make exactly the same 'calculations' without any external standardized concepts, without having science or math or even numeracy.

My point is, standardization is not something that is 'invented', it is something that is innate. The animal mind has built-in non-numeric universal standards of measurement that are applied continuously in day-to-day living, and that are consistent over time, over almost all instances of that animal mind.

I know in my mind, and I can very quickly calculate, for every stone I pick up, how much force and in what direction I need to throw it, in order to consistently, rock after rock, hit the same target. This precision requires an innate basic universal unit of measurement for mass, time, distance, direction, and speed that I use to do the calculations. Basic universal units that every human doing the same task with the same precision uses.

It is not, in fact, having a universal absolute unit of measurement that is the challenge, but it is about being able to communicate that standard absolute basic unit of measurement to others that humans in particular excel at.

But communication requires person-to-person contact. And there is the rub. For an 'absolute universal unit of measurement', there must be absolute universal inter-individual contact. Somehow, the individual needs to be in contact with other individuals, in order to communicate to them a basic unit that is inmate in their own thinking.

This could not be possible until global travel and intellectual conversation was established. There can be no universal standard of measurement until there is universal communication of that standard.

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