# How to create precise measurements from scratch

You are stranded on Earth as it was ten thousand years ago. You have access (say, through a brain implant) to all of current human knowledge. Assume that basic survival is no issue.

Starting from scratch, your task is to create a rod, out of any material you like, with a length of one meter. The length must be accurate to one nanometer. How long would this take? How much prerequisite technology would have to be developed? Considering you have no meter-related standard to compare against (other than the current definition of the meter and physical constants), is it even possible to complete the given task in a single lifetime?

• how would you know its exact to one nanometer tho, without another measuring device? Sep 5, 2016 at 8:41
• Ten thousand years ago, there was no standard yet, so you take any size rod and call it the meter. Sep 5, 2016 at 9:33
• @JourneymanGeek look up the SI definition. It's completely doable. It would take a lots of effort to reinvent the laser. But then it's pretty easy after that.
– Aron
Sep 5, 2016 at 11:49

This is a fascinating problem because it shows just how tricky it is to define units of measure. In school, we are often given the impression that the units are inviolate structures fundamental to nature, but reality shows otherwise.

This task would have been impossible before 1960. From 1889 until 1960, the meter was actually defined by a particular bar stored in Sèvres, France. Without access to it, it would be virtually impossible to construct a 1 meter object. Before that time, the meter was actually defined to be 1/10,000,000 of a quadrant along the Earth's meridian. Interestingly enough, the meter bar they constructed was actually 200um shorter than it should have been due to a miscalculation, but once the bar was struck, it became the meter.

From 1960 to 1983, the meter was redefined to be 1650763.73 wavelengths of light from a specified transition in krypton-86. This meant that, for the first time, one could have a definitive "meter" that was not bound to a physical object which could be damaged or worn down. This definition was replaced in 1983 with our present one, which is the distance light travels in a vacuum in 1/299,792,458th of a second. This definition locked the meter down to a physical constant (the speed of light), and the second.

Swallow the spider to get to the fly.... okay, how do we measure a second to within nanosecond precisions?

For the longest time, the "second" was measured as a fraction of the day. This was sufficient for centuries. However, the day actually varies slightly, so in 1956 we redefined it to be "the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time." Yes, this is how we do things in science.

Of course, it would be easy to lose track of exactly how long the period of year was back in 1900, so this was less than ideal. In 1967, after the invention of the atomic clock, it was redefined to be "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." What a mouthful!

So these numbers are incredibly precise. They need to be. If you want to measure the second accurate to 1 part per billion (one nanosecond) so that you can measure a meter to 1 part per billion (nanometer), you need all those sig figs. If you miss just 10 of those tiny transitions in your caesium atoms, you're off by a nanosecond!

At this scale, silly things start to matter. For instance, we noticed that time was traveling faster for some clocks at different altitudes because of relativistic effects. Yes, relativistic effects matter on these scales, so the second was re-clarified in 1997 to be the rate of an atomic clock operating at mean sea level! This had about a 0.1ns difference per second, so it shows up on the scales you care about.

So to answer your question, no. A single person is not about to make an accurate meterstick in their lifetime. Your first step would be to create an atomic clock, which calls for high purity components, high vacuums, and quite a lot of high precision machining. With that, you could acquire some caesium-133 and measure a second to a high enough precision. Then you could attempt to measure the speed of light using another expensive scientific instrument to create your meter.

Finally, you could create your meter stick. Did you know that this is not easy? The machinists and metrologists that build these high precision measuring devices are extraordinary. Hopefully your isolated human sent back ten thousand years happens to have spent his whole life mastering this art!

You could try to take a step back in history, and use the krypton definition. You could build an interferometer to do this measurement. However, the transition to measuring the meter based on the speed of light was partially done because the best scientists in the world were having trouble measuring more accurately than about 0.2nm. Shifting to a definition based on the speed of light let them measure frequencies, which were far easier. If the best scientists and metrologists of our world had trouble measuring accurately on the scale you are interested in, its highly likely that you'll have trouble with it 10000BC.

Fortunately, you don't need a kilogram definition. That one is still defined by the IPK in France, a lump of platinum irridium. There's a current effort to change this definition, redefining the kilogram as "1000/27.9769265325 · 6.02214179×10^23 atoms of Si-28. Yes... that qualifies as a "better" definition of the kilogram. Metrology is an insane art, but you have to respect their immaculate precision!

• I disagree. During my under grad I did an experiment to measure the transition line difference between two Na lines, we discovered it to be about 0.6nm. Using this fact, you could construct an interferometer to count the beating wavelengths to get a cavity size of a meter give or take 0.3nm. No atomic clock needed. Just smoke and mirrors.
– Aron
Sep 5, 2016 at 12:01
• That of course would cut a few hundred years off your approach. 😀
– Aron
Sep 5, 2016 at 12:03
• Just to add as well that it's not unlikely that the second will be redefined in the near future we'll move to a definition based on Ytterbium rather than Caesium. The transition frequency is in the optical rather than the microwave range and so offers better stability and performance. Sep 5, 2016 at 14:33
• @Aron What is the wavelength of the transition line you measured, accurate to 1ppb (9 significant figures)? Were you able to get that close? Sep 5, 2016 at 15:47
• @Aron The difference here is that any error you make in your initial measurement of the difference in wavelengths is a bias term, not random variable which varies between beats. Thus, if Earthbound scientists were to have measured the wavelength difference to be 0.6nm, while the "actual measurment" was .597000nm, that would generate a bias term. The final object you measure as a meter would be 5mm off! Interferometry is great for measuring the differences in length between two objects of very similar length, but it is less effective for making these sorts of measurements. Sep 5, 2016 at 17:46

Know your height, or any other size-measure? Take whatever is there (clay, wood, ...) and start churning out rods, a hairs breadth different. Hundreds, all in the eyeballed ballpark of 1m. Then hug them, or wait for nightfall. Thermal expansion will guarantee one of those to be the exact meter you need.

Task did not specify you had to point to a specific rod at specific time...

• Even a broken clock is right twice a day..... May 19, 2018 at 15:02
• The question didn't address thermal effects, so this answer is useless, but correct.
– cmm
Jan 21 at 2:38

If you knew your height, then it would be fairly easy to find the length of a meter.

However, generally people only know their height in meters to 3 or 4 significant digits. Getting the length accurate to a nanometer would be effectively impossible. Thus, you'd have to go back to the definition of the meter: 1/299 792 458th of the distance light travels in a second. You'd also have to know how long a second is: exactly 9,192,631,770 periods of a certain frequency of radiation from the caesium atom.

So, in effect, you'd have to build an atomic clock, an electronically-controlled (hand control wouldn't result in necessary accuracy) light source (preferably a laser), and a very, very long stretch of absolutely flat land in a vacuum (light travels at a different speed in air). Not to mention all the necessary technology to make refined metal, electronics, etc. You'd also have to find and purify caesium, which is rather uncommon.

I'd say its impossible in a lifetime.

• hah damn , I was gonna write this answer when i read the question. pretty much covers all the points I was gonna bring up Sep 5, 2016 at 7:23
• Your height also changes all the time: you shrink while standing up and stretch again when you're sleeping, so humans are not a good standard. Sep 5, 2016 at 9:36

If you have to be precise down to the nanometer, probably not. The meter, as we know it, is defined as "the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second." The meter was first defined as one ten-millionth the length of the prime meridian, a distance you are unlikely to be able to calculate without some advanced technology. An alternate method that might be more plausible, though still unlikely, would be to construct a pendulum with a half-period of one second. The distance that the pendulum swings is approximately one meter. Beyond that, there is really no sure way to tell a meter without having some kind of meter-related measurement.

If close enough counts, and if you have the right materials, you might be able to use a sapling. If you know how much a certain kind of tree will grow in 365 days, you can figure out how long it would take to grow one meter, then cut the tree. Similarly, you could look up/remember how long one or another bone is in an average however-old human and base your ruler on that. It still won't be perfect, but it will be close. And really, who is going to call you on it?

• The meter was actually defined as one ten-millionth of the distance from the North Pole to the Equator, which is one quarter of a meridian (any meridian, not just the Prime Meridian). Sep 5, 2016 at 0:59
• Yes, sorry I wasn't complete. The Prime Meridian through Paris from the Pole to the equator. But, yeah, any meridian would do. Sep 5, 2016 at 1:11

The easiest way to do it if you had access to all current Earthly knowledge at your hands and bronze age technology and people at your disposal (to mine and such the material) would be to do some simple volumetric math using multiple systems.

For example I would know the weight of iron, bronze, brass, copper, tin, etc per cubic meter or lbs per foot. and I can come up with about the right size for both off the top of my head. Since we can convert using ever greater accuracy if we couldn't convert from our third made up system to them both then to each other we would know that we were off and just work it out through testing and failing until we get the right dimensions.

Another way to do it, if you built a camera of some sort or had a cell phone on you that could is to just throw stuff off high places with a camera taking pictures as it fell. And again using several systems and your own you just convert and find the rate of fall which you'd know the number of once with your knowledge base, because after a certain point things stop accelerating.

Another way to determine it would be to look at the sun and measure it or moon as it moves across the sky which we know the distance of and thus could get a number from...

Ultimately though, all of the ways only would give you a meter to millimeter scale probably, but, again, once you have a rough estimate of that you can pretty easily cross reference measure to between multiple things as in the first option and and pretty easily get it pretty accurate.

I don't consider the measurement the hard part of your question, because assuming you had the tech to do it, its fairly simple given all the knowledge. Now if you asked me to machine the rod rather than tell if and when it is that precise length there would be a bigger problem, because that takes precision instruments which would require skills and materials to be built up on a civilization scale to get ahold of. Could you do it in a life time? Yes... if everyone listened to you and worked with you, you could, easily. The problem is that they wouldn't and so at best you'd only be able to write it down or try to convince those in charge that the current civ to listen to you.

• -1 Without old IPK you could never weigh anything accurately enough.
– Aron
Sep 5, 2016 at 12:05
• @Aron All you need is enough of a given metal that is pure enough to not cause too large of a difference in weight. And then forge them into cubes that are the correct ratios to each other and you should and then just compare and contrast different measurements. Impurities can be accounted for due to knowledge provided so even with a poor process you can still get really close to what you want. Not to mention most of the processes to purifying metals is also fairly easy and could be taught rapidly to artisans. Sep 5, 2016 at 12:26
• the problem is that you are side stepping the bootstrap issue. You are assuming you can measure a block of metal to the nm to then give a mass, then to get a distance.
– Aron
Sep 5, 2016 at 12:42
• @Aron No. Any random cube will do, because I just need to be consistent with my own system and then work with known ratios. Iron weighs x kg, tin weighs y kg, an iron cube and a tin cube should weigh some multiple of tin. Once you work out the ratio you can scale it up and down. Once you get that you can mess with getting the ratio between lbs, ounces and then inches and meters. Then you work on converting between the two. The conversion number has to be precise or it wont work, therefor any mess ups will show. So you just try until you get the correct ratio. Sep 5, 2016 at 12:55
• @Aron I told you how to get to THE meter. What I am talking about in this solution is using multiple points of reference that have only 1 solution. That's what you don't get. The only problem is the precision of the instruments. If you could get instruments to be that precise, as I said, there is no hardship in figuring out the measure to be accurate and by precise, I mean actually working at that scale, but it is far from impossible. All you need is a mold, a sharp blade, and some magnification of sufficient strength. It'd be impractical but you could do it. Sep 5, 2016 at 17:10

Assume that all materials, chemistry, etc is the same, you have basic technology and scientific knowledge, but that you have no artifacts: Not even your size.

Water is the same, so you can construct a thermometer with a Celsius scale.

Any suitable battery chemistry will give you a reference for a standard-Volt voltage scale.

Using the known e/m ratio of an electron, an e/m tube will give you a scale for a standard-Ampere current measurement.

Finally, the thermal properties of water will let you create standards for a liter and cc. From those, you can get operational kilograms and meters.