shared measurement units [closed]

How do individuals or small groups connected by a radio or similar connection, one or both having minimal tools agree on a system of measurement. Assume no communication problems. Do not assume shared culture or race (no assuming their feet or screwdrivers are the same length) precision should be at least good enough for trade and navigation.

For clarity, don't bother mentioning metrics or physical constants unless you can call a highschool graduate and tell him how to base a ruler on that over the phone.

Assume transportation difficulties, ship wrecks or distance or something. (the store is out of reach) Don't assume the individuals communication tools are things they built instead of purchased or found. Assume they are on the same planet, not necessarily Earth. Don't assume either knows where they are or has fast transportation and a way to trace the radio or whatever.

Don't assume either has a ruler, they might each be able to guess near the length of their radio in their favorite set of units.

I'm asking about what is possible. Does it maybe appear too story based because I'm trying to ask broadly to draw multiple usable answers so solutions will be of benefit to many?

Based on this being my first question, being on hold, and recieveing brilliant answers and comments that made it clear I had asked badly; rather than try to fix this I'm going to close and try again. I thank everyone for their responses.

closed as off-topic by sphennings, L.Dutch♦, AlexP, John Dallman, dot_Sp0TJun 11 '17 at 11:00

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• They both have enough tools and enough knowledge of physics to make a radio, don't they? Because if they simply bought their radios from the store they can go to the same store and buy a ruler and a weighing scale. – AlexP Jun 11 '17 at 7:19
• Ah, they are both on Earth? And one of them is shipwrecked? Then just send a rescue ship to fish them out and make sure it carries rulers and scales. And please edit the question so that we understand how this problem came about, because I for one cannot understand what's the difficulty. If they are both on Earth then there is no need to agree on units -- one will physically send their units to the other. – AlexP Jun 11 '17 at 8:03
• they can synchronize time intervals. And if they are on one planet the gravity is about the same in their case, so they can make a pendulum. Its frequency depends on the length of the rope and gravity, so they probably can realistically establish the same length with 1% precision. They can establish angular units by observing stars and the sun. time units over ratio. – MolbOrg Jun 11 '17 at 13:34
• I like the pendulum. How much error could on planet differances in gravity impart?(like between Marianas and Everest ) – Darkhorse Jun 11 '17 at 19:11
• +- 50 milligals in average en.wikipedia.org/wiki/File:Geoids_sm.jpg ; "Effective gravity on the Earth's surface varies by around 0.7%" - from wiki, Gravity of Earth – MolbOrg Jun 12 '17 at 3:39

The Hydrogen line. ~ 21 cm. Not so simple to measure, but it should be possible for any advanced space-faring race to compute and if radio works then we're in the same universe, at least with respect to the electromagnetic spectrum & the speed of light, so the result will the same. That takes care of length. Time can be derived as well (frequency of the Hydrogen line = 1420405751.7667 per second).

This was included on the Pioneer Plaque.

As I understand it (and I am not a physicist so I don't understand it 100% but that also means other non-physicists have a good chance of being able to understand it, including high school graduates), essentially this involves associating a well-defined physics phenomena - the transition of electrons in a hydrogen atom - with an electromagnetic signature that has been detected. That is the hard part - needs physicists working with space-age technology to figure out what it means, but once they figure out the concepts involved, there is a measurable physical constant associated with it - the wavelength of the electromagnetic signature. Anyone who knows the speed of light in a vacuum can translate a frequency into a wavelength. Plus, in this particular case it is a human-scale (and presumably other sentient life as well) number, not nanometers or light-years.

• computing requires what tools? humans may not count as an advanced space-faring race but we're reasonably bright and I'm relatively well educated, tell me how. – Darkhorse Jun 11 '17 at 4:55
• can you provide some more flesh to this answer? – L.Dutch Jun 11 '17 at 5:26
• I can, but not right now - time to get paid work done :-( – manassehkatz Jun 11 '17 at 5:32
• The hydrogen line is a very strong electromagnetic radiation spectral line which can be easily detected by any civilization which has radio. It is powerful enough to be detectable as noise by ordinary receivers in the UHF L band. Its wavelength and frequency are known to very great precision. – AlexP Jun 11 '17 at 7:30
• @Darkhorse: You don't understand. The wavelength and frequency of the hydrogen line are well known. One party says that for them the wavelength of the hydrogen line is 21.1061140542 centimeters; the other knows that for them it's 8.309493722 inches. Now they know how to convert one's centimeters to the other's inches. – AlexP Jun 11 '17 at 14:07

They're talking by radio - from that they'll have a frequency (from which to devise a time scale) and a wavelength (a distance scale) and then from that you can devise energies, temperatures and probably everything else.

For EM waves you have: $$c=f\lambda$$ With $\lambda$ as the wavelength and $c$ the speed of light. This is assuming they aren't so far apart as to have a red shift in the wavelength but you spoke about a shipwreck so I'm assuming they're on the same planet.

The speed of light is constant so the other two will be too.

• I like this from a simplicity point of view but how accurate to a wavelength are radios? Like will it be exact or do you have a range? I guess you could just pick the middle of that range. – FreeElk Jun 11 '17 at 8:32
• @FreeElk ±1ppm frequency stability is pretty easy, and we can certainly do better than that if necessary. At 1 GHz that means a stability of ±1kHz. (Compare for example the Yaesu FT-897 amateur radio transceiver, which with its optional temperature-controlled crystal oscillator attains a frequency stability of ±0.5ppm and operates up to about 450 MHz.) This doesn't necessarily mean that the indicated frequency will be equally precise, but most of the time, the accuracy of the displayed value is less important than the precision in maintaining the actual value. – a CVn Jun 11 '17 at 15:08