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If two species with no previous knowledge of one another, and no knowledge of each other's environments (say they're on the other side of a wormhole through which they can shoot a radio signal), what system of measurement would they use to communicate?

Someone once suggested to me that the period length of a hydrogen atom, which they said was 21 cm, would make a good universal measurement standard for beings with our basic scale. Not knowing any better, I accept their assertion. Binary seems like a good numeric base, with useful "higher" numeric bases of base 8 and base 16 being easy to agree on.

How about mass, though? And time? What could they communicate those ideas with to establish them?

Update:

One answer suggests the International System of Units. Skimming through the Wikipedia article, it provides measurements such as "metre (current): the distance traveled by light in vacuum in 1/299792458 second."

How would we communicate the 299792458 denominator for a second? For that matter, how do we communicate a "second"? Its definition is even more obscure.

I'm looking for a more straightforward unit of measurement, such as the aforementioned length of the period of a hydrogen atom. Also, the units of measurement should be useful at scales that are useful to our physical form and attention span. I'm presuming that any alien race we'd have much in common with would have physical attributes (scale, time sense) similar to ours. We may learn a lot from sentient quasars, but we would seem horribly impatient to them given that our lifespans are so short.

Clarification:

Based on comments and answers that have been provided, I think I was unclear with my question. Perhaps I should re-frame the question this way: What units of measurement could we concoct that would be useful to us in our day-to-day lives that are based on things occurring in nature and are observable no matter where you are? For some reining in of possibilities, I'll limit the "where" to our galaxy and relative acceleration.

The suggested unit of length I posited (which turns out to be the hydrogen line) is useful at our scale. If every length measurement we used on Earth was based on this, we would be no worse off than we are using meters or feet. We could call it the hyl, craft a symbol for it, and start measuring things. If aliens ever call, and ask what unit of measurement we use, we could say, "Oh, it's this, which you should be able to measure on your end and understand what we mean when we say hyl".

The bit about communicating with aliens is really just a different way to say "how do you determine it no matter where you are"? At least that's the way I meant it; perhaps that's a different question.

So, again, what other measurements could we use that are useful to us at our scale? Things that are about the size of a pound or a kilogram, a minute or an hour... or...

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    $\begingroup$ A better question is how to explain which way is left and which way is right. $\endgroup$
    – Samuel
    Commented May 1, 2015 at 21:33
  • $\begingroup$ @Samuel you can use the polarization of your radio signal to define handedness. A more advanced method would use CP violation to distinguish left and right. $\endgroup$
    – 2012rcampion
    Commented May 2, 2015 at 1:05
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    $\begingroup$ @Samuel, that's a different question, not necessarily better. $\endgroup$
    – J.D. Ray
    Commented May 4, 2015 at 17:09
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    $\begingroup$ Carl Sagan touched on this in the book "Contact". The movie basically skims over the entire issue, but the book had some specifics about how one might bootstrap scientific communication for sharing a construction plan which, at a glance, seemed plausible. I'll have to see later if I can find that specific passage in the book. $\endgroup$
    – user
    Commented May 5, 2015 at 7:46
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    $\begingroup$ All of these point to using the Natural Units as the reference units at least until we have established firmer communication. Problems with precision wouldn't be very big during this period. As for the size of those units, the Planck Length and Time are pretty darned small, but any alien entity should have developed its equivalent of scientific notation, so that shouldn't be a problem either. $\endgroup$
    – Jim2B
    Commented May 7, 2015 at 19:41

6 Answers 6

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The fundamental physical constants of our Universe

  • $ c $ speed of light in a vacuum - units $ \frac {distance}{time} $
  • $ G $ Universal gravitation constant - units - $ \frac {distance^3}{mass \times time^2} $
  • $ ℏ $ Reduced Planck Constant - units - $ energy \times time = \frac {mass \times distance^2}{time^2} $

You can manipulate these Universal constants to develop fundamental, Natural Units based upon the physics of our Universe and not based upon any reference object.

Planck Length $$ L_{Planck} = \sqrt{\frac{G * ℏ}{c^3}} $$
Planck Time $$ T_{Planck} = \sqrt{\frac{G * ℏ}{c^5}} $$
Planck mass $$ m_{Planck} = \sqrt{\frac{ℏ * c}{G}} $$

Planck units are a system of natural units that is not defined in terms of properties of any prototype, physical object, or even elementary particle. They only refer to the basic structure of the laws of physics: c and G are part of the structure of spacetime in general relativity, and ℏ captures the relationship between energy and frequency which is at the foundation of quantum mechanics. This makes Planck units particularly useful and common in theories of quantum gravity, including string theory.

There are many more Natural Units (and Universal Constants) at the link and we'd have to work through derivations for electric charge, magnetic fields, etc.

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    $\begingroup$ Your current derived units for length are meter seconds, for time you have seconds squared, and for mass you have kilogram seconds. Zero for three on derivations :/ $\endgroup$
    – Samuel
    Commented May 1, 2015 at 22:34
  • $\begingroup$ I found one of the errors but they're still not working out and I'm too tired to look at it tonight. $\endgroup$
    – Jim2B
    Commented May 2, 2015 at 1:15
  • $\begingroup$ You may just want to copy from the definitions of the Planck units or another system of natural units. $\endgroup$
    – 2012rcampion
    Commented May 2, 2015 at 1:19
  • $\begingroup$ Well dang, I guess I got it right on my second try after all. I was seeing those results but I though the sqrt(c^5) for instance didn't make sense. Because it's a sqrt of a distance and that didn't seem to make sense. $\endgroup$
    – Jim2B
    Commented May 2, 2015 at 2:23
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    $\begingroup$ @GaryWalker, 1 part in 10^4 might be huge in scientific terms, but for most purposes, it's plenty. $\endgroup$
    – Mark
    Commented May 3, 2015 at 0:26
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Actually the International System (SI) that most of the world already uses is designed in such a way that it would be simple to share with our alien friends.

The SI system has been systematically redefining it's basic units so that it is possible to recreate the units from the definitions themselves. Though this was not done to share with aliens, it is exactly what you need.

The Wikipedia page lists the history of the definitions. Of the 7 base units, only the mole and kilogram rely upon things not completely reproducible across the wormhole, and this will no doubt be changed in the near future by defining the mole as a simple quantity and mass in terms of a mole of a given isotope of silicon (most likely).

There are lower-tech approximates for many of the base units that could be determined in a well equipped high-school science labs.

Also note that a lot of careful thought has already gone into the process of redefining the SI units. They must be unambiguous, reproducible from the definitions and measures that can be made in the laboratory, and very accurately measured.

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  • $\begingroup$ The kilogram can be fixed to "the mass equal to that of 1000⁄12 x 6.02214×10^23 atoms of Carbon 12.". The mass of a fixed number of atoms is universal, it can reproduced by aliens. This video about how you go about producing such a thing on Earth explains why that's plenty accurate, more accurate than the standard kilogram. $\endgroup$
    – Schwern
    Commented May 7, 2015 at 18:25
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    $\begingroup$ As I stated in my answer, they seem to be planning on defining mass in terms of silicon -- IIRC the primary reasons being that we have good techniques for creating very pure crystals of silicon and crystals can be analyzed very precisely, so we can very precisely determine the number of atoms in a given volume more easily. $\endgroup$
    – Gary Walker
    Commented May 7, 2015 at 18:35
  • $\begingroup$ @Schwern: ...at temperature X Kelvin (plus the whole thermodynamic joy of converting average speeds of atoms into temperature). The change of mass resulting from increase of temperature factor is $1 \over {c^2}$ but that's still not zero. I believe a more universal unit would be a mass exerting given gravitational force F at distance d. It's hard to reproduce physically but trivial to convert to "local units". $\endgroup$
    – SF.
    Commented May 8, 2015 at 8:23
  • $\begingroup$ The imprecision re: determining gravitational force is far larger than the difference in relativistic vs. rest mass. At molecular speeds near room temperature we cannot measure the difference (though we can calculate it accurately) $\endgroup$
    – Gary Walker
    Commented May 8, 2015 at 9:10
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    $\begingroup$ The SI unit of measures is purely arbitrary - just as arbitrary as the more traditional foot, pound, second, etc. unit of measures. SI's breakthrough was using base 10 unit conversions. To aliens, SI will be just as arbitrary and strange as old imperial UOM. $\endgroup$
    – Jim2B
    Commented Dec 28, 2017 at 17:58
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If you want units that don't need big numbers in definition or in everyday measurements, you can use, together with your hyl (21.10611405413 cm):

Actually, I suppose that SI unit definitions were chosen to use precisely measured values and even gravitation constant, necessary for natural units, is much better known than neutron lifetime. Big numbers are just big numbers and not so hard to understand and barring a big number, definition of the second (the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom) is analogous to definition of the hyl (the length of the wave of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the hydrogen-1 atom).

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What do we have in common with the aliens? Integers (ie. we can both count and send numbers). Universal constants. Atoms. That's plenty, and it's already being taken advantage of here on Earth. Alien communication will benefit greatly from the terrestrial efforts of international standards to define units of measurements in absolute terms.

Mass can be sent as the number of atoms of a stable, common isotope. The Kilogram is currently being redefined as "the mass equal to that of 1000⁄12 x 6.02214×10^23 atoms of Carbon 12.". The mass of a fixed number of atoms is universal, it can reproduced by aliens. This video about the new Kilogram standard explains how you'd produce such a thing and why that's plenty accurate, more accurate than the standard kilogram.

From there, plus the speed of light, you can derive energy via E = mc^2.

Time can be transmitted the same way we measure it now, the number of oscillations of a chosen atomic particle.

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.

Once you have time, you can define length as how far light travels in a given time.

Electric charge is simply the charge of an electron or proton.

For temperature, the Cosmic Background Radiation can be used as a first order approximation. However, our current definition for the Kelvin works just fine.

1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F). In other words, it is defined such that the triple point of water is exactly 273.16 K.

There is only one triple point of water and it is at a certain temperature and pressure (you get pressure in the bargain). This neatly gets around the problem of using boiling or freezing as the benchmark as they are not fixed points, but change with both temperature and pressure.

This is all great to start with, but mass, length and time are all relative to your local spacetime warping. That is: gravity. These can be measured even with the slight gravitational anomalies on Earth, atomic clocks around the world fall out of sync. Fortunately, the differences in measurement from one planet to another will be very, very small. Ignoring spacetime warping gets you a very, very long way and is good enough for most science.

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I guess you're assuming that we are otherwise able to communicate, learn each other's languages, etc. Otherwise any attempt to establish common units of measurements will get bogged down in basic comprehension.

Something like a kilogram would be almost impossible to communicate. The definition of a kilogram is that it is the mass of a certain block of platinum at the national bureau of standards in Paris. If the aliens can't visit Paris to weight it, they're out of luck.

You could define mass in terms of the mass of a specific atoms, say Hydrogen. To scale it to something convenient for creatures our size, say the mass of 10^24 atoms of hydrogen or whatever convenient number.

For time I'd say to take the half life of some naturally occurring radioactive isotope.

Distance could then be the distance that light travels in a specified amount of time -- assuming we've got time worked out from the previous step.

Energy could be the amount of energy released by a specific chemical reaction. Or a nuclear reaction, I suppose.

Let's see, once you have time, mass, distance, and energy, I think most other units can be derived from those.

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  • $\begingroup$ Yes, I'm presuming some sort of language (or communication protocol) has been established, but I'd like to be able to base the idea on the smallest possible lexicon. Indeed, like in Close Encounters, tones should be able to establish series, which can be expanded into basic math expressions, and from there we're off to the races. $\endgroup$
    – J.D. Ray
    Commented May 6, 2015 at 18:43
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    $\begingroup$ How you could best build up to basic communication is a different question. I had some conversations with a couple of friends many years ago on using math. Presumably many aspects of math should be universal. But how do you go from "2+3=5" to concepts like "love" and "freedom", or even "gravity"? But as I say, different question. $\endgroup$
    – Jay
    Commented May 6, 2015 at 20:20
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I came across this question having sought the same exact thing!

I felt that measurements based on atomic weights and distances would be difficult to convey, and suffered from uncertainty in any event.

One constant I would work with is that of gravity; as one of the four fundamental forces, it can be assumed to be understood by any spacefaring race.

When considering any solid round body (for example, the Earth), if that body was thought of as having a small hole through its center to the other side, and a small mass (for example, a marble) through that hole, it would accelerate more and more, then pass the center and slowly come to a stop as it would reach the other side. (This, of course, assumes operation in a vacuum and ignores geothermal effects.)

The calculation is simple, and both races could agree that 1 pass would be equal to 1 unit of time.

On Earth, this traversal is 45 minutes... and no matter what size the body may be, that traversal will take the same length of time.

Ed. Note: This is not remotely true, but could still be a worldbuilding suggestion provided that the question doesn't depend on actual science.

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    $\begingroup$ While the gravitational constant is constant, the force of gravity varies based on mass. 1 pass, to use your terminology, would have a different value on Earth than, say, the Moon. $\endgroup$
    – Jakob Lovern
    Commented Feb 14, 2018 at 1:16

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