# What is the best unit of measure for the time portion of a non-earth-bound light“year”?

The question, Reference to Earth in Intergalactic Universe illuminates the shortcomings of the term "light-year", which defines a distance by mixing the universally constant speed of light in a vacuum with our far less universally recognizable measure of time known as a "year".

So my question is...

What measure of time would be universally constant and automatically recognizable by all species who achieve space-travel?

Some element's half-life seems like a good starting point, but which element and which isotope of that element?

Also, what would we call the resulting measure of distance? A "Light-HalfLifeOfFrancium233" doesn't exactly roll off of the tongue.

• You seem to talk a lot about element half-lifes. Would you prefer it to be an element's half-life that is used? – NL628 Dec 28 '17 at 5:46
• As soon as you start talking practical space travel, you're going to have to convert all of your spacetime to Lorenz invariants. – chrylis Dec 28 '17 at 6:03
• worldbuilding.stackexchange.com/questions/100907/… is a related question, also asked today. – computercarguy Dec 28 '17 at 14:45
• @computercarguy, I referenced (and linked to) that question in the opening line of my question. I added this question to focus on the specific issue of a universally (non-earth-bound) measure of time, which was not the focus of that previous question. – Henry Taylor Dec 28 '17 at 16:42

This same problem was faced by Sagan et al. when they made the golden records to travel on the Voyager probes. They decided to define time using the wavelength of light produced by a ubiquitous spin transition in Hydrogen molecules that I'm unfamiliar with. Still, if it's good enough for Sagan!

It would be just as natural to define length in this way. As I understand it, this 21cm wavelength microwave permeates the known universe (going through dust clouds even), and the stack exchange answer linked describes it as 'notorious'. A most charming description. In any case, the single unit is convenient for daily measurements, our homely lightyear is 2^55 (ish) of them, and the diameter of the known universe is about 2^91 of them.

I hope that helps, best of luck with your universe building!

Here is a Physics.SE link describing the Voyager records and the H2 spin transition. A Wikipedia article is here.

Edit: Thank you to Kingledion for the formatting edit, very appreciated! I embarrassingly only noticed on rereading that our OP additionally asked about a universal time. For this same Hydrogen line, a second is about 1.4Billion wave periods, or (perhaps more universal) 3 seconds is about 2^32 wave periods. 2^42 (important number) wave periods is about 51min, and a year is about 2^55.3 of them. If November and December were optional, more like 2^55. :)

• The Hydrogen frequency, as I've heard it called, appears in many other sources as well, I've seen it frequently. Upvoted. – Tom Dec 28 '17 at 9:12

There is no obvious one. There's lots that can be understood and interpreted, but then you run into the translation issue that what one civilization may find intuitive, another will not.

Consider converting "light-year" into something else, as you suggest the half-life of a given isotope. Humans might gravitate toward define a base universal measure--call it the Stellar Distance Unit--as the distance light travels in a vacuum in the period of the half life of the ruthenium-106 isotope. Why that one? Because its half-life is 373.59 days, which is just a tad longer than an Earth year, which makes the Stellar Distance Unit conveniently close to the light-year. A species on TRAPPIST-1g might consider thullium-170 to be the obvious candidate instead: at 128.6 (Earth) days half-life, it's just a tad longer than ten of the planet's orbits around TRAPPIST-1 (123.5 days). That assumes, of course, a base-10 counting system. They might use another entirely which would change what numbers they would find relevant.

Whatever the case, it's fairly easy to translate a given half-life into another language of a technological civilization so they know which one you're talking about, so why worry about trying to assume there's some standard everyone will agree with? If you're talking to another civilization, assuming they have access to basic calculators capable of doing conversions is a reasonable assumption to make, and they'll be able to convert a light-year into whatever unit they commonly use.

• Incidentally, the astronomical year used to define the lightyear is itself defined as a large multiple of the period of a particular electron transition of the cesium-133 atom (via the SI definition of a second). Why not a nuclear half-life? Because, being statistical in nature, those are much harder to measure than electron transition frequencies to extremely high precision. Why cesium? Because it happened to be easy to make cesium clocks (compared to clocks based on other elements) when the standardization was done. So we could call a light-year a light-2.900974e+17-cesium-transition... – Logan R. Kearsley Dec 27 '17 at 22:58
• For practical purposes, you don't need as much precision for measurements like a light-year. If you start getting down into fractions of a light-year such that the imprecision comes into relevance, you're probably better off using a different, more precise, base unit anyway. – Keith Morrison Dec 27 '17 at 23:06
• True. If we didn't already have a physically-grounded definition, we could use a less precise one. But, that's how it happened to work out--we needed a precise, physically-based definition for smaller measures, and the larger measure turned out to be defined in terms of those. I imagine that wouldn't be a terribly unusual way to do it, either--after all, it's convenient to only need one base unit that everything else can be defined in terms of, rather than independently defining distance units on different scales. – Logan R. Kearsley Dec 27 '17 at 23:41
• @KeithMorrison You do need as much precision as you most precise measuring devices. Distance measurement is very precise nowadays, so we need distance units with a lot of precision. In fact, distance and time measurement are a lot more precise than half life measurement. That's the reason half life hasn't been chosen to define time units here on Earth. – Pere Dec 28 '17 at 11:55
• Uhm ... changing the representation base has no effect on relative nearness. If we postulate a race choosing an isotope to approximately match their year, they will chose the same isotope no matter what base they count in. – dmckee Dec 29 '17 at 2:33

Planck length to a large power will suffice if you want a universal constant that is actually universal.

• which raises the question, " to what power? ". I think Plank length alone is too small to be useful. But most of our large multipliers seem obvious to us only because we count using base-10. – Henry Taylor Dec 27 '17 at 21:55
• @HenryTaylor we have HDD sizes shown in powers of 10 (seller's kilobyte is 1000 bytes) and in powers of 8 (OS kilobyte is 1024 bytes). Not really a problem if we know what bottom unit is and have computers to recalculate "some power" of different bases. – Mołot Dec 27 '17 at 22:18
• @Molot, that is a perfect example. I wonder if a 2.4% discrepancy in distances on a galactic scale is enough to keep us from finding each other? – Henry Taylor Dec 27 '17 at 22:22
• @Mołot: Nitpick, but 1024 is not a power of 8, it's a power of 2. 8^3 = 512, 2^8 = 1024. – jamesqf Dec 28 '17 at 2:50
• @jamesqf 1024 = 2^10. – Spencer Dec 28 '17 at 13:57

If you want to detach completely from non-universal measurements of time, you could measure things in intervals of the plank length. According to the wikipedia page:

The Planck length is believed to be the shortest meaningful length, the limiting distance below which the very notions of space and length cease to exist. Any attempt to investigate the possible existence of shorter distances, by performing higher-energy collisions, would inevitably result in black hole production. Higher-energy collisions, rather than splitting matter into finer pieces, would simply produce bigger black holes.

So it's a fairly universal constant, which, (assuming current theory holds) would translate to any civilization advanced enough to discover it. It's value is $1.616×10^{-35}\ meters$. Rather conveniently, there are $5.854×10^{50}\ plank\ lengths$ in a light year, so you could quite easily make up your own unit defined as $10^{50}\ plank\ lengths$ and have a similarly sized unit that's detached from any non-universal measurement of time.

The problem with this answer is that it uses our (relatively arbitrary) base 10 system. I recommend switching to a base 2 system, which gives us $~2^{169}\ plank\ lengths$ in a light year. This you can round to whatever you see fit. I would recommend going for either 128 or 256, as both are powers of two.

After this, naming depends on what you want to make your "standard length". In SI it's the meter, which is $~2^{34}\ plank\ lengths$. From there scale up with SI prefixes until you reach your stand-in for the light-year.

• To be fair to cultures with different number bases, I'd suggest factorials. 42! Planck units = 2.40021 years. – Anton Sherwood Dec 29 '17 at 0:51
• @Anton Sherwood + for using the truly universal constant 42 :-) – Radovan Garabík Dec 31 '17 at 18:15
• Perhaps a better idea: lcm(1, …, 120) Planck units = 1.633 year. – Anton Sherwood Jan 6 '18 at 8:15

The problem of finding a universal time unit has been addressed by physicists for a long time and the current best solution is exact to ten significant figures. The present definition of the second is "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 cesium 133 atom". Therefore we already have an universal unit of time: the period of that radiation.

Since this period is a very short time, a light period will be small: about 0.032612256 meters. For astronomical distances we should use a reasonable multiple. As one year is about $2.9·10^{17}$ periods, the light exaperiod could be a useful unit (1 light exaperiod = 3.44 light year).

It must be noted that the period has already been selected to define the second because it can be measured with large precision. Other natural phenomena, as Earth rotation aren't regular enough or measurable enough to provide a good definition of a time unit. That's true for half lives of unstable isotopes: they can't be measured with precision beyond a few significant figures.

Interestingly, adopting this period as base time unit could have some advantages that would ease transition:

• For astronomers, 1 light exaperiod is just a bit more than one parsec.
• For countries still not completely metricated, a light period is about one tenth of a foot, therefore transitioning to period units could be easier than metricating.
• For metricated countries, 30 light periods are close to 1 meter - more close than 3 feet are. Therefore, it's easier to translate both imperial and metric units to periods than to translate between imperial and metric units.

Furthermore, using the petaperiod (about 30 hours) instead of the old fashioned day could lead to a longer number of productive hours, although it could put some stress of circadian cicles of Earthlings.

• If you want the population of Earth in perpetual jetlag, that's a good idea. For most of humanity no, no it isn't. – Keith Morrison Dec 28 '17 at 2:50
• That period of time isn't "universal", it's one chosen because (a) we could make cesium atomic clocks, and (b) that number of transitions represent a unit of time that's sufficiently close to the previous definition of the second, which was "the fraction ​1⁄31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time". You'll note that definition is astronomical, and thus based on the Earth as well. That makes the second just as arbitrary a unit of time as any period less than a day. We just can define that purely arbitrary number really well. – Keith Morrison Dec 28 '17 at 6:20
• @KeithMorrison Sure, but when we get down to such details, does it really matter what the definition is? It would be perfectly possible to define a system of units similar to the SI units but the values of which have no relation to anything currently in use, call them something else, and use those instead. But for what purpose? After all, humans are creatures of habit; if we've got a perfectly good idea of roughly how long a second or a day or a century is, why not base our scientific units on those? As long as it's defined and measurable, I dare say the definition doesn't matter. – a CVn Dec 28 '17 at 11:37
• @KeithMorrison The second is arbitrary. The period of a given radiation from the cesium atom is not arbitrary, but an universal constant. And of course, it's only useful to people who can measure it, just as the second is only useful to societies which have clocks but useless to societies whose most fine time measuring device is the sundial. However, that doesn't make it less universal. – Pere Dec 28 '17 at 11:54
• @KeithMorrison I supposed it was self evident that the practical advantages of such a unit - like the 30 hours day - weren't to be taken seriously. Maybe I should reword that part. – Pere Dec 28 '17 at 11:59

## What is the best unit of measure for the time portion of a non-earth-bound light“year”?

There is none, because time is relative:

According to the theory of relativity, time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other, or by being differently situated relative to a gravitational field. As a result of the nature of spacetime, a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference. A clock that is under the influence of a stronger gravitational field than an observer's will also be measured to tick slower than the observer's own clock.

Even satellites in orbit around the Earth exhibit this phenomenon:

Such time dilation has been repeatedly demonstrated, for instance by small disparities in a pair of atomic clocks after one of them is sent on a space trip, or by clocks on the Space Shuttle running slightly slower than reference clocks on Earth, or clocks on GPS and Galileo satellites running slightly faster.

Thus, even the atomic clocks referenced in other answers are going to tick at different rates on different planets and different space ships.

All we can be sure of is that the arrow of time always points forward.

• While time, and indeed distance, are both measurements that vary according to the movement of the observer, it is also true that there are also certain invariants that are alway true, no matter what speed you are travelling when you make the measurement. One of these invariants is that the speed of light will always appear exactly the same to you, however you are moving, and in whichever direction you measure it. Therefore measurements based on that speed are perfectly sensible, whatever your reference frame. – Jules Dec 28 '17 at 16:36
• No need to go into orbit. My question Have we attempted to experimentally confirm gravitational time dilation? on Space Exploration has some details. – a CVn Dec 28 '17 at 20:33
• "All we can be sure of is that the arrow of time always points forward." Simply not true. The interval between two space-time events is the same to all inertial observers; move-over it is equal to the time experiences by an observer on an inertial trajectory between those events (i.e. the proper time between them) which means that it is quite easy for all observers to agree on the proper time between two events: everyone can measure it naturally in their own frame. – dmckee Dec 29 '17 at 2:37

## Assumptions

I'm assuming you are talking about time and distance within the same relative frame of reference.

## Earth Time

From Wikipedia: https://en.wikipedia.org/wiki/Second

The SI definition of second is "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"

## Earth Distance

From Wikipedia: https://en.wikipedia.org/wiki/Metre

The metre is defined as the length of the path travelled by light in a vacuum in 1/299 792 458 second

This comes out to be about 30.66 periods of Cesium 133

## Universe Time/Distance

If we were to "start over" time and distance could still be based on Cesium 133. Whatever the rest of the universe uses will be dependent on their technologies.

However, instead of an arbitrary count of Cesium 133, it would probably be something more universal like $\ 2^x$ periods of Cesium 133.

You could base your universal prefixes to those used in computers. That is, instead of kilo-,mega-,giga-, you would use bit-, byte-, word-.

Example Measurements

• 1 meter = Distance light travels in 30.66... Periods of Cesium 133

• 1 half-byte distance (~0.5 meters) = Distance light travels in $\ 2^4$ Periods of Cesium 133

• 1 light year = Distance light travels in $\ 28.9915 * 10^{16}$ Periods of Cesium 133

• 1 qword distance ( ~63.3 light years) = Distance light travels in $\ 2^{64}$ Periods of Cesium 133

• 1 second = $\ 9.1923 * 10^9$ Periods of Cesium 133

• 1 word time ( ~7.13 µs) = $\ 2^{16}$ Periods of Cesium 133

• 1 dword time ( ~467 ms ) = $\ 2^{32}$ Periods of Cesium 133

• 1 qword time ( ~63.3 years) = $\ 2^{64}$ Periods of Cesium 133

## Cesium 133

I'm only using Cesium 133 as a reference because that is how a second is officially defined.

Earth's Atomic clocks are improving. There is no doubt that the rest of the universe is using something else. Besides, Cesium 133 clocks may not have a high enough resolution for accurate FTL jumps. Eventually, time resolution could have the resolution of 1 plank-time - a slight variation to A.C.A.C.'s answer.

From Wikipedia: https://en.wikipedia.org/wiki/Atomic_clock

21st century experimental atomic clocks that provide non-caesium-based secondary representations of the second are becoming so precise that they are likely to be used as extremely sensitive detectors for other things besides measuring frequency and time. For example, the frequency of atomic clocks is altered slightly by gravity, magnetic fields, electrical fields, force, motion, temperature and other phenomena. The experimental clocks tend to continue improving, and leadership in performance has been shifted back and forth between various types of experimental clocks.