Mars has a solar day equal to 24 hours, 39 minutes and 35.244 seconds. This is 2.75% longer than an Earth solar day, and close enough to the period of the human sleep–wake cycle that it's plausible civil timekeeping on Mars might be based around it.
Once a (official or de facto) standard concept of civil timekeeping exists on Mars, what will be the first standard way to talk about the time of day among ordinary Martians? This market ignores questions about how a Martian calendar will otherwise be set up, it's exclusively about how Martians will talk about the time of day within a solar cycle. It also ignores the concept of timezones - resolution of any of the answers doesn't depend on whether everyone on Mars uses the same timezone or separate ones.
This requires there to be a concept of ordinary civilians who live on Mars and aren't there as employees of an Earth-based mission - we are asking about what system ordinary Martians will use for timekeeping day-to-day.
There may be multiple standards used in different jurisdictions on Mars, or among different groups of people. Whilst I'll try to resolve based on whichever seems to be the dominant one when such standards first emerge, if it's close I may wait to see if one reaches dominance. The spirit of the question is to resolve based on what most people actually use day to day, whether it's an official standard or not.
There are a few candidates that come to mind:
A day will be 24h×60m×60s using a "mars second" equal to 1.0275 SI seconds.
This will resolve YES if the solar day is divided into 24h of 60m of 60s each, where a second is a fixed interval of time defined with respect to fundamental constants such as atomic transitions. This Martian second need not be defined as 1.0275 SI seconds - it's fine if Mars defines their own standard with respect to a different atomic transition or whatever, as long as the result is a martian second that is 1.0275 SI seconds long. Mars need not use this same "Martian second" in engineering or physics, this question is only about civil timekeeping.
This answer will resolve YES regardless of whether leap seconds are used to keep the time system in sync with mean solar time (as opposed to just allowing for drift).
A day will be 24h×60m×60s where a "second" is a unit of angle rather than time, equal to 1/86400 of a revolution (i.e. the equivalent of Earth's UT1)
This is a system where a "second" isn't a unit of time at all, but a unit of angle of rotation of the planet with respect to the sun. The time duration corresponding to a second isn't fixed, and watches and clocks need to sync with astronomical observations of Mars' rotation on long timescales in order to know what time it is is this time system, even if they're as precise as atomic clocks. However, this system needs no leap seconds to stay in sync with mean solar time - it is mean solar time, essentially being constantly kept in sync.
A day will be 24 hours, 39 minutes and 35.244 SI seconds long
People will keep using SI seconds, and just deal with the fact that the day is not a whole number of hours long, and the last hour doesn't have 60 minutes, and the last minute doesn't have 60 seconds. Watches will tick over from 24:39:35 to 00:00:00.
Again, this answer resolves YES regardless of whether leap seconds are used to keep this time system in sync with mean solar time.
Time of day will be an incrementing number of SI seconds from 0 to 88775.244 (possibly rounded to an integer, with leap-seconds every 4 days or whatever, or no leap seconds and allowing it to drift)
Not too much to explain about this one. They'll count SI seconds. Maybe they'll keep the day to an integer number of seconds, and maybe they'll correct for the resulting error with leap seconds, or maybe they'll just allow for the drift compared to mean solar time.
A day will be 24h×60m×60s using SI seconds (and will drift with respect to mean solar time by ~40 minutes a day)
That is, they just use Earth days, and tolerate that sunrise and sunset move by 40 minutes a day.
Other
Feel free to recommend more, including systems not even approximately based around the Mars or Earth solar cycle. But we're looking for a description of how regular Martians will talk about time on a timescale comparable to or less than a Martian solar day, for example how they will schedule appointments a few hours out and communicate to each other when to meet.
This question's close date should be extended until Mars colonisation happens, and then long enough for de facto standards to be established among ordinary Martians.
Related questions
@PlasmaBallin @Shump suggested below 10 "hours" 100 "minutes" 100 "seconds", which still leaves ambiguous whether they're units of time or tracking the rotation of the planet, but yeah, happy to add things like that. And any given answer should still resolve YES whether the units are called "seconds" or not.
Maybe I should add a catch-all "some kind of decimal splitting of the day - fixed-length time units" and a "some kind of decimal splitting of the day - rotation-angle-tracking time units".
@chrisjbillington Yeah, I agree it doesn't really matter if they're called seconds or not, I was just thinking of something that would represent any way of splitting up the Martian day in a way that's completely unrelated to how we split up Earth's day. But maybe it would be better to only out down a specific option like decimal splitting, since otherwise the catch-all might be too broad if you want to later add more specific options that it overlaps with.
This isn't happening. A second is already a unit of angle equal to 1/1,296,000 of a revolution. We already have enough confusion just because the U.S. uses different units than the rest of the world - imagine how ridiculous it would be if we had two different definitions of a second as a unit of time and two different definitions of it as a unit of angle measure. This would be ridiculously confusing.
@PlasmaBallin A second in UT1 is 1/86400 of a revolution presently, and a second before 1960 was defined as a unit of time equal to 1/86400 of a mean solar day, so there is precedent here. "Mean solar day" turned out to be an incoherent idea since the rotation rate of the Earth is slowing, so the surviving idea from that is a unit of angle - if it's horribly ambiguous, it's already so!
@chrisjbillington But UT1 is a time standard. As far as I know, it doesn't define any units of angle, even if it bases certain units of time on certain angles of rotation.
If a second was defined as "the amount of time it takes for the planet to rotate 1/86400 of a revolution", that just defines a unit of time that doesn't have a fixed value (the length of a second increases as Earth's rotation slows down), not a unit of angle. I have never heard anyone use this notion of a second to refer to an angle.
@PlasmaBallin OK, well that's what I mean. I don't much mind if people call it a variable unit of time or a unit of angle, though to me it seems more accurate to describe it as the latter. UT1 is all about syncing up with the solar cycle, so it's measuring (some kind of average of) the earth's angle of rotation with respect to the line joining the earth to the sun.
@chrisjbillington I think the option is misleading then. It specifically says, "A second is a unit of angle rather than time," which implies that it would be used as, well, a unit of angle rather than time.
@PlasmaBallin Well it would be, that's what UT1 is doing, no? Even if you don't think of it that way. How would you recommend I get this point across in a non-misleading way, whilst ensuring the distinction between UT1 and e.g. TIA or UTC is clear?
@PlasmaBallin here's Wikipedia:
Universal Time (UT or UT1) is a time standard based on Earth's rotation.[1] While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle with respect to the International Celestial Reference Frame (ICRF), called the Earth Rotation Angle (ERA, which serves as a modern replacement for Greenwich Mean Sidereal Time). UT1 is the same everywhere on Earth. UT1 is required to follow the relationship
ERA = 2π(0.7790572732640 + 1.00273781191135448 · Tu) radians
where Tu = (Julian UT1 date - 2451545.0).[2]
So my characterisation is inaccurate in that I've just said "angle" when I should say "with respect to the line joining Mars to the Sun" or whatnot, though in practice the rotation angle w.r.t the celestial sphere would likely be used for the actual measurements.
@chrisjbillington There is already a name for the thing I think you're intending, so just use that: https://en.wikipedia.org/wiki/Timekeeping_on_Mars#Coordinated_Mars_Time
Also, a second in mean solar time isn't defined as 1/86400 of a revolution anyway (that would give you a sidereal day of 86400 seconds, not a solar day), so no matter what happens, a second on Mars is definitely not going to be defined that way either.
@PlasmaBallin Yes, I meant rotation with respect to the sun - edited the answer to specify this.
I could include the name, but since the other answers actually describe what they are, I think it's good to still do that.
@chrisjbillington I still think calling it "a unit of angle rather than time" is misleading. Maybe something like, "the time is defined based on the angle wrt the sun," rather than saying that seconds themselves are a unit of angle.
I think I'm going to agree to disagree at this point. It is a unit of angle. UT1 measures the angle between the prime meridian and the mean location of the sun in the sky when smoothing over some periodic motion. That's what UT1 is. Saying this to someone who doesn't already know what UT1 is I think is useful, because the fact that UT1 measures this angle instead of, well, actual time, is the fundamental difference between it and other time standards. "based on angle" is too vague, I want to tell them what it actually is, and it's 1/86400 of a rotation of the planet with respect to (some average of the location of) the sun. That is what a UT1 second is.
If anyone does know what UT1 is and would be confused by this, I've written "The equivalent of Earth's UT1" there too.
Really depends on sociopolitics. At the start I imagine they would be using Earth-derived time, but when they become less dependent on Earth I can't imagine they would want to keep using that.
Seconds as angle is really awful. How are computer systems supposed to handle variable-length seconds?
My guess for other would be a decimal-like system, something like 10 hours 100 minutes 100 seconds,
How are computer systems supposed to handle variable-length seconds?
Same way they do now! Syncing with a time server. Current Earth computer clocks are far too inaccurate for the variable-length to be meaningful anyway - it's not that variable. And even if computers all have atomic clocks in them in the future, they'll be able to calibrate to the current rotation rate as part of the syncing and be accurate for a long time in between syncs. Pretty sure computers are already doing this since their quartz crystals aren't perfect. It will be no different.
In fact you could point all Earth's computers at time servers in UT1 instead of UTC and apart from the transition being about as problematic as a leap-second (which currently computers have no good way to deal with), Earth computers would not be able to tell the difference.
UTC was a mistake and we should have all been using UT1 on Earth for civil time anyway.
FWIW, UT1 doesn't factor in all rotational motion of the Earth, just the long-term stuff. Periodic shorter-term fluctuations in the rotation speed of Earth are just ignored, I believe, we take the mean over them or something like that.
My guess for other would be a decimal-like system, something like 10 hours 100 minutes 100 seconds,
Want me to add it as an option? Though there are three options:
10 hours 100 minutes 100 seconds, where a "second" is 0.8877 SI seconds, and you insert leap seconds to keep it in sync with mean solar time
10 hours 100 minutes 100 seconds, where a "second" is 0.8877 SI seconds, and you don't insert leap seconds, accepting that it will drift with respect to mean solar time
10 hours 100 minutes 100 seconds, where a "second" is an angle equal to 1/100000 of a revolution
So far I've not distinguished between whether leap seconds are used or not in systems that use a fixed-length second, I don't think that's super relevant. So I guess you're interested in the first two options (which are the same if you ignore whether leap seconds are used).
The ability to keep in sync with solar time without leap seconds is one of the appeals of using mean solar time (i.e. variable-length seconds that are more like a unit of angle than of time).
@chrisjbillington I don't actually see what would be so bad about this, though. It would definitely be weird, but not any weirder than having to use different units of time than everyone on Earth.
@PlasmaBallin You won't be able to think about time differences across the boundary easily. You want 8 hours of sleep - when should you set your alarm for? Obviously you could have an alarm be set in the form of an "8 hours from now" setting, but then you can't set it in advance - etc.
You won't be able to schedule work shifts among employees that are e.g. an integer number of hours and all equal. Someone's going to get a shift that's a funky number of hours. Of course, payroll software can calculate it, but it's annoying to think about. I get a 30 minute break, when does it end? Oh it overlaps the end of day, better set a timer instead of just looking at my watch.
Like, all the problems are solvable, but things are simpler when your day has a whole number of hours. Why bother having hours if you don't have a whole number in the day?
@chrisjbillington I don't setting alarms is that big of a deal. You can treat the extra time as basically 40 minutes when calculating numbers that don't need to be precise. And breaks in work shifts would only apply to people who are working at about midnight. Really, I think the biggest problem it would create might just be that the time zones can't all be exactly 1 hour apart. You'd have to have one place where it jumps by 39 minutes and 35.244 seconds instead, which would be weird for the people living near the boundary of that time zone.
@PlasmaBallin The time difference between any two timezones would also be sometimes a whole number of hours* and sometimes not, depending on the time of day.
(or 15 minutes, or whatever resolution they decide to split up their timezones in)