[HN Gopher] A relativistic framework to establish coordinate tim...
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A relativistic framework to establish coordinate time on the Moon
and beyond
Author : croes
Score : 103 points
Date : 2024-07-11 08:11 UTC (14 hours ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| engineer_22 wrote:
| In the abstract they hint that without a common clock
| communication could be inhibited
| teruakohatu wrote:
| Do they? I don't see that in the abstract, they do state that:
|
| > This understanding also underpins precise navigation in
| cislunar space and on celestial bodies' surfaces, thus playing
| a pivotal role in ensuring the interoperability of various
| position, navigation, and timing (PNT) systems spanning from
| Earth to the Moon and to the farthest regions of the inner
| solar system.
| karmakaze wrote:
| > [...] and their inter-comparisons using clocks onboard
| orbiters at relatively stable Lagrange points as time
| transfer links is crucial for establishing reliable
| communications infrastructure.
| davidw wrote:
| "I was in favour of space exploration until I realised what it'd
| mean for date time libraries"
|
| https://x.com/joe_jag/status/510048646482894848?lang=en
| jiehong wrote:
| Nice!
|
| It made me realise that we currently live in a time that can
| never be accurately referenced outside the planet.
|
| So no software can ever truly define 2024-07-11T00:00 on Pluto.
|
| It also makes me think that the Mass Relais in Mass Effects could
| actually also be atomic clocks forming this galactic time grid of
| reference, so in-game lore seems less implausible.
| zokier wrote:
| The whole point of the paper is to show that we can model the
| time for various bodies to very high degree of accuracy.
| jiehong wrote:
| Indeed! My point being that it's gonna be true someday, just
| not yet.
| pfdietz wrote:
| Or even on/in the planet. The Earth's core is about a year
| younger than the Earth's surface.
| WorldMaker wrote:
| There are interesting theories about how to use constellations
| of Pulsars as galactic "atomic clocks". Pulsars are generally
| extremely predictable in their emissions and with a big enough
| constellation, you can do old fashioned triangulation to get
| relative distance between yourself and enough pulsars to sync
| to some sort of standard time based on synchronicities in
| pulsar timing.
|
| I've not yet seen a full proposed _standard_ for such a thing,
| but it 's also not far from how GPS itself works and how GPS
| forms its standardized time, which is synced to Earth based
| atomic clocks but includes more relativistic effects. Most
| cellphones actually use GPS time rather than "atomic time"
| today, because they need GPS services in general and also
| because cell towers use a variant of GPS time in their
| communications with cell devices for complicated three
| dimensional dances like tower to tower hand-offs.
|
| It's kind of neat how even "Earth time" at its most accurate
| involves relative effects and triangulation in some of our most
| used and trusted devices. (Even NTP sync of non-cellphones uses
| IP pings as an approximate for triangulation to try to reduce
| error in syncing a laptop or desktop to nearby atomic clock
| sources. Though at least today in most internet usage, the
| Internet Protocol is less impacted by relativistic effects.)
| zokier wrote:
| > how GPS itself works and how GPS forms its standardized
| time, which is synced to Earth based atomic clocks but
| includes more relativistic effects
|
| While the GPS satellites internal clocks might operate on
| whatever timescale, it is important to note that the time
| signal that is broadcast through GPS is strictly fixed offset
| from TAI without any additional relativistic shifts. And TAI
| is defined to use the geoid as reference frame.
|
| That is to say that if you have a clock synchronized to GPS
| signal then it should tick exactly at same rate as TAI and
| UTC.
| bloopernova wrote:
| Now I'm wondering just how timekeeping would work with distance
| and/or high relative velocity. Would you observe "ship time"
| until you returned to base, and would then sync ship to base
| time?
| ianburrell wrote:
| The ship would keep local time because that is easy to measure
| and fits with what people are doing. The point of establishing
| Moon time is that it is hard to keep using non-local Earth
| time.
|
| Keep in mind that there is difference between clock measuring
| seconds, and converting to days and times that requires
| choosing a calendar. The ship could use origin calendar,
| destination calendar to make people familiar, or some universal
| calendar. The problem with destination is that it won't sync
| properly until arrival. Or maybe they skew the calendar on the
| last leg.
|
| Also, don't need high relative velocity to have a difference.
| Considering relativistic space travel may be impossible; the
| only may be proposed warp drives.
| jerf wrote:
| That particular problem isn't necessarily materially different
| from the ships we already have that experience major time
| shifts every day. Time zones already create that problem and
| you can just look at the solutions we use today.
| hlieberman wrote:
| Missed opportunity to name it "stardate".
| jvanderbot wrote:
| It strikes me as surprising to imply that we don't have time-
| keeping standards for solar system exploration that take into
| account relativistic differences.
|
| the CSPICE toolkit from JPL/NAIF has a bunch of routines to
| calculate local time, local time of arrival of events from other
| places (light cone, I suppose?), down to the nanosecond.
| nynx wrote:
| That code exists for calculating those things does not mean
| there are timekeeping standards that support them.
| jvanderbot wrote:
| True, should have mentioned (as sibling comment did) that the
| code _uses_ several timekeeping standards to do those
| calculations.
| zokier wrote:
| There definitely are various timescales and standards that take
| relativity into account
|
| https://en.wikipedia.org/wiki/Barycentric_Coordinate_Time
|
| https://en.wikipedia.org/wiki/Ephemeris_time
|
| https://en.wikipedia.org/wiki/Coordinate_time
|
| Etc
| nickdothutton wrote:
| I wonder if Sci-Fi novels contain any info on time
| representation, reference, and distribution.
| bloopernova wrote:
| Kim Stanley Robinson's Mars trilogy mentions the longer Martian
| day. The extra 39 minutes were represented by a 39 minute
| midnight clock freeze between 12:00:00 and 12:00:01. It was
| never mentioned how this worked across the entire planet.
|
| Jack Campbell's Lost Fleet series (starting with _Dauntless_ )
| has a lot of time involved, due to military fleets/flotillas
| maneuvers at light-hour distances:
|
| Fleet A jumps into a system. Fleet B is 6 light hours distant
| across the system. B won't see light from A's arrival for 6
| hours. A won't see B's reaction for _12_ hours, less any
| distance covered. Ships can engage in combat at up to 0.2c
| relative velocity, at a maximum distance of about 1 light
| second.
|
| Fleet A accelerates to 0.1c, Fleet B does the same and they
| approach. Time to contact is 30 hours, and the books discuss
| how difficult it is for humans to rest and focus on other
| things during that time. Our instinctive
| fight/flight/fawn/freeze reaction doesn't translate well to
| waiting 30 hours!
|
| Fleet A and B approach, but because the ships take a few
| seconds to pivot/roll/yaw to maneuver, so there's a critical
| time period where A or B can change position and the opposing
| fleet won't have time to react before the fleets clash. This is
| used to great effect by the skilled fleet commander of the Good
| Guys.
|
| The lost fleet books also discuss maneuvering fleet formations
| when everyone is at light-minute or multiple light second
| distances. There's lots of orders like "at time 15, Echo One
| pivot formation down 30 degrees and starboard 15 degrees".
| Learning to bring all your firepower to bear on the enemy at a
| single moment, while denying them the same opportunity, is a
| very difficult skill to learn in these books.
|
| Aaand I've written way too much. And probably not done the
| fantastic combat in the lost fleet books any justice at all.
| gamegoblin wrote:
| These concepts would make for a killer PVP real time strategy
| game, good write-up
| bloopernova wrote:
| > These concepts would make for a killer PVP real time
| strategy game
|
| Yeah, I deeply hope someone can write it one day. I've
| tried thinking about how you'd model and calculate such
| behaviour, but it's mostly beyond me.
|
| Thank you for the compliment :)
| shagie wrote:
| NEBULOUS: Fleet Command ( https://store.steampowered.com/ap
| p/887570/NEBULOUS_Fleet_Com... - currently 35% off on the
| Steam sale which is ending Real Soon Now)
|
| It is a heavy game. https://youtu.be/eqn7F97M8XA
| shagie wrote:
| > Jack Campbell's Lost Fleet series (starting with Dauntless)
| has a lot of time involved, due to military fleets/flotillas
| maneuvers at light-hour distances:
|
| I'll also mention Dread Empire's Fall by Walter Jon Williams
| - https://en.wikipedia.org/wiki/Dread_Empire%27s_Fall
|
| You again deal with long communication distances and most
| fleet actions are done with missiles. This then has the
| challenge of "how do you control the missiles / select the
| targets at such distances (no AIs)" and there is a class of
| pilots that fly a 'pinnace' which is a small, one person ship
| that is capable of doing high acceleration to keep up with
| the missiles.
|
| During peace times, the pinnace pilots tend to be more about
| prestige and racing.
|
| There was also an instance of moving a jump point thingy that
| _really_ messed up a fleet action (since the fleet, traveling
| at high speed to the edge of the system missed the "go here
| to jump to the next system" and instead had to turn around
| and go back ... which represented a lot of time and
| acceleration (not all species in the universe don't have the
| same tolerance for acceleration).
| SaberTail wrote:
| In Vernor Vinge's _A Deepness in the Sky_ , ships in the far
| distant future are still counting time from the Unix epoch. The
| common belief in the novel, though, is that it's measuring time
| from when humans first became space-faring by walking on the
| moon. But I don't recall it mentioning that there's any attempt
| to account for relativity; ships all keep their own local time.
| ceejayoz wrote:
| The exact quote is on Wikipedia: https://en.wikipedia.org/wik
| i/A_Deepness_in_the_Sky#Interste...
|
| > Take the Traders' method of timekeeping. The frame
| corrections were incredibly complex - and down at the very
| bottom of it was a little program that ran a counter. Second
| by second, the Qeng Ho counted from the instant that a human
| had first set foot on Old Earth's moon. But if you looked at
| it still more closely ... the starting instant was actually
| about fifteen million seconds later, the 0-second of one of
| Humankind's first computer operating systems.
| WorldMaker wrote:
| There's a lot of fascinating discussion around Star Trek's
| Stardate and its seemingly universal metric calendar and times
| referenced as decimal units of day: How does it adjust for
| relativity? Why did they choose the epoch they seemingly chose?
| (Not that many days before Enterprise's 5-Year-Mission, and
| seemingly still years into Starfleet's existence.) How do you
| account for the various obvious real world facts that many
| episodes just picked numbers that sounded cool or random and
| didn't pay attention if they were in the right order in the
| season or overall timeline? (Is that relativistic problems
| creeping in?) They are called Stardates implying the base unit
| is a Day, but it is an Earth-like 24 hour day or was it
| something else, perhaps in a compromise with other Federation
| planets?
|
| From the TNG era onward the various Writer's Bibles took an
| approach of 10,000 days per season to make the math easy if a
| script was given a Stardate in the right season and plenty of
| room for all the scripts in a season to have their own
| Stardates. If the Stardate day is a 24 hour Earth day
| equivalent then seasons were expected to take roughly 3 earth
| years. Or was that a sign that the Stardate day was about a
| third shorter than an Earth day and "five-year mission" did
| still just refer to Earth standard years?
|
| There are all kinds of fan theories. Some weird things in
| canon. Some weirder things in the books and other bits of Beta
| and Gamma "canon".
|
| (I did a bit too deep of a dive into Stardates recently as an
| offshoot of getting the idea to try to display a Stardate-like
| calendar and date stamps in the configurable calendar system of
| the Fantasy Grounds TTRPG hosting application.)
| Rhapso wrote:
| It is very clear that relativity and time dilation due to
| relative velocity is not part of Star Trek cannon. They live
| in a "Toy" universe where everything is easy and quartz
| crystals can be used for FTL travel.
| nickdothutton wrote:
| And I can see already from the child comments you folks did not
| disappoint :-)
| akozak wrote:
| It's a neat idea that you could publish a paper like this that
| establishes a framework for thousands of years.
| alganet wrote:
| > yielding 58.721 ms/day
|
| Can someone kind explain this unit for me? microseconds per day.
|
| Does that mean that the relativistic difference is cummulative?
| In other words, does it add up over time?
| unholiness wrote:
| That's right. While a day passes on earth, a day minus 58.721
| ms passes on the moon (which is moving faster than the Earth).
|
| This multiplies, so after a million days a clock on the moon
| will read 58 seconds behind a clock on the earth.
| alganet wrote:
| Thanks!
| pdonis wrote:
| It's the other way around: while a day passes on Earth, a day
| _plus_ 58.721 microseconds passes on the Moon. The Moon clock
| gradually gets _ahead_ of the Earth clock.
|
| In an Earth-centered inertial frame, the Moon is moving
| faster than the Earth, but it is also at a very high
| altitude, and the altitude effect, which speeds up the Moon
| clock relative to Earth, is much larger than the speed
| effect, which slows it down.
|
| (Note that the above only takes into account the effects of
| the Earth's gravity. The paper also takes into account the
| effects of the Moon's gravity, which don't change the above
| answer qualitatively but do add small corrections
| numerically, so the 58.721 microseconds per day is not the
| actual value the paper ends up with.)
| alganet wrote:
| Cool, thanks!
|
| I'm assuming this affects clocks (and things) but not time,
| right? Time itself is no different on the moon (it's not
| the future there).
|
| I know this must be true otherwise we would be surrounded
| by time travellers by now. So, where does this cancels out?
|
| My intuition says that if we have two clocks, each clock
| with a display and a laser pointing to each other, and we
| put one of them on the moon and the other on earth, someone
| observing it from a third equidistant point would see both
| lasers blinking at the same rate.
|
| If that's true (I don't know if it is) both of your answers
| are kinda right, aren't they? From earth, the moon clock
| ticks slower compared to earth clocks, therefore it lags
| behind. From the moon, the moon clock ticks faster compared
| to earth clocks, therefore it skips ahead, and vice-versa.
| I am not sure though, I feel like I'm missing something.
| pdonis wrote:
| _> I 'm assuming this affects clocks (and things) but not
| time, right?_
|
| What's the difference?
|
| _> otherwise we would be surrounded by time travellers
| by now_
|
| I'm not sure what your reasoning is here.
|
| _> where does this cancels out?_
|
| I don't understand the question. What is supposed to
| cancel out?
|
| _> someone observing it from a third equidistant point
| would see both lasers blinking at the same rate._
|
| No, they wouldn't.
|
| _> From earth, the moon clock ticks slower compared to
| earth clocks_
|
| No, it ticks faster. That was my point.
| alganet wrote:
| Consider this scenario: - I get into a
| spacecraft, go into orbit around earth. - Once in
| orbit, I start accelerating until my clock ticked faster
| for long enough to be 1s ahead of earth. - Once I'm
| 1s ahead of earth, I capture transmissions my buddy sent
| to me of the stock exchange rates. - My buddy, on
| the ground, has a telescope and is ready to invest or
| sell stocks depending on whether I stop or keep
| accelerating. - My buddy now has knowledge about
| the future, I land and share the money we stole from the
| future with him.
|
| My intuition says this should be impossible, but it seems
| that I got the "why" wrong. Or maybe everything wrong.
| pdonis wrote:
| _> Consider this scenario_
|
| Let me re-describe your scenario properly:
|
| Your buddy sends you information about stock exchange
| rates when his clock reads 12 noon exactly. You are one
| light-second away from him, so his message is received by
| you at 12 noon + 1 second, his time. That is also 12 noon
| + 2 seconds, your time, but that doesn't matter; it's
| still information about rates when his clock said 12
| noon, not rates when his clock said 12 noon + 1 second, 1
| second after he sent the message.
|
| In other words, the fact that your clock ticks faster and
| gets "ahead" of your buddy's does not mean you receive
| information from your buddy's future.
| alganet wrote:
| Your example makes sense, the distance for light to
| arrive makes it impossible (also, the distance for the
| light from the craft to reach the telescope in step 4,
| it's a round trip).
|
| Going further than this is way above my skillset :D
| Thanks for the time to indulge my curiosity, I'll study
| more and try to develop a better intuition.
| pdonis wrote:
| _> the distance for light to arrive makes it impossible_
|
| If you mean the 1 second light travel time is the same as
| the 1 second clock difference, you can increase the clock
| difference by just spending longer in orbit. For example,
| you could wait until the clock difference was 1 hour.
| Then, if your buddy sent you a light signal at 12 noon by
| his clock, it would arrive at 1 pm + 1 second (1 second
| light travel time) by your clock. But it would still be
| telling you stock exchange rates at 12 noon by your
| buddy's clock, not 1 pm by your buddy's clock.
| pdonis wrote:
| _> Once in orbit, I start accelerating until my clock
| ticked faster_
|
| Note that this is wrong: you don't have to accelerate to
| make your clock tick faster. You just have to be in orbit
| at a high enough altitude for the speedup due to altitude
| to outweigh the slowdown due to your free-fall orbital
| speed.
| alganet wrote:
| I was under the impression that the speed in orbit
| matters, therefore accelerating matters.
|
| From the paper:
|
| > Ph0 is the effective gravitational potential in the
| rotating frame, which is the sum of the static
| gravitational potential of the Earth, and a centripetal
| contribution
|
| This is just so I can catch up with a specific desired
| dilation relative to earth.
|
| I don't want to make my orbit higher, on the contrary,
| the less distance the better so communication is faster.
| pdonis wrote:
| _> I was under the impression that the speed in orbit
| matters_
|
| It does.
|
| _> therefore accelerating matters._
|
| No, it doesn't. In a free-fall orbit, proper acceleration
| is zero; you are weightless. "Accelerate" would mean
| firing your rockets to change your orbit. You don't want
| or need to do that.
|
| It is true that there is a _coordinate_ acceleration for
| a body in a circular orbit, in coordinates centered on
| the Earth, but coordinate acceleration is irrelevant to
| what we are discussing.
|
| _> This is just so I can catch up with a specific
| desired dilation relative to earth._
|
| As I said, you do that by staying in an appropriate free-
| fall orbit for a long enough time. You don't need or want
| to fire your rockets.
|
| _> I don 't want to make my orbit higher, on the
| contrary, the less distance the better so communication
| is faster._
|
| But the lower your orbit, the less your clock speeds up
| relative to Earth clocks. And if your orbit is low
| enough, your clock will actually run _slow_ compared to
| Earth clocks (because the altitude effect no longer
| outweighs the effect of your orbital speed). For example,
| clocks on the ISS run slow compared to Earth clocks.
| alganet wrote:
| > "Accelerate" would mean firing your rockets to change
| your orbit
|
| That's almost what I meant! Spacecraft, acceleration to
| pick up speed (not to go higher), stock-exchange
| cheaters.
|
| I don't get the "don't need" or "don't want". It is part
| of my scenario. I also don't want a twin falling into a
| black hole, but it is a thought experiment that helps put
| things in perspective, specially for layman like me.
|
| I always heard of the scenario of the twin at the speed
| of light that remains younger. I am introducing an
| element of communication (originally, clocks with laser
| beams then stock exchange rates) into that scenario and
| trying to understand what the offsets mean.
|
| This is all above my paygrade, I know, so don't worry! I
| know I'm far from getting it and I don't want to bother
| :)
| pdonis wrote:
| _> Spacecraft, acceleration to pick up speed (not to go
| higher)_
|
| That would mean you would no longer be in a free-fall
| orbit, you would be moving faster than free-fall orbit
| speed, and your clock would run slower. Depending on how
| much you sped up, you might even end up having your clock
| run slower than Earth clocks.
|
| _> stock-exchange cheaters_
|
| Nothing you can possibly do with your rocket will enable
| you to cheat on the stock exchange. No matter what you
| do, you can't have your buddy's light signals contain
| information from his future.
|
| _> I don 't get the "don't need" or "don't want"._
|
| You don't need or want to fire rockets to speed up if
| your objective is to have your clock run as fast as
| possible relative to Earth's at a given altitude. Indeed,
| if you really want your clock to run as fast as possible
| relative to Earth's clock at a given altitude, you should
| use your rocket to "hover" motionless (meaning zero speed
| relative to Earth's center of mass) at that altitude, not
| to speed up relative to free-fall orbital speed.
| alganet wrote:
| > Nothing you can possibly do with your rocket will
| enable you to cheat on the stock exchange.
|
| I'm not trying to come up with an experiment that enables
| stock-exchange cheating. I'm trying to come up with a
| thought experiment that highlights the effect of speed on
| time dilation, with the purpose of understanding what the
| accumulation of "microseconds per day" means, and in the
| spirit of the paper posted I want to put an element of
| information/communication there (clocks with laser beams,
| stock exchange, doesn't matter what it is, for this
| purpose they're equivalent).
|
| > Depending on how much you sped up, you might even end
| up having your clock run slower than Earth clocks.
|
| So there is at least a component of the "microseconds per
| day" offset formula that contributes to a slowing down
| compared to what is being orbited, is that correct?
|
| If I got this right, speed matters but it is negligible
| compared to other factors for objects like the moon or a
| human made satellite. That's OK. Like I said, I don't
| want to actually cheat in the stock exchange, I want to
| understand that effect.
| pdonis wrote:
| _> a twin falling into a black hole_
|
| _> the twin at the speed of light that remains younger_
|
| Neither of these are actual scenarios in relativity. I'm
| not sure where you are getting them from but your
| information appears to be garbled.
|
| There is a so-called "twin paradox" in relativity (not
| actually a paradox so the name is a misnomer), where two
| twins who take different trips (in the original scenario,
| one stays at home and one travels out to a distant star
| and back again at high speed) can end up with one younger
| than the other when they meet up again. But neither twin
| can travel at the speed of light; that's impossible for
| an ordinary object like a person. And neither twin can
| fall into a black hole, because if they did they could
| never come back out to meet up with the other twin.
| alganet wrote:
| Nice, I'm glad you got the reference despite my lack of
| proper terminology. It's a thought experiment, no one
| actually wants a twin paradox, but it is worth thinking
| about it. I'm sure you get my point.
| doctorpangloss wrote:
| It might be easier to think about this as "if you are on
| the moon and point a telescope at a clock on earth, clock
| hands move slower on earth than on the moon." This is
| distinct from "all humans everywhere have a normative
| experience that the clock hands right next to them move
| at the same speed." Or "you never experience falling into
| a black hole, but you do fall in." You can also watch the
| movie Interstellar, it has clock hands moving slower in
| gravity wells as a minor plot point.
| IIAOPSW wrote:
| I think what you are trying to say here is that if both
| the Earth and Moon reference frame were blinking out a
| 1-second clock signal via a laser pointer to a neutral
| 3rd party reference frame, the third party would see
| pulses at 1-second intervals from both sources.
|
| This is false. Time itself is in fact progressing at a
| different rate in both frames, and a second in one is not
| the same as a second in the other.
|
| But, time still "works the same way" for both reference
| frames in the sense that its not like the clocks in one
| appear to move in "slow motion". An observer on Earth or
| the Moon still sees clocks ticking at one second per
| second, and objects appear to move and react in the
| ordinary physical ways at the same rate you expect them
| to. But this is because the observer is also an object in
| that reference frame, so their perception of everything
| is in the same "slow motion" as the objects they observe.
|
| Now, if an observer on the Moon was to watch an observer
| on Earth with a telescope or vice versa, then they would
| indeed see "the video playing at a slightly wrong speed".
| The effect is relative between observers, not local to an
| observer. That's why its called relativity.
| alganet wrote:
| Thanks! I'm not trying to say anything :D I'm just trying
| to understand it better. That's why I sprinkled all my
| comments with healthy doses of "I don't know". I really
| don't know.
|
| The 3rd party seeing blinks at the same rate was just a
| guess, I'm happy to learn that this guess is false.
| mr_mitm wrote:
| Moves faster than than the Earth relative to what? Isn't it
| the gravitational time dilation that is the relevant effect
| here?
| nh23423fefe wrote:
| its actually not a unit either. its a dimensionless ratio
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