I Researchers calculate how much faster time passes on the Moon

[pinball1970]

TL;DR Summary

A team of physicists with NASA's Jet Propulsion Laboratory at the California Institute of Technology has calculated more precisely how much faster time passes on the moon than on the Earth.

Fro phys.org

"The team in California has used math to calculate the difference in time passage between the Earth and moon, and also between both bodies and the solar system's barycenter.

In so doing, the team found that time on the moon ticks by at 0.0000575 seconds faster per day (57.50 µs/d) than it does on Earth. Based on that number, other calculations can be made—if a person were to live on the moon for 274 years, for example, they would be 5.76 seconds older than they would be had they lived on Earth all that time.

The work by the team is just the first step in establishing a standardized lunar time; meetings will have to be held between various entities to develop agreements, ensuring that everyone involved in lunar activity is on the same timetable."


paper here https://arxiv.org/abs/2406.16147

 

[anuttarasammyak]

The work by the team is just the first step in establishing a standardized lunar time; meetings will have to be held between various entities to develop agreements, ensuring that everyone involved in lunar activity is on the same timetable."

Has the standardized Earth time been established already ?

 

[pinball1970]

Has the standardized Earth time been established already ?

I took that as a given.

If they have accurately calculated that time on the moon is faster by a certain amount, it must be faster compared to a specific time on earth?

The paper is too far above my head unfortunately although I did look at it. Something for you guys.

 

[DaveC426913]

The team in California has used math to calculate

Ah yes - a marked advancement over the chicken bones and tea leaves of last year...

 

[pinball1970]

Ah yes - a marked advancement over the chicken bones and tea leaves of last year...


View attachment 348163

I nearly edited that but I thought I should quote directly.

It does read a bit naff.

 

[Vanadium 50]

I didn't read all 15 pages. Why is this interesting? Other than using math, of course.

 

[PeterDonis]

Has the standardized Earth time been established already ?

Yes, it's time on the geoid of the rotating Earth, as noted in the paper.

 

[DaveC426913]

I didn't read all 15 pages. Why is this interesting? Other than using math, of course.

"...ensuring that everyone involved in lunar activity is on the same timetable."

I think it's interesting that they seem to be anticipating a very active era of lunar ...er... activity.

Gotta keep them lunar trains running on time...

 

[Vanadium 50]

Good thing we had GPS and all these ppb-level corrections in 1969 or we never would have made it to the moon.

 

[Ibix]

It does sound a bit like a solution in search of a problem, doesn't it? Having a single well understood and clearly specified time standard would undoubtedly be useful if we were deploying GPS (LPS?) systems there, or doing other high precision relativity experiments. But we aren't, that I'm aware of.

Are there plans to put interferometric telescopes on the moon or something? Or LIGO type GW detectors?

 

[DrGreg]

if a person were to live on the moon for 274 years

A bizarre figure to choose as an example!

 

[Ibix]

A bizarre figure to choose as an example!

It's 100,000 days, which is a bit less arbitrary. Well, no less arbitrary, but at least round.

 

[DrGreg]

It's 100,000 days, which is a bit less arbitrary. Well, no less arbitrary, but at least round.

Ah I didn't realise. Explicable, but still a little bizarre. 27.4 years would have been a better example.

 

[pinball1970]

I didn't read all 15 pages. Why is this interesting? Other than using math, of course.

Yeah it's a new paper. I thought coordinating information between a fixed reference here and the moon would have been something of interest.

 

[pinball1970]

A bizarre figure to choose as an example!

Yeah. I don't know the long term plans of NASA

 

[Vanadium 50]

A bizarre figure to choose as an example!

We need an "oddly specific" emoji.

GPS (LPS?) s

GPS is fine. The moon is a globe.

 

[Ibix]

I thought coordinating information between a fixed reference here and the moon would have been something of interest.

I think it's a complex technical challenge, but kind of in the same sense a 100,000 piece jigsaw puzzle is. If you can do a 100 piece puzzle you can do the 100,000 piece one - if you have the patience.

The interesting question is why you would bother, and that section seems a bit light. The discussion at the end of the paper proposes some kinds of things you might use this for (a lunar GPS, basically, and then anything you'd use GPS for on Earth) but unless I missed something it all seems quite speculative. It's not "we need this for mission X", more like "this is an enabler for things that aren't even on the horizon yet".

GPS is fine. The moon is a globe.

One Star Trek novel (one of Diane Duane's, I think) had the Enterprise enter hephaestosynchronous orbit above Vulcan. I feel like there should be a better name than "lunar GPS"...

 

[Vanadium 50]

Isn't "geography of the moon" bad enough?

 

[pinball1970]

Isn't "geography of the moon" bad enough?

It's all relative I suppose.

 

[mathwonk]

mathematician weighing in here with arithmetic trivia. 274 years is a bit more than 100,000 days; in exactly 100,000 days the excess age would of course be about 5.75 and not 5.76. So the choice of time frame is still rather odd to me. I think I would have just said that in 100 years one ages a little over 2 seconds more.

 

[pinball1970]

mathematician weighing in here with arithmetic trivia. 274 years is a bit more than 100,000 days; in exactly 100,000 days the excess age would of course be about 5.75 and not 5.76. So the choice of time frame is still rather odd to me. I think I would have just said that in 100 years one ages a little over 2 seconds more.

They didn't include all the terms in the calculation either.

"...omitted O(c−4) terms in this expression, when evaluated at the Earth, contribute up to ∼ 9.74 × 10−17, too small to consider."

 

[Hornbein]

If is published then their goal has been achieved.

 

[ohwilleke]

Why is this interesting?

It builds intuition about the magnitude of gravitational effects on the passage of time in GR.

It is a bit like learning to use ºC without converting if you grew up using ºF. It helps to have benchmarks like normal human body temperature, room temperature, a chilly day, and a hot day to make sense of what the number mean through concrete examples.

I knew it was a small effect. But, without doing the math, I wouldn't have been able to guess if the effect was on the order of magnitude of a day, an hour, a minute, a second, or a microsecond per lifetime. Now I know: one or two seconds per lifetime. With a few more examples, in my head, I can better guess without calculating roughly what that kind of effect should be, as a reality check on any math that I do, and in deciding right off if this is a factor significant enough to include in a particular calculation.

 

[Vanadium 50]

It builds intuition about the magnitude of gravitational effects on the passage of time in GR.

Really? Whose intuition is better because of this? And why stop here? Why not Ganymede? Or Triton?

 

[ohwilleke]

Really? Whose intuition is better because of this?

Anyone he needs to understand how gravity impacts the passage of time.

And why stop here? Why not Ganymede? Or Triton?

Sure. And, maybe Jupiter, a white dwarf, and a few km out of the event horizon of Sgr A*. Intuition comes from examples, not rules. The more the merrier.

 

[Herman Trivilino]

Are there plans to put interferometric telescopes on the moon or something? Or LIGO type GW detectors?

I think they just want a standard that is as future-proof as possible.

 

[pinball1970]

In the interest of follow up (although I am aware that not many of you found it interesting/meaningful)

From the paper above.

"In conclusion, more work is needed to specify the details of the relativistic time and position transformations for various users in cislunar space (e.g., landers, orbiters, Earth-Moon Lagrange points). The introduction and maintenance of a self-consistent, fully-relativistic LCRS are essential for this purpose. Additionally, supporting this coordinate system for various practical applications (e.g., PNT services, frequency transfer, astronomy, lunar geology,fundamental physics) is crucial. This work is ongoing, and results will be reported when available."

This alert on Monday. https://iopscience.iop.org/article/10.3847/1538-3881/ad643a

From the abstract.

"This formalism is then used to compute the clock rates at Earth–Moon Lagrange points. Accurate estimation of the rate differences of coordinate times across celestial bodies and their inter comparisons using clocks on board orbiters at Lagrange points as time transfer links is crucial for establishing reliable communications infrastructure."

The first paper gives a difference of 57.5µs/d and this one gives 56.02µs/d

 

[jbriggs444]

crucial for establishing reliable communications infrastructure

The first paper gives a difference of 57.5µs/d and this one gives 56.02µs/d

High speed data circuits such as a DS-3 or an OC-3 have a frequency tolerance of 20 parts per million. That is 1.7 million microseconds per day.

Even on Earth, network links do not depend on externally synchronized clocks. One embeds timing information into the transmitted signal.

I've run reliable terrestrial communications networks without any need for externally synchronized clocks at the sub-microsecond level.

 

[pervect]

Has the standardized Earth time been established already ?

There are a number of standardized Earth times - the most relevant ones are probably TAI time, based on atomic clocks standardized to correct for altitude above sea level, https://en.wikipedia.org/wiki/International_Atomic_Time, and UTC time (the standard civil time), which differs from TAI time by a number of "leap seconds". The purpose of the leap seconds is to keep a version of the atomic time that is also synchronized to the Earth's rotation, as said rotation changes measurably. Rather than do this continuously, fixed offsets are added or subtracted from the atomic time as needed.

Traditionally, the Earth's rotation has been slowing down as it transfers angular momentum to the moon (via tidal interacations, but recently, for reasons that aren't entirely clear (there may be more current info on this out there if you do some research) the Earth's rotation has speed up.

There are a whole bunch of other time standards as well, if you really get into it. To name a few, TCB, TDB, GPS, and UT. There are some important ones I'm forgetting, all I can recall are the ICRS (International Celestial Reference Systems) and and GCRS (Geocentric Celestial Reference System), but those are coordinate system definitions which including both time and space. Those were adopted by the IAU, the Internatioanl Astronomical Union, most of the other time standards I mentioned are from the BIPM, the organization created by the treaty of the metre and the keeper of the SI standards.

https://spsweb.fltops.jpl.nasa.gov/portaldataops/mpg/MPG_Docs/Source Docs/USNO_Circular_5.1.pdf looks like it might be good reading if you want to get really technical.

 

[Vanadium 50]

Even on Earth, network links do not depend on externally synchronized clocks

Good thing, too. The speed in electronic cables varies by several ppm per degree. I expect fiber to be a little better, but mot much. You'd never keep sync across a city, let alone a country.

 

[WWGD]

Good thing, too. The speed in electronic cables varies by several ppm per degree. I expect fiber to be a little better, but mot much. You'd never keep sync across a city, let alone a country.

I believe some countries like Korea, have ultrafast internet countrywide. Maybe the can sync somewhat within the mega conurbation of Seoul. High population densities make it easier.

 

[jbriggs444]

I believe some countries like Korea, have ultrafast internet countrywide. Maybe the can sync somewhat within the mega conurbation of Seoul. High population densities make it easier.

What is the use case? For what applications is NTP insufficient? Yes, within a data center where latency is low, one can deploy protocols such as PTP and get sub-microsecond precision. https://www.broadcom.com/blog/time-synchronization-in-data-center-networks

Note that Seoul has a radius of about 15 km (50 microseconds).

In any case synchronization is a service provided by the network, not a prerequisite for building the network.

 

[Vanadium 50]

Sure, but why not just using the existing, self-symcing protocols? (Which is what I believe they do). Why bother rolling your own which is a) technically more difficlutt and b) provides no real advantage.

 

[WWGD]

Sure, but why not just using the existing, self-symcing protocols? (Which is what I believe they do). Why bother rolling your own which is a) technically more difficlutt and b) provides no real advantage.

I didn't make any suggestions; just brought it up as somewhat-related.

 

[jbriggs444]

Sure, but why not just using the existing, self-symcing protocols? (Which is what I believe they do).

Indeed.

One might think of classical RS232 serial. You agree on a baud rate at both ends, a number of start bits and a number of stop bits. Let's say one start bit, one stop bit, eight data bits and no parity at 300 baud.

When the sender has a byte to send, it raises the voltage for 1/300 of a second. That's the start bit. For the next 1/300 of a second, the sender sets the voltage corresponding to the low order bit in the byte. And so on for the next seven 1/300 of a second for the remaining seven bits. Then the sender raises lowers the voltage for a final 1/300 of a second. That's the stop bit.

Done. 10/300 of a second used. One byte transmitted. 300 baud gets you 30 characters per second.

The receiver only needs a clock that matches the transmitter to within 5 percent or so. You need to be accurate to within a fraction of one bit time per frame. For RS232 the frames are normally 10 bits.

Note that because both the idle condition and the stop bit are low voltage and the start bit is a high voltage, one is guaranteed to have a signal transition at the beginning of each character frame.

The framing for physical layers such as T1 are more involved and involve things like bit stuffing to ensure that have signal transitions at a reasonable rate. Those transitions let you re-synch the receive clock.

 

[Vanadium 50]

300 baud? How retro!

As you know, it may take some data for a new receiver to know "where it is in the stream". If every 8 bits is in a 10 bit stream, with bit 0 always 1 and bit 9 always 0 (or whatever), there may be multiple 0 -> 1 transitions that might be the start of a frame. But the next frame comes along, and the possibilities decrease. Even if you need 10 frames to figure out where you are, it's a fraction of a second.

Once you are synced, there's enough traffic to easily keep sync.

This global external syncing would save you a fraction of a second in the time between Power On and Ready, and possibly - possibly - let you use a frame with a little less overhead. At great expense.

 

[jbriggs444]

300 baud? How retro!

I started on an ASR-33 at 110 baud using an acoustic coupler. 1972 or so.

As you know, it may take some data for a new receiver to know "where it is in the stream". If every 8 bits is in a 10 bit stream, with bit 0 always 1 and bit 9 always 0 (or whatever), there may be multiple 0 -> 1 transitions that might be the start of a frame.

Not a problem if the line is idle when you hook up. An idle line is just sitting there at 0 volts.

In practice, I do not ever recall an issue. You could turn on a VT-100 connected to a cable was spewing data and it would just start displaying the text once the terminal was ready. You might have a gibberish character or two. [We did not use hardware flow control e.g. with RTS/CTS. I'd generally loop pin 4 back to pin 5 at the connector just in case the end point cared. Same with 6 and 20]

But the next frame comes along, and the possibilities decrease. Even if you need 10 frames to figure out where you are, it's a fraction of a second.

Yep.

 

[pervect]

This has gotten very long, so I'm going to make my main point in advance. That point is that one of the reasons we have so many standards is the relativity of simultaneity, a key feature of SR that is inherited by GR. For extremely high precision applications, when we adopt the concept of different ideas of spatial symmetry, we wind up with different notions of simultaneity.

Going a bit more into the weeds. I find that clock synchronization makes more sense from the viewpoint of a coordinate system, such as the GCRS and the ICRS.

I say this because that's what a coordinate system does - it includes not only clocks (which keep proper time) , but how to use them to specify locations and times. This ability implies the ability to synchronize clocks, by simply saying that clocks that share the same time coordinate are synchronized. It also addresses the rate issue - we can compare the rates of actual clocks to the rate of coordinate clocks, and perform appropriate adjustments as needed.

Thus, coordinates encapsulates not only how to keep track of time intervals, but also how to synchronize clocks and define coordinate numbers that represent time and place. The relativity of simultaneity comes into play here, that is why it is important to combine the discussion of spatial coordinates and time coordinates into a system of space-time coordinates. Definitions that do not include a complete coordinate system tend, unfortunately, to neglect the entire idea of simultaneity, which ultimateley winds up as a conceptual weakness.

The approach I am most familiar with is outlined in Misner's "Precis of General Relativity". https://arxiv.org/abs/gr-qc/9508043. I should not that it doesn't have an overwhelmingly high citation count, but it's key to my thought processes and I highly recommend it.

(1) dτ^2 = [1 + 2(V − Φ0)/c^2]dt^2 − [1 − 2V /c^2](dx^2 + dy^2 + dz^2)/c^2

....

Equation (1) defines not only the gravitational field that is assumed, but
also the coordinate system in which it is presented. There is no other source
of information about the coordinates apart from the expression for the met-
ric. It is also not possible to define the coordinate system unambiguously in
any way that does not require a unique expression for the metric. In most
cases where the coordinates are chosen for computational convenience, the
expression for the metric is the most efficient way to communicate clearly
the choice of coordinates that is being made. Mere words such as “Earth
Centered Inertial coordinates” are ambiguous unless by convention they are
understood to designate a particular expression for the metric, such as equa-
tion (1).

The IAU papers are very terse, but appear to follow the approach outlined by Misner, as they specify a metric associated with their various coordinate systems they define. The short version is that they specify using what is known as "harmonic coordinates".

The paper that originated this thread basically extends this to adding a Lunar-based coordinate system since we are talking about having people live there.

So, to recap, fundamentally, specifying a metric implies specifying a coordinate system. The metric can be thought of as a sort of mathematical "map" of space-time.

To recap my main point in more detail, I will point out again the role of the relativity of simultaneity. If one loosk at the transformation equations, clocks synchronized in the GCRS may not be synchronized in the ICRS, though the differences are tiny. To oversimplify, note that respecting the Earth's symmetry (axisymmetric for sure, and mostly spherically symmetric) does not respect a sun-based notion of symmetry.

This extra complexity with it's variety of coordinate systems is needed to realize the full accuracy of which General Relativity is capable of, though for many applications, one can get away with approximations which simplify things enormously. The extra complexity is really only needed for extremely precise work. For example, are as of yet few applications for Earth- based timekeeping where the lunar and solar tides have an important effect - as can be seen by Misner totally ignoring such effects in his equation (1), which is notably not necessary the same as any of the standards that I've mentioned.

There are applications in astronomy where we need to account for the varying distance of the Earth from the sun to account for effects on pulsar timing. As our timekeeping gets more and more precise, accounting for all the various effects will become more necessary to realize the full potential precision of the new methods.

 

[Nik_2213]

I sorta remember an analogous discussion about Martian time. That descended into near-farce as the embattled protagonists entirely over-looked the obvious...

Do you live on / near a coast with non-trivial tides ? Then you may have a 'Tide Clock', A 'standard' clock variously re-tuned to match the passage of Lunar' rather than 'Solar' time, it is a sufficient way to track 'Highs' and 'Lows'.

Yes, some areas have a single 'daily' tide, some the usual double, some a bizarre 'Double High' due reversing coastal currents. No big deal, local variants easily accommodated.

Whatever, you track *two* time-systems. Your analogue 'tide-clock' shows, at a glance, the coming and going of the sea, to extent allowed by Spring/Neap and Equinoctial variations, storm surges etc, Your UTC clock gives you the digital cue for weather forecasts, storm alerts, official reports, pub-hours, docking fees etc etc.

Equivalent on Mars is sun-rise, sun-set. They are 'loose' enough for 'analogue', would suit a tweaked 'Tide Clock'. Beats getting 'caught out' at night because you 'Murphied' precise correction the wrong way.
For 'official' stuff, you have UTC...

 

[pinball1970]

Really? Whose intuition is better because of this? And why stop here? Why not Ganymede? Or Triton?

Because NASA do not have plans to send astronauts there, yet.
Just a guess.

 

[Vanadium 50]

Because NASA do not have plans to send astronauts there, yet.
Just a guess.

Same comment as before:

Good thing we had GPS and all these ppb-level corrections in 1969 or we never would have made it to the moon.

Why is this important?
Why do you need to know the time to a better accuracy than a good wristwatch?

 

[PeroK]

Why do you need to know the time to a better accuracy than a good wristwatch?

Why do you need a wristwatch when you have a cellphone?

 

[pbuk]

Why do you need to know the time to a better accuracy than a good wristwatch?

So that you can build a radionavigation system. It's a bit difficult to measure time of flight of a radio signal with a wristwatch.

 

[Vanadium 50]

OK, next question. Why do you need a radio navigation system? And how good does it need to be?

Taking all the navigation problems we have had with spaceflight, and I'll let you throw in Mars, to get the statistics up, has there ever been a case where a "LPS" or "MPS" would have improved anything?

What problem is this trying to solve?

 

[Vanadium 50]

Let's look at it from a cost perspective.

Geosync costs an order of magnitude more then LEO. The world spends about $1B/year on GPS and GPS-like systems, and they are in 12-hour MEO orbits. So a Lunar Positioning System will likely cost a few billion a year to operate.

That's about what the ISS costs. Would LPS provide the same benefits as ISS? When ISS is deorbited in a few years, will some blue ribbon committee say "don't replace it. Build a LPS instead."?

 

[pbuk]

Let's look at it from a cost perspective.

TL;DR: orbiting satellites around the moon to build an LPS the way GPS works is not cost effective.

But GPS is not the only way to use ToF measurements for accurate positioning, see e.g. https://technology.nasa.gov/patent/LAR-TOPS-361

 

[pbuk]

What problem is this trying to solve?

Mapping of and positioning on and near the lunar surface. https://www.unoosa.org/documents/pdf/icg/2023/ICG-17/icg17.02.07.pdf provides some good context.

 

[Vanadium 50]

I find that document is more about what can be done as opposed to what should be done.

Maybe I should turn it around. How good do you think this needs to be? One nanosecond? Ten? 100 picoseconds? And then the obnoxious question - would you rather have this, a new space station, a new space telescope, or a Mars sample return?

 

[pervect]

Same comment as before:


Why is this important?
Why do you need to know the time to a better accuracy than a good wristwatch?

Getting serious for a bit, I am thinking that humanity might do astronomy (automated or otherwise) on the moon. Astronomers probably really use the ICRS nowadays (I am actually not positive what current practice is, that's my impression from my readings). For that application they probably eventually want the appropriate solar barycentric time, but we don't actually have clocks at the barycenter of the solar system for obvious reasons, on Earth we compute the barycentric time from local clock readings, local clocks on the surface of the Earth. There are some theoretical clocks at the Earth's center that we use to create and organize our timekeeping system (most notably how we synchronize clocks), but the actual clocks we use are typically on or near the Earth's surface. The most popular idea for common use seems to be adjusting the clock rate for a clock on the geoid (loosely speaking, a clock at sea level), and just ignoring the small effects of things like the lunar and solar tides. Theorretical standards that don't perform a rate adjustment exist, people tend to just not like them.

The issue becomes more acute when we have more than one instrument and associated atomic clock on the moon. It pretty much begs us to set up a system to handle it.

So it may not be premature to think about the appropriate theoretical framework.

The gravitational field of the moon is noticably lumpy, I suspect this might complicate things a bit more than it does for what we do on Earth.

We currently have quite a mess of time standards already, and adding in the desire to do accurate time measurments on the moon is going to add a bit more to the mess. Key things that relativity adds are the difference in clock rates for different observers, and the relativity of simultaneity. The rate issue is not the only one, the simulataneity issues are at least as important. Sadly, people unfamilair with the concept just see a fnord (https://en.wikipedia.org/wiki/Fnord) when I mention that.

 

[Vanadium 50]

OK, so lets consider this is needed for an observatory on the moon. LSST, to meet its goals, needs to know the time to about 60 μs.* Because the moon turns 30x slower, I only need to do 1/30 as well: 2 ms.

Holding that for a year requires an Allan variance of about 10^-7. (τ = 1 s) This is easy with a quartz oscillator.

I don't see that ppb corrections are necessary if my use case says I need to know the time only to ms.


* Actually, the length of the earth's day varies by many tens of microseconds per day. No timekeeping is good enough to achieve this because the earth is not spinning srably enough - you need to use something else, like reference stars.

(Edited to fix formatting)