Galactic Time-Keeping: Creating a Universal Calendar

[lpetrich]

Because of how accurate it's been possible to make atomic clocks, we now face a similar problem here on the Earth's surface and low Earth orbit, especially with the Global Positioning Satellites (GPS).

First, there's the question of the definition of time in general relativity, with its curved space-time. Viable GR alternatives like Generalized Brans-Dicke feature the same sort of curvature, but with different source terms, so this discussion will carry over into them. Every entity has its own proper time, but that alone gives us no way of relating them. Instead, one must define time in a way that gives every space-time point a well-defined time. Thus, time is defined from a foliation or splitting up of space-time into spacelike 3-hypersurfaces, where each hypersurface has a time value associated with it. For flat space-time, it is easy. The standard definition of time there involves flat and parallel 3-hypersurfaces, with time changing at constant rate in an orthogonal direction. Most GR definitions try to approximate that definition to within the limits of space-time curvaure. If there is a time-translation symmetry, as with the Schwarzschild and Kerr black-hole solutions, then one can use it to define an overall time. Likewise, the FLRW cosmology metric has a well-defined overall time in it.

Our Galaxy, like the Earth and its neighborhood, are well within the weak-field limit, so one must use a post-Newtonian expansion to define a standard foliation and a time coordinate. But there seems to be a generally-accepted foliation, one that makes the space-time metric look like the usual statement of the Parametrized Post-Newtonian metric. It's close to the flat-spacetime one.

But those preliminaries aside, let us look at Earth timekeeping.

Astronomers started out by using the Earth's rotation, but the orbits of the Moon and the planets showed variations that were closely parallel, so they switched to Ephemeris Time, the time associated with those orbits. The Earth's rotation's irregularities is what those variations were. Then in the 1960's, humanity had gotten laboratory clocks that could compete with astronomical measurements: atomic clocks. They now use as a reference International Atomic Time (TAI, from its French initials), kept by some 300 atomic clocks in some 30 national laboratories. Their measured times are compared to each other to get a more precise standard than any individual one.

TAI is intended as a realization of Terrestrial Time (English and French initials the same), the time at the Earth's sea-level surface (the "geoid").

This time can be extrapolated to infinity relative to the Earth while ignoring other objects, yielding Geocentric Coordinate Time (TCG). It flows faster than TT does, with an additional factor of 7.0*10^-10, meaning that clocks at infinity would look fast by that additional factor relative to the Earth's surface. That's about 22 milliseconds/year.

One can do the same with the Earth and the Solar System. Its Barycentric Coordinate Time (TCB) flows faster than Earth-surface time by an additional factor of about 1.6*10^-8. That's about half a second per year.

Doing that with the Solar System and our Galaxy yields an additional factor of about 10^-6 for extragalactic vs. Solar-System time. That's about 30 seconds/year. Over a century, that adds up to about an hour.

So time-rate variations within our Galaxy are not going to be very noticeable unless one does very precise timekeeping.

 

[mfb]

So time-rate variations within our Galaxy are not going to be very noticeable unless one does very precise timekeeping.

We frequently add leap seconds at the end of a year, so apparently we do.

 

[Jonathan Scott]

We frequently add leap seconds at the end of a year, so apparently we do.

Leap seconds don't affect the long term atomic time, TAI, but rather affect how we adjust UTC to match the slightly varying rotation of the earth.

 

[mfb]

Sure, I mentioned the leap seconds as an example that a difference of fractions of a second per year is so much we don't want it to influence our timekeeping. An atomic clock on moon or Mars would need a different tune to keep in sync with our clocks on earth, in the same way the GPS clocks have to take care about that.

 

[lpetrich]

TAI is an approximation of TT, Terrestrial Time, which is the proper time of a point on the geoid. That's the equal-potential surface that roughly corresponds to the Earth's sea-level surface.

To refer to its counterpart on Mars, one converts to the Solar System's coordinate time, TDB, along the way: (Earth) -> TDB -> (Mars)

 

[Khashishi]

There are two ways for standards to be created. The first is for some dominant regime to force everyone to use their system. The second is for a bunch of people to convene and agree on a standard. I guess that the first is more prevalent in history. So in this fantasy scenario you have set up, everyone would probably end up using the time system of the capital of the dominant force. If humans are the dominant creatures, then this might just be Greenwich mean time or something. To all the aliens, it's just an arbitrary number with no meaning, but presumably they know how to calculate it from their tables.

As far as time synchronization being path dependent, everyone will have to agree to take the shortest path between points. This is not simple to calculate, but presumably these advanced societies have mapped out the cosmological metric using some suitable FTL sensors.

 

[mfb]

You do not need FTL to calibrate time delays. We can do this on Earth and with satellites (otherwise the GPS system would not work), doing it for the whole galaxy would be no difference.

 

[dragoneyes001]

in the words of the Vogon constructor fleet: "No No no you've had three galactic years to address this..." if aliens with superior technology do come to Earth they may well be like us and consider humans on the same scale as humans did local animals when we discovered a new island and give us about as much deference as we did a turtle.

 

[Danger]

So time-rate variations within our Galaxy are not going to be very noticeable unless one does very precise timekeeping.

I am far too tired and far too sober to address your entire post. I'm going to have a beer and a nap. Rest assured, though, that I will return with some devious way to make your life miserable for you having posted that...

 

[Pete Cortez]

None of your questions make any sense without the existence of faster than light communications and/or travel and since those don't exist and are believed to be impossible, I don't see how there can be any meaningful answers to your questions.

Not necessarily. Maybe this community talks to each other on time scales measured in hundreds of thousands to millions of years.

 

[Pete Cortez]

Consider that the galaxy is 100,000 light years across. Say I want to schedule a meeting. In order for me to notify the whole galaxy AND give them reasonable time to come to the meeting place, I better set that meeting ~200,000 years in the future. And this is assuming that the inhabitants of the galaxy can travel very close to the speed of light. :D

In addition, participants from the other side of the galaxy can expect a 200,000 year round trip journey to attend my meeting...so this better be a pretty darn important meeting!

On the agenda: Should we have pie or cake for Mr. Poindexter's 4,523,917th birthday?

 

[Pete Cortez]

What ways might a civilization like this maintain an objective calendar-keeping system? I assume that if whatever the capital world of such a civilization would create a new calendar based on the orbital period of their own star, but would do you think this would be absolutely necessary?

About the only thing you need is an agreement on some minimum time unit and some reference event (which need not be fixed--a way of representing simultaneity will suffice). Everything else is just time zones.

 

[lpetrich]

This would be a reasonable issue only if one could travel faster than c or at least communicate faster than c. But if one could, let's imagine that one would want some external calibration, rather than use the timekeeping of the FTL systems. As some others here have pointed out, pulsars are the best Galaxy-wide time standards. They broadcast over sizable solid angles, they slowly spin down, and many of them have glitches in their spinning every now and then. The glitches may be especially useful as time references. The main problem is that pulsar broadcasts travel only at c, and in the scenario, that can be a long time. But if pulsar P1 is nearly the same distance away from C1 and C2, it can be used to synchronize C1 and C2, and if pulsar P3 is nearly the same distance away from C1 and C3, it can be used to synchronize C1 and C3, providing an overall synchronization between C1, C2, and C3. One may have to observe several pulsars, but it may be possible to build up a synchronization grid for colonies spread across several hundred light years, and even across our entire Galaxy. The grid would be constructed in much less time than it takes for pulsar signals to traverse them.

 

[lpetrich]

Now the politics. We can look at history for an indication of what one can expect.

The OP's scenario 2 is a central authority deciding it. That can make it relatively easy, since it can decide on a time standard for all its subjects. There may be some internal politics involved, with different worlds' delegations preferring standards that involve their worlds as primary references.

The OP's scenario 1 is lack of a central authority. We have some interesting historical precedent here. Most nations originally developed their own calendars, though many nations later adopted others' calendars. One of the first to adopt a calendar was Julius Caesar. Rome's native calendar was a lunisolar one, with an extra month added every now and then to keep the months in sync with the years. But officials were sometimes lax in that duty, and some of them gerrymandered the calendar by adding or omitting the extra month to favor or disfavor some other officials (Elfinspell: Censorinus, Part II: De Die Natali, [De Die natale], translated by William Maude, from the Latin. Online text of an early birthday book: a study on time and calendars during the Roman Empire.). Though Egypt likely started out with a lunisolar calendar, Egyptians some centuries earlier made that calendar a purely solar one with the months all being 30 days long and some extra days added to keep it in sync with the seasons. Julius Caesar adopted it, using Roman month names, adding the extra days to most of the months, and making February one day longer every 4 years. Two of the months ended up named after him and his successor Augustus Caesar. Some later Emperors tried to get months named after themselves, but that did not catch on.

Politics interfered with a later calendar reform. Over the centuries, it became apparent than the Julian calendar, as it's called, was a little bit too long, pushing its days ahead relative to the seasons. In 1582, Pope Gregory XIII decreed a solution. The first year of every century except for every fourth century has no leap-year day. That made the calendar in much better sync with the seasons. The Gregorian calendar, as it's called, was adopted by skipping some days. But there was a problem. Europe was having its Protestant Reformation, complete with Wars of Religion about which sect will be the official one of this territory or that. Catholics quickly adopted it, but Protestants refused to go along with it because it was some Catholic thing. But over 1700 - 1750, Protestant nations adopted this calendar. However, Eastern Orthodox nations did not adopt it until around World War I, though Russia got a new official belief system then also.

As Western political and commercial influence increased over the rest of the world, nations elsewhere also adopted the Gregorian calendar, and that calendar is now universal for all but various religious and ceremonial uses.

 

[lpetrich]

Here's how Greenwich Mean Time was adopted as a standard. Originally, for times shorter than a day, noon was when the Sun was on the meridian, the north-south line. But that produced problems. The Earth's orbit has a nonzero eccentricity and the Earth's spin north pole is not aligned with its orbit north pole. that makes the Sun seem to be speed up and slow down over a year. One can get around that problem with a "mean Sun" that moves at constant west-to-east speed. But there remains the problem that cities at different longitudes will have different time standards. Cardiff's time would be about 13 minutes behind London's time, Chicago's time about 55 minutes behind New York City's time, etc. As the railroad companies built their railroad lines, they adopted "standard times" for themselves. In Britain, they used London's Greenwich Observatory's time. The US's Pennsylvania Railroad used Pittsburgh's Allegheny Observatory time, etc. (Standard time - Wikipedia)

International Meridian Conference - Wikipedia -- in 1884, several nations sent representatives to Washington DC for that conference to straighten out their timekeeping, something that had been discussed in some previous international conferences. It wouldn't do for Britain to use Greenwich time, the US to use Allegheny time or whatever, with everybody having to do lots of awkward conversions. Here are the 26 nations that participated:

Austria-Hungary, Brazil, Britain, Chile, Colombia, Costa Rica, Denmark (absent), France, Germany, Guatemala, Hawaii (then independent), Italy, Japan, Liberia, Mexico, Netherlands, the Ottoman Empire, Paraguay, Russia, El Salvador, San Dominigo (now the Dominican Republic), Spain, Sweden-Norway, Switzerland, the United States, Venezuela

They all agreed on establishing a single standard prime meridian, a single standard zero longitude that would also serve as a source for a time standard. But they had a little bit of disagreement on where it would be. They voted 22 in favor, 1 opposed, and 2 abstaining about the Greenwich Observatory being on the prime meridian. The Dominican Republic rejected it and France and Brazil abstained. France did not adopt the Greenwich prime meridian until 1911. I think that they selected the Greenwich Observatory because Britain was the biggest seafaring nation back then, the one whose longitude measurements covered the greatest area. France's delegation preferred some neutrally-located prime meridian, one that passed through no major land mass, but that would have made it hard to build an observatory on it.

 

[lpetrich]

Now for non-temporal measures. Traditional measures have a variety of sources, like various body-part lengths (inch, foot, ell, cubit) and marked-off length (mile: "mille passuum", "1000 paces", counting both steps in a pace). They were often a chaotic mess. Consider A New and Complete System of Arithmetick: Composed for the Use of the ... - Nicolas Pike, Chester Dewey - Google Books Different nations had feet with different lengths, ells with different lengths, etc., and NP gave tables of their lengths.

But in the 17th and 18th centuries, various people discussed various rationalized systems of measurement units, often associated with some physical quantity, like the length of a pendulum with a period of 1 second. The French revolutionaries established a committee for rationalizing measurement units, and its members came up with the metric system (History of the metric system - Wikipedia, Metrication - Wikipedia). Introduced in 1795, it did not catch on very fast, but when Napoleon took over, he recognized its value and in 1912, he decreed versions of traditional units that were simple multiples or fractions of metric ones. But by 1840, the French government no longer supported them.

The metric system spread to other nations, and by the end of the nineteenth century, it had spread to most of Continental Europe and Latin America. By the early twentieth century, it had reached the former Russian Empire and some eastern Asian countries. By the 1960's, the main holdouts were the United Kingdom and ex-British-Empire countries, including the oldest one of them all, the United States. By the next decade, Britain, Canada, Australia, and New Zealand had gotten started. Now all that's left are the United States, Liberia, and Burma, and the latter two countries are starting also.

Though the metric system was invented in France, it has been governed by an international committee, the General Conference on Weights and Measures - Wikipedia, established by treaty in 1875. It has presided over redefinition of the meter from the length of a platinum rod to the distance between notches on a platinum-iridium rod to a certain multiple of a certain wavelength of an optical spectral line to the distance traveled when light travels for a certain time in a vacuum. It will consider in the next few years some further redefinitions, like defining temperature by fixing Boltzmann's constant the way that it has fixed the speed of light in a vacuum, and a similar sort of fixing to banish the last standard artifacts: the platinum-iridium cylinders that define the kilogram.