# Would time dilation make it impossible to accurately convert between calendars across the galaxy?

A hypothetical signal is emitted from a known exoplanet thousands of light years away. The signal marks the occurrence of an epoch-worthy event on that planet, and we (the receivers) want to know exactly when that transmission was sent in our own local timekeeping system, so we can can set up the conversion of time between the two calendars of the two different worlds.

An approximate answer is pretty simple - distance in light years between the stars / c. This doesn't consider things like the different orbital positions of the planets within their systems, and the movement of both stars within the galaxy over the thousands of years the message was in transit, but these things can theoretically be calculated, but there's one thing that makes me suspect the whole concept is doomed to fail:

Time dilation between the two stars. As they're in different orbits around the milky way, and travelling at 100's of km per second, one sun from the frame of reference of another will experience non-constant time dilation, as a result of the relative velocities slowly drifting over the centuries as the suns orbit the galactic centroid (assuming their orbital radius from centroid is non equal, and thus they have different orbital periods)

I've attempted to calculate this, and the factor is small (like off by $$10^{-7}$$), but this is significant if signal between those two worlds has to travel 1000's of light years, this could translate to the clocks being several hours out of sync and drifting over time as the time dilation factor changes as the suns orbit the galactic centroid.

This would seem to imply that the whole concept of creating a precise conversion between calender's across the galaxy is flawed. Is it? Or have I missed something?

This question is prompted by a question asked on the WorldBuilding stack exchange. Someone requested the transmit time of a signal from planet A in the local calendar of planet B, accurate to the nearest minute.

Time dilation is an issue even for terrestrial timekeeping. Atomic clocks are accurate enough to detect rate differences due to latitude and height above the geoid. It's also famously noticeable in GPS satellites.

It isn't a fundamentally unsolvable problem. You just define a coordinate time as the time standard, rather than the proper times actually measured by your clocks. You adjust the rate of the clocks to match the coordinate rate based on a mixture of theoretical calculations and real-time comparisons with other clocks. I don't know exactly how TAI, the terrestrial time standard, is defined, but it's a coordinate time.

You can maintain a similar system over thousands of light years in principle. It couldn't have atomic-clock precision or anything close to it, but it isn't doomed to drift out of sync.

• One candidate for a galactic time standard is that each planet applies a correction factor to factor out the effect of its own galactic orbiting velocity. With such a standard time in place there is opportunity for cross reference. For example, the largest gravitational wave events occur almost instantly; the final merger occurs in seconds. Each planet can send an archive of their observation records. The time coordinates of the records can be converted to galactic standard time, and by identifying matching events I expect the forms of timekeeping can be correlated to within seconds. – Cleonis Sep 19 '20 at 17:33

There is no concept of an absolute synchronisation in general relativity. There is only coordinate time, which is determined from a particular clock (or set of clocks) together with a particular procedure to relate time in one place with that in another. This is usually the radar method in the immediate vicinity of the Earth, and for greater distances requires an estimate of the distance travelled by a signal from the source. The nearest we have for large distances is cosmic time, but this is really only an approximation, ignoring the effects you mention. Likewise, we can talk of Galactic time, but again we only mean an approximation.

• It's not clear what you mean by 'only an approximation'. In radio astronomy there is the technology of Very Long Baseline Interferometry Quote: "Data received at each antenna in the array include arrival times from a local atomic clock, such as a hydrogen maser. At a later time the data are correlated with data from other antennas that recorded the same radio signal to produce the resulting image". I emphasize: the time correlation is at such a level of precision that actual interferometry is achieved. – Cleonis Sep 20 '20 at 3:54
• @Cleonis, the signals from the masar are correlated because the signals have the same source and travel almost exactly the same distance, but this says nothing about any absolute synchronisation between the masar and a clock on Earth. Your example has nothing to do with the definition of cosmic time, which I describe as an approximation, and which requires an estimate of the distance traveled by the signal. – Charles Francis Sep 20 '20 at 10:08
• There seems to be some babylonian confusion here. A clock on Earth can be of several designs, such as a cesium clock or a hydrogen maser clock. In your reply-comment you write about an astronomical source that you refer to as a 'masar'. A google search did not find such a word in use in astronomy. (Example of Very Long Baseline Interferometry usage: observation of quasars.) I write this only to notify - I recognize of course that independent of this particular detail you have made your disagreement quite clear. – Cleonis Sep 20 '20 at 12:12
• @Cleonis, Sorry about spelling. I refer to astrophysical masers (en.wikipedia.org/wiki/Astrophysical_maser) which are often used as sources in VLBI observations. The quote you used clearly referred to the same thing. The question has nothing to do with either the design of Earth clocks or the synchronisation of Earth clocks, but only to do with the notion of synchronisation between clocks separated on astronomical and cosmological distance scales. It remains that your example has nothing to do with the question. – Charles Francis Sep 20 '20 at 12:47
• ivscc.gsfc.nasa.gov/meetings/tow2013/Diegel.MW.pdf "During geodetic VLBI observations, signals emitted by distant sources of radio frequency energy (quasars) are received and recorded at several antennas. At each antenna (VLBI station) a very stable frequency standard (hydrogen maser) provides a reference signal that enables time tagging of the quasar signals as they are being recorded." – Cleonis Sep 20 '20 at 19:24