Physics Asked on February 4, 2021
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.
Answered by benrg on February 4, 2021
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.
Answered by Charles Francis on February 4, 2021
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