But does Alice and Bob need to agree that pulsars have the same period in both their respective reference frames? Is it not enough that they know the period of the pulsar in its frame of reference? Then, also knowing their own relative velocities and positions compared to the pulsar, that should alleviate the issue, no? If the time standard has then also picked an origo, the galactic frame of reference point in space and time, then everyone else should be able to calculate what that is, even in their own frame of reference.

@MichaelK even if they used a single pulsar as a clock, the problem of simultaneity remains. Alice may calculate her age as X rotations of the pulsar, and know that she was born before the release of Half-Life 3, and that's true for her. Bob will calculate Alice's age as Y rotations instead, and know that she was born after the release of Half-Life 3, and that's true for him. They only agree that things happened, but never when nor in which order, even if they adjust for each other's time dilation.

Actually the relative motion of the stars in the same galaxy is not very high, on the order of some hundred km/s. So relativistic effects would be minimal if we only want to sync time for planet dwellers. If we want to sync time between space ships traveling at relativistic speeds, we will have the problem described in this answer.

@TheSquare-CubeLaw Couldn't you resolve that issue by just straight-up having a preferred frame of reference in your fictional setting, the same way that resolves the problem of FTL breaking causality?

Relativistic distortion can be calculated and corrected for mathematically, just like we do with our GPS satellites.

@idran no, because all other frames that are moving fast enough relative to it disagree on the sequence of events. So any historical information tracking becomes useless for all but this priviledged frame.

@Nosajimiki you correct that for your frame, and you can calculate the correction for other frames, but the fact remains that things will happen at different orders and timestamps for other frames.

@TheSquare-CubeLaw actually, I thought about this further, and time-dilation is not even an issue because everyone is measuring time based on the Pulsar's local reference point, not thier own. A space second will feel longer on one planet than another, but they will all stay in sync. The only thing you need to correct for is the doppler effect which is not hard as long as you understand how fast you are moving towards/away from the pulsar.

@TheSquare-CubeLaw Oh no, I mean a privileged frame of reference in the physics of the universe, not a particular frame of reference that everyone has just chosen to use. Doesn't the simultaneity paradox disappear in a system of physics that actually does have a privileged frame of reference?

@Nosajimiki indeed but people would still disagree about sequences and timestamps. You tell me that dinosaurs were extinct when a certain supernova happened... I say that the supernova happened before dinosaurs went extinct. And we're both right. So if you want these ordered in a history book, you need one edition for each frame, or you need a priviledged frame that overrides history for the others.

@TheSquare-CubeLaw Ohh, wait, I just read the description of the science-based tag and realized I was misunderstanding it; I assumed it allowed for alternate physics systems. My bad, yeah, I withdraw my comments.

@TheSquare-CubeLaw If I see a Supernova today that is 20,000 LY away and you saw it from 19,900 LY away, 100 years ago, then we can both agree based on distance when it actually exploded (assuming our time increments are both based on the same clock like a distant pulsar). The UTC timestamp of the supernova would be today - 20,000 yr, the UTC timestamp of it reaching your planet would be today - 100yr, and the timestamp of it reaching me would be today. Those are 3 separate events, not 1, so there is not actually any disagreement about when each happened.

So, if I say some Jesus dude was born on my planet 18,000 yrs after the nova (not to be confused with 18,000 after I saw the nova), then you can determine that it was 1900 years before you saw the Nova, which was 2000 years ago.

@Nosajimiki this is what I have been trying to explain - if I am not im the same frame as you, I can (and depending on speed and position, probably will) see these things happening in different orders and timestamps. Jesus was born after the Nova for you, but before the nova for me from the other side side of the galaxy. Also even if we were equidistant to the supernova, we could count different timestamps for it just because we are at different speeds, even if we adjust for time dilation.

@TheSquare-CubeLaw Yes, but it is 3 different events which are easy to distinguish. You would say something like the Nova happened in 18,000 BCE or it was witnessed on your planet in 1900 CE. And any work that does not specify can generally be implied by context. More importantly, if I need to make it to a meeting in Gliese 667 in 3 days, no one is really going to care that the light reflected off the back of my ship won't get back to Earth for 20 years. We only care that my 2024.1370 is the same as the 2024.1370 there so that I arrive at my meeting on time.

@Nosajimiki what I jave been trying to say is that 2024.1370 is local and valid to you. It's not valid to anyone else moving at a fraction of c relative to you. It is your 2024.1370, not the galactic 2024.1370. If you wish to impose your own local time as the galactic one, people in other star systems will be able to use it to sync with you, but not among themselves.

@TheSquare-CubeLaw and what I have been trying to say is that no one is using local time at all. I can experience a different amount of local time between 2024.1370 and 2024.1371 than you will, and but we can design clocks that will tick in unison anyway. Local time will still be required for specific scientific purposes, but in the day to day of things, no one would really notice if a galactic second is a little longer or shorter in one place or another, just like no one notices that Gravity is a little stronger in some places on Earth than others unless doing precise ballistics calulation

If no matter where I go, or how I move, I'm always adjusting my clock to sync to the universal clock, then it will always speed up or slow down to compensate for my movement and position so that by the time I reach you, our clocks will be in sync.

@Nosajimiki for two travelers synching, yes. For 3 or more, no, because simultaneity is an illusion. Once again, for multiple denizens in the galaxy, the same events have different timestamps (even compensating for relativity) and different orders. 2024.1371 works for everyone and everything at your stellar system. But ask two different historians far from each other what happened when it was 2024.1371, and they will give you two mutually incompatible histories.