Wednesday, March 23rd, 2011
One area of mathematics that fascinates me is calendrical arithmetic. Turns out, like pretty much anything involving numbers, a bunch of very smart people have spent their entire careers publishing papers about clever mathematic tricks in this case relating to dates and times. Calendars are interesting to me because they’re pretty concrete — calendars are after all a practical, human endeavor — but if you’re clever, you can do a lot of interesting things with pretty simple mathematics.
A full run down of calendrical arithmetic is a bit beyond what I understand right now (someday I will read a textbook on this), so instead chew on this: today I was daydreaming about space exploration — like I do — and I wondered something along these lines:
How would two people, moving at relativistic speeds, arrange to get coffee together?
Star Trek’s fictional stardates were sort of a tongue-in-cheek nod to the conflict between absolute timekeeping and relativity. (As you are probably aware, if you travel very fast, like near the speed of light–fast, time will “move faster” for you1 — well known consequences of this being that you’ll travel “into the future” and things you’d see while riding your super fast bicycle would look very weird and probably slow.) While Star Trek is fascinating, its calendar ultimately serves the dramatic purposes of the show. I’m curious if anyone’s actually thought about this in earnest.
The closest I’ve come to a solution2 is to have the units of time no longer be fixed to the moving observer’s time — instead the perceived length your time unit would change depending on the ship’s speed. You can estimate clock drift using some sort of space speedometer (since the amount of time dilation varies by speed), and perform calibration via some kind of highly accurate laser signals or a well-known pulsar or something.
I don’t want to spend too much time thinking about this as I don’t have the appropriate mathematical tools at hand to accurately describe any solution, but pondering it entertained me for an afternoon. Plus, if anyone out there does know of any prior art, hopefully I’ll hear about it now.
This is assuming that you have FTL communication or that you’re deciding when to meet while in each others’ presence, before you set off on your respective relativistic journeys. ↩