So,... picking up where we left off, I, the intrepid hero, am sailing off to your right into the sunset, with my incredibly reliable gerbil keeping time for me. You, the diligent historian, will eventually reconstruct everything I'm seeing from all of the reports you'll get — from the cloud of NSA bugs that I'm flying through — into a big, happy space-time diagram in which:
- My time axis, everything that is happening "Here" according to me, is — as everyone would reasonably expect because I'm moving — slanted away to the right from your own natural, obvious, and vertical notion of "Here",
- My space axis, everything that is happening "Now" in my direction of motion, according to me, is, — as nobody expected prior to 1905, — slanted up from your own natural, obvious, and horizontal notion of "Now" and by the same angle,
that second item being what makes all the difference, ruins Galactic Empire stories, and happens to be the only thing you really have to remember about Relativity because it's enough to derive all of the other wacky effects you hear about.
Introduce a 3rd player, call her Alice, moving away from you to the left at exactly the same speed that I'm moving to the right.
Let's also give Alice a gerbil clock that is identical to mine. Same laws of physics applying to an incredibly reliable identical-twin gerbil running on its own identical gerbil-wheel. Thus far, everything Alice does mirrors what I'm doing, as far as you're concerned. Therefore she's got the same tilt to her time axis, her space axis, same spacing on all of her ticks, etc.
Rewind everything to when Alice and I were in the same place. Call that moment "here" and "now" for both of us. And then we zoom in on what happens in that first tick afterwards:
Look at all the events I consider simultaneous with my first tick. One of them is on Alice's ship, and it's somewhat before when she gets to her first tick. Meaning her first tick isn't happening fast enough, as far as I'm concerned. Which means I'm "seeing" her clock running slow — and a quick look at that grayed right triangle shows that it's by a factor of √1−v² — or, if you're one of those weirdos who insists on using stupid units that entail the speed of light being some c≠1, then it's √1−(v²/c²), whatever.
For you, this should be no mystery: my definition of "simultaneous" is fucked up in not being horizontal. And if we flipped things around and look at where Alice thinks my first tick should be, she can just as easily conclude that it's my clock that's running slow.
And if I tell you that second gray triangle to the right is just the first one rotated by 90°, then it's not too hard to see that the distances Alice and I are measuring in the direction of motion will likewise have to be fucked up and by exactly the same factor.
If you're getting the idea that my deciding that a bunch of events are all happening "now" is a pretty arbitrary thing, you wouldn't be far wrong. Apart from the moment we meet, I'm not actually there on Alice's ship, so one might reasonably conclude it doesn't actually matter what I think about her clock. In fact, we're never really going to be able to compare notes because if we stay on our ships and never fire our engines, we never see each other again.
It's also a fair bet that other observers will have yet other ideas as to which event on Alice's ship is one tick from now according to them. And then we're stuck in this rhetorical black hole where all opinions are equally valid as to where "one tick from now" actually is, leading us to conclude that the notion of "one tick from now" must actually be nonsense, therefore time doesn't exist, and everything decays into this heap of moral relativism, Satan wins, etc.
We can still salvage something. There may not be a universally agreed, absolute notion of when "one tick from now" is. But, everyone still has to agree on which event on Alice's ship Alice thinks is one tick from now and that Alice and all of her passengers, just like her gerbil, must be experiencing one tick's worth of physics in that whole time.
And if we arrange for one of her passengers, Dave, to jump ship at the point that I think of as being one tick from now, everyone (including me) can and must still agree that Dave could only have experienced one √1−v²th of a tick while aboard Alice's ship.
If we then have Dave immediately catch a ride with Bob, who is coming towards me with the same velocity as Alice is moving away, so that Dave can arrive back where I am just in time for my second tick, we can all similarly calculate that Dave only experiences another √1−v²th a tick, thus arriving back at my place somewhat younger than expected,…
…and that is what rubs it in our faces that time is not this Absolute Thing, i.e., the way Newton and Gallileo thought it was.
Einstein probably figured he was done at this point, but I'm sure he hadn't reckoned with the tenacity of 20th century SF writers, so I'm going to go a bit further with this and extend the diagram to the left (a whole lot).
Let's suppose for the sake of argument everything thus far is all happening out in space 500 light-years from Earth, and let's suppose there exists some magical Tachyon or Subspace Transmitter Ansible Thing that allows communicating with Earth in real time. Remember, Sinclair was able to talk to Geneva on Gold Channel and get immediate responses.
Do we need the super-genius Vulcan working out the Intermix Formula that's likely to make the ship go up in the biggest fireball since the last sun in these parts exploded, which is why nobody'd ever thought to try it before? Do we need freak sunspot activity interfering in just the right way with the unobtanium-powered stargate? Or do we need Mysterious Tech from the ancient, dead civilization that takes up the inside of an entire planet and can only be used for the one episode?
Or… maybe,… just maybe,… we can look at where Bob's and Alice's Now axes are.
If we know how to make a subspace transmitter, we could make two of them: One for Bob, one for Alice. The physics of it, whatever it is, should work just as well on their ships as on mine, so all I have to do is give my message ("Kill Dave.") to Bob when we meet, Bob sends it to Earth, Earth relays it to Alice and voilà: trivially easy time loop.
For extra fun, let's see just how incredibly fast Bob and Alice have to be going in order to send a message back in time, say, one whole day. That ought to be enough to wreak havok, right?
Stretch the diagram so that the Earth⟷Me distance is 500 light-years, and then we make each of the ticks 12 hours. 500 years to 12 hours is a ratio of 365,000 to 1. Which gives you an idea of just how thin all of those triangles really are. Which means it's enough if Alice and Bob are going 1/365,000th of the speed of light, which is,… wait for it,…
900 meters per second.
This is so ridiculously easy we don't even need spaceships. Earth Alliance pulls a couple of SR-71 Blackbirds out of cold storage and it's game over right there.
You say, "Fine, so we don't do real-time communication. But surely, we could still have something where the message to Star Fleet Command takes 2 weeks to get there?" This changes nothing. Rerun the previous problem and ask how fast Alice and Bob have to be going to get a message back in time 4 weeks plus one day. The answer comes out to around 24,000 m/s. Yes, that's a bit harder. It's roughly how fast the Earth moves in its orbit around the sun. I think we'll be able to manage that.
If the communication delay is anything less than 500 years (minus 12 hours), Alice and Bob can go fast enough to make up for it and get the message delivered in time (a day ago).
The problem with "Meanwhile, back on Earth,…" is this: If you are 500 light-years away from Earth, then "meanwhile" can, depending on how fast you're going and in what direction, refer to anything between the cord-cutting ceremony for a shiny, new Star Fleet Academy building in Marin City, California, and the first Spanish Explorers landing at Point Reyez 1,000 years earlier.
That much is not a problem so long as you and the Meanwhiles cannot actually talk to each other. But if you're relying on a Meanwhile for story purposes, then, chances are, you are assuming that they can. Why else would you be bothering with the happenings on Earth if it weren't going to affect your characters less than 500 years in their future?. And that's where you're going wrong.
Because once there's any kind of conversation along the "Now" lines, that means they all can talk to each other. Easily. And then the rogue Star Fleet cadets are teaching the Ohlone tribes how to make phasers, and would-be conquering Spaniards and causality all get toasted extra crispy.
Note that this is not an argument for FTL travel/communication being impossible. Just that if it were possible, in the sort of arbitrary and ubiquitous way that you would need for most Galactic Empire stories, then we're in Bill and Ted Land. Which we could actually be, for all we know, though, if so, I'd like to think we'd have noticed this by now. In any case, all of your stories then end up being unintentional time-travel stories, which will then consequently officially suck, because with two (2) pairs of stargates, a couple of non-FTL-but-really-fast ships, and a big enough fuel supply, you can fix anything…
…and then we spend the rest of the movie chasing down Biff's Sports Almanac.