Fuck it, let’s assume we can build jump gates.
Let’s say they’re just big enough to send a tiny unmanned drone through.
I hop into my space ship and accelerate with a conventional engine to 86% of light speed.
No violation of physics needed, just shitloads of energy.
I fly to another star, which takes 10 years from earth’s point of view.
Due to time dilation at 86% light speed, time in my space ship passes half as fast as on earth.
If someone on earth had a strong enough telescope, they could look at a clock on my ship and see that it ticks half as fast as the clocks on earth.
But in my frame of reference, earth moves away from me at 86% light speed.
So if I look at earth through a telescope, I see that the clocks on earth tick half as fast as mine.
There isn’t a universal time. Time is always relative to speed and this is no problem when the reference frames are separated.
I arrive at the star, after 5 years have passed on earth.
I activate a jump gate and send the drone through with a message. It arrives on earth instantly, 5 years after I left.
But from their reference frame, they could see my clock ticking only half as fast as theirs.
After earth’s 5 years, only 2.5 years have passed for the space ship they see.
They activate their jump gate and send the drone back with a reply.
It arrives instantly at the star, 7.5 years before my space ship gets there.
This is why FTL travel isn’t and will never be possible. Even with tricks like jump gates or wormholes, it creates time paradoxes.
That’s not how it works. You’re correct when you say that from your point of view it’s Earth’s clock going half speed and from Earth’s point of view it’s your clock going half speed while you’re traveling away from Earth (or Earth is traveling away from you, both are equally valid), but that’s only true as long as the distance between you and Earth continues to increase at 86% of the speed of light. As you decelerate at your destination your reference frame continuously changes until you’re back in the same frame as Earth (or nearly so, we can assume the two stars aren’t exactly maintaining their relative positions). While you’re decelerating, from your perspective Earth’s clock speeds up and goes faster than yours, how much is determined by your rate of change in relative velocity. Earth’s reference frame isn’t changing (ignoring movement around the sun, galactic center, the great attractor, etc.), so the Earth’s perspective on your clock doesn’t change, the Earth sees your clock gradually speed up as you “slow down” until it’s going the same rate, but never faster. So once you’re back in the Earth’s reference frame both you and the Earth will agree that your clock advanced 5 years while Earth’s clock (and your destination’s clock, adjusted for any relative movement between it and Earth) advanced 10 years. This assumes a constant 86% light speed and ignores the time accelerating at departure and arrival so let’s assume very fast acceleration so it doesn’t change more than a couple days.
Edit: this is all completely ignoring gravity based time dilation from the spaceship climbing out of Sol’s well and going down the destination’s well and only considers velocity based time dilation. It would be more correct if you only considered two spaceships in a void where one accelerates to relativistic speeds and then accelerates back into the reference frame of the other.
Assuming a mechanism exists that changes the universe from being singly connected to multiply connected (i.e., wormholes exist), it is possible to have wormholes permitting faster-than-light travel without time paradoxes, though some additional restrictions may apply.
We have already shown that wormholes connect across both space and time, so that a trip between star systems could take you hundreds of years into the future, and the return trip takes you hundreds of years back in time. And this is even before we throw in how time slips between planets when considering relativistic time dilation due to different speeds and gravitational potentials.
Fortunately, all the weirdness of different time rates and going backward and forward in time can be ignored by the average person. This is because you never need to go from one world to another, or back, across the vast gulfs of interstellar space. You just take the wormhole between them. All you ever need to worry about is the coordinate frame that goes across the wormhole. When considering this reference frame, you’re not hopping all over the place in time. If it takes ten minutes to cross the wormhole between the two planets, when you get to your destination world the clocks will read ten minutes later than they did when you left your departure world. By coordinating their time-keeping across the wormhole network, all of the worlds of the network can agree on a common time to coordinate their activities. This is all travelers ever need to worry about, and they can then ignore all the relativistic weirdness. Your network engineers will still need to keep track of relative time drift and how close a given configuration is getting to a time loop. But unless your protagonist is a network engineer, they can just ignore all that stuff. And, as an author, so can you! Assume your engineers are competent, you have good regulatory bodies and standards institutions, and don’t worry about any of this “time travel” that doesn’t actually let you cause paradoxes.
Fuck it, let’s assume we can build jump gates.
Let’s say they’re just big enough to send a tiny unmanned drone through.
I hop into my space ship and accelerate with a conventional engine to 86% of light speed.
No violation of physics needed, just shitloads of energy.
I fly to another star, which takes 10 years from earth’s point of view.
Due to time dilation at 86% light speed, time in my space ship passes half as fast as on earth.
If someone on earth had a strong enough telescope, they could look at a clock on my ship and see that it ticks half as fast as the clocks on earth.
But in my frame of reference, earth moves away from me at 86% light speed.
So if I look at earth through a telescope, I see that the clocks on earth tick half as fast as mine.
There isn’t a universal time. Time is always relative to speed and this is no problem when the reference frames are separated.
I arrive at the star, after 5 years have passed on earth.
I activate a jump gate and send the drone through with a message. It arrives on earth instantly, 5 years after I left.
But from their reference frame, they could see my clock ticking only half as fast as theirs.
After earth’s 5 years, only 2.5 years have passed for the space ship they see.
They activate their jump gate and send the drone back with a reply.
It arrives instantly at the star, 7.5 years before my space ship gets there.
This is why FTL travel isn’t and will never be possible. Even with tricks like jump gates or wormholes, it creates time paradoxes.
That’s not how it works. You’re correct when you say that from your point of view it’s Earth’s clock going half speed and from Earth’s point of view it’s your clock going half speed while you’re traveling away from Earth (or Earth is traveling away from you, both are equally valid), but that’s only true as long as the distance between you and Earth continues to increase at 86% of the speed of light. As you decelerate at your destination your reference frame continuously changes until you’re back in the same frame as Earth (or nearly so, we can assume the two stars aren’t exactly maintaining their relative positions). While you’re decelerating, from your perspective Earth’s clock speeds up and goes faster than yours, how much is determined by your rate of change in relative velocity. Earth’s reference frame isn’t changing (ignoring movement around the sun, galactic center, the great attractor, etc.), so the Earth’s perspective on your clock doesn’t change, the Earth sees your clock gradually speed up as you “slow down” until it’s going the same rate, but never faster. So once you’re back in the Earth’s reference frame both you and the Earth will agree that your clock advanced 5 years while Earth’s clock (and your destination’s clock, adjusted for any relative movement between it and Earth) advanced 10 years. This assumes a constant 86% light speed and ignores the time accelerating at departure and arrival so let’s assume very fast acceleration so it doesn’t change more than a couple days.
Edit: this is all completely ignoring gravity based time dilation from the spaceship climbing out of Sol’s well and going down the destination’s well and only considers velocity based time dilation. It would be more correct if you only considered two spaceships in a void where one accelerates to relativistic speeds and then accelerates back into the reference frame of the other.
Assuming a mechanism exists that changes the universe from being singly connected to multiply connected (i.e., wormholes exist), it is possible to have wormholes permitting faster-than-light travel without time paradoxes, though some additional restrictions may apply.
source: Galactic Library