Time Dilation. At what distance travelled does it become a thing?
October 25, 2019 1:01 AM   Subscribe

I'm writing science fiction. I've been trying to avoid faster than light speed travel, but it's become impossible to get the story to work without it. How do I calculate how time dilation affects my characters? I suspect I am drastically misunderstanding some basic aspect of time dilation so apologies in advance.

I've read up on why time dilation happens but the concept keeps eluding me. My grasp of mathematics isn't up to using any of the time dilation calculators I've found online. This is what I need to figure out:
Two characters - Let's call them Io and Bear - are in a spaceship that is somewhere outside our solar system (I still have to decide exactly where the space ship is. It needs to be about 150 years worth of travel away from Earth but that is a different question).
The spaceship is harvesting a debris field of alien waste it has discovered and is staying still in relation to that debris field for the foreseeable future.
Bear has access to some type of (sorry! Handwavey) wormhole travel tech that allows her to move (pretty much) instantaneously to a new destination. This wormhole-tech is separate from the spaceship. Bear will be leaving the spaceship behind . Bear has to choose. Is she going back to Earth, or will she go to an Alien Base?
I have to decide on the distances involved. From spaceship to Earth, and spaceship to Alien Base. I would like there to be significant consequences. Different amounts of time will pass for Io and Bear. If they were to meet again, one of them would be older (or one of them will have died of old age if enough time has passed).
Over what distances (from spaceship to Earth, or from spaceship to Alien Base) will time dilation be a thing? Assuming (pretty much) instantaneous travel? Who will have lived through a longer span of time and so be older?
I spent quite a lot of time reading up on time dilation, and I thought I understood the basics of why and how it happens more or less, but that was several months ago and I find that I no longer understand it and probably never really did. For now, I just need to roughly figure out what the consequences will be for my characters, to help me decide how far Bear will be travelling. I'm hoping to avoid paradoxes caused by FTL & time travel and communication but will probably have to resort to handwavey stuff to side-step that. I was really hoping to keep my story grounded by avoiding FTL travel but it's not working out that way. Anyone able to help?
posted by Zumbador to Science & Nature (21 answers total) 5 users marked this as a favorite
Since you are using an instantaneous form of travel, there is no time dialation. A SF book that deals with this is "Time for the Stars"
posted by Sophont at 1:26 AM on October 25, 2019 [7 favorites]

If you're going to have FTL travel, you're already in a universe which is not governed by real-life physical laws. That means that you get to choose what the rules are!

Would it help if you had an idea of how your narrative would be served by time dilation, which will tell you how much time dilation you want to happen, and work backwards from there?
posted by vincebowdren at 1:28 AM on October 25, 2019 [5 favorites]

Oh really? Maybe that's why I couldn't understand as I was assuming that time dilation would happen. Okay. Taking vincebowdren's suggestion. What if going to the Alien Base means that for every year Bear experiences at the Alien Base, Io lives 5 times that at the spaceship?
I'm also wondering whether I should abandon the wormhole instantaneous travel thing and use something that does take time.
posted by Zumbador at 1:43 AM on October 25, 2019

Every decent science fiction story needs exactly one plot hole big enough to drive a truck through. For many of them, this is FTL travel. If that's the one you pick, you get to make it work however you damn well please and your audience will let you get away with it as long as you're careful not to add two truck-sized plot holes.
posted by flabdablet at 1:53 AM on October 25, 2019 [4 favorites]

The easiest way to think about it is that time dilation happens because of acceleration. It's a side effect, mathematically speaking, of the speed of light being a constant and a maximum, and it depends on your velocity/acceleration. So if you're going to have faster than light travel, especially instantaneous travel, there's not going to be any way to make classical time dilation make mathematical sense or be mathematically correct. Instead you get to define what the rules are for that new realm of physics that your characters deal with.
posted by Lady Li at 1:58 AM on October 25, 2019 [1 favorite]

Time Dilation. At what distance travelled does it become a thing?

I think the thing you're missing is that time dilation isn't a function of distance, it's a function of speed, increasing as you get closer to the speed of light. It's fairly minor at small fractions of light speed, but increases more and more as you get closer to light speed.

E.g. while you're travelling at 90% of the speed of light, time passes about twice as fast for everyone else as it does for you. At 95% of the speed of light, it's about 3x. By the time you get to 99.9% it's more like 20x. This table and this graph may help you get the idea.

Distance comes into it only because of how long you spend traveling to get there, and therefore how much the time differences accumulate.

If you have some sort of FTL travel in the story, then you can basically choose how you want it to work, because from a physics perspective all bets are off.

But note that if you could hypothetically travel at the speed of light, extrapolating the physics would imply that time would basically stop for you entirely during the trip. In that case, time difference does actually become exactly equivalent to distance.

So if you want to go a bit more hard-SF, you could say that your instantaneous wormhole travel works that way. In that case, if a character stepped into the wormhole to travel somewhere 5 light years away, it would take 5 years to get there but no time would pass for them. If they then travelled back to where they started, everyone they knew would now be 10 years ahead of them.
posted by automatronic at 2:01 AM on October 25, 2019 [22 favorites]

I agree that if you have instantaneous travel, you're done, and if faster-than-light (FTL) travel is available, there's no point asking the question in the first place. But since you ask, if you DON'T have instantaneous or FTL travel, only plain old STL travel, the formula is Δtp = Δt0/c√(1-p2), where c is the speed of light and p is the percentage of the speed of light at which you're traveling. This leads to rather disappointing results: you need to be traveling at .9c to get enough time dilation to make a year's journey take only half a year, and .999c to make it take only 16 days (still a really long time to travel). Meanwhile, the same process makes the mass of your vessel increase, so at .999c you need 22 times more energy to move your ship, so you're also going to have to think about how your ship is propelled. It's probably a lot easier to posit some new technology we've never heard of to get around the problem.
posted by ubiquity at 2:07 AM on October 25, 2019 [3 favorites]

> automatronic: I think the thing you're missing is that time dilation isn't a function of distance, it's a function of speed, increasing as you get closer to the speed of light. It's fairly minor at small fractions of light speed, but increases more and more as you get closer to light speed.

Time dilation is also affected by gravitation. Time passes more slowly in a strong gravitational field than it does in a weak one.

This article points out something that may help to ground (heh) your understanding - time dilation affects passengers on commercial airline flights.

I would also agree with the folks saying that once you introduce FTL and instantaneous travel, you are playing so fast and loose with relativity that you can do pretty much anything you want. In fact, unless time dilation is important to your story, I'd suggest just ignoring it completely.
posted by Rock Steady at 4:31 AM on October 25, 2019 [2 favorites]

I was just reading about this topic, and the short answer as to why FTL makes physicists and writers throw their hands up is (a) it violates our current understanding of how the universe works, and (b) according to general relativity, if it did exist, it would break causality.

For more on (b), the relevant search terms are "FTL light cone." It's a super trippy bit of physics that I can't claim to fully understand, but it would affect FTL communications as well as space travel. It sounds like FTL may not be necessary for your story anyway, but if you do introduce it, you should feel free to do what most SF writers do and hand wave the physics.
posted by toastedcheese at 5:35 AM on October 25, 2019

Time dilation is also affected by gravitation. Time passes more slowly in a strong gravitational field than it does in a weak one

and in fact it's that effect, not so much the effect of straight-up relative speed, that's responsible for the famous Twins Paradox.

Consider: my twin hops in a spacecraft equipped with some ridiculous quantity of reaction mass and heads off for the stars. After a while, the spaceship has accelerated to some substantial fraction of lightspeed, and when we attempt to reconcile our clocks I find that his clock has ticked many fewer times than mine has. From where I sit, time on the spacecraft is passing more slowly than time here.

And the speed term in the time dilation equation is squared - it really is a speed, not a velocity - so even after he's turned around and is now screaming back here at near lightspeed, his clock will still be running slower. So when he eventually returns, he'd be really young and I'd be completely senile.

So when I first heard about this as a kid, my immediate question was this: speed is relative, right? The whole point of relativity is that there is no privileged frame of reference that can just be taken on faith as Not Moving. So from my twin's point of view it's me who is receding from him at near lightspeed, so from his point of view, my clock is the one that's ticked fewer times at any given point throughout the trip. So when he gets back, I'd be really young and he'd be completely senile.

Which is, of course, why this is held to be a paradox.

The resolution works like this: for as long as our speeds with respect to each other are indeed some substantial fraction of lightspeed, his clock will be running slow as judged from my point of view, and my clock will be running slow as judged from his point of view, and if we're going to arrange appointments we'll each need to take this into account. But once he's got as far out as he's going to go, and he slows down to the extent that our relative speed is now zero again even though he's at this vast distance, the clocks will therefore be running at the same rate again. And if that's all that time dilation boiled down to, then the total number of ticks registered on each clock would once again be equal at any given instant.

So if the speed-related dilation was the only thing going on, then on his return to Earth we would have seen it happen twice (once on the outbound leg, once inbound) but any time our relative speed is zero - which it would indeed be, after his return - then our clocks would have caught up with each other (twice!) and be in agreement, and there would be no paradox.

But as it turns out, one of us probably would be younger than the other after he'd done his round trip, because gravity.

The time dilation equation that ubiquity gives above is from Special Relativity, and Special Relativity is applicable only between reference frames that share a common gravitational field vector. To deal with time dilation in the presence of gravitational fields you need General Relativity, and General Relativity is gnarly.

For any part of the trip during which my twin's spacecraft was accelerating more than 1G, his clock would be running slower than mine, and this would be measurable from either of our viewpoints after applying the speed-related corrections required by SR. Whenever it was accelerating at less than 1G, my clock would be running slower than his as a result. In other words, which of us ends up older after his trip depends on how hard his craft accelerates, and for how long, and not on the fastest speed it ever attains with respect to Earth.

This, incidentally, is why the super-accurate, super-precise atomic clocks that GPS satellites carry don't run at the same rate as super-accurate, super-precise atomic clocks of exactly the same type when they're run here on Earth. Sitting on the surface of the Earth, an atomic clock is subject to a gravitational field with a strength of 1G (9.8m/s2); the satellites are in free fall, their local local gravitational field strength is therefore always zero, so their clocks run fast with respect to ours.

A weaker version of the same effect makes aeroplane passengers and mountaineers age ever so slightly faster than the rest of us: they're not in free fall (with any luck) but they're further from the Earth's centre of mass, so their local gravitational field strength is a little bit lower and their local time a teensy weensy bit faster.

Back to the spacefaring twin: the business with his clock measuring slow from here and mine measuring slow from there whenever our relative speed is ridiculous still feels weird and wrong and contradictory and paradoxical, even without the ultimate age discrepancy thing. The key to understanding how both measurements can be right at the same time is to realize that simultaneity is simply not a concept that works between observers at high relative speeds; once he's moving at high speed relative to me, his "now" and my "now" are not the same "now".

A consequence of Relativity's unification of space and time into spacetime is that here and now have to get unified into herenow. Splitting them back out again can only be done by ignoring this kind of anomaly or by using the equations that reconcile it.

This has consequences that are fun to contemplate after a doob or three.
posted by flabdablet at 6:02 AM on October 25, 2019 [9 favorites]

While I agree with the general thrust that FTL travel means time dilation is already out of the window, I can see one option that might work, if you need a time delta between Bear and Io: Rather than have Bear "jump" to an Alien Base, have them jump to an Alien Ship instead. This vessel would be travelling at high speed relative to the salvage field, with time dilation occurring between the two character's frames of reference.
posted by Nice Guy Mike at 6:13 AM on October 25, 2019

I found this video from Fermi Labs really helpful to explain why you can't travel faster than light based on current understanding of physics. I think you may already have an answer, but it may give you a few ideas.
posted by willnot at 6:56 AM on October 25, 2019 [1 favorite]

Erm, gravitational time dilation is a separate and distinct phenomenon from motion dependent time dilation, which happens regardless of whether there is any acceleration involved or not. There are several YouTube videos that help sort out the confusion by reformulating the scenario to avoid the whole "turning around and coming back" bit that leads the mind astray when considering these issues.

Personally, I'd do without the FTL and go with some kind of high-thrust evolution of ion drives or an Orion-type pulse "rocket." Why? Because it's completely unnecessary to getting yourself across the universe within your lifetime, thanks to the length contraction that comes along with the high gamma values that give you the time dilation in the first place.

There is a really neat constant acceleration calculator that lets you punch in a magnitude in terms of gee and will spit out the proper time intervals, observed time intervals, and apparent distances traveled over the entire trip and the relevant phases of the journey for observers in the origin, destination, and ship reference frames. Even better, it handles the fly by case as well.

Interested amateurs are likely to have their mind bent, even those of us that think we have a decent handle on relativity.
posted by wierdo at 6:57 AM on October 25, 2019 [3 favorites]

gravitational time dilation is a separate and distinct phenomenon from motion dependent time dilation, which happens regardless of whether there is any acceleration involved or not

Indeed it does. But the key points about relative speed dependent time dilation, and the things to keep in mind when trying to wrap one's head around the Twins Paradox, are that (a) it applies only for only as long as the relative speed does and (b) it's symmetric: observers working in either reference frame will see the clock that's moving with respect to that frame as the one that's running slow. There is no sense in which one of the clocks is "really" running slow and the other is not, other than with respect to a specified reference frame.
posted by flabdablet at 7:13 AM on October 25, 2019 [1 favorite]

I just want to add that the definitive popular* text on this is still, as far as I know, Black Holes & Time Warps by Kip S. Thorne.

* There's still a LOT of calculus involved, by necessity, but the book is written in such a way that lay readers can skip over the equation-heavy bits and still understand everything. That's how I read it back in high school.
posted by tobascodagama at 9:07 AM on October 25, 2019 [1 favorite]

Solely because it seems to me like there are at least two reasonable ways of interpreting the statement that "[Time dilation] applies only for only as long as the relative speed does," is true in the sense that once our high gamma adventurer returns to our reference frame our respective clocks will again tick at the same rate. The difference in elapsed time as recorded by our respective clocks does not.
posted by wierdo at 10:37 AM on October 25, 2019

once our high gamma adventurer returns to our reference frame our respective clocks will again tick at the same rate. The difference in elapsed time as recorded by our respective clocks does not.

My high-gamma twin never left my reference frame, because that's not a thing that can be done with reference frames. Closest he can get is simply failing to use my reference frame, on the basis that for most of his trip, a different reference frame within which his ship is stationary yields simpler descriptions of local measurements.

If I'm observing the ticking of my twin's clock over a live radio link between us, what I'm going to see is that on the outbound leg of his trip the apparent tick rate of that clock will slow down, and on the inbound leg it will speed up. That's not time dilation, that's just the Doppler effect.

He'll see the same thing with respect to my clock. When he gets back, then provided there's been no gravitational time dilation going on, clocks that started off with the same readings will have them again.
posted by flabdablet at 2:24 AM on October 26, 2019

Aside from the part about your high gamma twin measuring a total round trip time for 5 light years out and back of under 8 years despite never having exceeded the speed of light and your having measured between 12 and 13 years that you left out, and both of you agreeing that your twin is now younger than you, yes.

There is observational evidence to support the reality of the results of such calculations despite the apparently obvious absurdity. There are plenty of resources on the Internet that explain better than I can (especially when I've been woken up by a dog after very little sleep) why the apparent paradox is not actually a paradox.
posted by wierdo at 4:50 AM on October 26, 2019

I present to you (someone else's work) The Relativistic Rocket.
posted by wierdo at 4:57 AM on October 26, 2019

The Twin Paradox, from the same collection, covers what I've been trying to explain but much more thoroughly and with many fewer errors. Don't listen to me, listen to Michael Weiss. Thanks, wierdo.
posted by flabdablet at 7:35 AM on October 26, 2019

Time dilation in non-FTL (but approaching that speed) space ships was well covered in Poul Anderson's Tau Zero.
posted by CCBC at 2:17 PM on October 26, 2019

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