FTL Time Dilation

Orianna2000 · Nov 8, 2012

If I remember correctly, with the theory of relativity, if you're traveling faster than light, moving away from a planet, time slows down for you, so that years might pass on the planet's surface, while it's only been a few weeks for you, on the ship. Is that correct? (I think this was the basis for the original Planet of the Apes film.)

Is there any specific ratio for this? For instance, if you travel for three weeks at FTL, three years will have passed on the planet you left behind. Or can it be fudged, based on your story's specific needs? My female MC has been left behind by the male MC, who's flown off in his spaceship. After a period of time, he changes his mind about leaving, turns around and goes back, only to find that several years have passed for the female MC. The amount of time can be adjusted, but I'd like for her to have gotten a doctorate of science in the interim, so I'm thinking it'll need to have been at least six years. (She was already in university.) Given that time frame, how long would the male MC have hesitated before turning his ship around?

If this is all theoretical and can be utterly fudged, that's fine. I just wondered if there was a set ratio that I need to follow or if I'm free to make something up.

waylander · Nov 8, 2012

The equations http://www.phy.olemiss.edu/HEP/QuarkNet/time.html are for travel at a significant fraction of the speed of light - the closer you get to lightspeed the greater the dilation effect. Whether these hold for FTL is a moot point as, in the real world, FTL has not been demonstrated.

amschilling · Nov 8, 2012

http://en.wikipedia.org/wiki/Time_dilation

They have formulas there. It gave me a headache just thinking about calculating it, lol.

As far as fudging, it'll depend on your readers. Hard-core Sci-Fi fans will bash you if you're not close. Like Sheldon Cooper level of fans. Others won't notice if you're fudging it, and/or will use a little thing called suspension of disbelief to buy the time dilation you claim.

lbender · Nov 8, 2012

Not an expert, but I know enough to know that FTL is still fiction. Therefore, any time dilation theory is still theory. There may be some esoteric mathematical proof - again, not an expert - but you can pretty much do as you want. Most people will neither know nor care.

RichardGarfinkle · Nov 8, 2012

Here's a thread in Science Fact on Relativity (yes, I started it. I admit it).
http://absolutewrite.com/forums/showthread.php?t=246228

Time Dilation occurs at slower than light speed and the factor is
1/sqrt(1 - v[SUP]2[/SUP]/c[SUP]2[/SUP]) where v is the speed the object is traveling at and c is the speed of light, and sqrt means square root.

Relativity does not allow for FTL travel at all. Time dilation, however, has been measured so it's not just theory.

Orianna2000 · Nov 8, 2012

I have dyscalculia, so math disagrees with me. I really wasn't cut out to be a science fiction writer, but my romance novel takes place on another planet, so I kind of have to use a little science. It's driving me bonkers.

Okay, is it generally accepted that if you go faster than light, time dilation will still occur? Or is the popular theory that time dilation will cease once you break the speed of light barrier? I could say that his ship isn't quite FTL, if that would be more plausible. It would mean it's a lot slower to get anywhere, but it's still doable.

I want to be realistic and all, but as I said above, math is not my friend. I would need to hire someone to do the calculations for me, or else just fudge it and hope nobody calls me on it.

RichardGarfinkle · Nov 8, 2012

If you go FTL, you are violating the theory that has time dilation in it, so you can basically make up how you want it to work.

You don't need math to write SF. You might to write hard SF, but there's no obligation to do that.

FTL is an SF trope. There are a few theories that allow for it, but all of them have problems. Your best bet is to make up an FTL that you find useful.

The simplest is hyperspace wherein the drive takes the ship out of the universe so it can make a shortcut.

Are the particulars of time dilation important to your story?

King Neptune · Nov 8, 2012

Orianna2000 said:
I have dyscalculia, so math disagrees with me. I really wasn't cut out to be a science fiction writer, but my romance novel takes place on another planet, so I kind of have to use a little science. It's driving me bonkers.

Okay, is it generally accepted that if you go faster than light, time dilation will still occur? Or is the popular theory that time dilation will cease once you break the speed of light barrier? I could say that his ship isn't quite FTL, if that would be more plausible. It would mean it's a lot slower to get anywhere, but it's still doable.

I want to be realistic and all, but as I said above, math is not my friend. I would need to hire someone to do the calculations for me, or else just fudge it and hope nobody calls me on it.

There is a discontinuity at the speed of light, and it is thought that it is impossible for something to accelerate from slower than light to faster to light. The Lorenz Transformation (which Garfinkle gave) is only for slower than light. If the Lorenz Transformation holds true for faster than light, then time would go backwards. That is an interesting starting point.

If you want the scenario that you mentioned, then you should have the male go at 99% of c or faster, but not for very long. You can set up a spreadsheet for the relationship that will allow you to try different speeds and distances versus that time for the female to complete a degree.

RichardGarfinkle · Nov 8, 2012

King Neptune said:
There is a discontinuity at the speed of light, and it is thought that it is impossible for something to accelerate from slower than light to faster to light. The Lorenz Transformation (which Garfinkle gave) is only for slower than light. If the Lorenz Transformation holds true for faster than light, then time would go backwards. That is an interesting starting point.

Not quite. If you apply the Lorenz Transformation to a speed greater than light, time (and length and mass) become imaginary which does not have any physical meaning (unless you make one up).

Orianna2000 · Nov 8, 2012

The particulars aren't important, only the fact that the male MC leaves, is gone for a few weeks from his POV, and when he returns for the female MC, it's been six years for her. I don't mind saying that his ship travels at 99% of light speed, if that's necessary.

I know nothing of spreadsheets, so unless it's dead easy, I don't know if I could use them to calculate the time dilation.

Torgo · Nov 8, 2012

RichardGarfinkle said:
If you go FTL, you are violating the theory that has time dilation in it, so you can basically make up how you want it to work.

You don't need math to write SF. You might to write hard SF, but there's no obligation to do that.

FTL is an SF trope. There are a few theories that allow for it, but all of them have problems. Your best bet is to make up an FTL that you find useful.

The simplest is hyperspace wherein the drive takes the ship out of the universe so it can make a shortcut.

Are the particulars of time dilation important to your story?

Have you read Charlie Stross's Eschaton books (Singularity Sky, Iron Sunrise)? That's partly an attempt to grapple with space opera that has FTL, and thus causality violation. Closed timelike curves and that sort of thing.

Torgo · Nov 8, 2012

Orianna2000 said:
The particulars aren't important, only the fact that the male MC leaves, is gone for a few weeks from his POV, and when he returns for the female MC, it's been six years for her. I don't mind saying that his ship travels at 99% of light speed, if that's necessary.

In SF that's fine to do. It's the SF premise of The Forever War by Joe Haldeman.

waylander · Nov 8, 2012

If you use a hyperspatial jump for most of the distance travelled, the ship carrying the MC could still travel at a significant fraction of c to get to the jump point, and thus be subject the the time dilation effect.

RichardGarfinkle · Nov 8, 2012

Torgo said:
Have you read Charlie Stross's Eschaton books (Singularity Sky, Iron Sunrise)? That's partly an attempt to grapple with space opera that has FTL, and thus causality violation. Closed timelike curves and that sort of thing.

No, I haven't. I'll see if I can pick them up (i'm off to a con this weekend so i'll have a look around for them).

Orianna2000 · Nov 8, 2012

Ah, that makes sense. Say, he needs to travel slower than light speed until he gets out of the solar system. Then he can punch it. But he doesn't get that far, because he realizes he loves the MC and doesn't want to leave her behind, so he turns around and goes back. I need to account for his return journey, too, if I make any sort of attempt at calculating things.

Torgo · Nov 8, 2012

RichardGarfinkle said:
No, I haven't. I'll see if I can pick them up (i'm off to a con this weekend so i'll have a look around for them).

Part of the setup - recounted early, so v mild setting spoilers - is that we invented quantum computers, so calculations can be done simultaneously and violate - I think locality? - so you get, in some circs, the answer 'before' you asked the question. So the computer bootstraps itself up to a godlike AI which exists in the future as well as the present, and we get FTL, and then because FTL travel implies time travel the One Commandment is "Thou shalt not violate causality within My historical light cone." It's all very niftily worked-out and plausible if you concede only a few SF premises.

King Neptune · Nov 8, 2012

RichardGarfinkle said:
Not quite. If you apply the Lorenz Transformation to a speed greater than light, time (and length and mass) become imaginary which does not have any physical meaning (unless you make one up).

As I understand it, imaginary numbers in speed and location calculations of stars, etc. are taken as the time. It certainly would be interesting to accelerate something through the speed of light. The energy requirement might be infinite, which would have strange consequences, if it could be done.

Smiling Ted · Nov 8, 2012

Orianna2000 said:
Ah, that makes sense. Say, he needs to travel slower than light speed until he gets out of the solar system. Then he can punch it. But he doesn't get that far, because he realizes he loves the MC and doesn't want to leave her behind, so he turns around and goes back. I need to account for his return journey, too, if I make any sort of attempt at calculating things.

Just remember:

1. Time dilation happens with slower-than-light travel that approaches light speed.

2. The same theory (Relativity) that predicts time dilation also predicts that it is impossible to travel faster than the speed that light achieves in a vacuum.

3. Time dilation has been proven to exist. Many times.

4. One implication of Special Relativity Theory is that if you somehow could travel faster than light, you would also travel backwards in time.

5. The closer you get to the speed of light, the more massive you become (although you wouldn't notice it), and the more energy is required to increase your speed further - ultimately, it requires infinite energy to achieve light speed.

Those are the basics.

Orianna2000 · Nov 8, 2012

Got it, thanks.

Trebor1415 · Nov 8, 2012

"I could say that his ship isn't quite FTL, if that would be more plausible"

The problem with this is that without FTL drives much SF just won't work because the distance that needs to be travelled from one solar system to another, for instance, is longer than the human lifespan. For non-FTL travel SF writers have postulated "generation ships" that would travel for hundreds or thousands of years and the people who arrive at the destination are the descenants of the ones who left.

RichardGarfinkle · Nov 9, 2012

King Neptune said:
As I understand it, imaginary numbers in speed and location calculations of stars, etc. are taken as the time. It certainly would be interesting to accelerate something through the speed of light. The energy requirement might be infinite, which would have strange consequences, if it could be done.

I'm afraid you're combining two different parts of relativity. There's a way of talking about spacetime intervals which is phrased using imaginary numbers but that doesn't apply to their appearance in the Lorenz contraction. It's basically an artifact of trying to fit spacetime interval to look more like Euclidean distance.

Short version in flat spacetime (that is spacetime with no matter in it) each point (called an event) has four coordinates (x,y,z,t). One way to calculate spacetime interval between an observer at (0,0,0,0) and an event is
x[SUP]2[/SUP] + y[SUP]2[/SUP] + z[SUP]2[/SUP] - c[SUP]2[/SUP]t[SUP]2[/SUP] (for various reasons one more often uses -1 times this, but this version fits the current confusion better).

If this quantity is less than 0 then the event is perceivable by the observer or vice versa depending on whether the event happens before or after the observer's event (the separation is said to be timelike). If it's greater than 0 the event is not perceivable by the observer because not even light can get from the event to the observer or the observer to the event. If it's 0 the interval is called null or lightlike and only light (something else moving at lightspeed) can connect the event and the observer.

If you don't like the negative signs in the above calculation and want a distance formula that looks more like standard Euclidean distance
x[SUP]2[/SUP] + y[SUP]2[/SUP] + z[SUP]2[/SUP] + t[SUP]2[/SUP] then you can change the coordinate system so that the coordinates of the event are written as (x, y, z, ict). Where i = sqrt(-1). It produces the same effect but is largely useless beyond this calculational trick.

Imaginary numbers are used frequently in physics but mostly in the middle of calculations they're supposed to be gone from the results when you have to go from math back to reality.

The infinite energy thing means that if FTL is possible, we won't get there by just accelerating. It also takes an infinite amount of time (from an outside observer's frame of reference) to get from any less than c speed up to c.

blacbird · Nov 9, 2012

When I was in basic training in the U.S. Army, I once had a drill sergeant yell at me that I needed to get something done yesterday. Does that count?

caw

onesecondglance · Nov 9, 2012

Read The Forever War. Time dilation is a major plot line, it's not very long, and it has one of the best endings I've ever read.

Orianna2000 · Nov 9, 2012

So FTL is the way to go--once he's out of the solar system--but he can't break the light barrier by accelerating. So he'll, what, just fold space or something? I can make up any sort of method for achieving FTL, because it doesn't exist, right? Hyperspace, folded space, wormholes, etc. I can just pick something at random and work it into the story?

I know there's a book out there on how to deal with these kinds of plot issues. I got a similar one on how to write about time travel, for my previous novel. Never thought I'd need one on FTL drives, but maybe I'll go see if Amazon has it.

Oh, I found this time dilation calculator online. The trouble is, you have to know which equations (such as velocity) to punch into it, in order to get your answer. I just want to know, if it's been six years for the female MC waiting back home, how long has it been for the male MC traveling at near-lightspeed, heading out of the solar system? (Needs to include his return journey, since he goes back for her.) If anyone can definitively answer this question for me, without drowning me with math equations, you'll get acknowledged in my author's notes.

(I'd prefer to say it's been at least a week for him, maybe several. Long enough for him to regret his decision to leave, agonize over it, then finally turn the ship around and go back. But I'll go with whatever the real answer happens to be, even if it means he was only gone a few hours from his perspective.)

Torgo · Nov 9, 2012

I asked a similar question a while back; I had an idea for a story about interstellar con artists who stop on a planet at the dawn of the native civ and seed it with religious prophecy, then zoom off for six subjective months and come back a couple of thousand years later in the planet's history; a big fake Second Coming, letting them scoop up lots of loot. I think someone pointed out that if you have godlike tech like FTL you're probably not interested in loot all that much, but it's still one I think about from time to time.

FTL Time Dilation

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