# If time dilation can slow time down, is there away to speed time up?

Okay, I know the title is really confusing but I couldn't find words to explain it sorry. Pretty much what I mean is, if I can get in a lightspeed spaceship moving away from earth, time slows down for me. So one year for me will be 20 earth years or what ever. But is there away were I can reverse this? Where if I get on that same craft and travel for a year but it only will be a few months on earth? I know this is just a random thought.

No, there is not way to have the reverse effect in special relativity. This is because an object being at rest maximizes the time that elapses for it in relativity (a consequence of the lagrangian formulation of special relativity). So if your question is you have your friend sit on earth for a few (say three) months, and you want to know what is the most you can age in the time it takes your friend to wait three months, then the answer is three months, and this is accomplished by sitting on earth doing nothing.

In general relativity, you can use a gravitational field to accomplish what you want. Assuming you are already on earth, you just need to go a region of lower spacetime curvature, such as outer space, and then wait there. Time will pass faster for you, and if you wait long enough, more time will have passed for your friend than for you when you come back to earth. This was illustrated in the movie Interstellar, where we saw a man on a spaceship age much faster than the people on the surface of the planet being orbited.

• You could also accelerate everyone else to near light speed, although that might be impractical. Dec 12, 2016 at 17:40
• @JahanClaes You are clearly an evil genius. Dec 13, 2016 at 0:23
• @JahanClaes That's the most correct answer so far haha. Dec 13, 2016 at 0:54

The answer, as others have said, is generally 'no' (see caveats below). There is a lovely geometrical reason for this, which is the point of this answer.

## Without gravity

So first of all consider flat spacetime -- no gravity -- and think about two events -- points in spacetime -- which are timelike separated: one of the events is in the future of the other or, to be precise, you can get from one event to the other without travelling at the speed of light.

So, for instance, $e_1$ might be 'here, now' and $e_2$ might be 'here, in a week', or $e_1$ might be 'here, now', and $e_2$ might be 'in New York, in an hour'.

So, now consider all the possible ways we can get between $e_1$ and $e_2$: geometrically, these are all the possible timelike curves passing through $e_1$ and $e_2$: they must be timelike because we can't go faster (or even as fast) as light.

There are lots of these curves, here are three of them: But there is one special curve, which is in red in the diagram: a straight line between $e_1$ and $e_2$. And now we can crank up Euclid: there is always exactly one such curve between any two events. This curve has the special property that it is the one in which there is no acceleration: that's pretty much how a straight line is defined in fact.

However unlike in euclidean geometry this straight line is not the shortest curve between the two points it connects: it's the longest. In particular it is the curve which has the largest proper time: the curve which, if you follow it between two events, you will experience the longest time. All the other curves -- the curves which are not straight, and on which, if you follow them, you will experience acceleration -- are shorter, and you will experience less proper time when you follow them.

And this is why, in special relativity, you can't experience any longer time than the time you would experience by following the straight line between the two events. (It is also how the twin 'paradox' works: only one twin can follow the geodesic, and the other twin therefore experiences less time.)

## With gravity

Is this still true in the presence of gravity? In general yes, it is, but the situation is more complicated.

First of all, spacetime is no longer flat so we can't cheat and use results from Euclid: we need to create a whole definition of what a 'straight line' is, which is a geodesic. But geodesics have the properties we need: they are local maxima of proper time, you experience no acceleration when you follow them. Additionally, they exist given some mild constraints on the spacetime.

It's easy to see what geodesics look like on Earth, where there is gravity. Consider two events, 'here, now' and '100 metres over there, in 10 seconds time'. There are lots of timelike curves which connect these two events: you could drive a car between one and the other, and (if you are Usain Bolt) you could run between them. All of these trajectories will involve acceleration. But there's one that won't: you could fire a projectile in such a way that it followed a ballistic trajectory and arrived 100 meters over there, in 10 seconds. And there is a unique such trajectory which you can calculate (it's about $50\,\mathrm{m}/\mathrm{s}$ at $78^{\circ}$ from the horizontal I think).

This trajectory is the geodesic between those two events, and, just as in flat spacetime it is the curve which has the longest proper time: a projectile following that trajectory will experience the maximum proper time between these two events.

But now there are some other questions: are geodesics in curved spacetime unique the way that straight lines are, and if they aren't is there a longest one (or a set of longest ones) rather than being able to find ones with unbounded length? I am not completely sure what the answer to this question is: although I suspect very strongly that the answers are 'no' and 'yes' in physically plausible cases (see comment to this answer for an example).

## Caveats: pathological spacetimes

Finally it is possible to construct pathological spacetimes, where there is no longest-proper-time timelike curve, but I think the construction of one shows how physically weird such things would be.

Here's how you could construct one: take a flat spacetime, and in it two spacelike surfaces which do not intersect (so for instance, using some obvious coordinate system, pick $t=0$ and $t=10$ as the two surfaces). Now identify these surfaces. For any two timelike-separated events $e_1$ and $e_2$ between these surfaces you can now construct timelike curves which start from $e_1$, pass $e_2$, and then loop back into the past of $e_2$ through the identified surfaces. And you can iterate this process: there's no upper bound on how long such a curve can be, and someone travelling on it will therefore experience arbitrarily large proper times. Here's a picture of how this construction looks: the dotted lines are the identified spacelike surfaces. But this spacetime is causality-violating in a seriously horrible way: it's definitely not something you'd like to think of as physically plausible.

• If you are in orbit around earth and you want to go to the antipodal in some fixed amount of time, you can pick whichever direction you want to orbit the earth, so there are infinitely many geodesics by symmetry, and they will all have the same time. If your destination is offset from the antipode, you can still have two geodesics, but they won't have the same time. Dec 13, 2016 at 0:45
• @NowIGetToLearnWhatAHeadIs Yes, doh, I have amended my answer. The thing I really wanted to specify was that it should be hard to find a sequence of geodesics between two events with no upper bound on their lengths. Thank you.
– user107153
Dec 13, 2016 at 1:49

Being in a gravitational field is equivalent to accelerated frame... So we may accelerate towards the earth (in 0 g surrounding, so that acceleration causes us to experience gravity pulling us back in direction opposite to that of we are accelerating towards), so that while we experience the flow of time normally, time in front of us gets slow. And therefore, the time on earth will flow slow, causing few months to pass while we travel years in our time frame.

Time dilation, doesn't slow the time.... it is just that if you travel with the speed of light, you will do a very large amount of work in a very small amount of time, and hence we say that time seem to have been stopped, but in real it does not stop at all. I will explain it as that, if you are traveling around the earth in an jet you will complete one trip approximately in 40-50 hours, while traveling with speed of light you cover the same distance about 7.5 times in only 1 second..(Now, this difference is a huge one, just thing about it,,you have covered a distance which could take you about 40-50 hours in only about $1/7.5$ of a second) so therefore we say that time had stopped because once again you have done a lot amount of work in a very very small amount of time and hence time seems to stop(but never stops..).

• This is not true.
– Eva
Dec 12, 2016 at 17:02
• What? In what universe? This is false. Dec 14, 2016 at 0:41
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