# Space traveler and time dilation

## Main Question or Discussion Point

Maybe some one can help clear up a problem. According to Wikipedias article on time dilation

“In the case that the observers are in relative uniform motion, and far away from any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock.”

Which I can accept but this does not seem consistent with the “time slowing down for a space traveler” situation. If the space traveler is moving fast relative to the earth the people on earth will see that time is passing more slowly for traveler. The traveler will think that the time on the earth is moving more slowly. So what happens when he gets back to earth he’s been observing that earth time has been moving more slowly so he would be older that earth time would suggest. But also for the earth people the travelers time would have been passing more slowly so he should be younger. Which is a contradiction.

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phyzguy
George Jones
Staff Emeritus
Gold Member
If the space traveler is moving fast relative to the earth the people on earth will see that time is passing more slowly for traveler. The traveler will think that the time on the earth is moving more slowly. So what happens when he gets back to earth he’s been observing that earth time has been moving more slowly so he would be older that earth time would suggest.
Yes as the traveler moves away from Earth, he sees visually time on the Earth passing more slowly, but when the traveler is on the trip back to Earth, he sees visually time on the Earth passing more quickly. The net result is that upon arrival back on Earth, the traveler finds that the Earth has aged more than he has.

See

thanks everyone. I'll get reading then.

What I'd like to know is: if you went "all the way around the Universe", i.e. it was a 4-D sphere, and passed your starting point again without ever having undergone acceleration, how would the paradox be resolved? A wormhole would have the same problem in GR.

Ah "the twins".. I don't know about the time dilation or the paradox.

I don't know their acceleration or anything but this topic sure never gets old =)

What I'd like to know is: if you went "all the way around the Universe", i.e. it was a 4-D sphere, and passed your starting point again without ever having undergone acceleration, how would the paradox be resolved? A wormhole would have the same problem in GR.
As Universe is curved, then that can be answered in SR framework, only n GR framework. But the situation is not symmetric in GR because the world line of such observer is more curved.

What I'd like to know is: if you went "all the way around the Universe", i.e. it was a 4-D sphere, and passed your starting point again without ever having undergone acceleration, how would the paradox be resolved? A wormhole would have the same problem in GR.
You dont really need to go around the universe to resolve or simulate the problem - there is one round trip voyage where both twins remain in their own inertial frame for the entire round trip - yet their clocks show different lapsed times when the traveling twin returns - no general relativity involved and no curvature - a polar orbiting satellite will do - simple construct a 100 mile high tower on the South Pole and put a satellite in polar orbit at an elevation of 100 miles - a clock on top of the tower remains fixed in the non rotating earth centered inertial reference frame and the clock on board the satellite remains in the inertial frame of the orbiting satellite - start the clocks as the satellite passes the tower and stop them when it passes by after completing one orbit - the two clocks will not have logged the same amount of time.

You dont really need to go around the universe to resolve or simulate the problem - there is one round trip voyage where both twins remain in their own inertial frame for the entire round trip.
In SR if the twins part and reunite then at least one of them has been moving non-inertially at some time.

What sort of motion a round trip of the universe entails I do not know. It depends on the global geometry of the universe.

Matheinste.

Yes as the traveler moves away from Earth, he sees visually time on the Earth passing more slowly, but when the traveler is on the trip back to Earth, he sees visually time on the Earth passing more quickly. The net result is that upon arrival back on Earth, the traveler finds that the Earth has aged more than he has.

Gorge Jones,
You have posted this comment several times in this forum, now. It is absolutely wrong. If you believe it, you have a serious misunderstanding of Special Relativity.

I am shocked that the other members of this forum are letting you get away with this.

Ich
George Jones' comment is not wrong. Maybe you are confusing relativistic doppler effect and time dilation? George explicitly talks about the former.

phyzguy
George Jones and Ich are correct. Attached is a picture I downloaded from among the plethora of explanations on the web. You can see that on the way out, the twin on the rocket sees two years pass on Earth, while four years pass for him. On the way back, he sees 8 years pass on Earth while four years pass for him. So when he returns, 10 years have passed on Earth while 8 years have passed for him, so the twin on the rocket is younger.

#### Attachments

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George Jones and Ich are correct. Attached is a picture I downloaded from among the plethora of explanations on the web. You can see that on the way out, the twin on the rocket sees two years pass on Earth, while four years pass for him. On the way back, he sees 8 years pass on Earth while four years pass for him. So when he returns, 10 years have passed on Earth while 8 years have passed for him, so the twin on the rocket is younger.
If you do calculations to compensate for doppler effect, then you'll see that time passes slower in both directions (outbound and inbound). It's just that at the turnaround point at half way and decelleration to stop back on earth that perceptions of simultaneity will shift significantly in a small amount of time. This accounts for a huge 'jump' forwards in time on earth, as seen by the traveller, as he turns around.

Thus, even though earths clocks have been ticking slower on both the outbound AND inbound journey, the 'jump' forwards in time as simultaneity shifts means that the earthlings will have still aged more.

George Jones
Staff Emeritus
Gold Member
Gorge Jones,
You have posted this comment several times in this forum, now. It is absolutely wrong.
How is it wrong?
This accounts for a huge 'jump' forwards in time on earth, as seen by the traveller, as he turns around.
A huge jump in coordinates is not actually seen visually by the traveler. There is a big difference between what is seen visually, and what happens to coordinates.

phyzguy
A huge jump in coordinates is not actually seen visually by the traveler. There is a big difference between what is seen visually, and what happens to coordinates.
This is absolutely correct. If the twin on the rocket had a telescope trained on Earth, he would see no jump. He would simply see things start to happen faster as he turned around, because he is now starting to "catch up" with the outward propagating wave fronts coming from Earth. Look again at the space-time diagram I posted a few posts ago.

DrGreg
Gold Member
Re: Space traveller and time dilation

You dont really need to go around the universe to resolve or simulate the problem - there is one round trip voyage where both twins remain in their own inertial frame for the entire round trip - yet their clocks show different lapsed times when the traveling twin returns - no general relativity involved and no curvature - a polar orbiting satellite will do - simple construct a 100 mile high tower on the South Pole and put a satellite in polar orbit at an elevation of 100 miles - a clock on top of the tower remains fixed in the non rotating earth centered inertial reference frame and the clock on board the satellite remains in the inertial frame of the orbiting satellite - start the clocks as the satellite passes the tower and stop them when it passes by after completing one orbit - the two clocks will not have logged the same amount of time.
This analogy doesn't work in either special or general relativity.

In special relativity, ignoring gravity, the south pole pole would be inertial and the "satellite" would be accelerating.

In general relativity, the south pole pole is accelerating and the satellite is inertial.

This is absolutely correct. If the twin on the rocket had a telescope trained on Earth, he would see no jump. He would simply see things start to happen faster as he turned around, because he is now starting to "catch up" with the outward propagating wave fronts coming from Earth. Look again at the space-time diagram I posted a few posts ago.
I'm basing this on a model of what happened after calculating to remove the doppler effect and time it takes for light to travel, as i stated originally (probably not very well). I find that when people are trying to understand, the doppler effect and all that confuses the issue. People typically want to know what is 'really' happening, rather than what it looks like by the time the light has reached you.

So i guess what i mean is that if you plotted space and time coordinates on a graph for the whole journey then what the traveller would see is the earth taking a large jump forwards in time at the turnaround point (assuming its instantaneous).

my question is, can a Wick rotation be made 'physical' ??

i mean you are in a metric $$t^{2}-x^{2}$$ space and time

and you 'rotate' your reference system to get a new metric $$t^{2}+x^{2}$$ which is purely Euclidean and there is no distinction between space and time

JesseM
I'm basing this on a model of what happened after calculating to remove the doppler effect and time it takes for light to travel, as i stated originally (probably not very well). I find that when people are trying to understand, the doppler effect and all that confuses the issue. People typically want to know what is 'really' happening, rather than what it looks like by the time the light has reached you.
But that isn't what's "really happening" in any meaningful sense, it's just what's happening in one particular non-inertial rest frame for the traveling twin--specifically one constructed in such a way that the definition of simultaneity in this non-inertial frame always matches up with the definition of simultaneity that would be used in the traveler's instantaneously co-moving inertial rest frame at that instant. Unlike with inertial frames, though, there isn't any one "correct" way to construct a non-inertial rest frame for a non-inertial observer, there are an infinite number of different coordinate systems you could construct for such an observer and none of them would be considered physically "preferred".

Ich
Aaron_Shaw said:
So i guess what i mean is that if you plotted space and time coordinates on a graph for the whole journey then what the traveller would see is the earth taking a large jump forwards in time at the turnaround point (assuming its instantaneous).
SR does not support coordinate systems with a "jump forward in time". The very notion of such a jump is IMO much more misleading that the additional mentioning of visual effects. Especially if stated in a post supposed to describe what's 'really' happening. This is exactly the kind of voodoo that laymen love to hear, but it burns out their brains. It'd destroy my brain too if I had to understand how such a 'real' jump forward in time is caused by an acceleration manoever of a probe some lightyears away.

SR does not support coordinate systems with a "jump forward in time". The very notion of such a jump is IMO much more misleading that the additional mentioning of visual effects. Especially if stated in a post supposed to describe what's 'really' happening. This is exactly the kind of voodoo that laymen love to hear, but it burns out their brains. It'd destroy my brain too if I had to understand how such a 'real' jump forward in time is caused by an acceleration manoever of a probe some lightyears away.
Well i could be way off then, but i'm getting at the point that on the outbound journey the earth clock runs slower, and it also runs slower on the inbound journey. If this is the case then how does the earth clock end up being older than the travelling clock? Because at the periods in between the two non accelerating frame journeys, where acceleration occurs, the simultaneity wil shift as the speed isn't staying constant. So at time right BEFORE turn around the earth clock might read 25 seconds, but at the moment right AFTER turnaround (an instantaneous one) the earth clock will read significantly more than the expected 25 seconds, for example, 180.

Of course the traveller would SEE the clock read something different. But if the traveller knows he is X light years away, and he knows the speed of light, he would conclude that the clock reading he can currently see actually occured a certain amount of time earlier.

So baring that in mind, he might conclude that the two clocks read as follows:

Travelling clock - Earth clock
0 0
10 5
20 10
30 15
40 20
50 25

TURNAROUND

60 180
70 185
80 190
90 195
100 200

If this is complete rubbish then i'm keen to figure it out properly. But the way i currently see it is that it's 2 journeys which can be modelled by SR. The 2 journeys don't result in a paradox when the traveller is back at the start because in between there has been a part of the journey not handled by SR, where the idea of simultaneity between the two frames has changed due to the change in relative velocities.

I'm aware, btw, that my use of terminology is not proper. I'm still getting used to it.

Ich
If this is complete rubbish then i'm keen to figure it out properly.
No, it's not rubbish. It's a change of coordinate systems. You understand it clearly, different notions of simultaneity point to different events on the earth's worldline as happening "now".
But such a thing cannot happen in a single inertial system. It's not part of SR.
And a "jump forward in time" is nothing real. Rather, different numbers are assigned to events. It's more to do with bookkeeping than time warps.
i'm getting at the point that on the outbound journey the earth clock runs slower, and it also runs slower on the inbound journey. If this is the case then how does the earth clock end up being older than the travelling clock?
Forget about "clocks running slower". That's Lorentz Ether language. Of course, A cannot run slower than B while B runs slower than A. This sort of language is incompatible with SR.
I know that's how they teach it. Forget it. Look at your diagrams. There's a triangle, and there's a triangle inequality (in our case the non-straight path being shorter). That's true no matter in which frame you view it.

Your math is correct. But there's no such things as slowing clocks, contracting metersticks, or planets jumping forward in time. SR is about relations of objects, not changes happening to them.
Take the geometric viewpoint, there are projections, slices, different paths (time dilation, length contraction, twin paradox), not broken clocks.

No, it's not rubbish. It's a change of coordinate systems. You understand it clearly, different notions of simultaneity point to different events on the earth's worldline as happening "now".
But such a thing cannot happen in a single inertial system. It's not part of SR.
And a "jump forward in time" is nothing real. Rather, different numbers are assigned to events. It's more to do with bookkeeping than time warps.

Forget about "clocks running slower". That's Lorentz Ether language. Of course, A cannot run slower than B while B runs slower than A. This sort of language is incompatible with SR.
I know that's how they teach it. Forget it. Look at your diagrams. There's a triangle, and there's a triangle inequality (in our case the non-straight path being shorter). That's true no matter in which frame you view it.

Your math is correct. But there's no such things as slowing clocks, contracting metersticks, or planets jumping forward in time. SR is about relations of objects, not changes happening to them.
Take the geometric viewpoint, there are projections, slices, different paths (time dilation, length contraction, twin paradox), not broken clocks.
Ok... this is interesting. I've not heard anyone say this before, so it looks like i'm going to have to consider things differently; after i get some sleep : )

Thanks.

P.s. sorry if i've hijacked your thread, OP, it looked like it was winding up.

Re: Space traveller and time dilation

This analogy doesn't work in either special or general relativity.

In special relativity, ignoring gravity, the south pole pole would be inertial and the "satellite" would be accelerating.

In general relativity, the south pole pole is accelerating and the satellite is inertial.
A satellite in orbit is a perfectly good inertial frame - the traveling twin stays in orbit - all clocks are at the same gravitational potential (100 miles above the earth) - so there is no general relativity issues and there are no accelerations once the orbit is established and the first measurement is taken on the flyby.