Exploring the Twin Paradox: Understanding Time Dilation and Relativistic Speeds

[Orcinus]

Okay maybe it's not just the Ender's Game series, and maybe its actually a cornerstone [STRIKE]fact[/STRIKE] [STRIKE]belief[/STRIKE] [STRIKE]theorem[/STRIKE] [STRIKE]postulation[/STRIKE] thing of relativity, but still!
In the story Ender travels in ships which go at relativistic speeds. By doing so, centuries go past but he hardly ages at all. I don't get this.

As he approaches c, time for him slows down, and outside everything speeds up. So he would travel... a long way, in (for him) a short time. As v = s/t, he would still travel the same distance but the time to do so would decrease through relativity, to such a degree that he would (or could) go faster than light. Trying to reword this: Though to an observer at (for example) his destination, it actually takes him centuries to travel light years, to him its not nearly as long. So an observer can travel faster than light, but no-one else can?

If Ender (E) travels towards his destination (D) at relativistic speeds, D will observe E's time to slow down because E's traveling so fast, conversely E will observe D's time to speed up. However, relative to E, D is in fact the one traveling very fast, and so E will observe D's time to slow down and conversely D will see E's time speeding up. What?!

Also, 1st post! I know its bad form to post more than one topic at a time (especially a first time poster), but some other stuff's been bugging me for a while as well, so if I'm allowed to ask more than one question (if not, I'll ask again later, I just don't want to spam):

• Could you measure time in metres?
• What the **** is gravity? (link to something might be easier than an explanation)
• Is the centre of the universe the beginning of the universe?
• If mass is energy, is energy mass? In other words would something with more energy always have more mass? Building on that, what about gravitational potential energy: would something on the Earth have potential energy based on the displacement between it and the supermassive black hole at the centre of the galaxy and hence if it was knocked towards it, that E_p would turn to E_k, thereby meaning it has that potential energy stored in its... mass?

 

[ghwellsjr]

Okay maybe it's not just the Ender's Game series, and maybe its actually a cornerstone [STRIKE]fact[/STRIKE] [STRIKE]belief[/STRIKE] [STRIKE]theorem[/STRIKE] [STRIKE]postulation[/STRIKE] thing of relativity, but still!
In the story Ender travels in ships which go at relativistic speeds. By doing so, centuries go past but he hardly ages at all. I don't get this.

As he approaches c, time for him slows down, and outside everything speeds up. So he would travel... a long way, in (for him) a short time. As v = s/t, he would still travel the same distance but the time to do so would decrease through relativity, to such a degree that he would (or could) go faster than light. Trying to reword this: Though to an observer at (for example) his destination, it actually takes him centuries to travel light years, to him its not nearly as long. So an observer can travel faster than light, but no-one else can?

If Ender (E) travels towards his destination (D) at relativistic speeds, D will observe E's time to slow down because E's traveling so fast, conversely E will observe D's time to speed up. However, relative to E, D is in fact the one traveling very fast, and so E will observe D's time to slow down and conversely D will see E's time speeding up. What?!

When you talk about what E and D observe, do you mean what they actually see or do you mean what they determine theoretically from Special Relativity without regard to what they can see?

 

[Orcinus]

Well, not in the story, I made that up.
I got that situation by regurgitating what I've heard before(eg. ww(totallynotalinkmodguy)w.youtube.com/watch?v=sYOO2mOjo9s&t=14m57s), that if you travel towards someone, than relativity apparently says that time appears slower for you to someone else. But... hmmm... so maybe light travel has something to do with it? But that would have the opposite effect wouldn't it?
...
Theoretically.

Also: OMG 2 view 1 post! Fastest thread reply I've seen evar.

 

[Dale]

Hi Orcinus, welcome to PF!

You may be interested in the following page:
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

Basically, if you measure time according to the person in a relativistic space-ship, and distance according to the people outside the space-ship, then you can indeed get a ratio with units of speed and a value greater than c. However, that ratio mixes measurements from two different frames, so it does not contradict the fact that the space-ship is traveling slower than c in all reference frames.

 

[ghwellsjr]

Well, not in the story, I made that up.
I got that situation by regurgitating what I've heard before(eg. ww(totallynotalinkmodguy)w.youtube.com/watch?v=sYOO2mOjo9s&t=14m57s), that if you travel towards someone, than relativity apparently says that time appears slower for you to someone else. But... hmmm... so maybe light travel has something to do with it? But that would have the opposite effect wouldn't it?
...
Theoretically.

Also: OMG 2 view 1 post! Fastest thread reply I've seen evar.

You're going to have to be a little clearer in your responses. I'm asking you when you use the word "observe" do you mean what observers actually see with their eyes and/or instruments or do you mean what they calculate theoretically from SR based on a lot of information that they presume to be true but that they cannot have any knowledge of?

And, yes, it does have everything to do with light travel.

 

[phinds]

Orcinus, try this:

www.phinds.com/time dilation

 

[Orcinus]

Thanks for the insanely fast replies.

@DaleSpam, okay, I think that makes sense. So that means a fast moving body will measure distances differently to one static in relation to what they're measuring. Oh yeah of course, I remember that bit now. To someone else it would appear the ship is really short... but that would also mean they're measuring with "short" instruments. And oh dear, I thought I might be getting close to real maths by doing the highest yr 12 maths there is, but I got lost at the first term on that link (what's a sinh? Don't bother answering that).

@ghwellsjr I do mean what they theoretically calculate from SR.
Though if it was to do with light: If a ship were traveling towards you and you saw bob drop his drink and lean over to pick it up, the light from him dropping it would travel at 1c which is far faster than the ship. The light from him picking it up though would be released from a position ahead of where he dropped it, though still traveling at 1c. This would be like Doppler, and the illusion would be that bob appeared to drop it and pick it up faster to you than to him. But this Doppler has the opposite effect to the specific relativity I've heard about, so I assume that the phenomenon I'm thinking about is indeed a bending of time and not just an illusion else why is it discussed when speaking about relativity. ie, what does light have to do with it? That's fighting the effect, not causing it.

e: Or maybe not Doppler at all there phinds
2nd Edit: I thought light would be irrelevant cause I wanted bendy time not illusory time, light weasels its way in a way I didn't expect due to the limited nature of c. So the converse's I mentioned aren't true, E sees D slow, and D sees E slow? (please say yes cause that makes sense)

 

[ghwellsjr]

@ghwellsjr I do mean what they theoretically calculate from SR.
Though if it was to do with light: If a ship were traveling towards you and you saw bob drop his drink and lean over to pick it up, the light from him dropping it would travel at 1c which is far faster than the ship. The light from him picking it up though would be released from a position ahead of where he dropped it, though still traveling at 1c. This would be like Doppler, and the illusion would be that bob appeared to drop it and pick it up faster to you than to him. But this Doppler has the opposite effect to the specific relativity I've heard about, so I assume that the phenomenon I'm thinking about is indeed a bending of time and not just an illusion else why is it discussed when speaking about relativity. ie, what does light have to do with it? That's fighting the effect, not causing it.

Then your earlier statements in your first post are incorrect where you said that the different observers see the other ones times being sped up. Everyone determines that the other moving observers and their clocks are going slower than their own, not sped up.

You also need to take into account length contraction so your traveler determines that he gets where he's going not because he exceeds the speed of light but because he doesn't have very far to go.

 

[harrylin]

[..] As he approaches c, time for him slows down, and outside everything speeds up. So he would travel... a long way, in (for him) a short time. As v = s/t, he would still travel the same distance but the time to do so would decrease through relativity, to such a degree that he would (or could) go faster than light. Trying to reword this: Though to an observer at (for example) his destination, it actually takes him centuries to travel light years, to him its not nearly as long. So an observer can travel faster than light, but no-one else can?

Everyone measures everything material as moving slower than light speed. However time goes slower for a fast traveler, such that the speed of light has the same effect for the traveler as an infinite speed in classical mechanics.

If Ender (E) travels towards his destination (D) at relativistic speeds, D will observe E's time to slow down because E's traveling so fast, conversely E will observe D's time to speed up. [..]

The special thing in relativity is that the same effects are observed with all inertial reference systems. Thus, if E uses D's reference system then E will measure the same as D. But if E uses instead his "rest frame" as reference during a time of constant velocity, then his units and clock synchronization will be different from those of D, such that E will also measure D's time to be slowed down (and nobody can prove the other "wrong").

PS I see that you now realize that in your second edit:

2nd Edit: I thought light would be irrelevant cause I wanted bendy time not illusory time, light weasels its way in a way I didn't expect due to the limited nature of c. So the converse's I mentioned aren't true, E sees D slow, and D sees E slow? (please say yes cause that makes sense)

Yes indeed, just as we elaborated.

 

[Orcinus]

Okay thanks guys, that works.

Thus, if E uses D's reference system then E will measure the same as D. But if E uses instead his "rest frame" as reference during a time of constant velocity, then his units and clock synchronization will be different from those of D, such that E will also measure D's time to be slowed down (and nobody can prove the other "wrong").

I'm not sure about this bit. Just to bring in another illustration to confuse things, when they put that atomic clocks on the plane and left the other where it was, which one was behind? Because they were both traveling fast in relation to each other.

 

[harrylin]

Okay thanks guys, that works.

I'm not sure about this bit. Just to bring in another illustration to confuse things, when they put that atomic clocks on the plane and left the other where it was, which one was behind? Because they were both traveling fast in relation to each other.

There also gravitation effects played a role. Mutual time dilation works for inertial frames - thus you were right with your second edit, as I said - but there is no such symmetry when one of them changes velocity and the other not. For that case the only inertial frame calculation gives you the correct answer. See for the first discussion section 4 of:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

This is also commonly discussed under the topic "twin paradox", see this forum as well as http://en.wikipedia.org/wiki/Twin_paradox

 

[Nugatory]

Just to bring in another illustration to confuse things, when they put that atomic clocks on the plane and left the other where it was, which one was behind? Because they were both traveling fast in relation to each other.

This is the famous "Twin Paradox", about which much has been written on this forum - although I suggest that you start with http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParadox/twin_paradox.html. But with said...

They both measure the other clock running slow, for exactly the reason that you state: they're both moving relative to each other. Indeed, the situation is completely symmetrical, so it would be surprising if they didn't both the see other one affected in the same way.

Now you're asking which one is "really behind", and that's a trickier question. If you think about what it really means, you'll realize that you're asking "If I look at both clocks at the same time, which one will display the earlier time?" However, different observers in different frames moving relative to one another have different ideas of what time it is (it kinda has to be this way because their clocks are ticking at different speeds) so clock readings taken at the same time by one are not necessarily at the same time for another. Thus, it perfectly possible for both of them to measure the other's clock as running more slowly than their own.

To create an apparent paradox, you have to change the speeds of one or both clocks to get them into the same reference frame so we can read both clocks at the same time. Do this, and you'll find that relativity predicts (see the link that I posted above) a perfectly consistent answer.

BTW, I've bolded the phrase at the same time throughout this post because just about all relativity "paradoxes" come from being imprecise about this concept. If you can systematically root it out of your thinking (note how it was hidden in the question about which clock was behind) special relativity gets a lot easier.