Is the Twin Paradox Truly Unresolvable from Speedo's Perspective?

[Michio Cuckoo]

According to Lorentz, time is always dilated.So think of two twins, Speedo and Goslo.

- Goslo stays on Earth and drinks tea.
- Speedo gets into a rocket, zooms off into outer space and zooms back.Imagine YOU are Speedo. You zoom off, and when you return to Earth, you find that Goslo is 20 years older than you.

Both of you were the same age when you left, but now he's way older. This means he must have aged faster. But how could Goslo appear to age faster, when time is always dilated?!.
Discuss this but only consider Speedo's point of view. Because if you are Speedo, what would you see?

 

[Jonathan Scott]

Let's look at an equivalent scenario in ordinary space, involving two ants. Both ants start at A in this diagram:

 A
 |\
 | \
 |  *1
 *2  \
 |    B
 |   /
 |  /
 | /
 |/
 C

Initially ant *1 is crawling towards B and ant *2 at the same speed towards C. If either ant looks at the other, it sees the other ant progressing more slowly in its own forward direction than itself. Then ant *1 reaches B and turns towards C. After the turn, both ants STILL see the other ant moving more slowly than themselves in their own direction. Ant *2 reaches C first, but there is no contradiction involved. Note that as ant *1 turned the corner at B, it saw ant *2 going from being behind it to being ahead of it.

Apart from a minus sign in the relationship between time and space, the maths of the twin paradox is very similar to this.

 

[Michio Cuckoo]

Let's look at an equivalent scenario in ordinary space, involving two ants. Both ants start at A in this diagram:

 A
 |\
 | \
 |  *1
 *2  \
 |    B
 |   /
 |  /
 | /
 |/
 C

Initially ant *1 is crawling towards B and ant *2 at the same speed towards C. If either ant looks at the other, it sees the other ant progressing more slowly in its own forward direction than itself. Then ant *1 reaches B and turns towards C. After the turn, both ants STILL see the other ant moving more slowly than themselves in their own direction. Ant *2 reaches C first, but there is no contradiction involved. Note that as ant *1 turned the corner at B, it saw ant *2 going from being behind it to being ahead of it.

Apart from a minus sign in the relationship between time and space, the maths of the twin paradox is very similar to this.

So if I'm Speedo, as I turn my rocket back to Earth, Goslo will "suddenly" become older? Is that what you're saying?

I want people to think about this from Speedo's point of view.

 

[ghwellsjr]

Speedo will see Goslo's clock ticking slower than his own during his outbound portion of the trip. At the same time, Goslo will see Speedo's clock ticking slower than his own. They each see the other one's clock ticking slower than their own by exactly the same amount.

Then when Speedo turns around, he immediately sees Goslo's clock ticking faster than his own. So exactlly half the time Speedo sees Goslo's clock ticking slower than his own and exactly half the time he sees Goslo's clock ticking faster than his own.

However, Goslo does not see Speedo's clock go from ticking slow to ticking fast at the half-way point of the trip, because he has to wait for the image of Speedo turning around to propagate from that distant location to himself, so he continues to see Speedo's clock ticking slower than his own for much more than half the trip. Eventually, near the end of the trip, he sees Speedo turn around and now he sees Speedo's clock ticking faster than his own until Speedo gets back to him, In fact, they both see each other's clock ticking faster than their own by exactly the same amount during this last portion of the trip.

Now when Speedo gets back, since he watched Goslo's clock tick slow and fast for exactly half the trip, and since Goslo watched Speedo's clock tick slow for most of the trip and fast for a very short time, Goslo will see that Speedo is much younger than himself when they reunite.

It's really very simple, OK?

 

[Jonathan Scott]

Speedo will see Goslo's clock ticking slower than his own during his outbound portion of the trip. At the same time, Goslo will see Speedo's clock ticking slower than his own. They each see the other one's clock ticking slower than their own by exactly the same amount.

Then when Speedo turns around, he immediately sees Goslo's clock ticking faster than his own. So exactlly half the time Speedo sees Goslo's clock ticking slower than his own and exactly half the time he sees Goslo's clock ticking faster than his own.

However, Goslo does not see Speedo's clock go from ticking slow to ticking fast at the half-way point of the trip, because he has to wait for the image of Speedo turning around to propagate from that distant location to himself, so he continues to see Speedo's clock ticking slower than his own for much more than half the trip. Eventually, near the end of the trip, he sees Speedo turn around and now he sees Speedo's clock ticking faster than his own until Speedo gets back to him, In fact, they both see each other's clock ticking faster than their own by exactly the same amount during this last portion of the trip.

Now when Speedo gets back, since he watched Goslo's clock tick slow and fast for exactly half the trip, and since Goslo watched Speedo's clock tick slow for most of the trip and fast for a very short time, Goslo will see that Speedo is much younger than himself when they reunite.

It's really very simple, OK?

Although this description appears to be correct, there is a big difference between what we actually see (by means of light or similar) and how we measure time and space, and that could cause confusion.

What we see varies continuously, as described above. However, we plot the location of events in our own time and space by assuming that what we see was delayed by the time that light took to reach us, or by doing equivalent calculations based on earlier events.

When the moving twin turns around, the main effect this has is that "now" at a distant location as calculated by light travel time in his own new frame of reference jumps suddenly, as described by the Lorentz transformation. This means that the point in the other twin's life (or "world line") that corresponds to "now" for the turning twin is suddenly shifted, in the same way that the point on ant *2's path that is level with ant *1's progress suddenly switches so that ant *2 is now ahead.

Yes, it works as if Speedo effectively sees Goslo as suddenly being older after he turns, because the point in Goslo's life which corresponds to "now" from Speedo's point of view has suddenly shifted. (Be careful of which way round "older" and "younger" go for the space-time version, as the switched signs mean that the straight line in the space-time case corresponds to the most proper time, not the least).

 

[Michio Cuckoo]

Then when Speedo turns around, he immediately sees Goslo's clock ticking faster than his own.

But how is that possible? Isn't time always dilated?

 

[Michio Cuckoo]

Although this description appears to be correct, there is a big difference between what we actually see (by means of light or similar) and how we measure time and space, and that could cause confusion.

Let's assume Speedo and Goslo can perceive each other using insta-beams, which travel at infinite speed.

So Speedo and Goslo can perceive instant time-dilation of the other twin.

If Speedo is using insta-beams, he will always witness time dilation, NEVER time compression, so he will always see Goslo as younger.

 

[Jonathan Scott]

But how is that possible? Isn't time always dilated?

As I just said, what you see isn't the same as what you calculate to be happening. When you are moving towards a signal or away from it, you see the signal sped up (known as "blue shift" ) or slowed down (known as "red shift").

 

[Jonathan Scott]

Let's assume Speedo and Goslo can perceive each other using insta-beams, which travel at infinite speed.

So Speedo and Goslo can perceive instant time-dilation of the other twin.

If Speedo is using insta-beams, he will always witness time dilation, NEVER time compression, so he will always see Goslo as younger.

By "infinite speed" you presumably mean in such a way that the beam takes exactly zero time to pass between two points in space. However, this property depends on the velocity of the frame of reference, in the same way that being level with the other ant depends on the direction of travel. A beam which is takes exactly zero time to travel between two points in one frame of reference (which means their separation is "purely spacelike") can take a positive time to traverse the same distance in another frame of reference and a negative time in another (so it is received before it is sent).

 

[Dale]

According to Lorentz, time is always dilated.

This is not true. According to Lorentz, moving clocks are always time dilated in an inertial frame.

Do you understand the importance of that distinction?

 

[Dale]

I want people to think about this from Speedo's point of view.

Speedo is non-inertial, so there is no standard definition of what his point of view is. You have to define it explicitly. In particular, you have to define what convention speedo adopts for determining simultaneity in his frame and for determining distance in his frame.

 

[ghwellsjr]

Speedo will see Goslo's clock ticking slower than his own during his outbound portion of the trip. At the same time, Goslo will see Speedo's clock ticking slower than his own. They each see the other one's clock ticking slower than their own by exactly the same amount.

Then when Speedo turns around, he immediately sees Goslo's clock ticking faster than his own. So exactlly half the time Speedo sees Goslo's clock ticking slower than his own and exactly half the time he sees Goslo's clock ticking faster than his own.

However, Goslo does not see Speedo's clock go from ticking slow to ticking fast at the half-way point of the trip, because he has to wait for the image of Speedo turning around to propagate from that distant location to himself, so he continues to see Speedo's clock ticking slower than his own for much more than half the trip. Eventually, near the end of the trip, he sees Speedo turn around and now he sees Speedo's clock ticking faster than his own until Speedo gets back to him, In fact, they both see each other's clock ticking faster than their own by exactly the same amount during this last portion of the trip.

Now when Speedo gets back, since he watched Goslo's clock tick slow and fast for exactly half the trip, and since Goslo watched Speedo's clock tick slow for most of the trip and fast for a very short time, Goslo will see that Speedo is much younger than himself when they reunite.

It's really very simple, OK?

Although this description appears to be correct, there is a big difference between what we actually see (by means of light or similar) and how we measure time and space, and that could cause confusion.

Wow, this is the first time I ever heard anyone apologize for the Relativistic Doppler explanation of the Twin Paradox. It exactly and precisely describes the Point of View of each twin and is fundamentally the raw measurement that each one makes of the other ones clock. Any other explanation requires arbitrary assumptions about how we measure time and space and different assumptions lead to different "measurements". So please don't denigrate my perfectly valid explanation of what each Twin sees. Isn't that fundamentally what "Point of View" means?

What we see varies continuously, as described above. However, we plot the location of events in our own time and space by assuming that what we see was delayed by the time that light took to reach us, or by doing equivalent calculations based on earlier events.

Yes, all based on assumptions, we get out what we add into the situation.

When the moving twin turns around, the main effect this has is that "now" at a distant location as calculated by light travel time in his own new frame of reference jumps suddenly, as described by the Lorentz transformation. This means that the point in the other twin's life (or "world line") that corresponds to "now" for the turning twin is suddenly shifted, in the same way that the point on ant *2's path that is level with ant *1's progress suddenly switches so that ant *2 is now ahead.

Your ant explanation claims that just because I turn my head, I can cause another person's age to change abruptly, even to the point of him getting younger.

Yes, it works as if Speedo effectively sees Goslo as suddenly being older after he turns, because the point in Goslo's life which corresponds to "now" from Speedo's point of view has suddenly shifted. (Be careful of which way round "older" and "younger" go for the space-time version, as the switched signs mean that the straight line in the space-time case corresponds to the most proper time, not the least).

And what if Speedo turns around again, does Goslo suddenly become younger?

Now I'm not saying that your explanation is invalid because it's not, but it is based on assumptions that are totally arbitrary and totally unnecessary in an explanation based on Einstein's assumptions (postulates) and his definition of a Frame of Reference. There is no need to have Speedo change frames just because he changes his speed or direction of travel.

So what causes confusion is claiming that one explanation is not as valid as another. They can all work as long as we understand what the assumptions and definitions are that we use in each of them. But every explanation will agree with the Relativistic Doppler explanation.

 

[ghwellsjr]

Then when Speedo turns around, he immediately sees Goslo's clock ticking faster than his own.

But how is that possible? Isn't time always dilated?

Haven't you ever experienced Doppler shift when, for example, an emergency vehicle passes you and you suddenly hear the pitch of the siren drop? A similar thing would happen if you could take a high speed video of a fast moving object passing close by you. You would see the colors change and if there was a visible clock, you would see it change its tick rate. You would never see it jump in time though.

Time dilation is an explanation that is provided in Special Relativity based on a clock's motion in an inertial (non-accelerating and non-changing Frame of Reference). During the first half of the trip, if you analyze the situation from a frame in which Goslo is at rest, his clock ticks normally while Speedo's is time dilated and ticks slower. If you analyze the same situation from a frame in which Speedo is at rest, then his clock ticks normally while Goslo's time is dilated and his clock ticks slower. If you continue analyzing in the same frame, you will get a consistent result.

 

[jartsa]

Speedo will see Goslo's clock ticking slower than his own during his outbound portion of the trip. At the same time, Goslo will see Speedo's clock ticking slower than his own. They each see the other one's clock ticking slower than their own by exactly the same amount.

Then when Speedo turns around, he immediately sees Goslo's clock ticking faster than his own. So exactlly half the time Speedo sees Goslo's clock ticking slower than his own and exactly half the time he sees Goslo's clock ticking faster than his own.

However, Goslo does not see Speedo's clock go from ticking slow to ticking fast at the half-way point of the trip, because he has to wait for the image of Speedo turning around to propagate from that distant location to himself, so he continues to see Speedo's clock ticking slower than his own for much more than half the trip. Eventually, near the end of the trip, he sees Speedo turn around and now he sees Speedo's clock ticking faster than his own until Speedo gets back to him, In fact, they both see each other's clock ticking faster than their own by exactly the same amount during this last portion of the trip.

Now when Speedo gets back, since he watched Goslo's clock tick slow and fast for exactly half the trip, and since Goslo watched Speedo's clock tick slow for most of the trip and fast for a very short time, Goslo will see that Speedo is much younger than himself when they reunite.

It's really very simple, OK?

If we use non-relativistic Doppler shift of light here, then the result is incorrect: no time dilation.

If we use relativistic Doppler shift here, then the result is correct: time dilation.

The difference between non-relativistic Doppler shift and relativistic Doppler shift is that in relativistic Doppler shift time dilation is taken account.

EDIT: Or should say: non-relativistic frequency shift of ticking, and relativistic frequency shift of ticking.

EDIT2: I mean: If we calculate clock ticks assuming the clock is time dilated, then we get less ticks, if calculate clock ticks assuming the clock is not time dilated, then we get more ticks, and therefore a Doppler shift based explanation is not really an explanation.

 

[Jonathan Scott]

Your ant explanation claims that just because I turn my head, I can cause another person's age to change abruptly, even to the point of him getting younger.

Note that "turning" in the ant case is equivalent to a velocity change in the space-time case. This has the effect of changing the point in the other person's time line which is considered equal to "now" locally. You can't see someone "now" anyway, so the concept of what their age is "now" is a projection anyway.

And what if Speedo turns around again, does Goslo suddenly become younger?

Yes, if by "turns around" you mean changes velocity to move in the original direction. Nothing happens to Goslo of course, but Speedo's "now" mapped on to Goslo's time line has changed.

 

[Nugatory]

So if I'm Speedo, as I turn my rocket back to Earth, Goslo will "suddenly" become older? Is that what you're saying?

I want people to think about this from Speedo's point of view.

You will find a really excellent explanation at http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParadox/twin_paradox.html.

As others have already pointed out, you have to be careful with that phrase "Speedo's point of view". When Speedo says that he "saw" Goslo and Goslo's clock, he is actually saying that light rays from Goslo and Goslo's clock hit his retina; these light rays tell Speedo about Goslo's state of affairs when the rays left Goslo, and by the time they get to Speedo, something completely different could be going on with Goslo.

Ghwellsjr has given you a spot-on accurate explanation of what Speedo "sees"; this is basically the "Doppler Shift Analysis" of the FAQ I linked to above.

We can also analyze the situation by having both twins try to figure out what was going on for each twin at various points during the experiment. The best way to do this is for each twin to keep precise records ("When my clock read T, I saw my twin moving at speed S towards/away from me, and the distance between us was D"), and when they get back together they can compare notes and come up with a consistent view of events in which Speedo ended up experiencing less time than Goslo. This leads to the "Spacetime Diagram Analysis" in the FAQ I linked to above, and is pretty much what Jonathan Scott was explaining in his first post. (I think it's also what you were trying to do with your "insta-beams", but that's a topic for a different post).

[And, just to stave off any possible misunderstanding: The two analyses are not conflicting viewpoints, competing theories, or a suggestion that there is any disagreement about what's going on in the twin paradox. They are both using the exact same physics and understanding of how the universe works - one just spends more time analyzing the behavior of light rays passing between the two twins than does the other]

 

[Michio Cuckoo]

This is not true. According to Lorentz, moving clocks are always time dilated in an inertial frame.

Do you understand the importance of that distinction?

So if I undergo acceleration, I can actually witness Time Compression?!

Enlighten me, master.

 

[Q-reeus]

So if I undergo acceleration, I can actually witness Time Compression?!

Enlighten me, master.

If by time compression you mean 'everyone else's clocks go faster' then sure - hop onto the periphery of a rotating carousel. Your clock unambiguously ticks slower than for 'stationary' observers.

 

[Janus]

So if I undergo acceleration, I can actually witness Time Compression?!

Enlighten me, master.

Yes. For example, If you were in the tail of an accelerating rocket, you would see a clock in the nose run fast compared to your own. The longer your rocket, the greater the difference in time rate. Conversely, if you were in the nose, you would see the clock in the tail as running slower.
This also applies to clocks outside of the rocket and not accelerating with you. Clocks in the direction you are accelerating will run faster, and ones in the opposite direction will run slower. This is in addition to any time dilation caused by relative velocities. The difference here is that these "outside" clocks will not see any additional effect on you due to your acceleration and will only see the time dilation due to your relative velocity.

 

[SinghRP]

I am late. Looks like the discussion has gone well beoynd the scope.
Please see the Pseudogravity thread and my statements.
George Gamow in his popularization series "Gravity" (Dover, 2002; p. 126) addresses this twin paradox. (Here he missed a point though. He ignored the effect of the Earth's own gravity.) Good luck.

 

[Nugatory]

Let's assume Speedo and Goslo can perceive each other using insta-beams, which travel at infinite speed.

So Speedo and Goslo can perceive instant time-dilation of the other twin.

If Speedo is using insta-beams, he will always witness time dilation, NEVER time compression, so he will always see Goslo as younger.

Although we use this "Let's assume..." style of though experiment all the time, there is a pitfall: Whatever we assume has to be at least theoretically possible, or the results of the argument will be very misleading. For example, if I start with "Let's assume that 2+2=5, ..." I can come up with all sorts of strange weird paradoxes that prove nothing except that my starting assumption is inconsistent with reality.

The problem with your hypothetical insta-beam is that if it's going to do what (I think) you want it do, all observers have to see the transmission and the reception happen at the same time. That's no more possible than 2+2=5, so logical reasoning about what people using instabeams would observe is bound to lead to impossible paradoxes.

I suspect that what you're trying to do is get rid of the distracting arguments about how hard it is for the two twins to compare the passage of time when they're in different places and forced to communicate with light traveling at a finite speed. If that's what you want, you'll be better served by the space-time diagram approach I mention in my previous post.

 

[Michio Cuckoo]

I suspect that what you're trying to do is get rid of the distracting arguments about how hard it is for the two twins to compare the passage of time when they're in different places and forced to communicate with light traveling at a finite speed. If that's what you want, you'll be better served by the space-time diagram approach I mention in my previous post.

Thanks. That's what I was trying to do.

A lot of people have given me all sorts of crazy explanations, the Doppler Shift, and that the Doppler Shift is equivalent to Time Compression; that Time Compression is actually possible in an accelerating frame, despite what Lorentz said; and that Goslo suddenly becomes older when you turn around.

I need help.

 

[Nugatory]

Thanks. That's what I was trying to do.

A lot of people have given me all sorts of crazy explanations, the Doppler Shift, and that the Doppler Shift is equivalent to Time Compression; that Time Compression is actually possible in an accelerating frame, despite what Lorentz said; and that Goslo suddenly becomes older when you turn around.

I need help.

Read that FAQ that I pointed you at... That will get you through this...

The Doppler Shift is a spot-on accurate explanation of what the twins "see", as it describes how the light rays passing between the two twins behave.

Goslo doesn't "suddenly become older", he sees the days and weeks and months and years of his life ticking steadily by at a constant rate just as we'd expect. Speedo has the same experience with his life. What's happening at the turnaround is that Speedo is changing reference frames, hence changing his notion of how readings on Goslo's clock relate to readings of his own clock.

Don't sweat the gravitation and acceleration stuff until you've got the basic space-time diagram and Doppler effect pictures of the paradox down cold.

 

[Dale]

So if I undergo acceleration, I can actually witness Time Compression?!

If you use a non inertial coordinate system you can indeed "witness time compression".

Good examples have already been mentioned, rotating reference frames and Rindler coordinates.

 

[Dale]

A lot of people have given me all sorts of crazy explanations, ... that Time Compression is actually possible in an accelerating frame, despite what Lorentz said;

Lorentz never said what you claim he said.

 

[ghwellsjr]

Speedo will see Goslo's clock ticking slower than his own during his outbound portion of the trip. At the same time, Goslo will see Speedo's clock ticking slower than his own. They each see the other one's clock ticking slower than their own by exactly the same amount.

Then when Speedo turns around, he immediately sees Goslo's clock ticking faster than his own. So exactlly half the time Speedo sees Goslo's clock ticking slower than his own and exactly half the time he sees Goslo's clock ticking faster than his own.

However, Goslo does not see Speedo's clock go from ticking slow to ticking fast at the half-way point of the trip, because he has to wait for the image of Speedo turning around to propagate from that distant location to himself, so he continues to see Speedo's clock ticking slower than his own for much more than half the trip. Eventually, near the end of the trip, he sees Speedo turn around and now he sees Speedo's clock ticking faster than his own until Speedo gets back to him, In fact, they both see each other's clock ticking faster than their own by exactly the same amount during this last portion of the trip.

Now when Speedo gets back, since he watched Goslo's clock tick slow and fast for exactly half the trip, and since Goslo watched Speedo's clock tick slow for most of the trip and fast for a very short time, Goslo will see that Speedo is much younger than himself when they reunite.

It's really very simple, OK?

If we use non-relativistic Doppler shift of light here, then the result is incorrect: no time dilation.

If we use relativistic Doppler shift here, then the result is correct: time dilation.

The difference between non-relativistic Doppler shift and relativistic Doppler shift is that in relativistic Doppler shift time dilation is taken account.

EDIT: Or should say: non-relativistic frequency shift of ticking, and relativistic frequency shift of ticking.

EDIT2: I mean: If we calculate clock ticks assuming the clock is time dilated, then we get less ticks, if calculate clock ticks assuming the clock is not time dilated, then we get more ticks, and therefore a Doppler shift based explanation is not really an explanation.

You have to read carefully what I said. I didn't mention time dilation at all. I didn't even mention relativity. I didn't say it was Doppler, relativistic or normal. I was explaining what each twin sees or views. Isn't that the fundamental meaning of "Point of View"?

Now if it was normal Doppler then what I said would be incorrect, wouldn't it? Because I said that at the end of the trip, they each see the other ones clock having accumulated a different amount of time and that wouldn't be true for normal Doppler.

I'm trying to get Michio Cuckoo to understand what the scenario is before he tries to create non-existent problems for it. I'm presenting the raw data measurements that any viable theory has to explain.

 

[jartsa]

You have to read carefully what I said. I didn't mention time dilation at all. I didn't even mention relativity. I didn't say it was Doppler, relativistic or normal. I was explaining what each twin sees or views. Isn't that the fundamental meaning of "Point of View"?

Now if it was normal Doppler then what I said would be incorrect, wouldn't it? Because I said that at the end of the trip, they each see the other ones clock having accumulated a different amount of time and that wouldn't be true for normal Doppler.

I'm trying to get Michio Cuckoo to understand what the scenario is before he tries to create non-existent problems for it. I'm presenting the raw data measurements that any viable theory has to explain.

I see. We are talking about what Speedo sees. OK I trust that simply putting Speedo's speed into relativistic doppler shift formula, tells us what frequencies Speedo sees.

 

[Michio Cuckoo]

You have to read carefully what I said. I didn't mention time dilation at all. I didn't even mention relativity. I didn't say it was Doppler, relativistic or normal. I was explaining what each twin sees or views. Isn't that the fundamental meaning of "Point of View"?

Now if it was normal Doppler then what I said would be incorrect, wouldn't it? Because I said that at the end of the trip, they each see the other ones clock having accumulated a different amount of time and that wouldn't be true for normal Doppler.

I'm trying to get Michio Cuckoo to understand what the scenario is before he tries to create non-existent problems for it. I'm presenting the raw data measurements that any viable theory has to explain.

So as Speedo undergoes acceleration, he sees the rest of the stationary universe undergo Time Compression; and that is why Goslo ends up older?

 

[ghwellsjr]

So as Speedo undergoes acceleration, he sees the rest of the stationary universe undergo Time Compression; and that is why Goslo ends up older?

I don't say that. I say that as Speedo undergoes acceleration at the half-way point of his trip, he immediately sees an increase in the rate at which Goslo's clock ticks but this is only because he is moving toward the images of Goslo's clock that were already in transit toward him. It's just a Doppler shift. But Goslo doesn't see any such change until way later when the images of Speedo undergoing acceleration finally reach him. It's this imbalance in the time that each one sees the other ones clock ticking slower then faster that allows them to see a difference in the accumulated times on each others clock.

 

[Michio Cuckoo]

I don't say that. I say that as Speedo undergoes acceleration at the half-way point of his trip, he immediately sees an increase in the rate at which Goslo's clock ticks but this is only because he is moving toward the images of Goslo's clock that were already in transit toward him. It's just a Doppler shift. But Goslo doesn't see any such change until way later when the images of Speedo undergoing acceleration finally reach him. It's this imbalance in the time that each one sees the other ones clock ticking slower then faster that allows them to see a difference in the accumulated times on each others clock.

So Goslo's clock ticking faster as seen by Speedo is a result of the Doppler effect.

This means that from Speedo's reference frame, he can still apply Time Dilation to Goslo.

Therefore, the only explanation as to how Goslo got older is that as Speedo changed his direction, he also switched to another world line, and he observes a time gap, i.e. Goslo suddenly becomes older.

Amirite?

 

[Dale]

This means that from Speedo's reference frame, he can still apply Time Dilation to Goslo.

First, you have to define Speedo's reference frame. As I mentioned in post 11 there is no standard way of doing so, which means that you have to be explicit.

What exactly do you mean when you say "Speedo's reference frame".

 

[A.T.]

Therefore, the only explanation as to how Goslo got older is that as Speedo changed his direction, he also switched to another world line, and he observes a time gap, i.e. Goslo suddenly becomes older.

Comparing distant clocks depends on certain conventions. According to the usual one, time flows at different rates at different positions in an accelerating frame (just like in a gravitational field, see Equivalence principle). So yes, in the accelerating frame of Speedo time is running very fast at the very distant position of Goslo, allowing Goslo to age quickly.

This observed non-uniform aging of Goslo is just a consequence of the non-inertial frame of Speedo. Describing the world from non-inertial frames is always "strange", even in classical mechanics where suddenly inertial forces appear. In Relativity non-inertial become a bit more "strange".

 

[ghwellsjr]

I don't say that. I say that as Speedo undergoes acceleration at the half-way point of his trip, he immediately sees an increase in the rate at which Goslo's clock ticks but this is only because he is moving toward the images of Goslo's clock that were already in transit toward him. It's just a Doppler shift. But Goslo doesn't see any such change until way later when the images of Speedo undergoing acceleration finally reach him. It's this imbalance in the time that each one sees the other ones clock ticking slower then faster that allows them to see a difference in the accumulated times on each others clock.

So Goslo's clock ticking faster as seen by Speedo is a result of the Doppler effect.

This means that from Speedo's reference frame, he can still apply Time Dilation to Goslo.

Therefore, the only explanation as to how Goslo got older is that as Speedo changed his direction, he also switched to another world line, and he observes a time gap, i.e. Goslo suddenly becomes older.

Amirite?

Again, please note that I have been talking about what each twin actually sees, not how you can resolve what happens according to an arbitrary non-inertial reference which to me is a pointless exercise and shouldn't be pursued until you thoroughly understand how you can resolve what happens from an arbitrary inertial reference frame. Do you understand how to analyze the situation from an inertial reference frame, for example, one in which Goslo remains at rest throughout the scenario?

 

[AntonL]

And which twin aged?

Suppose the two twins are each in their respective spaceships traveling at some or other high speed as measured in reference system C, so A and B stay young while C ages.

A & B do not know about C so let's forget about C and just look at A & B in their respective reference frames

A & B sync their clocks:
1) A sees B depart at some high speed and return, A aged and B remained young
but also at the same time
2) B sees A depart at some high speed and return, B aged and A remained young

So whoever ages depends into which spaceship you place the reference frame.

Now if above is all gibberish then SR is to blame. Sorry I rephrase: The science must be correct it is just that I do not understand SR. Maybe someone can give me a nice logical explanation and proof to explain to me which clock actually slowed down when A and B meet again.

PS:Now let's go back to reference system C and relativity says A & B clocks tick slower than C's clock.

3) Now A sees B depart but actually B slows to C so B clock is faster than A, but in reference system A, B clock is slower than A

As I said, I am totally but I am sure their must be an explanation forthcomming

 

[Dale]

A & B sync their clocks:
1) A sees B depart at some high speed and return, A aged and B remained young
but also at the same time
2) B sees A depart at some high speed and return, B aged and A remained young

So whoever ages depends into which spaceship you place the reference frame.

This is not true. All inertial frames will agree which is younger when they return. Once you have completely specified the problem in anyone inertial frame you can determine what happens in any other.

The science must be correct it is just that I do not understand SR. Maybe someone can give me a nice logical explanation and proof to explain to me which clock actually slowed down when A and B meet again.

Just use the following formula to calculate the time accumulated for A and for B. The formula is valid in any inertial frame:
http://en.wikipedia.org/wiki/Proper_time#Mathematical_formalism

PS:Now let's go back to reference system C and relativity says A & B clocks tick slower than C's clock.

3) Now A sees B depart but actually B slows to C so B clock is faster than A, but in reference system A, B clock is slower than A

As I said, I am totally but I am sure their must be an explanation forthcomming

Just pick any inertial frame, use the formula above, and look at the result. Then, Lorentz transform to any other inertial frame, and do the same. Compare the results.