# The Twin Paradox can't be resolved.

1. May 19, 2012

### 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?

2. May 19, 2012

### Jonathan Scott

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

Code (Text):
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.

Last edited: May 19, 2012
3. May 19, 2012

### Michio Cuckoo

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

4. May 19, 2012

### 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?

5. May 19, 2012

### Jonathan Scott

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).

Last edited: May 19, 2012
6. May 19, 2012

### Michio Cuckoo

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

7. May 19, 2012

### Michio Cuckoo

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.

8. May 19, 2012

### Jonathan Scott

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").

9. May 19, 2012

### Jonathan Scott

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).

10. May 19, 2012

### Staff: Mentor

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?

11. May 19, 2012

### Staff: Mentor

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.

12. May 19, 2012

### ghwellsjr

Wow, this is the first time I ever heard any one 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?
Yes, all based on assumptions, we get out what we add into the situation.
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.
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.

13. May 19, 2012

### ghwellsjr

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.

14. May 19, 2012

### jartsa

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.

Last edited: May 19, 2012
15. May 19, 2012

### Jonathan Scott

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.

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.

16. May 19, 2012

### Staff: Mentor

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]

17. May 19, 2012

### Michio Cuckoo

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

Enlighten me, master.

18. May 19, 2012

### Q-reeus

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.

19. May 19, 2012

### Janus

Staff Emeritus
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.

20. May 19, 2012

### SinghRP

I am late. Looks like the discussion has gone well beoynd the scope.
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.

21. May 19, 2012

### Staff: Mentor

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 travelling 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.

22. May 19, 2012

### Michio Cuckoo

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.

23. May 19, 2012

### Staff: Mentor

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.

24. May 19, 2012

### Staff: Mentor

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.

Last edited: May 19, 2012
25. May 19, 2012

### Staff: Mentor

Lorentz never said what you claim he said.