Can time dilation cause confusion in the twin paradox?

[lrubin28]

Hi,

In the often cited example of a person in a rocket traveling past Earth at high speed - I think I understand that both the person on Earth and on the rocket could view the other as being the party that's actually moving. And so if they could view the other party, they would both see the other moving in slow motion. And I guess there is an assumption that time is relative to the observer. So if the rocket travels 10 years at speed near c, and then turns and spends another 10 years getting back to Earth, those 20 years in space may reflect say 100 years on earth. The original Earth person will be 100+ years old, and the space-person 20+ years old. But if time were relative to the other originally, now it seems that Earth time has become an absolute reference frame. I feel like I'm totally comparing apples and oranges, but can't figure out why. Does this make sense (my question)?

 

[Nugatory]

then turns

Those two words make a huge difference in the problem. The turnaround and the fact the two observers seaparate and rejoin while not a maintaining a constant velocity relative to one another turns the problem into the famous Twin Paradox. Googe for "Twin Paradox", search this forum for it, and above all else read the FAQ at http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[elusiveshame]

What if the rocket never "turns around", but always continued in an arc, then slowing down when approaching the starting position, or would that be the same thing?

 

[Khashishi]

Same thing. The point is that the rocket accelerates at some point, while the Earth remains in free fall. Only the details change if the rocket is accelerated throughout the journey or only during a short period.

 

[Nugatory]

What if the rocket never "turns around", but always continued in an arc, then slowing down when approaching the starting position, or would that be the same thing?

The "Spacetime diagram' section of that FAQ I pointed you at is the easiest way of analyzing that situation, although the Doppler-based analysis also works. Because of the continuously changing direction of travel you'd need some calculus either way.

 

[DaveC426913]

What if the rocket never "turns around", but always continued in an arc, then slowing down when approaching the starting position, or would that be the same thing?

The short answer to this is that, in order for them to first compare clocks at the beginning AND then again at the end of the run, they need to at some point in in close proximity. There is no way to do this without at least one of them changing their direction of motion and accelerating.

 

[ghwellsjr]

Hi,

In the often cited example of a person in a rocket traveling past Earth at high speed - I think I understand that both the person on Earth and on the rocket could view the other as being the party that's actually moving.

A more precise way of saying this is that in the rest frame of one party, the other party is moving. And Time Dilation applies to the party that is moving according to a frame.

Let me make some spacetime diagrams to illustrate. Here is one showing the rest frame of the rocket covering a time period from -10 years to +10 years. The moment when the rocket travels past Earth, is depicted as the blue dot at the origin of the diagram. The dots represent one-year increments of time:

Notice that the dots are aligned with the Coordinate Time of the diagram which means that there is no Time Dilation because the rocket is not moving in its own rest frame.

Now we can transform the coordinates of the events (dots) of the rocket to see the Time Dilation at a speed of just over 98%c:

Since this is the Earth's rest frame, we can add it in:

And so if they could view the other party, they would both see the other moving in slow motion.

You are thinking that they can each see the Time Dilation of the other party which is not the case. Look at this diagram which shows some of the images of each party as they are propagated at the speed of light to the other party. These are shown as thin lines. I have left off the thick red line that shows the worldline of the rocket since it would obscure the details of the light signals. Just imagine that the red dots are connected by a thick red line:

​

Look in the lower left corner. You see how the image of the red rocket that is emitted at the rocket's time of -10 years propagates up and to the right and encounters Earth at its time of -1 year. So for the next year on Earth, it will see the approaching rocket go through 10 years of the rocket's clock. This is 10 times fast motion, not slow motion.

Similarly, when the rocket gets to the -1 year, it can see the image of the Earth at its time of -10 years and it will see the Earth at ten times fast motion as they both approach the origin where they pass each other.

But after they pass each other, things change dramatically. Now they each see the other one in slow motion but still it is not the rate of Time Dilation which is about 1/5. Instead, they see each other at 1/10. It takes each of them 10 years according to their own clock to see 1 year pass on the other ones clock.

And I guess there is an assumption that time is relative to the observer. So if the rocket travels 10 years at speed near c, and then turns and spends another 10 years getting back to Earth, those 20 years in space may reflect say 100 years on earth. The original Earth person will be 100+ years old, and the space-person 20+ years old. But if time were relative to the other originally, now it seems that Earth time has become an absolute reference frame. I feel like I'm totally comparing apples and oranges, but can't figure out why. Does this make sense (my question)?

Let's depict this with a couple more diagrams. They both show the rocket traveling away for 10 years and then traveling back for 10 years while Earth accumulates 101 years (instead of 100 years as I wanted to make the light signals line up better). The first diagram shows how the rocket views the Earth's time:

Notice how during the first 10 years of the rocket's clock, it sees Earth aging by only 1 year, just as in the previous diagram but when the rocket turns around, it immediately sees the Earth aging at 10X high speed so that during the second 10 years of the rocket's clock, it see Earth aging by 100 years for a total of 101 years.

Here's the same scenario but showing how Earth views the rocket's clock:

Notice how the first ten years of Earth time is just like two diagrams ago. Earth is seeing the rocket's clock running one-tenth of its own time but this keeps up for 100 years of Earth time during which it sees the rocket aging by 10 years. Then it sees the rocket turn around and for the last year of Earth time, it sees the rocket's time at 10X and so it completes the total aging for the rocket at 20 years.

Does this help you understand Time Dilation?

 

[phinds]

What if the rocket never "turns around", but always continued in an arc, then slowing down when approaching the starting position, or would that be the same thing?

Google "twin paradox with circular motion"

 

[elusiveshame]

The "Spacetime diagram' section of that FAQ I pointed you at is the easiest way of analyzing that situation, although the Doppler-based analysis also works. Because of the continuously changing direction of travel you'd need some calculus either way.

I don't believe you pointed that at me, but I will definitely check it out :) I will also look into the Doppler based analysis as well. So much information!

The short answer to this is that, in order for them to first compare clocks at the beginning AND then again at the end of the run, they need to at some point in in close proximity. There is no way to do this without at least one of them changing their direction of motion and accelerating.

Ah, that makes sense. Thanks for that!

Google "twin paradox with circular motion"

Will do! I figured I wasn't the first to ask that question, but I wasn't sure how to phrase it (or anything similar to it), so thanks for that bit of info :)

 

[PhoebeLasa]

Here's a link to a previous thread that had a lot of discussion and alternative opinions about the Twin "Paradox":

https://www.physicsforums.com/threads/acceleration-and-the-twin-paradox.779110/

 

[lrubin28]

Thanks for all of these replies! And GHWells thanks for taking all of that time to write your response. I have to reread yours again but I wanted to ask a question based on the reference Nugatory provided. I read the reference, and am not sure if I have this right.
This is what I think I read...
1) Frames must be inertial (constant motion only) in order to invoke SR.
2) If the frames are inertial, and the rocket travels say 10 years near light speed, the twin in the rocket will have aged less than the twin on earth. (Does this mean that this person is effectively traveling into the future? Because if he stops the rocket after traveling 10 years near light speed, he might be at say 2020, while his twin on Earth is at 2050 in Earth years? Does this mean that if planet Earth traveled at near light speed, everyone would essentially live 7 times (roughly) longer than on Earth, but to them it would feel merely like 1 lifetime would feel to one person on a stationary Earth?)
3) If the Earth twin is watching his rocket based twin travel 10 years away at near light speed and then turns around and comes back, with a super powerful telescope the Earth twin would see his brother barely age while traveling away from Earth, but once the twin turns around and heads back to Earth at the same speed, the Earth twin would see most of the aging taking place while his brother is returning? So even though the Earth bound brother has aged a lot more, the rocket brother still ages but the aging process would mostly be seen on the return journey. This would all be because we are talking only about what we actually see. Meaning that if the Earth brother looks at the rocket brother immediately at the end of ten years of travel, and supposing the rocket brother has only had 2 years go by, that means that from Earth his brother might only look to have aged by some factor less than 2 years because of the Doppler effect? And this would mean that although you could travel into the future, you couldn't travel into the future back on Earth. Or I guess you could travel partly into the future on Earth if you turned around and came back.
Not sure I have any of that correct, but the parts about turning the rocket around taking say 80-90% of the entire trip's time is a little hard to wrap my head around. It just doesn't make that much sense to me, because I don't see how either brother would describe the experience as turning around for 80-90% of the time. Or maybe I'm just not understanding it...

(Most of these questions popped up for me after seeing Interstellar)

 

[lrubin28]

The short answer to this is that, in order for them to first compare clocks at the beginning AND then again at the end of the run, they need to at some point in in close proximity. There is no way to do this without at least one of them changing their direction of motion and accelerating.

So if they traveled in a gigantic circle, couldn't they travel at the same speed and same direction? Why does it only hold true if youre traveling in a straight line. I guess all the explanations explain why, but I don't intuitively get it. Travelling say 100 light years in a straight line is totally different than traveling 100 years in a circle. Even if they're traveling the entire way at the exact same speed? That doesn't really make any sense to me, which I guess shows that I don't understand it...

 

[phinds]

So if they traveled in a gigantic circle, couldn't they travel at the same speed and same direction? Why does it only hold true if youre traveling in a straight line. I guess all the explanations explain why, but I don't intuitively get it. Travelling say 100 light years in a straight line is totally different than traveling 100 years in a circle. Even if they're traveling the entire way at the exact same speed? That doesn't really make any sense to me, which I guess shows that I don't understand it...

Traveling in a circle mean that OF NECESSITY you are accelerating. That is, you can't travel in a circle without accelerating then whole time you are traveling in the circle. I say again, Google "twin paradox with circular motion"

 

[ghwellsjr]

Thanks for all of these replies! And GHWells thanks for taking all of that time to write your response. I have to reread yours again but I wanted to ask a question based on the reference Nugatory provided.

Why don't you go ahead and reread my response again (or as many times as it takes for you to understand it) and then see if you still have questions.

I read the reference, and am not sure if I have this right.
This is what I think I read...
1) Frames must be inertial (constant motion only) in order to invoke SR.
2) If the frames are inertial, and the rocket travels say 10 years near light speed, the twin in the rocket will have aged less than the twin on earth. (Does this mean that this person is effectively traveling into the future? Because if he stops the rocket after traveling 10 years near light speed, he might be at say 2020, while his twin on Earth is at 2050 in Earth years? Does this mean that if planet Earth traveled at near light speed, everyone would essentially live 7 times (roughly) longer than on Earth, but to them it would feel merely like 1 lifetime would feel to one person on a stationary Earth?)
3) If the Earth twin is watching his rocket based twin travel 10 years away at near light speed and then turns around and comes back, with a super powerful telescope the Earth twin would see his brother barely age while traveling away from Earth, but once the twin turns around and heads back to Earth at the same speed, the Earth twin would see most of the aging taking place while his brother is returning? So even though the Earth bound brother has aged a lot more, the rocket brother still ages but the aging process would mostly be seen on the return journey. This would all be because we are talking only about what we actually see. Meaning that if the Earth brother looks at the rocket brother immediately at the end of ten years of travel, and supposing the rocket brother has only had 2 years go by, that means that from Earth his brother might only look to have aged by some factor less than 2 years because of the Doppler effect? And this would mean that although you could travel into the future, you couldn't travel into the future back on Earth. Or I guess you could travel partly into the future on Earth if you turned around and came back.
Not sure I have any of that correct, but the parts about turning the rocket around taking say 80-90% of the entire trip's time is a little hard to wrap my head around. It just doesn't make that much sense to me, because I don't see how either brother would describe the experience as turning around for 80-90% of the time. Or maybe I'm just not understanding it...

(Most of these questions popped up for me after seeing Interstellar)

It's a little hard to tell whether your understanding is correct but I would just make some general comments::

1) When you're learning SR, always think in terms of a single Inertial Reference Frame to completely describe and analyze your scenario. The objects/observers/clocks can independently travel at any speeds (short of c) and their Time Dilation is based on their current speed as determined by the gamma factor.

2) You should only compare accumulated age differences between observers/objects/clocks after they depart and reunite. While they remain separated, their ages difference are frame dependent.

3) Learn to use (or at least appreciate) the Lorentz Transformation process to see what a scenario looks like according to a second Inertial Reference Frame. It is helpful to make a spacetime diagram for in-line scenarios. Remember, light travels at c along the 45-degree diagonals no matter how you transform between frames.

4) Doppler allows you to determine what each observer actually sees and must be the same in every frame.

5) SR works just as well with non-inertial frames but they don't provide any new understanding of what any observer actually sees and, unlike inertial reference frames, there is no standard way to specify them.

 

[harrylin]

Same thing. The point is that the rocket accelerates at some point, while the Earth remains in free fall. Only the details change if the rocket is accelerated throughout the journey or only during a short period.

Sorry that's mistaken - as a matter of fact, the first "twin" traveler example concerned a traveler who does a "free fall" turnaround:
- https://www.physicsforums.com/threa...on-is-not-relative.670653/page-8#post-4275033

What matters is that compared with the traveler, the stay-at home is almost unaccelerated, and thus approximately in inertial (or, "galilean") motion.

[..] 1) Frames must be inertial (constant motion only) in order to invoke SR.

Right: SR uses so-called "galilean" reference systems. In those systems, Newton's first law of classical mechanics holds perfectly.

2) If the frames are inertial, and the rocket travels say 10 years near light speed, the twin in the rocket will have aged less than the twin on earth. (Does this mean that this person is effectively traveling into the future? [..]

You probably mean: if the stay at home is inertial.
Then, yes indeed: you can in that way "travel to the future" - but you cannot go back to the present!