# B Does your age only change when accelerating?

1. Apr 19, 2016

### idea2000

After looking at the "doppler effect" explanation of the twin paradox, I'm under the impression that the difference in the age of the two twins has to do with the part of the diagram where one of the twins is accelerating. But, my question is, what about the "coasting" part of the diagram? So, if I were to accelerate two particles in exactly the same way, but, allow one of the particles to coast 10 more years in the lab frame, but stop the other one immediately after acceleration, would they both end up aging the same amount? If we cut out the coasting part of the diagram in the middle, would that make a difference?

2. Apr 19, 2016

### Orodruin

Staff Emeritus
The part of the diagram where the twins have constant velocity is of utmost importance to the differential ageing. The acceleration does not enter into it other than as a means of changing rest frame.

3. Apr 19, 2016

### idea2000

How come both frames see each other's time as slowing down during the coasting phase of the diagram? What do they see during the acceleration phase? During the coasting phase, are both frames symmetric? How can one frame age more than the other when they are both symmetric during the coasting phase?

4. Apr 19, 2016

### robphy

5. Apr 19, 2016

### idea2000

I'm very confused about one aspect. In that thread you mentioned, one of the posters says that the travelling twin's perspective is not symmetrical to the home twin. Can we say the two perspectives are asymmetric even during the coasting phase? Or does this hold only during the acceleration phase? I have seen a "doppler" effect explanation where the change in ages between the two frames happens during the acceleration phase only. The travelling twin, in this explanation, sees the earth twin's heart rate speed up during the acceleration phase, but, during the coasting phase, their heart rates are the same. Both twins see the other twin's heart rate as slower than usual. Do the frames need to be symmetric during the coasting phase in order to satisfy any kind of assumption or postulate of sr? For example, that all frames are the same and there is no preferred frame of reference?

6. Apr 19, 2016

### Staff: Mentor

So you are focusing on the Doppler effect explanation. The way to do this would be to calculate the Doppler shift for each part of the altered trip.

Personally, I think it is more difficult than the spacetime interval explanation.

7. Apr 19, 2016

### PeroK

Thinking about the twin paradox is probably the hardest way to learn SR. Better to do things the other way round!

I'm not sure there any magic words that can help you or anyone really understand. Everything makes sense once you understand SR. But not the other way round. Even if you manage to grasp the essence of the paradox, you still won't understand SR. You'll probably just think you do. And then another paradox will cause the whole house of cards to come tumbling down.

8. Apr 19, 2016

### idea2000

Why are there so many explanations for the same thing? =)

I'm really just wondering if the perspectives have to be symmetric during the coasting phase. Does this need to be satisfied so that there is no preferred frame of reference?

I have learned sr to the degree where I am comfortable with the concept of proper time and how every frame measures the same spacetime interval, they just measure different time and space intervals. My greatest source of confusion came when I started reading these pop sci books and how this twin sees this and that twin sees that. Does all this really follow from the math? Can you really see the other twin's heartbeat getting faster? Or is all this stuff just an attempt to explain the math? And are all these attempts consistent with each other?

9. Apr 19, 2016

### PeroK

If you understand SR, why do you care?

But, if you understand SR, the twin paradox isn't a paradox at all. It's just a rather simple problem.

10. Apr 19, 2016

### idea2000

I didn't say that I understood sr, I just said that I've learned sr to the point where I am comfortable with the concept of proper time, which is still far from understanding sr. The reason that I care is because when famous people write books, I'm not sure what to believe. They obviously understand more than I do, so I give them the benefit of the doubt.

Are all these explanations valid? Or should we just trust what the math tells us?

11. Apr 19, 2016

### Orodruin

Staff Emeritus
This is a very common confusion with beginners in relativity - to confuse what you actually see with what is going on in a given inertial frame (i.e., accounting for the finite speed of light). What you would actually see (as an observer) would be very related to the Doppler analysis. This is not what we talk about when we talk about time dilation. Time dilation is based upon observations relative to a large number of synchronised watches at relative rest in an inertial frame.

I do suggest you go to the original insight article and look at the geometrical interpretation. As you may not be surprised about, I like it a lot ...

12. Apr 19, 2016

### jartsa

Seeing objects is not complicated at all:

1: When you see an object, you always see that the object has some velocity.
2: When you see that an object has some velocity, you always see that the light from the object has some Doppler shift.
3: When you see that an object has some Doppler shift, you always see that the object has a changed heart beat or a changed tick rate, i.e. changed time.

And here's an asymmetry:
When you start moving, you see that the universe around you changes its state of motion immediately.
When you start moving, all the universe does not immediately see that you have started moving.

Last edited: Apr 19, 2016
13. Apr 19, 2016

### pervect

Staff Emeritus
You might also look at https://www.physicsforums.com/threa...on-implies-relativity-of-simultaneity.805210/

The ultra-short answer is that the relativity of simultaneity is a logical necessity to understand symmetrical time dilation (by which I mean that according to A, B's clock is slow, and that according to B, A's clock is slow).

I attempt to explain what "The Relativity of Simultaneity" means in the above thread. If the concept were familiar, mentioning the name alone would be sufficient. Frequently, though, the name isn't familiar and the concept needs to be explained - which is what I attempt to do. In addition to giving my own explanation, I try to give some references to some published sources that talk about the issues.

The other threads mentioned by other posters may also be helpful. Different approaches may "click" with different readers. Knowing the name "Relativity of Simultneity" is also helpful as it will aid in searches for more information about the topic.

14. Apr 19, 2016

### Staff: Mentor

Well, I am not sure that they are symmetric during the coasting phase since "the coasting phase" itself is longer for one than for the other. You would have to define things carefully to make it symmetric. I think that you could do it, but it isn't trivial.

Yes, all of this is just various attempts to translate the math into natural language. They are all consistent with each other exactly insofar as they are consistent with the math.

15. Apr 20, 2016

### Stephanus

First of all (and as I had already had too many from PF) this has nothing to do with acceleration. Altough acceleration plays a role, but very little. It's about changing frame of reference.

Suppose you (A) have a friend (B) who keeps sending you a signal/sec.

So, you're receiving B signal, 1 signal / sec. Now B travels 0.6c.
Now after 1 sec, B arrive at C.

When will this signal reach you?
So, in 1 sec B will be as far as 0.6ls from you. So this signal will arrive at you at 1.6 sec.
So, from the original 1 sec for a signal, you'll have 1.6 sec for a signal.
No, wait. This is not SR.
B "experiences" time dilation wrt A (what ever "experiences time dilation means")
wrt means With Respect To
And I see that you have understood SR
So you must know that 1 sec for B isn't 1 sec for A
So 1 sec for B is 1.25 sec for A, you can check the explanation in Lorentz Factor in Wiki.
So in 1 sec wrt B, B will send it's signal. But where is B actually? B of course would be at 0.75 ls away from A wrt A. How would A know that B is 0.75ls away from A? A can then check to his friend C whom A knows exactly at 0.75 ls away from A.
A can then ask C "Do you meet B? What is your clock (C) reading when you see B? Can you see B's clock reading? What?
C will answer. I meet B when my watch shows 1.25 sec.
I see B clock 1 sec.
Now when will this signal reach A? This signal will reach A at 0.75 (AB distance wrt A) + 1.25 (A's clock) = 2 second.
So when B travels away from A, A will see that B clocks ticking half it's rate. And B will see A's clock is as slow as half B's clock as well
This you can check for yourself in relativistic Doppler Effect $k = \sqrt{\frac{1+v}{1-v}}$
And this goes also if B is APPROACHING A, the effect is reversed. A will see B's clock ticking twice faster then A's. And vice versa, B will see A's clock ticking twice faster as well.

====================================================================================
Okay, so much for Doppler.
Now we have k = 2.
So, suppose.
A and B meet.
Then B travels away from A at 0.6c to C 300 ls away.
When B reaches C, how many signals from B that A receives and vice versa?
Traveling 0.6c for 300 ls away takes 500 secs.

So A will receive 250 signals from B. A has sends 500 times, but A only receives 250 times from B. It's ok. It's the effect of Dopples (plus relativity, otherwise, A will only has 125 signals)
So does B, B will receive 250 signals from A.
This is SYMMETRICAL

Now B travels B to A.
When B reaches A, h
ow many signals from A that B receives and vice versa?
Because two partys are approaching each other, B will receive 1000 signals.
And A will receives 1000 signals

-------------------------------
No, that's not the case!
A will not know that B is traveling to A until 300 secs later!
Because it's B who does the traveling!
Imagine that right now you travel to the Sun, you'll imediately see the Sun gets bigger, right. But if the sun is doing the traveling, you won't know the sun gets bigger until 8 minutes later.
--------------------- this is 'asymmetry of twins paradox ------------------

A still receives 150 signal from B for 300 secs, and then A will receive signals from B every 0.5 sec.
How many signal that A have from B after that?
So.. B will be at 120ls away from A. It takes another 200 secs for B to reach A. A will only have 400 signals from B.
------------------------------------------
Okay, I'll summarize for you.
From B point of view.
B1. From A to C, B receives 250 signals.
B2. From C to A, B receives 1000 signals.

From A point of View
A1. From A to C, A receives 250 signals.
A2. From C to A (the first 300 sec), A receives 150 signal.
A3. From C to A, the rest 200 sec, A receives 400 signals.

Ok, so let's analyze it deeper.
From B point of view.
B1. For 500 second, B see that A ages 250 seconds.
B2. For 500 second, B see that A ages 1000 seconds.

From A point of view
A1. For 500 seconds, A see that B ages 250 second
A2. For 300 seconds, A see that B ages 150 second
A3. For 200 seconds, A see that B ages 400 second.

The symmetry is B1 and A1
B2 and A3 in also symmetry.
But the trick is in A2.
Hope you can understand it as I did 1 year ago

16. Apr 20, 2016

### Battlemage!

My understanding of it is this:

If you are racing someone from a starting line to a finish line, and you spend one second of your journey turning slightly so you are not going at a perpendicular path, and then spend three hours traveling along this path, you'll have traveled a lot more distance to get to the finish line.

Did all the additional time on your trip occur during the short span you were turning? Nope. The change in direction was crucial but the extra distance and time spent on the journey were during your angled straight line path.

Space time diagrams for twin paradoxes look like that too. What is important isn't the acceleration so much as the fact that you changed reference frames.

Also there is a symmetry between the twins but it is kind of an inverse symmetry.

An example that illustrates why the acceleration is not when the aging difference occurs and why there is still a symmetry between the two twins from the perspective of what the twins actually SEE rather than in terms of various clocks at rest in between them. Feel free to critique everyone!

Think of it like this: if you calculate the time it will take the moving twin to get to the destination, you know his total trip will be twice that for him. Meanwhile, when he gets there according to his own frame, the person at home will still see him traveling there, since it takes time for the light signal to reach her. She will see his trip take longer, and by the time he gets there to her he is already on his way back in his own frame. That means to her his clock is going to have to run fast when she finally sees him coming back, but by then he would have already been on his return trip for quite a while, and all the while HE will be seeing HER clock moving fast for more ticks (because again, she won't see him coming back until he has already been on his return trip for quite some time). Likewise, on his way back he will see her clock as it was in "the past" as well.

The symmetry is that the amount of time each sees the other's clock moving fast or slow is proportional to each other.

Some details:

If t is the proper time for the trip, the traveler sees .5t has passed when he gets there. Let's say an Earth observer will see it take 1.25t for the total trip. But since light takes time to reach Earth, she will see that more than half the time for the trip to take from her perspective will have passed when she sees him reach the destination. Let's say for this example that it takes a total of time of t for her to see him reach the destination, which means she sees his clock moving twice as SLOW as her clock (it takes him .5t on his clock and t on her clock). Then on the way back she will have to see his clock move .5t in only .25t of her time (since in his frame the trip up takes as long as the trip back- on her clock t of the total 1.25t is already spent, which means HIS .5t must occur in only .25t of her time). That means now she has to see his clock move twice as FAST as hers for the amount of ticks that .5t gives on his clock.

But symmetrically, when he reaches the destination at .5t on his own clock, due to the signal taking time to reach him, he will see that only .25t has transpired on the earth clock, which means he sees HER clock as moving slowly. His return trip will take .5t on his own clock, but since the total trip from an Earth observer must take 1.25t, on his way back a total of t time must pass on Earth in only .5t of his own time, which means on the way back he will ALSO see her clock moving twice as fast as his. The key difference is that she will see his clock move twice as fast as hers for only .2t, while he will see her clock move twice as fast as his own for .5t, which means he sees her go through more ticks with faster time (hence she ages more). (Or alternatively, you'll notice that Earth sees the traveler's clock run slow for t amount of time, while the traveler only sees Earth's clock run slowly for .5t)

In this way it is symmetrical, but you'll notice the numbers are different. Earth's clock will be moving at a fast rate for more "ticks" than the spaceship's clock will. And not only that, IT IS NOT DURING THE ACCELERATION that this occurs. As far as I can tell this is exactly why the space ship twin will have aged less. It certainly will match the specific number of years difference between them every time.

17. Apr 20, 2016

### idea2000

Thanks for all your replies, I appreciate them a lot. =)

I've found a video that seems to illustrate the concepts that people have been posting in this thread.

I'm still confused about what he says at about 8:10 in the video, though. He seems to put the aging for the coasting periods together to show that there is no age difference during the periods where there is no acceleration. Is this correct?

Thanks for any replies in advance!

18. Apr 20, 2016

### Battlemage!

The only place where there is an acceleration is the POINT midway through the trip (the point labeled 4), but your video shows that the aging difference occurs along an INTERVAL (all the red dots).

Point 4 is the only place he accelerates, yet the aging difference occurs in Earth's frame from point 4.5 to point 7.5, and in the spaceship's frame from point 4.5 to 5.5.

The acceleration causes the traveler to change reference frames, and the different reference frame directly causes the time discrepancy.

As an analogy, the acceleration is like when you're driving and you take a turn to a road that causes you to take a longer trip. You're only turning for a few seconds. It's the PATH you take that makes the trip longer- the DIRECTION. With the twin paradox the acceleration changes your reference frame, and it's moving in the new reference frame that directly causes the age difference, as can be seen in your video by looking at the intervals with the red dots.

Last edited: Apr 20, 2016
19. Apr 21, 2016

### idea2000

Okay, I have a better understanding of what you are trying to say now. The mistake we make when analyzing these scenarios is by assuming that the twins are seeing each other at the same age. What pervect, and stephanus, and you were trying to show me, was that they are NOT seeing each other at the same age. So, when earth twin sends a signal from 1, on his axis, we think that he must be sending that signal to space twin's 1, when, he's not. He's sending the signal to space twin's 2. And when space twin is sending a signal from 2 to earth twin, we think he's sending the signal to earth twin's 2, or, at least, back to 1, but, he's not. He's sending the signal to earth twin's 4.

The difference in aging arises when he changes direction, but, not only at the acceleration point, but, also beyond that point as well. So, if he decided not to slow down and turn around, and he had just kept going along the same worldline, he would have sent a signal from his 3 to earth twin's 6. And earth twn would have sent a signal to his 12 (not shown on the diagram). But, because he turned around, earth twin sent to his 6, instead. You could also create a scenario where the space twin would slow down to be in the same frame of reference as earth twin, and just keep moving along. When you look at his worldline in this case, he would just be horizontal to earth twin. And you could just keep plotting the lines like you were doing before.

Seems like you could resolve almost any basic paradox in sr this way. Since, I'm guessing that these paradoxes usually revolve around what happens first and what happens next.

Special thanks to Battlemage, and Pervect, and stephanus for all the help they gave me! And for spending so much time creating their explanations! =)

I really appreciate everything. =)