B Does your age only change when accelerating?

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.

 

You may be interested in recent subthread of another thread...
https://www.physicsforums.com/threa...he-twin-paradox-comments.842793/#post-5446549

 

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.

 

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.

 

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 ...

 

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.

 

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.

 

Perhaps I can help you from a layman point of view.
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.

But, let's forget about Twins Paradox. Why don't we talk about Doppler.
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, how 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

 

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.

 

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.