[Origin]

How much difference is caused by the changing reference frames?

Reread reply #1

Is it quantifiable?

Yes, reread reply #1.

Is there any other causes?

No.

If there are more than one changes of reference frames, what difference do those extra changes cause?

It seems you do not know what a inertial frame is.  If something is moving at a velocity that is different than you, then it is in a different inertial frame.
In your example the twins left earth, this was the first change of inertial frame.  The twins move at a constant velocity and then stop and meet up at Alpha Centauri, that is the second inertial frame change.

[hamdani yusuf (OP)]

How much difference is caused by the changing reference frames?

Reread reply #1

Is it quantifiable?

Yes, reread reply #1.

Is there any other causes?

No.

If there are more than one changes of reference frames, what difference do those extra changes cause?

It seems you do not know what a inertial frame is.  If something is moving at a velocity that is different than you, then it is in a different inertial frame.
In your example the twins left earth, this was the first change of inertial frame.  The twins move at a constant velocity and then stop and meet up at Alpha Centauri, that is the second inertial frame change.

You misunderstood my questions and Halc's answers. Reply #1 only addressed half of the question, which is reasonably hasn't touched the paradoxical part.
Perhaps the misunderstanding can be avoided if we use the term "switch of inertial frame" instead of "change of inertial frame"

[Origin]

You misunderstood my questions and Halc's answers. Reply #1 only addressed half of the question, which is reasonably hasn't touched the paradoxical part.

Sorry, I must be misremembering the questions and answers, I will go back and check.

No, I did not misremember, it is very clear that in the OP you asked 2 questions and reply #1 answered those questions.

Question 1:  Classical physics calculation predicts that they'll arrive at Alpha Centauri simultaneously.  Does special theory of relativity predict the same?
Answer:  Classical in what sense?  Classical physics refers to non-quantum physics. I think you mean Newtonian physics, not classical.  Yes, every theory (including Newtonian) says they get there simultaneously. This is an objective fact, true in any reference frame.

Question 2:  How old are they when they meet up at Alpha Centauri?
Answer:  As computed above, 9y2m and 8y respectively.

I did in fact understand your 2 questions which were quite clear.  I also understand the answers Halc gave and I agree with those answers.

[hamdani yusuf (OP)]

Half way to what?  No, he simply rides Earth for 5 of his years.  λ=1.091 for 0.4c, remember?  So that's going to take 5λ years in the frame we're using, which is 5.455 years. 5.455 years at 0.4c takes him 2.182 ly away from where he started, which isn't particularly halfway to anything.

It's may not be a critical issue, but Lorentz factor is usually represented by gamma symbol γ instead of lambda λ.

[hamdani yusuf (OP)]

Sorry, I must be misremembering the questions and answers, I will go back and check.

No, I did not misremember, it is very clear that in the OP you asked 2 questions and reply #1 answered those questions.

Reply#1 answered time dilation experienced by twin A and B as observed/calculated by earth observer.
No paradox is found here, because it only described half of the story.

Reply#9 answered time dilation experienced by twin B as observed/calculated by twin A.
Here, twin A is treated as in a single inertial frame of reference.

Reply#15 is supposed to answer time dilation experienced by twin A as observed/calculated by twin B. But he refused to give numeric result, on the account that twin B switched his frame of reference.

[hamdani yusuf (OP)]

The video below tries to solve twin paradox using acceleration.

But this video below doesn't touch the paradox yet. It only describe time dilation observed by earth twin, without being bothered by travelling twin's perspective.

[Origin]

Reply#1 answered time dilation experienced by twin A and B as observed/calculated by earth observer.
No paradox is found here, because it only described half of the story.

The answer is also as observed/calculated by the twins.  You need to understand this part before moving on.

Let's describe the same case from twin A's perspective. He stays in his own reference frame, while Alpha Centauri moves closer at 0.4c.

This statement is incorrect.  Twin A does not stay in his own constant inertial frame.  He starts in earths frame, accelerates to the cruising frame then decelerates to Alpha Centauri's frame.  Twin A knows that he is accelerating away from earth and it is not earth accelerating away from him.  Twin A, twin B and the earth all agree that twin A is the one that accelerates.

The problem with your threads in general is you ask a question and receive an answer that you don't fully understand.  Instead of asking questions to clarify the original answer you ask questions that further complicate the issue which then leads to more complications until you are so confused that you deduce no one understands anything.  That ain't a good way to learn.

[Halc]

This is also incorrect since the conclusion is abstract (mental, not physical) unless they are in each other's presence, in which case it is called 'differential aging', which is the unequal comparison of clocks physically in each other's presence.

Do you mean that A's clock will be equal to B's clock at the destination point?

No. 8y is not equal to 9y 2m.  Why would you suggest otherwise?

So, you are not confused if the problem can be simplified to 0 or 1 inertial frame change, but you start to get confused with 2 or more inertial frame changes. Cmiiw.

As I said before, doing it via frame changes just adds complications, requiring multiple formulas, some of those being more complicated.

Using what I showed, no frame change is made ever. You pick just one and stick with it.

The confusion comes from asymmetrical results produced by symmetrical situations.

The situation was never symmentrical, and if it is (like the one in one of your recent threads), then the result is very much symmetrical. But adding more characters just adds more complications which is inadvisable if you cannot in any way understand even the simplest case.

How much difference is caused by the changing reference frames?

None actually, since a change of reference frame is a mental abstraction, not physical. A mental change doesn't in any way alter what actually happens.

The other half is asymmetrical results between the twins, which means that one of them will observe time contraction of the other twin, instead of time dilation.

There is no such thing as 'time contraction'. There is time dilation, but you speak of this time contraction as if it is something different.

t's the cause of this supposed asymmetry which created disagreement among physicists.

You're making up facts. There's no conflict when different physicists explain it in different ways since none of the explanations are wrong. But the way I showed seems the most simple, and requires but the one equation.

Halc's answers. Reply #1 only addressed half of the question, which is reasonably hasn't touched the paradoxical part.
Perhaps the misunderstanding can be avoided if we use the term "switch of inertial frame" instead of "change of inertial frame"

I didn't touch on a paradoxical part because there isn't one.
The misunderstanding can be best avoided if we avoid switching inertial frames altogether, as I suggested in post 1.It only leads to confusion if you don't understand how to do it right, and doing it right that way is considerably more complicated than sticking to one frame as I suggested.

Lorentz factor is usually represented by gamma symbol γ instead of lambda λ.

I stand corrected on that one

Reply#15 is supposed to answer time dilation experienced by twin A as observed/calculated by twin B. But he refused to give numeric result, on the account that twin B switched his frame of reference.

I instead encouraged you to work it out yourself. Even an attempt with mistakes would have been a learning experience, and we could have helped. But you declined since apparently learning anything isn't your goal. Hence my not bothering to reply much anymore.

The answer is easy. If 'the frame of B' is used, 8 years are logged by twin A, and 9y2m by twin B.

The video below tries to solve twin paradox using acceleration.
But this video below doesn't touch the paradox yet. It only describe time dilation observed by earth twin, without being bothered by travelling twin's perspective.

The first is a terrible video. It has many errors, such as asserting that they see each other age more slowly, which is only true when they watch each other recede. The twins scenario is not in any way about what anybody sees. Then they try to explain things via gravity which is utterly wrong. This is a special relativity scenario in which gravity is never taken into consideration.

The second video isn't much better. It say 'time slows down as you approach the speed of light'. That's just wrong. 'I move at nearly light speed relative to a muon created in the upper atmosphere. It doesn't make time slow down to me. He then attempts to reference an invalid frame of a light-like worldline, which is obfuscation at best, and wrong at worst. He never actually gets back to the twins after that.

There are good videos out there, but hunting down bad ones seems a favored pasttime to those that don't want to learn. Take the advice of other posters and find a good physics text if you actually want to learn this, which I suspect you don't. Stay away from you-tube, pop sites, and especially social media.

Let's describe the same case from twin A's perspective. He stays in his own reference frame, while Alpha Centauri moves closer at 0.4c.

This statement is incorrect.  Twin A does not stay in his own constant inertial frame.  He starts in earths frame, accelerates to the cruising frame then decelerates to Alpha Centauri's frame.

His statement is pretty much my words from post 9. The statement doesn't suggest that any planet undergoes any acceleration. I was talking about the frame in which A is stationary for the entire duration of the exercise. Everybody 'stays in' this frame since it is impossible to exit an inertial frame. To 'be in' a frame is simply to have valid and unique coordinates to your event in that frame. So acceleration doesn't necessarily cause a change of frame, since a frame is simply an abstract choice, and the simplest choice is to never switch frames. So the other players (planets, twin B) are still in this frame, they're just not stationary relative to it.

Relative to that frame, which we've called 'A's frame', Alpha Centauri moves closer to twin A at 0.4c. There's no suggestion that it needed to accelerate to do so since it was always moving at that speed relative to that frame, as was Earth. Yes, twin A needed to accelerate to a halt in that frame, but that fact is irrelevant since he spent zero duration at that alternate speed. Acceleration computations do not figure into the simplified method I suggested in at the top.

[Origin]

Relative to that frame, which we've called 'A's frame', Alpha Centauri moves closer to twin A at 0.4c. There's no suggestion that it needed to accelerate to do so since it was always moving at that speed relative to that frame, as was Earth. Yes, twin A needed to accelerate to a halt in that frame, but that fact is irrelevant since he spent zero duration at that alternate speed. Acceleration computations do not figure into the simplified method I suggested in at the top.

I agree. 
I am trying to help Hamdani understand this but it is very difficult because he asks question after question either ignoring or not understanding the answers.  I have no idea if he even understood the original answer in reply #1.

It almost seems that his goal is to sow confusion, I doubt that is the actual goal but that seems to be what happens in all his posts. 

[hamdani yusuf (OP)]

How does he know?

Twin A knows that he is accelerating away from earth and it is not earth accelerating away from him. 

[hamdani yusuf (OP)]

The problem with your threads in general is you ask a question and receive an answer that you don't fully understand. 

I received several different answers and tried to figure out which one is the most correct. Your problem is inability to distinguish them and think that they are the same. You can't come up with a solution if you can't even identify the problem in the first place.

[Origin]

How does he know?

I assume you are asking how does the twin know he is the one accelerating.  So again we are moving even farther away from the original question which I am not sure you ever understood the answer.
All inertial observers agree the twin is the one accelerating since acceleration is absolute.  Or to put it more simply the twin can feel himself accelerate or he can read an accelerometer telling him he is accelerating.

[hamdani yusuf (OP)]

acceleration is absolute. 

Where did you get that from?

[Origin]

I received several different answers

The answers seem consistent to me.  I think you may only be happy when your confused.

You cannot learn special relativity on a forum.  As I suggested earlier if you really want to understand SR, look up "SR Stanford" or "SR Yale" on Youtube, both are quite good overviews.

[hamdani yusuf (OP)]

No. 8y is not equal to 9y 2m.  Why would you suggest otherwise?

What does this mean?

the conclusion is abstract (mental, not physical)

[hamdani yusuf (OP)]

There is no such thing as 'time contraction'. There is time dilation, but you speak of this time contraction as if it is something different.

Twin A finds twin B as younger than himself, hence he says that B experience time dilation.
On the other hand, Twin B finds twin A as older than himself, hence he says that A experience time contraction.

[Origin]

acceleration is absolute. 

Where did you get that from?

Physics...
Here is a link from the University of California https://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html#:~:text=Velocities%20are%20relative%20but%20acceleration,space%2Dtime%20is%20always%20flat.
From the link:
Velocities are relative but acceleration is treated as absolute.  In general relativity all motion is relative.  To accommodate this change, general relativity has to use curved space-time.  In special relativity space-time is always flat.

If you want to discuss your original question I am willing to do that but I am done with you dragging this discussion "into the weeds".

[hamdani yusuf (OP)]

The answer is easy. If 'the frame of B' is used, 8 years are logged by twin A, and 9y2m by twin B.

What does it mean, unambiguously?

[hamdani yusuf (OP)]

You're making up facts. There's no conflict when different physicists explain it in different ways since none of the explanations are wrong. But the way I showed seems the most simple, and requires but the one equation.

Not just a different way, but different interpretation of the cause.
Lorentz' relativity interpretes time dilation is caused by relative motion against stationary aether. Thus no paradox is generated. Clocks stationary to the aether tick the fastest.

Einstein's 1905 Relativity dismissed aether, hence the paradox came up. Since there is no more universal reference, it's no longer clear which clock ticks faster.

Einstein's 1921 relativity reintroduced aether, with some modifications. It no longer carries some physical characteristics. It was then renamed to space-time continuum.

It seems like not many of us are aware of those distinction. But we can't just erase history of science.

[Origin]

What does it mean, unambiguously?

What about Halc's answer did you find ambiguous?