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How much difference is caused by the changing reference frames?
Is it quantifiable?
Is there any other causes?
If there are more than one changes of reference frames, what difference do those extra changes cause?
Quote from: hamdani yusuf on 26/09/2023 22:22:03How much difference is caused by the changing reference frames?Reread reply #1Quote from: hamdani yusuf on 26/09/2023 22:22:03Is it quantifiable?Yes, reread reply #1.Quote from: hamdani yusuf on 26/09/2023 22:22:03Is there any other causes?No.Quote from: hamdani yusuf on 26/09/2023 22:22:03If 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.
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.
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.
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.
Quote from: Halc on 23/09/2023 14:44:05This 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?
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.
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.
The confusion comes from asymmetrical results produced by symmetrical situations.
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.
t's the cause of this supposed asymmetry which created disagreement among physicists.
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"
Lorentz factor is usually represented by gamma symbol γ instead of lambda λ.
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.
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.
Quote from: hamdani yusuf on 25/09/2023 15:03:10Let'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.
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.
Twin A knows that he is accelerating away from earth and it is not earth accelerating away from him.
The problem with your threads in general is you ask a question and receive an answer that you don't fully understand.
How does he know?
acceleration is absolute.
I received several different answers
No. 8y is not equal to 9y 2m. Why would you suggest otherwise?
the conclusion is abstract (mental, not physical)
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.
Quote from: Origin on 28/09/2023 15:21:22acceleration is absolute. Where did you get that from?
The answer is easy. If 'the frame of B' is used, 8 years are logged by twin A, and 9y2m by twin B.
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.
What does it mean, unambiguously?