No. 8y is not equal to 9y 2m. Why would you suggest otherwise?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?
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.I didn't touch on a paradoxical part because there isn't one.
Perhaps the misunderstanding can be avoided if we use the term "switch of inertial frame" instead of "change of inertial frame"
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.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.
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 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.
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.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.
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.
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