Jorrie, fascinating stuff!

I have a doubt however: after your Fig. 2 you said "... and the reunion happens 12.5 years later on the calendars of the chosen reference frame" as is also shown on the figure.

Are we supposed to believe that an observer sitting stationary in your "chosen" reference frame would have aged 12.5 years, compared to the 10 and 8 years of your twins?

Guest wrote: "Are we supposed to believe that an observer sitting stationary in your "chosen" reference frame would have aged 12.5 years, compared to the 10 and 8 years of your twins?"

No, we are absolutely not supposed to believe that! No observer in the chosen reference frame (fig. 2) can be present at both Pam's departure event and the reunion event, so we cannot say how any observer stationary in the reference frame would have aged during Pam's journey.

Say we had two stationary observers with clocks synchronized by Einstein's method, Jack at the origin and Jill at 7.5 l.y. away. Jack is present at the start of Pam's journey and Jill is present at the reunion.

If Jack and Jill exchange messages afterwards (waiting 7.5 years for the signals to cover the distance) and compare the date and time of departure and reunion, they will calculate a time interval of 12.5 years.

However, Jim, who made the 0.6c journey between the two events will not agree with Jack and Jill's calculation, because his clock and calendar tells him that the journey took 10 years. Since Jim was present at both events without being accelerated, we better believe him!

Hope it clears the uncertainty!

Jorrie

Math is easy in special relativity, but I have difficulties to understand the philosophy...

I have never been able to understand why Pam must be the one who changes frames instead of Jim?

I mean that above given discontinuing worldline has merely transferred information from previous article's diagram which was drawn from Jim's point of view. It demonstrates effect of different inertial frames, but differency is already decided to be Pam's, from Jim's point of view. So I can't take it as a root-cause explanation.

What exactly is the reason why I can't initially start drawing from Pam's point of view? Assuming that (as far as Pam can see and detect) it is Jim who moves fast away, turns around, and returns (even thought third party observer, like absolute universe, would disagree with this interpretation).

Pam feels the g's, while Jim does not, so their situations are different. That acceleration of Pam's causes her to follow a different (shorter) path through spacetime. The 'lazy path' is the longer path.

-J

Okay...

I have realized difference in acceleration, but always seen it (as source of effects) to be more in scope of generic theory than special theory...

So, when I have been told that special theory of relativity alone can be used to solve twin problem, I have felt that some information is missing

I can't edit, had to write another reply...

So my mistake is that I take special theory alone and try to be completely ignorant things that are not in scope of it, or things that require special treatment because of not being in scope, and still trying to solve problem by seeing movement and velocity alone.

Question is, is my reasoning correct or incorrect that if only thing I know is special theory of relativity, Twin Paradox can't be fully explained? Does initial understanding of changes in g-forces as basis of selecting inertial frames be a valid concept inside special theory (or was it one of the reasons why work continued immediately towards general theory )

(Hmm... Sounds like things that I could find out from your website as well, but you know what people are - lazy and unconcerned)

Accelerated movement is today considered to be covered by the special theory, although it was not like that immediately after Einstein published the special theory. It is actually a sort off link between the special and the general theory, which in any case fully encompasses the special theory. The full general theory is only required where gravity plays a role.

Accelerated movement can be treated as an 'infinite' progression of momentary inertial frames, between which the transformations of the special theory (Lorentz transformations) can be used. IMO, people who insists that acceleration is not needed for explaining the twin paradox are missing some crucial point: changing from one inertial frame to another cannot happen without acceleration being present.

-J

Thank you very much. Now it is all clear.

Keyword was a difference between Einstein's original papers and later additions. I was most likely thinking contents of the Einstein's first papers about the theory of relativity (can't remember much of their specific contents, thought), while modern articles about Twin Paradox include modern definitions when they talk about solution using special theory.

It was a little bit humiliating to have problems understanding this little thing, while not having problems understanding some much more complex feeling issues. Ummm... Same kind of problems... I, of course, do have a lot of problems with understanding, but usually I get over them eventually