[hamdani yusuf (OP)]

Whose second?

In my early scenario, everything is measured by the midway observer, because it's where the symmetry is guaranteed.

[hamdani yusuf (OP)]

If you want to use a 4 ly distance and a velocity of 0.999c, then  the AC clock reads 3.996 yrs when ES leaves Earth according to ES,

Your statement seems to imply that earth travelling twin can see events on Alpha Centauri in the future which midway observer hasn't been able to observe yet. Cmiiw.

[Janus]

If you want to use a 4 ly distance and a velocity of 0.999c, then  the AC clock reads 3.996 yrs when ES leaves Earth according to ES,

Your statement seems to imply that earth travelling twin can see events on Alpha Centauri in the future which midway observer hasn't been able to observe yet. Cmiiw.

Pay attention.   I already pointed out that what he would SEE would be the same thing as what someone on Earth would see at that moment: Events that occurred at AC 4.3 years ( by the AC time measure) prior to the AC ship leaving.

The Earth observer sees this and uses it to work that the AC ship is also leaving at that moment in the Earth-AC rest.  Hwe can do this either by being aware of the setup with the signal originating at the midpoint, or waiting 4.3 years until he sees the AC ship leave, and working backwards.
The Earth ship, moving at 0.8c relative to both the Earth and AC, and seeing that same light has to come to a different conclusion:  That in order to be seeing this light from AC at this moment, the clock at AC has to already be reading 3.44 yr past when the AC ship left at that same moment.

Grasping the relativity of simultaneity is key to understanding SR. It really is the first thing you need to come to grips with before proceeding to anything else.

[hamdani yusuf (OP)]

If you want to use a 4 ly distance and a velocity of 0.999c, then  the AC clock reads 3.996 yrs when ES leaves Earth according to ES,

Your statement seems to imply that earth travelling twin can see events on Alpha Centauri in the future which midway observer hasn't been able to observe yet. Cmiiw.

Pay attention.   I already pointed out that what he would SEE would be the same thing as what someone on Earth would see at that moment: Events that occurred at AC 4.3 years ( by the AC time measure) prior to the AC ship leaving.

The Earth observer sees this and uses it to work that the AC ship is also leaving at that moment in the Earth-AC rest.  Hwe can do this either by being aware of the setup with the signal originating at the midpoint, or waiting 4.3 years until he sees the AC ship leave, and working backwards.
The Earth ship, moving at 0.8c relative to both the Earth and AC, and seeing that same light has to come to a different conclusion:  That in order to be seeing this light from AC at this moment, the clock at AC has to already be reading 3.44 yr past when the AC ship left at that same moment.

Grasping the relativity of simultaneity is key to understanding SR. It really is the first thing you need to come to grips with before proceeding to anything else.

Perhaps you can avoid confusion by using more consistent and succinct words.
You can rewrite this statement,

the AC clock reads 3.996 yrs when ES leaves Earth according to ES,

to

the AC clock reads 3.996 yrs when ES leaves Earth as calculated by ES,

to distinguish the interpretation that it were what's actually read/seen by ES.

[hamdani yusuf (OP)]

Just in case you've missed to read this question.

What's the reading of the travelling clock by midway observer, one second before passing the mid point, and one second after passing it?

Whose second?

In my early scenario, everything is measured by the midway observer, because it's where the symmetry is guaranteed.

To be clear, I'm not trying to propose a new theory here. Just like the OP's question, I want to know what are actually described by currently most accepted/mainstream theory, and what their implications and consequences are.

[Janus]

If you want to use a 4 ly distance and a velocity of 0.999c, then  the AC clock reads 3.996 yrs when ES leaves Earth according to ES,

Your statement seems to imply that earth travelling twin can see events on Alpha Centauri in the future which midway observer hasn't been able to observe yet. Cmiiw.

Pay attention.   I already pointed out that what he would SEE would be the same thing as what someone on Earth would see at that moment: Events that occurred at AC 4.3 years ( by the AC time measure) prior to the AC ship leaving.

The Earth observer sees this and uses it to work that the AC ship is also leaving at that moment in the Earth-AC rest.  Hwe can do this either by being aware of the setup with the signal originating at the midpoint, or waiting 4.3 years until he sees the AC ship leave, and working backwards.
The Earth ship, moving at 0.8c relative to both the Earth and AC, and seeing that same light has to come to a different conclusion:  That in order to be seeing this light from AC at this moment, the clock at AC has to already be reading 3.44 yr past when the AC ship left at that same moment.

Grasping the relativity of simultaneity is key to understanding SR. It really is the first thing you need to come to grips with before proceeding to anything else.

Perhaps you can avoid confusion by using more consistent and succinct words.
You can rewrite this statement,

the AC clock reads 3.996 yrs when ES leaves Earth according to ES,

to

the AC clock reads 3.996 yrs when ES leaves Earth as calculated by ES,

to distinguish the interpretation that it were what's actually read/seen by ES.

Since by this point of the thread I had already mentioned at least twice that ES would, at that moment, see the same thing as Earth would, I don't think that my wording here is really at issue, as its meaning is quite clear when taken in context with what had been said earlier.

[Origin]

I don't think that my wording here is really at issue, as its meaning is quite clear when taken in context with what had been said earlier.

For some reason Hamdani likes to go over the same ground again and again, he's done that in many of his marathon threads.

[hamdani yusuf (OP)]

Since by this point of the thread I had already mentioned at least twice that ES would, at that moment, see the same thing as Earth would, I don't think that my wording here is really at issue, as its meaning is quite clear when taken in context with what had been said earlier.

They become different 1 second later. That's why the distinction becomes important.

[hamdani yusuf (OP)]

I don't think that my wording here is really at issue, as its meaning is quite clear when taken in context with what had been said earlier.

For some reason Hamdani likes to go over the same ground again and again, he's done that in many of his marathon threads.

Maybe you can help him answer my question.

Just in case you've missed to read this question.

What's the reading of the travelling clock by midway observer, one second before passing the mid point, and one second after passing it?

Whose second?

In my early scenario, everything is measured by the midway observer, because it's where the symmetry is guaranteed.

[hamdani yusuf (OP)]

Maybe you can help him answer my question.

https://www.doubtnut.com/question-answer-physics/a-stationary-observer-receives-a-sound-from-a-sound-of-freqeuency-v0-moving-with-a-constant-velocity-11393557
The formula shown there suggests that right at mid point, cos θ = 0, and the observer gets original frequency.
I think this can be a clue.

[hamdani yusuf (OP)]

I don't think that my wording here is really at issue, as its meaning is quite clear when taken in context with what had been said earlier.

For some reason Hamdani likes to go over the same ground again and again, he's done that in many of his marathon threads.

Maybe you can help him answer my question.

Just in case you've missed to read this question.

What's the reading of the travelling clock by midway observer, one second before passing the mid point, and one second after passing it?

Whose second?

In my early scenario, everything is measured by the midway observer, because it's where the symmetry is guaranteed.

If a formula has really been accepted to be the solution, then it should not be a problem to input different values of the variables in it, and get an answer. I'm curious why it isn't the case.

[Origin]

Let's start with the simplest frame of reference first, which is the midway observer. What will he observe when he meet both travelling twins? At that moment, what's shown by his own clock, and the clocks brought by the travelling twins?

Assuming the mid way point is exactly 2 ly and the twins acceleration was instantaneous:
Twins speed 0.999c.  From the frame of the observer at the mid point the elapsed time on the clocks would be:
1.  Mid point clock - 2.002 years
2.  Earth twins clock - 0.0894 yrs
3.  Alpha Centauri twin - 0.0894 yrs

[hamdani yusuf (OP)]

Let's start with the simplest frame of reference first, which is the midway observer. What will he observe when he meet both travelling twins? At that moment, what's shown by his own clock, and the clocks brought by the travelling twins?

Assuming the mid way point is exactly 2 ly and the twins acceleration was instantaneous:
Twins speed 0.999c.  From the frame of the observer at the mid point the elapsed time on the clocks would be:
1.  Mid point clock - 2.002 years
2.  Earth twins clock - 0.0894 yrs
3.  Alpha Centauri twin - 0.0894 yrs

Thanks for giving quantitative answers.
How did you get those numbers?
Did you involve Doppler effect?
Do you think these represent the mainstream view of science community?

[Origin]

Thanks for giving quantitative answers.
How did you get those numbers?

Sorry, I didn't see your reply.
For the mid point observer's clock:  2 ly/.999 c
For the space ships:  t' = sqrt{1 - ({v^2}/{c^2})

Did you involve Doppler effect?

No, it is not involved in this case.

Do you think these represent the mainstream view of science community?

Yes, I think I did the math correctly.

[hamdani yusuf (OP)]

It makes me curious where did Janus get his Doppler effect and accumulation of time difference from.

[Origin]

It makes me curious where did Janus get his Doppler effect and accumulation of time difference from.

Janus definitely knows what he is talking about, however I don't know which of the many different questions he was answering.  I believe that I correctly answered your specific question.

[hamdani yusuf (OP)]

It makes me curious where did Janus get his Doppler effect and accumulation of time difference from.

Janus definitely knows what he is talking about, however I don't know which of the many different questions he was answering.  I believe that I correctly answered your specific question.

Let him explain himself when he has the time to spare.
Meanwhile, what will be seen by the travelling twins during that meeting point? Will they see the clocks to have the same values as observed by midway observer?

[hamdani yusuf (OP)]

The Twin Paradox: What is it Really All About

Since the discovery of the special theory of relativity in 1905 due to weird phenomena like time dilatation and length contraction, people started to find many possible paradoxes within the theory.
The most famous of them all is the Twin paradox which is still discussed today. In this video, we take a look at what is really weird and paradoxical about this scenario and why this happens, and whether it can be solved purely within the special relativity framework or we need something more (like general relativity).

In summary, it says that the difference is due to equivalence principle.

[Origin]

In summary, it says that the difference is due to equivalence principle.

I guess you will never be able to understand the twin 'paradox' with all the different explanations on Youtube.

[Halc]

The Twin Paradox: What is it Really All About

What it is about has already been well explained. Most you-tube videos on the subject contain mistakes. The one you provide is blatantly wrong in several areas.

In summary, it says that the difference is due to equivalence principle.

Which is blatantly wrong since the EP is about the local equivalence of acceleration and gravity, and the twins thing has nothing whatsoever to do with gravity, and it isn't local.

A minor mistake is made at about 5:10 where he says that both observers see the clock of the other running slow at all time. This is false. A directly receding clock is seen to run slow, and an approaching one is seen to run fast. This is one of the ways to explain the paradox. What he seems to mean here is that the other clock is computed to run slow. It takes a computation to account for the light travel time. One does not see the other clock run at half speed in either direction.

The bigger mistake comes when GR is invoked.at 9:10 and he says that there's no measurable difference between an accelerating rocket and a uniform gravitational field, and that there are no tidal forces for either. All this is very wrong. There are tidal forces in a continuously accelerating rocket, and the acceleration field is not uniform. There is no such thing as a uniform gravitational field under GR. Such a field would have a valid tensor, and there is no valid tensor with the properties described. Newtonian physics allows it (with an infinite 2D sheet of mass say), but GR does not.