[hamdani yusuf]

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]

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.

[yor_on]

It's about being in different frames of reference to me. Think of the muon example in physics for it. And if you want to define it to something as simple as an acceleration then?

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

you can also take a look at this one.   https://physics.stackexchange.com/questions/165179/does-light-itself-experience-time-dilation

[yor_on]

The only thing we don't define as 'accelerating' are mass less particles as light. They create a recoil though as they 'leave' which we then define to conservation laws. Everything else being of 'proper mass' or whatever one might want to call it, will have an acceleration as far as I know. We also define a carousel as 'accelerating' although it has a constant uniform speed, but we don't define infalling light, f.ex towards earth, the same way. Instead we refer to that as blue and red shifts, which will be observer defined.
=

Gravity is an example of an equivalence to mass or if you like, 'acceleration', in relativity, So is gravity time dilated? And photons, or light, is defined as a speed, a 'constant' speed. so when that 'photon' follows its geodesic, gravity 'bending the path' as defined by us?

Another example: Think of that twin traveling, as defined by you and your common 'origin'. His time, and everything being in a same reference, 'slows down' relative your own clock. Aka becoming younger than you once back. So what happens to that rockets 'velocity', as defined by you?

So no, it's not only about accelerations, although they definitely play a big role. But it also depends on your definitions. For example, if one agree on that accelerations, gravity and mass are equivalences, describing the same thing from although from different angles? Blue & red shifts being massless equivalences to different 'speeds' (including accelerations) described in a 'proper mass reference frame'?

that whole thing becomes a question
=

The funny thing, accepting the above, is that you might be able to reach a conclusion much like Newton did about 'time'. An locally 'absolute time' of no variance intrinsically, with other permutations of it described through 'frames of reference', 'masking' that invariance.

[hamdani yusuf]

It's about being in different frames of reference to me.

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?
Before these questions are answered, it's useless to switch to other frames of reference and pursue more complex questions.

[yor_on]

Observers always have a unique frame of reference. Where the twin experiment uses it by letting them leave and come back to an ''ideal' common frame of reference. We all become unique 'observers' if one f.ex use NIST gravitational time dilation experiments to define what frames of reference means.

[yor_on]

All of it comes from the same thing. Lights speed in a vacuum which is what special relativity build on. Where gravity comes into it first in General relativity, 'warping' space, giving different 'lightpaths' / geodesics. Frames of reference becomes a very complex definition to me :)
=

The only thing that twin experiment brings with it is the idea of time being malleable. But to do it right you will need to create a 'global' frame of reference for it. An unyielding time and space with the eye of a God watching it / ours. Somewhat like Newton. And Einstein himself defined it as no such frame can exist. So it's still 'observer dependent' that twin experiment

That's actually one of the trickiest parts of relativity. That no frame of reference can be a more 'privileged frame' than any other, no matter what I may think of the universe I observe. Which actually, turned around, and in a very backhanded fashion means that all frames of reference 'intrinsically' or 'locally' could be seen as equivalent

[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]

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]

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]

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?