[hamdani yusuf (OP)]

How do you read a clock or a ruler without your eyes?

ask AI to read them out loud, or use direct brain interface.

[hamdani yusuf (OP)]

What if there is another twin travel to the opposite direction with the same speed? And another one in perpendicular direction?

Direction is irrelevant to time dilatation. What matters is relative velocity, i.e. the vector that describes their rate of separation.

What do you think about my calculation below?

In the example in the video, the gamma factor is 2, which means the speed is around 0.866c.
In case of another twin travels with the same speed but opposite direction, the relative speed between them will be around 0.9897c, according to relativistic velocity addition. The gamma factor is around 7.

In the video, one of the twins travels 20 years to the right and then 20 years back with speed 0.866c, according to earth reference. At the end of the journey, earth clock shows 40 years, while the travelling clock shows only 20 years.
I added a third twin, having similar journey with the first, but goes to the left from earth. Due to symmetry, his journey should end at the same time as the first twin, with his clock also shows 20 years.

But relative speed between the travelling twins produces gamma factor of 7. Thus during the constant velocity of 20 years in their own clock, they see the other travelling clock to increase by 20/7 years. Thus the remaining increase of the clock occurs during the frame jump, which amounts to 120/7, making the total of 140/7 years or 20 years.

[hamdani yusuf (OP)]

In chronological order,  here's what a travelling twin's timeline.

At the beginning, all clocks are 0.

During outbound journey, his own clock increases by 10 years. In his calculation, earth clock increases by 5 years. While the other travelling twin's clock increases by 10/7 years.

During short period of turn around, earth clock jump from 5 to 35 years. While the other travelling twin's clock jump from 10/7 to 130/7 years.

During return journey, his clock increases by 10 years. In his calculation, earth clock increases by 5 years. While the other travelling twin's clock increases by 10/7 years.

At the end of the journey, both travelling clocks show 20 years, while earth clock shows 40 years.

[hamdani yusuf (OP)]

During short period of turn around, earth clock jump from 5 to 35 years. While the other travelling twin's clock jump from 10/7 to 130/7 years.

Earth clock jumps by 30 years, while the other travelling clock jumps by 120/7 years.
How are those numbers calculated?
They should depend on the distance and change of velocity. When the distance is zero, there's no time jump, just like at the start of the journey.
The other travelling clock is further than the earth clock during the turn around. But somehow it undergoes less time jump. Where did I miss?

[alancalverd]

change of velocity.

Oh dear. That's called "acceleration", which some of our correspondents say is irrelevant.

[hamdani yusuf (OP)]

change of velocity.

Oh dear. That's called "acceleration", which some of our correspondents say is irrelevant.

Those who said it's irrelevant argued that the observer who changes his velocity can be replaced by two observers with different velocities, one is the same as initial velocity, while the other is the same as final velocity. They meet at turn around point. Don and Mahesh used this argumentation.

[hamdani yusuf (OP)]

What if there is another twin travel to the opposite direction with the same speed? And another one in perpendicular direction?

The formula for perpendicular velocity addition is:

https://en.wikipedia.org/wiki/Velocity-addition_formula
In our case, vx=vy=0.866c.
For convenience, I used spreadsheet to calculate.
putting the number to the left formula gives 0.247c
putting the number to the right formula gives 1.732c
Either result doesn't seem to be correct. It shouldn't be slower than the individual velocity. It shouldn't be higher than c either. Can someone show where the error is?

[alancalverd]

They meet at turn around point.

...and cannot synchronise their clocks because v_rel >0.

[hamdani yusuf (OP)]

They meet at turn around point.

...and cannot synchronise their clocks because v_rel >0.

Why not?
The clocks were already synchronized before the experiment begun. They were identically manufactured at the meeting point. And then moved to their respective starting points for the experiment symmetrically.

[hamdani yusuf (OP)]

During short period of turn around, earth clock jump from 5 to 35 years. While the other travelling twin's clock jump from 10/7 to 130/7 years.

Earth clock jumps by 30 years, while the other travelling clock jumps by 120/7 years.
How are those numbers calculated?
They should depend on the distance and change of velocity. When the distance is zero, there's no time jump, just like at the start of the journey.
The other travelling clock is further than the earth clock during the turn around. But somehow it undergoes less time jump. Where did I miss?

I want to make sure that this unexpected result is not caused by typo.
In the original case, inertial earth observer didn't see time jump of travelling clock during the turn around. But the travelling twin did see time jump of earth clock during the turn around. It shows that time jump is determined by velocity change of the observer only.

[alancalverd]

Why not?

Time dilatation.
If identical clocks are moving relative to one another, you can't tell the time shown at B simply by looking at clock A.

[hamdani yusuf (OP)]

Why not?

Time dilatation.
If identical clocks are moving relative to one another, you can't tell the time shown at B simply by looking at clock A.

Do you think that symmetry always break down? What determines the time difference?

[hamdani yusuf (OP)]

(Personally, I think the OP is diving off into Twins' Paradox etc, with ever increasing complexity, when they don't really grasp the significance of the basics of relativity. I think the explanations need to get simpler, not more complex.)

Perhaps you can point out which basics of relativity I've missed out in my calculations with symmetrical twin travellings?

[alancalverd]

Do you think that symmetry always break down?

It does, by theory and experiment. Nothing to do with what I think.

[varsigma]

I live in a country that has two languages. One could be called the Maori tongue, which they call Te Reo.

In Te Reo, the sound at the end of a word is where you 'locate' the word. Words imply action or movement and aren't static descriptive things as in English. The meaning is fluid, and this isn't surprising given their ancestors were ocean explorers.

So in my country, a university is a Wananga, or Waananga. You take this apart, so the last sound (phonemic syllable), is 'nga', which translates variously as 'here', 'this way', etc. another word 'tenei' translates as 'this is', so you also get 'here is'--fluidity of meaning.

The rest of wananga is I believe a contraction of 'waha', meaning voice, or 'from the mouth', etc. and the 'a' connecting the two makes 'nga' into 'anga' meaning 'facing' (a direction), 'open', or 'unadorned, naked'.

So the whole word 'wananga' translates as 'voices facing (each other) here', i.e. a public forum. Polynesian languages are simpler than the one we use.

'The Maori language' -- 'Te Reo Maori', translates as 'the normal language'. Ironic just a little.

[alancalverd]

 

I live in a country that has two languages.

Lucky man! Next best place to heaven - apart from the odd earthquake.

given their ancestors were ocean explorers.

I gather that "canoe" can have umpteen meanings, dependent on context. Very economical!  A bit like teenspeak, which seems to consist of "whatever" and up to two other words that change every week.

[hamdani yusuf (OP)]

Do you think that symmetry always break down?

It does, by theory and experiment. Nothing to do with what I think.

The asymmetry can then be used to determine absolute frame of reference.

[alancalverd]

Or, to put it another way, relative velocity. There is no absolute frame of reference.

[hamdani yusuf (OP)]

Or, to put it another way, relative velocity. There is no absolute frame of reference.

In case of symmetrical motions, average relative velocity is zero. Thus no net difference in time dilation between the clocks. Which mean they can be synchronized while immediate relative velocity is not zero.

[varsigma]

I gather that "canoe" can have umpteen meanings, dependent on context. Very economical!

That's my understanding of waka, where in Hawaiian it's vaka. Not surprising because Hawaii and NZ were the last places on the map, sort of.

So a waka or whaka  means a canoe. But canoes carry people and people carry stories around. So a waka is a thing that moves people and stories--legends, myths such as a god, Maui, who fishes land out of the sea--from place to place.

Te reo uses pa for a place, repeat that and papa means places, but also movement. Hence one's ancestry is whakapapa;;  carrying stories and people around.

p.s. an algebraicist might say that pasting these phonemes together is tensoring them to modify the meme. There is a linguistic order (grammar) imposed. Te Reo is a Maori treasure, all words are gifts you are supposed to "look after", because you give them back. That's a nice way to close things, Closure comes at the end, the terminals locate the meme.