The 12 earth years observed by the traveling twin (assuming they can observe the earth and count how many times it orbits the sun, but that isn't a requirement), takes 10 years of local time for that twin. However, this condition expires when both twins are again in the same frame of rest.chinglu said:
The traveling twin aged 10 years.
No, the twin accepts that the elapsed time for their journey was less than the elapsed time on the earth because of relativistic effects. The effect is called time dilation, but really that's only a convenient label. It's convenient because everyone "understands" time, even if they don't understand relative time, or frame-dependent time, etc.chinglu said:
The travelling twin indeed sees the earth orbit the sun 12 times, but for them it happens in 10 years of their time. There is no contradiction because, in spite of their observations, they don't age 12 years, but their twin does.chinglu said:
Yes, I see what you are trying to say, Chinglu. But you are forgetting that the traveling twin 'measures' each Earth orbit 'year' at 10/12th the 'value' in his now-slowed clock measuring device accumulating a 'year's worth of seconds which in total is 10/12th the total of the stay-put twins clock seconds count for that same orbit.
I should add that this is only true if the two clocks are at rest relative to each other (comoving). If instead the two clocks have different worldlines and are at the "same place" momentarily, then they can disagree on where that place is located, relative, of course, to some other reference.
Yes, I see what you are trying to say, Chinglu. But you are forgetting that the traveling twin 'measures' each Earth orbit 'year' at 10/12th the 'value' in his now-slowed clock measuring device accumulating a 'year's worth of seconds which in total is 10/12th the total of the stay-put twins clock seconds count for that same orbit.
So, yes, the traveling twin measures the Earth going around 12 times too, but in his own traveling state the aging of that year in biological and clock process/count amounts to a 'year' being 10/12ths 'process time' as the stay-put 12/12 process time 'year'.
In other words, HIS 'aging value' for EACH 'year' of those 12 years is shorter for each Earth-sun orbit cycle than the stay-put twin's value for each year. The two 'values' are NOT the same even though the number of orbits is the same number for both.
When they re-unite this will become obvious as the 'aging value of 12 orbits' is LESS for the traveling twin. The two orbit counts were the same in absolute NUMBER/CYCLES, but NOT the same 'aging value' for each of the 'orbit units' counted.
Good luck!
What Im trying to say is that, it takes 1 second for an atomic clock at sea level to measure 1 second. A dilated clock takes a faster or slower time to measure 1 second, depending on the time dilation the clock is experiencing. The problem I see is from the clocks frame of reference, the detectors time should also be dilated and the clock must be synchronized with all the other clocks experiencing TD for time dilation to exist.
G'day cobber
Great explanation - in that I understood clearly what you are saying .. often not the case with these things.
I don't want to preempt chinglus reply, and I would be very interested to see it, but meanwhile, I have a question - what defines the 'travelling' twin ?
Let's remove then from earth and spaceship and put then on two similar asteroids. Same 'travelling' scenario as above.
When they meet up again, it could be deduced from the above that they are both younger than each other. How does that work out ?
And please, make your explanation no more complex than the above if you could.