Consider the twins, John and Jim, of the same age of 20 yrs. living on earth.
John decides to make a trip to a distant planet X, which is 8 light years from earth.
He boards a spaceship S1 going towards planet X at time t=0 from earth. S1 moves with a speed 0.8 times the speed of light.
When he reaches the planet X, he finds it too cold than he anticipated from thermal imaging device and refuses to jump out.
Luckily he finds another spaceship S2 going towards earth with the same speed that of S1. Wasting no time, he jumps into S2 from S1 and returns back to earth.
When he meets his brother Jim on earth, they are astonished as they are not of the same age any more. One was much older than the other.
Determine who was younger and by how many years.
John decides to make a trip to a distant planet X, which is 8 light years from earth.
He boards a spaceship S1 going towards planet X at time t=0 from earth. S1 moves with a speed 0.8 times the speed of light.
When he reaches the planet X, he finds it too cold than he anticipated from thermal imaging device and refuses to jump out.
Luckily he finds another spaceship S2 going towards earth with the same speed that of S1. Wasting no time, he jumps into S2 from S1 and returns back to earth.
When he meets his brother Jim on earth, they are astonished as they are not of the same age any more. One was much older than the other.
Determine who was younger and by how many years.
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Jim watched John's ships S1 and S2 take 20 years to make the round trip, so he was 40 when John came back. However, John's clock was slowed relative to Jim by a factor of 0.6, so that to John it seemed like only 12 years. Hence, he was 32 when he came back to see Jim. If technology existed to allow John to make this trip at 0.8c, I don't think they would have been astonished about the age difference.
Edit: Supernova Sam, if you are at rest and I am moving at some velocity v relative to you, then my clock ticks at a rate slower than you by the gamma factor, γ = √(1-(v/c)²). Since John was travelling at a constant speed of 0.8c relative to you during his whole round trip, his clock was running slower than you by a factor of γ = 0.6. Remember, planet X is 8 light years from Earth and Jim on it, and S1 & S2 traveled at 0.8c relative to Earth and Jim on it, so that in Earth's and Jim's time, the round trip took 20 years. However, it was not 20 years for John travelling on S1 & S2, but γ(20) = (0.6)(20) = 12 years.
The Twin Paradox is called a paradox because this is one of the most confusing aspects of Special Relativity. The first thing people say is, "yeah, but relative to John, Jim looked like HE was speeding away at 0.8c and came back at 0.8c, so why wasn't Jim the one who'd be younger, if there equations of Special Relatively were correct? Really, shouldn't both Jim and John be at the same age by the time they got back together?" There is unfortunately no easy answer to that, because it is John that "jumped" from one moving frame to another, namely from ship S1 to S2, while Jim back on Earth did no such thing. That is the difference, the situation is not symmetric. In fact, it's these kinds of pesky problems that pushed Einstein into developing a more general version of Special Relativity that would include accelerated frames. In General Relativity, there is no paradox, when acceleration is taken into account.
Edit: Supernova Sam, if you are at rest and I am moving at some velocity v relative to you, then my clock ticks at a rate slower than you by the gamma factor, γ = √(1-(v/c)²). Since John was travelling at a constant speed of 0.8c relative to you during his whole round trip, his clock was running slower than you by a factor of γ = 0.6. Remember, planet X is 8 light years from Earth and Jim on it, and S1 & S2 traveled at 0.8c relative to Earth and Jim on it, so that in Earth's and Jim's time, the round trip took 20 years. However, it was not 20 years for John travelling on S1 & S2, but γ(20) = (0.6)(20) = 12 years.
The Twin Paradox is called a paradox because this is one of the most confusing aspects of Special Relativity. The first thing people say is, "yeah, but relative to John, Jim looked like HE was speeding away at 0.8c and came back at 0.8c, so why wasn't Jim the one who'd be younger, if there equations of Special Relatively were correct? Really, shouldn't both Jim and John be at the same age by the time they got back together?" There is unfortunately no easy answer to that, because it is John that "jumped" from one moving frame to another, namely from ship S1 to S2, while Jim back on Earth did no such thing. That is the difference, the situation is not symmetric. In fact, it's these kinds of pesky problems that pushed Einstein into developing a more general version of Special Relativity that would include accelerated frames. In General Relativity, there is no paradox, when acceleration is taken into account.