00:01
For this problem, we have twins that are traveling to a distant planet that is 12 light years away from earths.
00:13
The first twin is traveling with a speed of 0 .9 times the speed of light.
00:21
And the second twin is traveling with a speed of 5 times the speed of blood.
00:28
So for this problem, the first twin is traveling with a higher speed, and then it will arrive at the planet earth.
00:46
And once this first twin is there, it's going to be oppressed relative to the earth and will ages at the same rate as people.
01:03
Back on the earth.
01:05
So as measured by an observer on the earth, the dilated time intervals that we are going to call t -e -delta -t -1 and delta t2, these are going, these are given by this following formula, which is the dilatation of time is equal to the proper time t -0 -t0.
01:35
Over one minus the velocity, the square of the velocity over the speed of line square.
01:47
Now, the proper time interval delta t sub zero, and in this case we will have delta t for between one and delta t's zero for between two.
02:05
This because they are both traveling, with the speak nearly the speed of light.
02:11
So they will experience time dilatation.
02:15
When they, these times, are the times they nature by themselves during their journey.
02:23
So, and so this, we can, from the previous equation, we can solve for delta t01, which is the proper time of the first twin, which is delta t1 times one minus the velocity of the twin one over the speed of light.
02:58
So we also have for this in the same form for the twinned two, but with the velocity of this second twaint.
03:12
Now, there is an additional aging that the first twin undergoes between the time of his arrival at this planet and the arrival of the second twin.
03:32
And this is the difference between the time of the second twin journey and the time of the first twin's journey.
03:41
And these are both measured by an observer on the earth.
03:47
And this is one additional, additional aging, and this is equal to delta c2 minus delta t1.
04:02
We use this because these are the times measured by an observer on earth.
04:09
Now, we are going also to use that definitions of these two equations from an observer on earth is just very straightforward.
04:25
This time is equal to the distance to the planet over the velocity of the first twin.
04:37
Meanwhile, for the other two is the distance over the velocity.
04:41
Of the second twin.
04:43
So now set all of these equations, we need to solve the first question for this problem.
04:58
That is, the first question is, according to the theory of special relativity, what is the difference between their ages when they meet again at the earliest possible time? so when the second twin arise at this planet, the final age of the first twin is given by this.
05:22
We are going to say that the age one of the first twin is going to be the initial age, the beginning age, and they begin with on earth.
05:43
That is 19 years old plus the delta, the proper time, the first twin measured by himself during the journey.
05:56
This is the proper time of the first twin plus the additional agent.
06:06
That is the difference.
06:08
It is different.
06:09
Then we sum this.
06:12
Additional agent.
06:15
This additional agent is because the, when the first twin arrived at the planet, he needs to wait for a little longer until the second twin arrived.
06:31
So the second for the second twin, we have that his age is the initial, the initial age, plus the proper time he measures by himself during the journey...