# Relative Twin Tango

1. Sep 26, 2007

### Remnant

My cousin stated that "Two twins born at the same time. Twin "A" remained on earth, and twin 'B" other be sent out in space(he did not specify where), and when twin "B" came back to earth he would be 3 years younger than twin A. Could someone specify what he meant by that.

I am not sure if he was talking about relative time. That twin B would be 3 years younger before he came back to earth and began catching up in relative time when he started heading back to Earth. If someone could specify my post, disprove my thought as maybe just a misunderstanding (its been many years since i heard my cousin tell me that statement). It would be much appreciated

2. Sep 26, 2007

### HallsofIvy

Staff Emeritus
First, time dilation does not depend upon direction. If twin B will be 3 years younger after his trip away from earth, he will NOT regain that time coming back. If he travels back at the same speed at which he went away (relative to the earth), one could argue that he would have to be 6 years younger when he arrives back on earth. I suspect in this case it is meant that B will be 3 years younger than A when he arrives back on earth.

One could also argue that, since speed is relative, twin B sees himself as stationary and twin A as moving away at the same speed and so twin A should be 3 or 6 years younger when they get back together. That is referred to as the "twin paradox" (and cannot be solved by saying what one gains going out one loses coming back!).

Resolving that paradox involves two different things. First, in order for twin B, who was initially stationary on earth, to leave, he must undergo an acceleration- inertial frames don't apply. In order to come back, he must also undergo an acceleration. The other point is that A remained on earth, subject to its gravitational field- and that also has its effect. That involves going into general relativity which is far beyond me!

3. Sep 26, 2007

### Remnant

Thank you for your input, i think that it was implied from my cousin that, 3 years was the time that it took for the twin to return to earth. I appriciate your time on this subject

4. Sep 26, 2007

### JesseM

Just so you know, the time dilation formula says that in the Earth's frame of reference, a ship moving at speed v would be slowed down by a factor of $$\sqrt{1 - v^2/c^2}$$, where c is the speed of light. So if the twin were to travel away from the Earth and back maintaining a speed of 0.8c, and the trip lasted 5 years according to clocks on Earth, then the clocks on the twin's ship would be slowed down by a factor of $$\sqrt{1 - 0.8^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6$$, so the traveling twin would only have aged (0.6)*(5 years) = 3 years when he returned to Earth.