1. Dec 13, 2011

### Snip3r

This question about the twin paradox(twins A,B). I hope everyone knows the statement. I have read explanations for this but they differ. Some authors say twin(say B) who takes the trip accelerates so he cant be an inertial frame of reference. Some say it has nothing to do with acceleration and it can be solved by time dilation,length contraction and relativity of simultaneity. Okay this brings me a lot of doubts

a)Which explanation is correct?(it doesnt have to be practically possible)
b)those who say acceleration is the culprit, if you can blame the other guy as moving when in constant velocity why cant you do the same for acceleration?
c)are there any frames in universe which can be validated as inertial?for example if you say earth is one it is certainly not because it revolves around itself,sun,galaxy etc. Like wise if you take a point in space(or any where else) how can you be sure its not accelerating or revolving etc?

2. Dec 13, 2011

### Fredrik

Staff Emeritus
a) It depends on what you need explained. If you only want to know what SR says about the final ages of the twins, the answer is an unambiguous "the astronaut twin is younger". If you want to know what's wrong with the incorrect argument for why they should have the same age, both of the explanations you mentioned are correct. The time dilation formula doesn't apply, since the astronaut's world line isn't the time axis of any inertial coordinate system. However, you can compensate for the error introduced when you apply it, by also taking relativity of simultaneity into account.

b) Experimentally, because an accelerometer will display something other than 0 when you're accelerating. Mathematically, because acceleration is defined as a measure of the deviation from geodesic motion. The Earth twin's motion is a geodesic (according to SR) and the astronaut twin's motion is not. ("Being a geodesic" is a a coordinate-independent property of a curve).

c) Here it looks like you want the answer given by GR rather than SR. (SR describes a universe without gravity). If your accelerometer displays 0 no matter which way you turn it (i.e. if you're in free fall), it's possible to define a local inertial coordinate system that has your world line as the time axis, but it gets less like an inertial coordinate system in SR the farther you go from the event that you took as the origin of the coordinate system.

Last edited: Dec 13, 2011
3. Dec 13, 2011

### mathman

The simplest way to look at is without acceleration as such. However the traveling twin has to change velocity during the round trip.

Ignoring practical problems, he can start out at almost light speed leaving the earth, getting to his destination in almost no time (in his reference frame). Then he stops and returns to earth at almost light speed, again in almost no time (in his reference frame). The net result is that he hardly ages during a trip that in earth years take a long time.

The reason it takes him almost no time is a result of the Lorentz contraction of the distance along his path.