The twin paradox


The twin paradox

Consider an experiment involving a set of twins named Andrew and Brian. When they are 20 years old, Andrew sets out on a journey to Planet X, located at 20 lightyears from Earth. His spaceship is capable of reaching a speed of 0.95c relative to the inertial frame of his twin brother back home. After reaching planet X, Andrew immediately returns to Earth at the same speed, 0.95c. Upon his return, Andrew is shocked to discover that Brian has aged 42 years and is now 62 years old. Andrew, on the other hand, has aged only 13 years.

Which twin is the traveler and which is really younger as a result of the experiment? 

From Brian’s frame of reference, he was at rest while his brother traveled at a high speed. From Andrew’s perspective, it is he who was at rest while Brian was on the high speed space journey. According to Andrew, he himself remained stationary while Brian and Earth raced away from him on a 6.5 years journey and then headed back for another 6.5 years. This leads to an apparent contradiction. Which twin has aged the most?

 

Resolving the paradox: Special theory of relativity deals with inertial frames of reference moving relative to each other at uniform speed. However, the trip in this paradox is not symmetrical. Andrew, the space traveler, must experience a series of accelerations during his journey. As a result, his speed is not always uniform and so, he is not in an inertial frame at all times. Even if you disregard the non-inertial frames during the initial/final acceleration and the turning point, Andrew must be in a minimum of 2 different inertial frames. He cannot be regarded as always being at rest (cannot claim that he is in one inertial frame throughout the whole journey) while Brian is in uniform motion because to do so would be an incorrect application of the special theory of relativity. Therefore, there is no paradox.

Note: Since Andrew cannot claim that he is in one inertial frame throughout the whole journey, his claim (of he himself remaining stationary while Brian (+Earth) raced away) falls through.

Note 2: There is a slightly more rigorous treatment of the paradox which can be found at http://home.earthlink.net/~owl232/twinparadox.pdf. (Requires the knowledge of spacetime diagram) This addition is kindly provided by a reader, Danny.

 

Animation of twin paradox:

 

Back To Special Relativity


Mini Physics

Administrator of Mini Physics. If you spot any errors or want to suggest improvements, please contact us.

Leave a Comment