Inertial Frames, Relativity, Equivalence Principle and the Twin Paradox

Question

I am very unsatisfied with how people resolve the twin paradox. As a little background, here is what the Wikipedia article about the paradox states...

In physics, the twin paradox is a thought experiment in special relativity involving twins, one of whom takes a space voyage at relativistic speeds and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as moving, and so, as a consequence of an incorrect[2][3] and naive[4][5] application of time dilation and the principle of relativity, each should paradoxically find the other to have aged less. However, this scenario can be resolved within the standard framework of special relativity: the travelling twin's trajectory involves two different inertial frames, one for the outbound journey and one for the inbound journey.[6] Another way to understand the paradox is to realize the travelling twin is undergoing acceleration, which makes them a non-inertial observer. In both views there is no symmetry between the spacetime paths of the twins. Therefore, the twin paradox is not actually a paradox in the sense of a logical contradiction. There is still debate as to the resolution of the twin paradox.[7]

So obviously, we can argue that either of the twins can claim they are stationary and the other twin is moving. That is where the paradox arises: Either of them may have seen the other twin as aged.

The way people resolve this is by saying that since the space twin "accelerated" and changed reference frames, we have an asymmetric situation.

But why should we consider the twin moving through space to be accelerating? We could also say, by the same principles of Gallilean relativity that the twin on Earth was the one accelerating and NOT the twin travelling through space.

Like every argument that certain kinematic property must be attributed to one twin can be transformed to those of the other twin, based on the reference frame.

So either:

• There is a Universal Reference frame (which is perhaps wrong)
• There is no difference in how they aged

What I think is that although you may not see the twin speeding away from you age, i.e. the speed of the information of the twin aging would dilate, the actual speed of aging wouldn't. Infact, nothing actually dilates time. All that dilates is the speed at which information (through light) travels if anything.

What am I missing here?

Answer 1

What you are missing is that you cannot attribute the acceleration to the stay-at-home twin in the way you have supposed. The asymmetry is fundamental.

The reason one twin ages less than the other is because they have followed a kinked path through spacetime that has a shorter duration than the straight path followed by the other twin. Acceleration is relevant because it is what causes the travelling twin to deviate from the straight path.

Consider a purely spatial analogy. You and I are standing together 100m away from a bar purveying the most delicious craft beers. You walk directly to the bar. I, having partaken of too many fortifying stimulants already, veer off at 45 degrees to my intended course and only after the half way mark do I realise my mistake and take corrective action, turning 90 degrees to meet you at the bar. In those circumstances, you walked 100m to the bar, while I followed a path of around 141m. The fact that I followed the longer path necessarily involved acceleration which allowed me to change direction at the half way mark.

In the twin paradox, the stay-at-home twin takes the direct route between the start and end of the experiment, while the travelling twin follows the kinked path. The geometry of spacetime being what it is, the kinked path has a shorter duration than the straight one, hence that twin ages less.

You can, if you like, take acceleration out of the picture all together, and forget about the twins too, by just considering the geometry of the two paths through spacetime. The maths will tell you that the kinked path is shorter than the straight one.