← Special Relativity

Saturday, January 22, 2022

## The Setup

Say there are two observers: Observer $O$, who stays on Earth, and Observer $O'$, who flies at a high velocity to a local star (several lightyears away), turns around, and returns to Earth.

Since each perceives the other moving with respect to themself, they will claim the other's time is passing slower (time dilation).

When observer $O'$ returns to Earth, who would be younger? Observer $O$ would claim $O'$ is younger since observer $O'$ moved with respect to Earth, whereas $O'$ would claim $O$ is younger since the Earth moved with respect to $O'$ 's rocket.

## The Solution

### Why the setup does not make sense

The twin paradox is not actually a paradox. The issue lies in how the situation is framed. It is not possible for observer $O'$ to remain in an inertial reference frame for the entire journey since they must, at some point, turn around and come back to Earth. Therefore, at some point they accelerated and the laws of physics no longer applied the same.

### Who would actually be younger?

Observer $O'$ would be younger upon returning to Earth, since they accelerate when they turn around and return to Earth. This is different than observer $O$, who was in an inertial reference frame for the entire time.