I'm trying to build some intuition to some basic concepts in Special Relativity. The following is a thought experiment from one of my lectures.
Here are the statements:
(1) According to Alice, her light signal reaches Charlie before the light signal sent by Bob.
(2) According to Alice, her light signal reaches Charlie at the same time as the light signal sent by Bob.
Here's my thought process:
- It's clear to me that one of the big points in Special Relativity is that light moves at the same speed in all inertial frames. So, both signals would hit Charlie at the same time.
- However, according to Alice it would perhaps be the case that her signal hits Bob first. In Alice's inertial frame, Charlie and Bob are moving at speed $-v$. However, due to their initial positioning, Bob is moving away from her and Charlie is moving towards her.
- However, what's immutable is that both light signals were emitted when Alice and Bob were at the same $x$ position. Therefore, according to Alice both signals hit Charlie at the same time. It doesn't matter if she's closer to Charlie by the time this happens.
Am I going wrong somewhere in my thinking?