system
Given the following post, respond as if you're commenting on Reddit:
human
How can velocity be relative when the speed of light is constant?

Ever since I read somewhere in a book that the speed of light is constant, I never understood how that worked with velocity being relative; the two are mutually exclusive.
gpt
The speed of light is the same for all frames of reference. So, if a space-ship is flying towards the Earth at half the speed of light, and it turns on its headlights, then from the Earth's frame that light is approaching at the speed of light - not 1.5x the speed of light. From the space-ship's perspective, the Earth is approaching the space-ship at half the speed of light, and the light from the space-ship's headlights are approaching the Earth at the speed of light.

This doesn't add up if you use the classic formulae for adding velocities. And this is the core of how relativity was derived. If the speed of light is constant for everybody, then space and time and velocity must work differently from our old classical assumptions. This is where you break universal time, you get time dilation and length contraction, and you can't just add two velocities like you used to. With these new equations of space and time and motion, you end up without any contradictions.