Undergrad Speed of Light from Car Headlights & Brake Lights

[Tony Sims]

So there is lots of information on the Internet specifying that the speed of light from the headlights of a car traveling at 30mph is C and not C+30 because it is impossible to travel faster than light but what about the speed of light from the brake lights pointing backwards? Am I right in thinking that this would be C-30 or is it still C?

 

[russ_watters]

Welcome to PF!

The speed of light measured by any inertial (non-accelerating) observer in a vacuum is C. Just C. Always C.

There is probably a related question you will think to ask soon which relates to how you add velocities for objects. For example, say you have, two rocket ships on opposite sides of Earth traveling toward Earth at 0.8 C. Do they measure their speed relative to each other to be 1.6C? Nope:
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel.html

 

[Herman Trivilino]

So there is lots of information on the Internet specifying that the speed of light from the headlights of a car traveling at 30mph is C and not C+30 because it is impossible to travel faster than light

It's the other way around. It's impossible to travel faster than light because the speed of the light from the headlights doesn't depend on the speed of the car.

In other words, you start with the postulate that the speed of light is independent of the speed of the source. If you're an observer standing beside the road, and the car is moving along that road, you will always measure the same value $c$ for the speed of the light coming from the headlights. This is equivalent to the car being at rest and you moving towards or away from it. Therefore no matter how fast you move, you will always measure the same value $c$ for the speed of light.

From there you can deduce that speed $c$ must also be your maximum possible speed. It goes something like this. Imagine chasing after a beam of light. No matter how fast your pursuit the beam will always recede from you at speed $c$. Therefore you can never catch it.