Is the speed of light constant relative to the observer? Hypothetically, I am standing at the front of a train. The train is traveling 100 mph. I shine a flashlight pointing forward in the direction the train is traveling.
Is the light from the flashlight traveling at 670,616,629 mph or (670,616,629 mph) +the speed of the train (100 mph) = 670,616,729 mph.?
The light travels at 670,616,629 mph according to an observer on the train and also at 670,616,629 mph according to an observer on the ground.
The speed of light is the same for all inertial observers, despite their relative motion. Velocities don’t actually “add” the way you would think they should based on our everyday experience at low velocities. The formula for combining velocities in Special Relativity is more complicated than simple vector addition. At low velocities it reduces to the familiar addition but at high velocities $c$ acts as the “speed limit”.
If you are curious about the correct velocity-addition formula, see Wikipedia.
