# Is the speed of light constant relative to the observer? [duplicate]

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.?

• – John Rennie May 13 '20 at 17:31
• Since you were frustrated by the reaction to your first question, I wanted to give you an answer to this one. The question would be fine except for the fact that it has already been asked many times on this site. In general you are expected to spend a few minutes searching to see what has already been asked on whatever topic you are interested in. Otherwise the site gets clogged with repetitive questions. – G. Smith May 13 '20 at 17:43

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”.
• In the first equation, take $v’$ to be the speed of the light relative to the train, $u$ the speed of the train relative to the ground, and $v$ the speed of the light relative to the ground. When $v’$ is $c$, $v$ is also $c$. The formula is more interesting when you have a train moving at, say 2/3 the speed of light and someone on the train throws a ball at 2/3 the speed of light. See how fast the ball will move relative to the ground. It won’t be 4/3 of $c$; it will be less than $c$. – G. Smith May 15 '20 at 16:19