Light as a Constant: Examining the Paradox

[matt4584]

How can light be a constant for any observer? I understand how it fits into equations and what not, but how can it be a constant. If I throw a baseball forward at 10m/s in a train going 40m/s. I perceive it as 10, an observer on the ground would perceive it as 50. Why doesn't the same apply to light? Is there anything else it doesn't apply to?

 

[Nugatory]

How can light be a constant for any observer? I understand how it fits into equations and what not, but how can it be a constant. If I throw a baseball forward at 10m/s in a train going 40m/s. I perceive it as 10, an observer on the ground would perceive it as 50. Why doesn't the same apply to light? Is there anything else it doesn't apply to?

You are mistaken about the baseball example: in fact the observer on the ground measures the speed of the baseball to be very slightly less than 50m/s.

If the speed of the train is $u$ and the ball is thrown at speed $v$, its speed relative to the ground will not be $u+v$, it will be $(u+v)/(1+\frac{uv}{c^2})$. This formula has been verified by experiment.

It would be a good exercise to try calculating this for the speeds in your example; you will quickly see why in daily life we never notice that $(u+v)$ is not exactly correct. It's also worth seeing what happens when you set $v=c$, shining a light forward in the moving train.

 

[phyzguy]

How can light be a constant for any observer? I understand how it fits into equations and what not, but how can it be a constant. If I throw a baseball forward at 10m/s in a train going 40m/s. I perceive it as 10, an observer on the ground would perceive it as 50. Why doesn't the same apply to light? Is there anything else it doesn't apply to?

Because that's the way the universe works. None of us built it. We just found it this way. Cool, isn't it?

 

[DaveC49]

matt4584 the classic observation of this is the Michelson Morley experiment where light beams were sent parallel to the rotation of the surface Earth which is also pretty close to the direction of motion of the Earth about the sun and normal to the direction of rotation of the Earth and its direction of rotation about the sun. The velocity of light is measured to be the same in both directions, which it would not be if a medium through which the Earth moved in its motion about the sum had existed. (See https://en.wikipedia.org/wiki/Michelson–Morley_experiment) for more detail. The Kennedy-Thorndike experiment (https://en.wikipedia.org/wiki/Kennedy–Thorndike_experiment) directly confirms that the speed of light is constant and with the Ives Stilwell experiment (https://en.wikipedia.org/wiki/Ives–Stilwell_experiment) confirms the Lorentz transformation of special relativity.