Question

Kurt is measuring the speed of light in an evacuated chamber aboard a spaceship traveling with a constant velocity of \(0.60 c\) with respect to Earth. The light is moving in the direction of motion of the spaceship. Siu- Ling is on Earth watching the experiment. With what speed does the light in the vacuum chamber travel, according to Siu-Ling's observations?

Short answer

Answer: The observed speed of light according to Siu-Ling's observations is c (the speed of light in a vacuum).

Step-by-step solution

Principle of relativistic velocity addition

The principle of relativistic addition of velocities states that if object A is moving at velocity \(v_A\) relative to object B, and object B is moving at velocity \(v_B\) relative to object C, then the velocity of object A relative to object C, \(v_{AC}\), can be calculated using the formula: \(v_{AC} = \frac{v_A + v_B}{1 + \frac{v_A v_B}{c^2}}\) In our case, the spaceship (object B) is moving with a velocity of \(0.60c\) with respect to Earth (object C), and the light (object A) is moving with a velocity \(c\) with respect to the spaceship. We want to find the velocity of the light (object A) with respect to Earth (object C), which is \(v_{AC}\).

Substitute the given values into the formula

Now, we will substitute the given values into the formula for relativistic addition of velocities: \(v_A = c\), \(v_B = 0.60c\), and \(c\) is the speed of light in a vacuum. \(v_{AC} = \frac{c + 0.60c}{1 + \frac{c(0.60c)}{c^2}}\)

Simplify the expression for \(v_{AC}\)

Let's simplify the expression: \(v_{AC} = \frac{1.60c}{1 + 0.60} = \frac{1.60c}{1.60}\)

Calculate the final result for the speed of light according to Siu-Ling's observations

Now we can find \(v_{AC}\): \(v_{AC} = \frac{1.60c}{1.60} = c\) The speed of light according to Siu-Ling's observations is \(c\), the same as the speed of light in a vacuum. This is expected because, according to the principles of special relativity, the speed of light is the same for all observers, regardless of their relative motion.