Chapter 15, Problem 15A

If you were traveling in a high-speed spaceship, would metersticks on board appear contracted to you? Defend your answer.

To determine

Whether meter stick on board in space-shift appear contracted or not when person was travelling in high-speed space-ship.

Answer to Problem 15A

There is no change in the length of meter stick on board seen by the observer inside the space-ship.

Explanation of Solution

Introduction:

According to special theory of relativity, the ultimate speed for all matter is the speed of light.In order to describe the motion of particle, frame of reference plays a crucial role. The basic postulate of relativity is that,‘all the laws of physics are same in inertial frame of reference.’ The Inertial frame of reference is the frame where Newton’s laws of motion are obeyed by the particle (non-accelerating).Ina non-inertial frame of reference,Newton’s laws of motion are not obeyed by the particle (accelerating).

When moving object is seen by the stationary object in the inertial frame of reference on the earth, the moving object seems to be contracted along its direction of motion. The amount of contraction depends on the velocity of the particle comparable to the inertial frame of reference. When space-shipis moving seen by the stationary observer on the earth, length of meterstick in the space-shiplooks like contracted. The amount of contraction in length is given by,

  $L=L_0\sqrt{1-\frac{v^2}{c^2}}$

Where,

L_o =Original length of the object in inertial frame of reference.

L = Length of the object seen by an observer when object is in motion.

v = velocity of the object with respect to ground observer.

c = Speed of the light.

As the speed of the object increases, the contraction in length of object increases.Since there is no relative speed of the meter stick with respect to observer in the space-ship,therefore, according to postulate of relativity, there is no change in the length of the meter stick seen by the observer inside the space-ship.

Conclusion:

According postulate of relativity, there is no relative speed of the meter stick with respect to observer in the space-ship. Hence there is no change in the length of meter stick on board seen by the observer inside the space-ship.