Because of time dilation, you observe the hands of your friend’s watch to be moving slowly. How does your friend view your watch—as running slowly, running rapidly, or neither?
Solution 26E Introduction: In relativistic speed, the time elapsed between two events is appeared to be “stretched” or “dilated”. This phenomenon is known as “time dilation” in relativity. Length contraction is another phenomenon in relativistic speeds. T 0 The mathematical expression for time dilation is, T = v 1 c Where, T - Dilated time between two events T0 Actual time between two events v - relative speed of the reference frames c - Speed of light Step 1: Due to the time dilation effect, you observed your friend’s watch is moving slowly. In fact, the hands of the watch are moving as slow when both of you are moving with relativistic speed. So, according to the frame in which you belongs to, it is appeared that your friend is moving with relativistic speed and this is the reason behind the slow motion of his watch due to the time dilation effects. Similarly, according to the frame in which your friend belongs to, it is appeared that you are moving with the same relative speed as you experienced on him. So, for him, your watch is also in slow motion since you are appeared to be in relativistic speed due to time dilation effects. Conclusion: So, in relativistic speed, both of their watches will experience time dilation effects and for both of them, the watches should be in slow motion.