If two people are moving in opposite directions at the same speed and they start their watches at the same time, will their watches show the same time or different times?

If two people are moving in opposite directions at the same speed and they start their watches at the same time, will their watches show the same time or different times?

Aditya Raj Anand

Saturday, 1 February 2025

Physics

If two people are moving in opposite directions at the same speed and they start their watches at the same time, their watches will eventually show different times due to the effects of time dilation, a phenomenon predicted by Einstein's theory of special relativity.

According to the theory of special relativity, time dilation occurs when an observer is moving at a significant fraction of the speed of light relative to another observer. When two people are moving at high speeds in opposite directions, each observer will perceive the other person's clock to be running slower than their own.

This means that as they continue to move away from each other, the person observing the other will see their clock ticking more slowly. When they eventually reunite, they will find that their watches show different times. The effect is typically only significant when the speed difference between the two observers is a substantial fraction of the speed of light, which is much faster than everyday speeds.

In practical terms, for everyday speeds, the effects of time dilation are extremely small and not noticeable. They become significant only at speeds that approach a significant fraction of the speed of light, which is much faster than any normal human motion.

If two people are moving in opposite directions at the same speed, and assuming they are both moving at speeds much less than the speed of light, their watches will show the same time. This is because the effects of time dilation due to their relative motion are negligible at everyday speeds.

However, according to Einstein's theory of relativity, time dilation becomes significant only at speeds approaching the speed of light. In the scenario where they are moving at ordinary speeds (e.g., walking or driving), the time dilation effect is so small that it would be imperceptible.

So, for all practical purposes, the two people’s watches will show the same time when they compare them. But if they were traveling at a significant fraction of the speed of light (close to 30,000 km/s or more), their watches would show different times due to time dilation, with the person moving at a high speed experiencing time passing more slowly relative to the other.

If two people are moving in opposite directions at the same speed and they start their watches at the same time, will their watches show the same time or different times?

If we consider only classical physics (Newtonian mechanics), both watches will always show the same time because time is absolute in this framework.

However, in the context of special relativity, the answer depends on the details of their motion:

1. If both people move at the same constant speed in opposite directions (relative to some initial reference frame, like the ground), and there are no accelerations involved, then in their own frames, their watches will continue to tick normally. Due to the symmetry of the situation, each person will perceive the other's clock as ticking more slowly (time dilation), but if they later reunite, their clocks will show the same time.

2. If they change speeds or one of them accelerates to reunite, then asymmetries arise due to acceleration, and their clocks may show different times when they meet again. This is similar to the twin paradox, where the twin who undergoes acceleration (changing frames) ends up with less elapsed time.

So, under purely symmetric motion at constant speed, the watches will agree if they reunite. But if there is acceleration involved, the clock readings could differ.