Close Encounters With the Effects of Time Dilation How does it feel to be going speeds near that of the speed of light What is it like to return to Earth to find that your best friend who was the same age as you is now older than you You might talk to a man named Bob Smith. Bob recently returned from his trip to the edge of the universe and we were fortunate enough to talk to Bob about what he experienced on his journey. We also got the opportunity to talk with Bob's close friend, Jill, who eyewitnesses the effects of time dilation on Bob. Ten years ago today, Bob Smith boarded his spaceship and journeyed to the edge of the universe studying its distance and other properties unknown to man. The day Bob left, his friend Jill was standing by his side to bid him farewell. As Bob took off into space Jill noticed something very peculiar, Bob's ship had seemed to have shrunk in size.
" It was astounding ", said Jill. "The ship appeared to be half the length it was before! " Bob, who was traveling at 87% the speed of light, on the other hand, did not notice this change in length at all. How could this be, you may wonder Well, we talked to renowned scientist, Alberta Einstein and she came up with a theory for us. The viewed length for an observer on Earth is equal to the actual length multiplied by the square root of the quantity one minus velocity squared divided by the speed of light squared.
In equation form that is. So if the length of Bob's ship on Earth was 53 meters, then to someone standing on Earth viewing the ship in space, the ship would appear to be approximately 26 meters or half the actual length of the ship. This would then verify that what Jill saw was actually the truth. While Bob was in the ship he measured his mass and surprisingly it was more tha he had measured it to be on Earth. Bob's mass on Earth was 77. 2 kgs.
When he measured it in space it was sizably greater. So again we asked Alberta if and why this could possibly be. Again she was able to provide us with an equation to explain this phenomenon. Bob's new mass is equal to his mass on Earth divided by the square root of the quantity 1 minus his velocity squared divided by the speed of light squared.
In equation form that is. So since Bob's mass on Earth is 77. 2 kgs. , then his mass on the ship is 593. 8 kgs. As we see, his mass was increased by approximately seven times! Wow! One last thing we should look at is the comparison of Bob's age and Jill's age after the trip.
To a person on Earth, Bob's trip seemed to take only ten years. When Bob left, both he and Jill were both 18 years of age. So, when Bob returned from his trip Jill was 28 and amazingly Bob was younger than Jill. How on Earth could this be possible you may ask Let's ask Dr.
Einstein once more for her input on this situation. According to Alberta, the time elapsed in Bob's frame of reference is equal to the actual time on Earth multiplied by the square root of the quantity one minus his velocity divided by the speed of light squared. So in equation form that's. Therefore, to Bob, the trip seemed to last only about 4. 9 years (or to make it simpler, 5 years).
So when Bob came back he was only 23 years old as opposed to Jill who was now 28 years of age. Quoting Bob, " Relativity is a very peculiar thing! It can very strange effects on simple things such as mass, length and time. If I would have known it would slow the aging process, I would have stayed out much longer! Book me another flight to the moon!