VACETS Regular Technical Column

"Science for Everyone"

"Science for Everyone" was a technical column posted regularly on the VACETS forum. The author of the following articles is Dr. Vo Ta Duc. For more publications produced by other VACETS  members, please visit the VACETS Member Publications page or Technical Columns page.

The VACETS Technical Column is contributed by various members , especially those of the VACETS Technical Affairs Committe. Articles are posted regulary on [email protected] forum. Please send questions, comments and suggestions to [email protected]

Mon, 1 May 1995

Spacetime-Travel & Relativity

Calvin: "Dad, will you explain to me the theory of relativity."

Dad: "Sure, son. The theory of relativity says that time slows down when you move at high speed."

Calvin: "Can you give me an example?"

Dad: "Like, you gain three hours on a seven hour flight (from DC) to Los-Angeles. Of course, it only works when you fly Westward."

Calvin: "That's not what mom said."


That "Calvin and Hobbes" comic strip was one of my favorites that I read many years ago. I think it is appropriate to start the spacetime-travel mini-series with a few lines from the comics with Calvin, a kid who has wild imaginations and often dreams of traveling to some unknown planets or going back in time.

Yesterday, sitting at home watching the movie "Back to the future", a sudden thought flashed in my mind. I thought about going to Hollywood to borrow the time machine and then I'll travel back in time to fix things, to prevent the bad things to happen, to make this world a better place to live. And then I realized that the time machine was just some fantasy idea that can only happen in science fictions. In real life, there can never be a time machine that can bring some one back to the past to change things. What has happened in the past will forever remain in the past and one can never change it to some thing else.

While sitting in the front of the TV feeling blue, I got a rare visit from the white-hole-who-knew-it-all friend of mine. Do you remember him? He is the full-of-hot-air guy who thinks he knows everything but actually knows nothing. I could smell the trouble and the long night laying ahead. This guy doesn't come to some one's house to have a beer and a friendly chat like most of us do; he comes because he wants to show off who knows what coming out of his hot-air-brain.

-- Do you remember our discussion half years ago about the astronomical stuff, the Olbers' paradox, the black holes and white holes?

I really do smell trouble now. I don't remember what we were discussing about and how it turned out; but if this guy comes to my house bringing some stuff to argue about then it can only mean one thing, that is, he has lost some argument earlier and now wants to revenge. I'd better divert his thoughts to other things now.

-- Want a beer?

-- Bud, please. After our discussion about the stars half years ago, I got interested in it and read some books on the astronomical stuff. I bet I know more about time travel, the stars and black holes than you now.

Wow! This bubbly head friend is really bragging. And it is not easy to shake him off the subject.

-- Yeah! Spit it out, my friend.

-- Do you know anything about the theory of relativity? It says that time slows down when you move at high speed. If you keep giving your money to the airlines like you do today then some day you will be younger than me and will have to call me "big brother"...

This "big brother" thing brought me back to the old college time when we first met. This empty brain guy thought I was younger than him and he talked to me like a big brother to a little kid, until... I asked him his age and it turned out that he was born one day after me. Our roles were then reversed and he has always regretted that. It looks like he is trying to prove that he is older than me. He started to write some formulas down on a piece of paper. There was something that looked like [t=t'/sqrt(1-v^2/c^2)] or something similar to that where "t" and "t'" are the time intervals measured by a stationary observer and a moving observer, respectively; "v" is the speed of the moving observer, and "c" is the speed of light. He went on...

-- It says here that when you are flying, you will age more slowly than me, and soon, you will be younger than me.

I didn't believe him a bit; that is, I believe there will be some time dilation but it effect would be so small that it will not make any difference on my age. We worked out the numbers and it turned out that even if I were to spend all my time flying on an airplane at an average speed of 600km/hr, I would be only 10 micro-seconds younger per year. Unless we both could live for a billion years or so, he would never be younger than me. Beside, I did not even take into account that when I flew high up in the sky, I would feel less gravity and therefore, would age a little bit faster. My empty head friend did not like the answer and he alone worked the numbers again and it came out the same. Round one: you lose, my friend. He looked upset.

-- So, the time dilation does not have any significant effect on any thing on earth at all.

-- My friend, you are wrong again. It does not affect my age, but it is not insignificant in everything on earth. I have a friend who is the elected president of VACETS and whose works involve the satellite communication and navigation system. I bet he knows how important the time dilation from both relativity and gravitational effects is to satellite navigation. I think you lose again, my friend.

My hot air head friend's head seemed to get even hotter. It looks like we are going to stay up all night.

-- Alright, so you won. But, instead of flying on an airplane, you get into a spaceship and zip away at near the speed of light to some star system and then zip back to earth. I bet you will then be younger than me.

-- Would you give me some numbers so I can easily visualize what you are talking about?

-- Suppose you fly in some spaceship at a speed of 0.8c to a star system 8 light-years away. After getting there, you turn around and come back to earth, also at a speed 0.8c. Working out the relativity equations, I will age 20 years during that span while you will only be 12 years older. So that after the trip, you will be 8 years younger than me and then you will have to call me "big brother".

-- Where in the hell do you get the energy to accelerate a spaceship to a speed like that? Out of the empty space? And even if some physicists say that the empty space does contain a huge amount of energy (this may be true), we don't have the technology to extract the energy out of the vacuum to power the interstellar spaceships yet. It may be a thousand years or so before we can build a spaceship like that, and you and I will be long dead by then, and you will forever be younger than me... Put that technologically impossible stuff aside, just look at the relativity equations, if I'm in the spaceship moving at 0.8c, you will see the clock in my ship moving at a rate equals sqrt(1-0.8^2) = 0.6 the rate of your clock on earth. So for a round trip of 20 years of your time, it is only 12 years of my time. But have your ever considered that, in my point of view, in my spaceship, I will see my ship remain stationary while the earth and you are moving at a speed of 0.8c and also your clock is moving at 0.6 the rate of my clock. So that I would age twelve years after the trip but I would see you only 12*0.6 = 7.2 years older. Is it paradoxical for both of us seeing the other aging more slowly? Then who will really be younger?

Of course I know the answer. I just only wanted to make him look foolish. He looked at the equations, at me, at the beer. His face seemed to be redder. It was probably the alcohol, or maybe his anger. He frowned. He tried to answer but nothing could come out of his mouth. I felt sorry for him, so I gave him the answer.

-- There is no paradox in the problem. For me, making a round trip in a spaceship with a speed of 0.8c, I would see 12 years passing by while you, my angry friend, would see 20 years going by. The paradox arises because in the problem I gave you, I left out one thing: that is, my point of view from the spaceship is from the accelerated reference frames and not from an inertial reference frame, and it can not be treated as simple as your point of view from an inertial reference frame, earth. Working with accelerated reference frames requires the general theory of relativity and it is much harder to do. However, it does not matter what reference frame one uses, the answer will always come out the same: after the round trip, I will be 12 years older and you will be 20 years older. And it means that you will probably die before me. You lose again, my friend.

My friend seemed to cool down a little bit now. A mysterious smile appeared in his face. The anticipated long night is just beginning. I think I need another beer.

(To be continued.)

Duc Ta Vo, Ph.D.
[email protected]

For discussion on this column, join [email protected]

Copyright © 1996 by VACETS and Duc Ta Vo


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Spacetime-Travel and Relativity (Part 1)

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