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.)
