The Twin Paradox Song Music
and Lyrics by Peter Cranson
Lying awake, I was thinking just the other night,
what if I was traveling at .8 times the speed of
light,
and if I had a twin, and he was just the same as
me, (let's call him Max)
and I left him on the earth and took a rocket out to Alpha Centauri.
Now, Alpha Centauri is a star
located 4 light-years away from earth.
That means, it takes light from Alpha Centauri 4 years to get here, even
though it is traveling at 186,000 miles PER SECOND. That is 7 times around the earth in just one second. Now the question is, how long would it take
me to get there if I was flying at .8 times the speed of light? (which is just
a little slower) Well,
let's see what
Max would say.
Me zipping away, is the first thing Max would
see.
Then he'd go to his chalkboard and calculate
mathematically,
that a trip like mine at .8 times the speed of
light should take 5 years and then,
You need to multiply by 2 because I want to come
home again, and that makes 10
How do we get 10? Well, if I traveled 4 light-years to Alpha
Centauri at light-speed, it would take 4 years. You can think of it mathematically. 4 light-years/1 light speed= 4years and the light factors
out. If you calculate 4light-years/.8
light speed, you get 5 years. And of
course that is only half the journey, so multiply by 2 and Max thinks that a
round trip to Alpha Centauri will take 10 years.
After 3 years I notice that something has gone
awry,
Because I look out my window and Alpha Centauri
goes zipping by.
I got real mad I said, "My math was bad," I had to
calculate just what I did wrong
I turned around instan(tan)taneously, and headed
back to where I started from.
So, why the inconsistency?
Why does it only take me 3 years to get to Alpha Centauri when Max thinks it
should take 5? Well, it's because a
problem arises when I travel at speeds approaching light speed compared to
Max. I am in a moving reference frame,
while Max is in an inertial reference frame.
Every single object in the universe has its own reference frame, but
they are only inertial reference frames when there is zero force on the object
and it maintains constant speed in a straight line. Light in these reference frames ALWAYS travels at light speed
compared to you. If
you're moving
toward it-if
you're moving away from it.
What ends up changing is the amount of time that passes for you compared
to other observers.
Just
imagine if Max was holding a fire cracker and it went off as I went by, we’d
both agree what time we see the fire cracker as it went off, but if I’m going
really fast, and it explodes after I’ve past, I won’t see it happen ‘til the
light catches up to me.
The property I’ve just
described is called SIMULTANEITY. It
shows that an event that occurs at one time in Max’s reference frame, will
happen at a different time in mine. Lines
of simultaneity can be seen on the diagram in the inner jacket of this CD. Every event that intersects that line appears
to me to happen at the same time, even if it doesn’t for Max. We will both see the event, but not at the
same time. Because I’m moving away from
the event, it takes longer for me to see the light from events that happen in
Max’s reference frame. Therefore,
time passes
slower for me than for him. This is
called TIME DILATION. The formula for this is as follows: the time
that passes for me equals the time that passes for him times the square root of
one minus my velocity squared over the speed of light squared. This is known as the LORENTZ TRANSFORMATION.
And so because I’m
flying at .8 times the speed of light compared to Max, the time inside my
reference frame is passing at a factor of .6.
For a trip that Max would think would take 10 years for me at .8c, I’d
only age 6 years, and he’d age 10.
So, when I get back to earth,
it’s true that I’m now 4 years younger than my twin. Amazing! But why isn’t it
the other way around? Technically, Max
travels away from me at the same speed that I travel away from him, so why
isn’t he younger than me? The reason is
in the reference frames. Max’s frame is
inertial, but mine breaks the rules establishing the definition. I change direction, speed, and therefore
must have some force acting on me.
Trying to do the Twin Paradox backward only results in a confusing mess…
Trust me…
Lying awake, I was thinking just the other night,
What if I was traveling at .8 times the speed of
light,
Well, now we’ve heard the song, and we know just
what goes on,
And since we’ll never
fly that fast, we’ll have to put our trust in these calculations.
However,
the time dilation effect it is minimally noticeable at slower speeds, and has
been experimentally confirmed as well, so it makes sense to believe what I’ve
been talking about.
If you enjoyed this
song, and would like to know more about the Twin Paradox, take a class in
Relativity at Syracuse University, or visit your local library.
IT’S
ALL PHYSICS!!!
Special
Thanks to: Prof. Donald Marolf at Syracuse University, for
letting me do this as my final project in Physics 312. Anna for believing in me. Chris for helping
me record this, and showing me that I can publish my own material when no one
else will. Kevin for helping me explore
the physics of Ping-Pong. Anna again
just because. My family. Casio for use of their beats in the Dance
Remix. Hendrik A. Lorentz for his
formulae. Calculus, which I still can’t
do well. And all them crazy physicists
who have paved the way for the rest of us.
All Music Arranged by Peter Cranson
Produced by Peter Cranson
Recorded at Chris’ Room Studios
Drawings and Cover Art by Peter Cranson
