| MadSci Network: Physics |
Hi Jesse,
That's a good follow up question. I gotta say that this paradox is incredibly confusing to me, and any answers I give you are going to be so oversimplified, they might be considered wrong. There's the short answer, and the simple answer. No long answer this time.
The short answer is that there is a solution to the near lightspeed twin paradox, and involves three frames of reference and accounts for periods of acceleration. It can be read here. I'll admit that I don't entirely understand it, but it sounds credible.
The simple (yeah, right) answer is that for a trip at light speed, the
outside observer will see the trip take the full length of time. (at
almost light speed, a 8 light year round trip will take 8 years.)
However, the outside observer will see the clock on the ship running
slower than the observer's clock.
The passenger (travelling near the speed of light) will see their clock
run normally, but the distance to the destination will shrink, and they
will reach their destination faster than they planned. Rather than the 4
light year distance, the passenger will measure the distance shorter and
shorter the faster he/she is going. So in theory, when the person is
travelling at 100% light speed, the nose of the ship will be at the
destination, and the tail of the ship will be at the liftoff. This is
wacky, because an external observer will see the ship shorten in length.
This is another
paradox that makes my brain hurt.
The bottom line is that if you are travelling at light speed, you are
actually in every point along your path at once. So you're travelling
zero distance, but you're doing it in zero time. (The math takes a
vacation at this point because you're dividing by zero.)
Hope this helps!
Jeff Yap
Mad Scientist
Links:
Twin Paradox
More Twin
Paradox
Time Dilation/Length
Contraction
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