### Re: relativity question related to question id:1102456893.Ph

Date: Tue Feb 8 14:01:28 2005
Posted By: Jeff Yap, Physics Teacher
Area of science: Physics
ID: 1107566562.Ph
Message:

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