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RE: starship-design: Relativity
> L. Parker writes:
> > I was in Chapter 5, specifically, Figure 5-8. It seems
> illogical that the
> > worldline indicated could approach zero, but that does
> seem to be what is
> > represented.
> > Lee
> It's not so much that the interval along the curved worldline
> zero; it's that the curved worldline has _less_ interval than the
> straight one, or that a clock carried along the curved worldline
> experiences less time than a clock carried along the straight
> one, even
> though both start and end with the same events. Curved worldlines
> correspond to paths of objects undergoing acceleration.
I get it, I wasn't thinking of the worldline quite right before.
> In general a more curved worldline has less interval than a
> less curved
> one. So yes, the higher the acceleration and the closer to c the
> object gets during its round trip, the less time it experiences.
But I still had the right idea.
> Mathematically, this counterintuitive result is the consequence of the
> non-Euclidean geometry of spacetime; drawn on a sheet of paper with
> (locally) Euclidean geometry, it's initially hard to get used to the
> idea that the longer line is the shorter interval. Note the equation
> that they show with figure 5-8; it's the basis of doing a
> line integral (if you're familiar with calculus -- otherwise I'm
> probably about to lose you).
No, I still can follow Calculus, just don't ask me to actually do any!
Thanks Steve, more questions later...