# 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
> approaches
> 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
> non-Euclidean
> 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...

Lee
```