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*To*: "'Steve VanDevender'" <stevev@efn.org>*Subject*: RE: starship-design: Relativity*From*: "L. Parker" <lparker@cacaphony.net>*Date*: Wed, 12 Jan 2000 06:37:50 -0600*Cc*: <starship-design@lists.uoregon.edu>*Importance*: Normal*In-Reply-To*: <14460.118.410985.569402@tzadkiel.efn.org>*Reply-To*: "L. Parker" <lparker@cacaphony.net>*Sender*: owner-starship-design@lists.uoregon.edu

> 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

**References**:**RE: starship-design: Relativity***From:*Steve VanDevender <stevev@efn.org>

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