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- Xref: sparky sci.math:13100 sci.physics:16411
- Newsgroups: sci.math,sci.physics
- Path: sparky!uunet!zaphod.mps.ohio-state.edu!darwin.sura.net!jvnc.net!nuscc!scip1061
- From: scip1061@nuscc.nus.sg (Marc Paul Jozef)
- Subject: Re: How do you draw a straight line?
- Message-ID: <1992Oct13.141730.16511@nuscc.nus.sg>
- Organization: National University of Singapore
- References: <1992Oct12.220926.19323@galois.mit.edu>
- Date: Tue, 13 Oct 1992 14:17:30 GMT
- Lines: 39
-
- jbaez@riesz.mit.edu (John C. Baez) writes:
- : In article <1992Oct12.083128.29023@nuscc.nus.sg> scip1061@nuscc.nus.sg (Marc Paul Jozef) writes:
- : >jbaez@riesz.mit.edu (John C. Baez) writes:
- : >: In article <1992Oct8.115013.2533@nuscc.nus.sg> scip1061@nuscc.nus.sg (Marc Paul Jozef) writes:
- : >: >
- : >: > The spacetime metric of GR defines geodesics
- : >: >in spacetime. A string or a rod or whatever
- : >: >define world*sheets* in spacetime; `straightness'
- : >: >of a line has nothing to do with geodesics of GR.
- : >:
- : >: While it's true that over time a rod covers a 2-dimensional surface
- : >: in spacetime, the closest thing there is to a straight (spacelike) line
- : >: in GR is a spacelike geodesic.
- :
- : > So what?
- : > The correspondence may be `close', but it can
- : > never be precise (except in static spacetimes
- : > which have a unique timelike Killing-field,
- : > so that there is a unique 3+1 splitting of
- : > spacetime).
- :
- : So what? Close is the best you can do when it comes to trying to
- : find a reasonable notion of straight lines on a curved spacetime.
- : Close is good enough when it comes to the everyday notion of a "straight
- : line", which assumes that line is not too long compared to
- : characteristic length scale of the curvature.
-
-
- As there is no natural mathematical curve corresponding
- to a physical line, the best you can do is to forget
- about the correspondence :-)
- As you say, spaceTIME is curved, but that is trivial:
- the worldcurves of two satelites traversing the same geo-stationary
- orbit in opposite directions cross more than
- once. What does this have to do with spatial curvature?
- (spacetime remains just as curved when you
- have euclidean frames all over the place).
-
-
-