On 1/2/2014 8:00 PM, LizR wrote:
On 3 January 2014 15:52, Jason Resch <jasonre...@gmail.com <mailto:jasonre...@gmail.com>> wrote:


    On Thu, Jan 2, 2014 at 9:31 PM, LizR <lizj...@gmail.com 
<mailto:lizj...@gmail.com>>
    wrote:

        Jason,

        You may be missing the fact that the acceleration of the space 
traveller is what
        causes the twin paradox.


    I would say it is not so much the acceleration that explains the paradox, 
but the
    fact that no matter how you rotate the paths, you always see a kink in the 
path Pam
    takes.


May I venture to suggest this is the same thing :-)

That's not exactly wrong - but it tends to make it confusing. It's like saying a road from A to B is longer than as-the-crow-flies because of its curves. Yeah, that's true; but if you want to calculate how much longer you see that the rate of excess distance is proportional to the first integral of the curvature and so the total excess is the second integral of the curvature - which is just the distance. So it boils down to unstraight lines are longer than straight lines. All the specific details of acceleration get integrated out so it's easy to see that a broken line (infinite accelerations) is just longer. Or in spacetime, unstraight worldlines are shorter than straight ones. To phrase it in terms of acceleration misleads people into thinking about the stressful effects of acceleration and how that could affect a clock,...

Brent

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