On 3 January 2014 17:30, meekerdb <meeke...@verizon.net> wrote:
> On 1/2/2014 8:00 PM, LizR wrote:
>
> On 3 January 2014 15:52, Jason Resch <jasonre...@gmail.com> wrote:
>
>> On Thu, Jan 2, 2014 at 9:31 PM, LizR <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,...
>
> I bow to your superior knowledge. I wasn't thinking about the aging
effects of acceleration (as in the Heinlein story where they have to fly to
Pluto at 3G) but just the fact that the course changes are the only way the
twin paradox can be enacted - that is to say, it's what breaks the symmetry
that otherwise exists between one ref frame's measurements and another's.

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