Re: The Twin Paradox

From: Franz Heymann (notfranz.heymann_at_btopenworld.com)
Date: 03/01/05 

Date: Tue, 1 Mar 2005 20:45:52 +0000 (UTC)

"The Ghost In The Machine" <ewill@sirius.athghost7038suus.net> wrote
in message news:usfef2-hnn.ln1@sirius.athghost7038suus.net...
> In sci.physics, sthfrnth
> <sthfrnth@gmail.com>
> wrote
> on 28 Feb 2005 07:36:39 -0800
> <1109604999.721516.138140@z14g2000cwz.googlegroups.com>:
> > A pair of twins, Adam and Eve, are thinking of what will happen
to
> > their ages if one of them will go away from Earth on a space
journey.
> > Will Eve for example be younger, older, or have the same age as
her
> > brother if she leaves Earth with a space-ship and then returns
after
> > some time?
>
> Depends on Eve's acceleration. Near as I can figure, if Eve
> experiences 1g acceleration [*] (after liftoff) for the entire trip,
> she'll age at the same rate as Adam, who stays on the Earth and
> experiences 1g acceleration thereon. However, I've yet to do
> detailed calculations -- note that at 1g acceleration, the time
> to accelerate to lightspeed (assuming Newtonian math, which isn't
> right) is close to a year; 365.2425 * 86400 = 3.1557 * 10^7 sec,
> c = 2.99792458 * 10^8 m/s, and g = 9.805 N/kg or m/s/s.
>
> Adam might experience some confusion as he'll *not* see 1g
> acceleration on Eve's spacecraft, after a time, as Adam sees
> Eve's time slow down and lengths shrink.
>
> The usual formulation of the Twin Paradox involves squishing Eve
> into meat jam first -- which would render the point more
> or less moot, as no one is all that concerned regarding the
> age of meat jam. :-) However, were Adam and Eve something along
> the lines of, say, pi mesons, one gets very interesting results,
> and such results are readily shown in the lab, AIUI.
>
> [rest snipped]
>
> [*] note that the acceleration vector will change direction at least
> twice during the trip.

It is possible to perform a thought experiment which demonstrates the
twins story without any accelerations. All that is required is one
world line corresponding to a stationary object and a series (2 are
enough) of world lines corresponding to motions at constant speed,
plus a good pair of lungs so that one traveller can shout the time of
day to another one en passant. As long as these two intersect each
other, and each of them also intersects the world line of the
stationary object, the proper time intervals can be compared to show
that the moving clocks ticked slower than the stationary clock. 

-- 
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley

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