Re: [Phys-l] twin paradox question

[John Denker <jsd@av8n.com>]

On 12/18/2010 06:36 PM, Michael Barr wrote:
> I have always wondered something about the twin paradox.  If one twin is
> moving away from the Earth at high speed time moves slower for him compared
> to his brother.  If the brother on Earth were able to see his brother on the
> fast moving ship everything would appear in slow motion.  Here is my
> question.  If the on the fast moving space ship were to look at the Earth is
> it moving away from him at a very high speed too.  So doesn't everything on
> Earth appear to be moving in slow motion compared to time on the space ship?
>   So, why upon return is the traveling twin young and the twin that stayed on
> Earth old? 

Like all paradoxes, that one comes from misstating the
laws of physics.  The general rule isthat the correctly-
stated laws of physics do not contain paradoxes ... and 
the traveling twins are certainly no exception to this rule.

The usual advice applies:  Draw the spacetime diagram.

As others have pointed out, if you are just worried about
the symmetry of the situation, if one twin goes away and
then comes back, that twin undergoes heavy acceleration
at the turn-around point, while the other twin is
unaccelerated, and this breaks the symmetry in a big way.

Draw the spacetime diagram.

The claim that "moving clocks run slow" is not a good way to 
understand relativity.  A better approach -- the spacetime
approach -- has been available for more than 100 years.

Two twins running around comparing the behavior of two
different clocks is not different in principle from two
twins driving around in cars and comparing the behavior
of two different odometers.  This is diagrammed and 
explained in detail at 
  http://www.av8n.com/physics/odometer.htm

In relativity, there is no such thing as absolute velocity, 
but there is absolute acceleration, and acceleration-at-a-
distance has a big effect.  This is related to the breakdown 
of simultaneity-at-a-distance, which is the part of relativity 
that students are most prone to under-appreciate.  On the
other hand, if/when students learn that relativity is nothing
more -- or less -- than the geometry and trigonometry of
spacetime, then this contribution becomes unforgettable,
because of the close analogy between velocity (e.g. a
rotation in the x/\t plane) and an ordinary spacelike
rotation (e.g. a rotation in the x/\y plane).  This is 
explained and diagrammed at
  http://www.av8n.com/physics/odometer.htm
Additional details can be found at
  http://www.av8n.com/physics/spacetime-trig.pdf

Draw the spacetime diagram already.