Natural Science Forum / Physics / Research / February 2005

There are two key points about the twin paradox. The first point is
that when Alice turns around she knows the moment that she turns and
all incoming data changes at this instant. Bob cannot detect that a
turn has occurred until x/v seconds later. The situation is highly
ASYMMETRIC. It is not a symmetrical problem such as would occur if both
Bob and Alice turned at a prearranged moment.

The second point is to understand that the twin paradox lies in the
relativity of simultaneity rather than simply in the time dilation
effect. When Alice travels away from Bob she finds that clocks that had
been synchronised along Bob's x-axis are no longer synchronised.  The
amount by which they are out of sync is called 'phase'.  The 'phase',
or amount by which clocks differ gets bigger the further Alice travels.
Phase is given by (vx)/c^2.

Phase means that if we try to represent Bob and Alice's time and space
coordinates on the same diagram it will appear as if, from Bob's point
of view,  Alice's x-axis slopes upwards in time compared with Bob's,
the slope being v/c^2.  From Alice's point of view Bob's x-axis also
slopes upwards. But what happens at the asymmetric turn around? The
moment that the turn occurs Alice notes that Bob's x-axis swings wildy
to the opposite slope. However, because of the asymmetry, Bob notices
the wild swing in x-axes x/v seconds after the event occurs in his time
frame. A graphical explanation is shown at:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#gap

A more detailed view is given at:

http://www.users.globalnet.co.uk/~lka/Image18.gif

and a detailed explanation at:
http://www.users.globalnet.co.uk/~lka/conz2b.htm

Getting back to your example of Pluto, Earth and 'the guy'.  If Pluto
was travelling towards earth at 50 m/s and 'the guy' was moving away at
50 m/s you can see that because none of them turn around there is no
twin paradox. In the case of an SR approximation to circular motion
where Pluto buzzes past earth in the north-south direction then returns
and 'the guy', at the moment Pluto goes past earth launches off in the
other direction then returns then there should be no time difference
between Pluto and 'the guy' because BOTH Pluto and 'the guy' have made
simultaneous turns with the same change of velocity. Both Pluto and
'the guy' will have clocks that are discrepant from earth clocks by the
same amount (having been synchronised as they passed earth).

Best Wishes

Alex Green

There are two key points about the twin paradox. The first point is
that when Alice turns around she knows the moment that she turns and
all incoming data changes at this instant. Bob cannot detect that a
turn has occurred until x/c seconds later. The situation is highly
ASYMMETRIC. It is not a symmetrical problem such as would occur if both
Bob and Alice turned at a prearranged moment.

The second point is to understand that the twin paradox lies in the
relativity of simultaneity rather than simply in the time dilation
effect. When Alice travels away from Bob she finds that clocks that had
been synchronised along Bob's x-axis are no longer synchronised.  The
amount by which they are out of sync is called 'phase'.  The 'phase',
or amount by which clocks differ gets bigger the further Alice travels.
Phase is given by (vx)/c^2.

Phase means that if we try to represent Bob and Alice's time and space
coordinates on the same diagram it will appear as if, from Bob's point
of view,  Alice's x-axis slopes upwards in time compared with Bob's,
the slope being v/c^2.  From Alice's point of view Bob's x-axis also
slopes upwards. But what happens at the asymmetric turn around? The
moment that the turn occurs Alice notes that Bob's x-axis swings wildy
to the opposite slope. However, because of the asymmetry, Bob notices
the wild swing in x-axes x/v seconds after the event occurs in his time
frame. A graphical explanation is shown at:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html#gap

A more detailed view is given at:

http://www.users.globalnet.co.uk/~lka/Image18.gif

and a detailed explanation at:
http://www.users.globalnet.co.uk/~lka/conz2b.htm

Getting back to your example of Pluto, Earth and 'the guy'.  If Pluto
was travelling towards earth at 50 m/s and 'the guy' was moving away at
50 m/s you can see that because none of them turn around there is no
twin paradox. In the case of an SR approximation to circular motion
where Pluto buzzes past earth in the north-south direction then returns
and 'the guy', at the moment Pluto goes past earth launches off in the
other direction then returns then there should be no time difference
between Pluto and 'the guy' because BOTH Pluto and 'the guy' have made
simultaneous turns with the same change of velocity. Both Pluto and
'the guy' will have clocks that are discrepant from earth clocks by the
same amount (having been synchronised as they passed earth).

Best Wishes

Alex Green

No.
You appear to have forgoten the surface sped of the earth.