Jack Martinelli wrote:
In:
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_spacetime.html
I understand and accept the experimental evidence that shows that the
Twin
Paradox is not a paradox. I understand the Lorentz xforms. I've
done the
derivation myself. But the explanation that John gives seems to
ignore
"inertial" and the view from both frames.
John shows a diagram where Stella travels away from Earth, turns
around and
comes back to Earth where Terence & Stella compare clocks. What he
doesn't
show is the same diagram where Stella is at rest in her frame and the
Earth
leaves and comes back. Why? In Stella's frame the Earth travels the
same
distance out and back & it's world line is the same distance. If
acceleration is the key to understanding it, I'm not getting it. I
understand the asymmetry, but how is this key?
The army of clocks doesn't help either since Stella can carry just as
many
if not more. Clocks don't vote anyway.
E.g., Terence has one clock & Stella has 10^100 Clocks. Why would
Stella's
clocks not be the ones who age more than Terence's.
It has to do with what the clocks are trying to tell you. A clock is
simply a book keeping mechanism of the "present time". In relativity,
an observers "present time" is the set of simultaneous events relative
to that observer. This set forms a (3d) plane in Minkowski space-time.
Here is Baez's space-time diagram:
|\
| \
T | \ Stella in leg 2
o | \
r | \
r | | <--- acceleration
e | /
n | /
c | /
e | /
|/ Stella in leg 1
During the first leg, Stella's simultaneity plane sweeps through
torrence's worldline at a constant angle as follows. (Excuse the ascii
art).
|\
| \
T | \
o | \
r | \
r | | <--- acceleration
e | /
n | _--/ <--- Stella's simultaneity plane here sloping down.
c |_-- /
e | /
|/
During the second leg, Stella's simultaneity plane has a different
angle.
|\
| \
T |-__ \
o | -__\ <--- Stella's simultaneity plane sloping up
r | \
r | | <--- acceleration
e | /
n | /
c | /
e | /
|/
So as you see, when stella arrives to meet Torrence at the end of the
second leg, Torrence will have aged relative to stella. How did this
happen since according to SR both were moving away relative to each
other?
The answer lies within the acceleration phase. Since stella
accelerated, she switched reference frames. Mathemetically this U-turn
rotates stella's simultaneity plane such that it sweeps through
Torrences time-line at a rather large rate. In essence the Twin
Paradox can never actually materialize as in order for Torrence and
Stella to compare themselves, at least one observer needs to switch
reference frames. It is the switching which resolves the paradox.
Regards,
Jack Martinelli
http://www.martinelli.org
.
