Re: Continue: Travel Twin
- From: "JanPB" <filmart@xxxxxxxxx>
- Date: 23 Feb 2006 19:05:50 -0800
jacksuyu@xxxxxxxxx wrote:
right, I understand they will have different feeling about the
acceleration.
But I still can't understand how acceleration works in aging?
It doesn't "cause" aging. Acceleration merely makes it possible for a
trajectory with differing accumulated proper time to _rejoin_ the other
(inertial) path again.
Note that the observed mutual clock rates are coordinate-based
quantities and as such have no absolute meaning. Only elapsed proper
times have absolute (coordinate independent) meaning.
The standard analogy: two cars going from A to B, one of the cars takes
a longer route through C, like this (use fixed font):
A
| \
| \
| \
| \
| \
| \
| C
| /
| /
| /
| /
| /
| /
B
They both drive at the same speed.
The driver going from A to B sticks out his left hand through the
window at the right angle and notices the car going from A to C is
lagging behind his index finger.
The opposite is also true for the AC-portion: if the driver going from
A to C sticks out his right hand at right angles he'll see the A-to-B
car lagging behind his index finger.
A "mutual distance contraction". Notice it's a coordinate phenomenon,
just like with mutual time dialtion and the twins.
As the second driver makes the turn at C he notices that the A-to-B car
suddenly "jumped" ahead of him - the other driver seemed to have
accelerated briefly to reposition himself _ahead_ of his index finger.
Again, this is a coordinate phenomenon, just like the "sudden aging" of
the home twin. Nothing physically happens at that moment to the A-to-B
car or the home twin.
What's not coordinate-dependent is the total distance travelled (which
corresponds to the total elapsed times) as shown by the two odometers
(which corresponds to the twins' clocks). The A-C-B car accumulated
more miles than the A-B car. The structure of 3D space in which we live
is such that it allows this. We call this "Euclidean geometry".
So I guess your question is really: "what exactly is the mechanism
behind space and time that trajectories of objects are allowed to
accumulate proper time according to Minkowskian geometry?" The answer
is not known besides the usual "that's what the structure of spacetime
is". So what would be needed is some theory more fundamental than SR
which would imply this spacetime structure. But do we really have such
"more fundamental" theory that would explain even the Euclidean
structure of *space* which alone is responsible for A-B/A-C-B
configuration? Do we even hear any complaints on this newsgroup about
some "inexplicable" reasons for the "Euclidean-ness" of space? [I'm
ignoring all the curved spacetime stuff here for the sake of the
argument.] No, we don't. So the argument then goes: "why are people
getting so upset about the same thing on spacetime"?
This is a huge philosophical can of worms which I won't go into. One
camp says that geometry is enough, the other says geometry is merely
reification for certain measurement procedures and results, etc. etc.
Throw in Plato and Roger Penrose with his "world of ideal objects" and
have fun.
--
Jan Bielawski
.
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