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[Phys-L] Re: "moving clock runs slower" (yes)



Rick Tarara writes:

Excuse me if I bring this back to the level of those of use who introduce
special relativity to our HS, and Gen-Ed (and our other INTRO courses for
that matter) where 4-vectors and different algebras (normal algebra for that
matter) are not going to be useful. I'm back to the twins reunited on
earth--with one much younger than the other. The only conclusion I can
really latch onto here is that the twin who was moving, relative to earth,
had a slow moving clock.

Here is another scenario. I, after studying physics, set off for Alpha
Seti-6, a mere 30 light years away. I know that the speed of light is the
galactic speed limit and I am pretty damn sure that the universe does not
contract and expand (despite appearances) when I move, especially because it
does not do so when I sit still and others move. I arrive at AS-6 with an
hour having passed on my trusty Dick Tracy wrist watch. To be sure, AS-6,
looked to be awfully close to the earth during my flight, BUT I know it is
30 light years distance. How can I come to any conclusion other than my
watch (and my biological clocks) ran very slowly during the trip?

Rick ALMOST answers his own question here. Frankly, it has always
astonished me that people make such a fuss out of how to resolve the
twin "paradox" precisely because, it is SO easy to see why things
work out the way they do using the idea of length contraction.

Both twins determine the time for the trip by dividing the distance
traveled by the relative velocity. Since the stay at home twin
determines that it is "really" a larger distance, he finds that the
trip "really" takes longer. Q.E.D.
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