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On 05/19/2016 02:52 PM, Donald Polvani asked:
why couldn't
the people at the top carry their clock down the mountain, again find that
it is 20 nanoseconds ahead of the clock at the bottom and so claim that they
had traveled back in time?
====
I believe the time dilation result, but
I'm not sure about the traveling to the future interpretation
That's essentially the right answer. The actual physics is reasonably
easy to understand ... but there are lots of "interpretations" running
around that are completely non-understandable.
Here's a parable:
Starting from Point A, Moe hops into his car and drives away.
Also starting from the same point, at the same time, Joe hops
into his car and drives away. Some time later they meet at
Point B.
Simplicio examines the the odometers on the two cars and finds
that Joe traveled a longer distance. He is upset by this. He
claims there is a definite distance between A and B, and an
odometer measures distance, so the readings should be the same.
He thinks somebody is lying, or one of the odometers is broken.
The problem is that there are two different kinds of distance:
-- A ruler can be used to measure the straight-line distance
between A and B.
-- An odometer however measures the distance along the path
actually traveled, even for non-straight paths. This explains
the discrepancy: Joe traveled a more circuitous route.
The underlying principle of logic here has been known for
thousands of years:
Ask a different question, get a different answer.
"The" distance as measured by a ruler is different from "the"
distance as measured by an odometer.
And by the way, the fact that Moe traveled a shorter distance
does not mean that it is possible to travel a negative distance.
Moe did not travel the longer path and then "undo" some of it.
The point of this parable is simple: Clocks are more like odometers
than like rulers. A clock measures the elapsed time along the path
that was actually taken. This depends on the path, as surely as
distance depends on the path. The clocks in the two cars will
show different elapsed time, depending on the velocities and the
gravitational potentials they encountered along the way.
BTW, the fact that one elapsed time is less than the other does
not mean it is possible to have negative elapsed time.
Bottom line: Clocks are like odometers, not rulers.
Postscript: As has been pointed out a bazillion times, it
really pays to think about such things using the /spacetime/
point of view. To be sure, the fourth dimension is not quite
the same as the other three, but it is a lot more similar than
it is different. A tremendous amount of your intuition about
geometry and trigonometry can be extended into the timelike
direction. For example, the analogy to odometers makes clocks
much less mysterious.
IMHO it is a tremendous pedagogical blunder to tell students
that relativity is weird and paradoxical. It's not. Most of
what relativity has to say is completely reasonable, prosaic,
and familiar.
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