Length is not an instrinsic property of an object.
I've seen a number of threads where posters have difficulty with a
basic concept having to do with length. What I hope to do here is to
move the point of discussion from length to simultaneity, where it
belongs.
Length is defined by an agreed-on procedure. It is not an innate
property of an object.
For an object at rest in the measurer's frame, it's easy.
1. Place a precalibrated ruler alongside the object.
2. Take note of the calibrated mark at one end of the object.
3. Take note of the calibrated mark at the other end of the object.
For an object moving in the measurer's frame, though, it's a bit more
tricky.
1. Hold up a precalibrated ruler parallel to the object's motion.
2. At a certain time mark, t0, take note of the calibrated mark at one
end of the object.
3. At the VERY SAME time mark, t0, take note of the calibrated mark at
the other end of the object. Why is this last step so important? A
moment's thinking will tell you that if there is a delay between 2 and
3, the object will have moved, sliding along its path. Depending on
which direction the object is going, you will end up with a number
that is either longer or shorter than the object's length measured if
it were at rest. So SIMULTANEITY is key to the definition of length of
an object, especially in a frame where the object is moving with
respect to the measurer.
There is no other workable definition of length other than this
operational one.
Ah, there's the rub...
For once we agree that simultaneity is crucial to the DEFINITION of
length, then the real issue is that simultaneity is not something that
two measurers moving with respect to each other will agree on. The
"relativity" of length is directly attributable to the "relativity" of
simultaneity.
Now, if folks want to talk about why simultaneity is not an inherent
property of two events...
PD
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