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

Paul Draper wrote:
Length is defined by an agreed-on procedure. It is not an innate
property of an object.

You are basically discussing variations on a PUN. You fail to
distinguish between two different meanings of "length":

length(1): the intrinsic length of an object.

length(2): the value some observer measures for the length of
some object.

Mostly you discuss length(2), but occasionally use length(1) and get
confused (as above). Yes, length(2) depends on a specified measurement
procedure, and for the usual procedure to measure the length of a moving
object differently-moving observers can obtain different values for the
length(2) of a given object.

But an object such as a ruler inherently has a length(1), and this is an
intrinsic property of the object.

Note, please, that length(1) is an invariant, whereas length(2) is not.

[Here I use length(2) in the abstract -- the value from any
specific measurement is invariant (as are all measurements).
This is sometimes called a frame-dependent invariant.]

Note that length(1) is often/usually called "proper length", to avoid
this pun. It is defined as the measured value of length(2) performed in
the usual way in the object's instantaneously-comoving inertial frame.


[...]


Tom Roberts

Tom Roberts wrote in message ...
Paul Draper wrote:
Length is defined by an agreed-on procedure. It is not an innate
property of an object.

You are basically discussing variations on a PUN. You fail to
distinguish between two different meanings of "length":

length(1): the intrinsic length of an object.

length(2): the value some observer measures for the length of
some object.

Mostly you discuss length(2), but occasionally use length(1) and get
confused (as above). Yes, length(2) depends on a specified measurement
procedure, and for the usual procedure to measure the length of a moving
object differently-moving observers can obtain different values for the
length(2) of a given object.

But an object such as a ruler inherently has a length(1), and this is an
intrinsic property of the object.

Note, please, that length(1) is an invariant, whereas length(2) is not.

[Here I use length(2) in the abstract -- the value from any
specific measurement is invariant (as are all measurements).
This is sometimes called a frame-dependent invariant.]

Note that length(1) is often/usually called "proper length", to avoid
this pun. It is defined as the measured value of length(2) performed in
the usual way in the object's instantaneously-comoving inertial frame.


[...]


Tom Roberts

I'm not sure I wholly agree with the pedagogical value of this
approach. Even in my "interpretation", length(1) is an artifact of it
being at rest in the measurer's frame. I think it's very important to
get across to folks that the length of an object is a procedural
result that HAPPENS to be maximum when the object is at rest with
respect to the measurer. Or said just slightly differently, ...that
happens to be equal to the invariant interval when the object is at
rest with respect to the measurer. Or still differently yet, ... that
happens to be equal to the proper length when the object is at rest
with respect to the measurer.

The problem with the term "proper length" is that it conveys that the
definition of length is different or more substantial somehow or more
"proper" when the object is at rest, compared to when it is moving.
The same would be true if we said the x-component of a 3-vector became
more "proper" if the vector had no y or z components. Saying such
confuses people and gives them the impression that something dramatic
has happened when the vector moves off-axis or we rotate the reference
frame. Do you see what I mean?

PD