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