Re: Androcles and Draper resume Einstein 1905

From: Timo Nieminen (uqtniemi_at_mailbox.uq.edu.au)
Date: 01/15/05 

Date: Sun, 16 Jan 2005 07:29:22 +1000

On Sat, 15 Jan 2005, PD wrote:

> Timo Nieminen wrote:
> > On Fri, 14 Jan 2005, Androcles wrote:
> > > "Gregory L. Hansen" <glhansen@steel.ucs.indiana.edu> wrote:
> >
> > > > If I may *** in, I think Draper's point was that when K watches
> k
> > > > measure
> > > > the length, he won't agree that it was a measurement of the
> length!
> > > > And
> > > > vice versa. So when k gives K a measured length, K will say
> "Your
> > > > number
> > > > is smaller than mine, but I don't know what the hell it is. I
> watched
> > > > you
> > > > do it, and that's not how to measure a length."
> > > >
> > > That's fine, but k is carrying out an illegitimate procedure. I
> had
> > > previously
> > > agreed with Paul that the measurement can only be carried out when
> > > the rod to be measured and the measuring rod were relatively at
> rest.
> > > Observer K will not agree with observer k's guesstimate,
> > > as you point out, but observer k himself will be uncertain.
> >
> > So, then you have agreed that only what is called in SR the "proper
> > length" is to be accepted as the length of an object.
> >
> > The proper length being invariant in SR (and Galilean relativity as
> well),
> > the answer follows trivially that observers k and K agree that the
> proper
> > length of the rod is the same.
>
> Though this is the way it is commonly taught, I find this distasteful
> because it leads away from the main point: that length is defined by a
> procedure and is not an inherent property of an object. Or, said more
> generally, the distance between two events is not an inherent property
> of those two events.
[cut]
> "Proper length", to me anyway, has the same pedagogical risk as "rest
> mass". "Proper length" gives the impression that there's really only
> one frame where length can be measured and that length is poorly
> defined in other frames. That's not the case. It's semantics, I know,
> but it seems important somehow.

Well, I wouldn't define the "proper length" to be the "length of an object
as measured in reference frame X". Androcles stated this was the
definition agreed on by the two of you.

Much better to simply define length as the distance between the positions
of the two ends of the object, when those two positions are measured
simultaneously. That's just what Gregory said, and so I'll answer your
reply to his comment here.

No inertial frame is better than any other for determing when those
measurements need to be made in order to be simultaneous. That's basically
why, in general, different lengths will be measured in different inertial
reference frames.

I think one also should be careful with the term "observer". Is it used to
mean an observer, or is it used to mean "inertial reference frame"? Since
an inertial reference frame is not at all the same thing that is meant by
observer in common English usage, and since "frame" (or even IRF if you
prefer) work well as short versions of inertial reference frame, why use
"observer" unless an actual "observer" is intended? 

-- 
Timo
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