Re: Androcles and Draper resume Einstein 1905

From: PD (pdraper_at_yahoo.com)
Date: 01/15/05 

Date: 15 Jan 2005 04:50:28 -0800

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.

What everyone can agree on is the spacetime interval, and that's what
has physical meaning. For spacelike-separated events, there is a frame
where the distance between these events happens to equal the interval,
and that distance is what some folks call the "proper length". Said
more colloquially and relevantly to the current case, there is a frame
where the measured length of the rod happens to equal the interval, and
that's what's sometimes called the "proper length".

"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.

PD