law...@ludwig.llnl.gov (William S. Lawson) wrote:
>In article <4ofrl9$
...@news.umsl.edu>, ph
...@newton.umsl.edu (Phil Fraundorf) writes:
>|> I am hence
>|> curious what these record speeds are in units
>|> of "traveler velocity", or lightyears per
>|> TRAVELER year where distance is measured in
>|> context of our more or less inertial rest frame.
>|> This traveler velocity u is of course nothing
>|> more than the spatial 4-velocity or g*w, where
>|> g=gamma=E/mc^2=1/Sqrt[1-(w/c)^2]. In terms of
>|> particle energy, u = Sqrt[g^2-1].
>From that last formula, it should be clear that the gamma factor is
>a perfectly good way of expressing what you want at high energy. The
>record is probably from one of the large electron synchrotrons.
That's a good guess for particles accelerated by us. A similarly
titled thread in sci.physics.particle/.accelerators has more
specifics on this. The traveler velocity concept itself,
i.e. dx/dT in lightyears per traveler year, is one in practice that
students seem able to pick up on quickly, well before (if ever)
they are ready to deal with multiple inertial frames and Lorentz
transforms.
As you know, folks have used this quantity
for a long time without giving it a name (it actually
has much better transformation properties than inertial
coordinate velocity since it is the spatial component
of the 4-vector velocity), but they have not (as far
as we can tell) ever really considered its definition
as a non-coordinate velocity in the context of a single
inertial frame. In addition to its nice transformation
properties, multiply by rest mass and it tells your
physical intuition what the particle's relativistic
momentum is!
>|> By way of example, for the electrons in our 300 kV
>|> Philips EM430ST transmission electron microscope,
>|> g = (300+511)/511 = 1.587, so that u = 1.232 lightyear
>|> per traveler year (or "roddenberries").
>I am a Roddenberry fan myself, but this ain't gonna fly.
Calling it lightyears per traveler year works fine.
Of course, when you start solving practical problems
an abbreviation other than c is helpful to avoid
confusion when comparing coordinate and traveler forms
of the same velocity. Try saying 1[rb]=0.707[c]
the long way, & you'll see what I mean.
I think relativists may prefer to come up with an
official and abiding name for [ly/tyr], e.g. like
[Wheelers] given that the Taylor/Wheeler book
Spacetime physics is one of the few I've seen with
the chutzpah to experiment with new ways to cast the
old equations for educational purposes.
For the moment, present day students seem to like [rb].
I suspect its mnemonic value stems from the connection in
our language between the concept of high speed and
the word "hotrod", because "berries" are well-defined
little packages and this provides a well-defined
value near light speed to really mark the transition
between relativistic and non-relativistic regimes, and
because it reminds them of the Star Trek series which,
like traveler velocity, ignores the lightspeed limit
to which inertial velocity is held.
The goal is certainly not to endorse Star Trek's
lack of awareness of the nature of (3+1)D spacetime!
Perhaps by using this "frame dependent" approach to
defining different times, awareness of these
things can become more widespread even in
secondary schools, so that future creative
fiction will more often reflect the
differences in the clock behavior of inertial
and accelerated observers.
Find more on "pre-transform" applications for
traveler velocity in the "frame-dependent relativity"
stuff at <http://www.umsl.edu/~fraundor/a1toc.html>.
Cheers! /philf :)
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//P.Fraundorf Phys&Astr/CME 3145165044 ph...@newton.umsl.edu
\\U.Missouri-St.Louis MO 63121 http://www.umsl.edu/~fraundor
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