From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon May 26 2003 - 11:39:36 MDT
Hal wrote
> [mailto:owner-extropians@extropy.org]On Behalf Of Hal Finney
> Sent: Saturday, April 19, 2003 5:36 PM
>
> Lee Corbin writes:
> > I was explaining a typical thought experiment to an
> > acquaintance in order to convey why mass increase
> > occurs.
>
> Actually, in modern treatments of Special Relativity, relativistic mass
> increase is no longer considered to be the best way of understanding
> the phenomena.
I (Lee) had written
> > Okay, so you are approaching a solar system at speed v
> > in your rocket ship, and you see a planet orbiting a
> > star. You are traveling perpendicularly to the plane
> > of the orbit of the planet. So imagine that the planet
> > is orbiting the star like the tip of a minute hand is
> > orbiting the center of a clock on the wall, and you are
> > walking towards the clock straight on.
> >
> > Now because physical processes happen in that solar
> > system in your frame of reference more slowly than they
> > do in the that solar system's frame, you observe that
> > the planet is moving around its star not very fast. In
> > fact, judging from the usual mass of that kind of star,
> > its amazing how slowly that planet is revolving about it.
> >
> > So using some typical formulas, you calculate the mass
> > of the star, and find it to be rather picayune. But
> > hold on! Special relativity predicts that your measurements
> > of the star should make it *more* massive, not less. Paradox!
> Teachers downplay the notion of "relativistic
> mass" because it leads to so many confusing situations like the one
> you describe. Instead, they use the idea of "relativistic momentum"
> which is equal to rest mass, times velocity, times the "gamma" parameter,
> 1/sqrt(1-v^2/c^2). By sticking with momentum and energy, you don't have
> to imagine that mass increases.
Yes, I had seen this more modern treatment in some books.
In fact, they were quick to credit Newton himself with
this insight: Newton emphasized that acceleration is
equal to the change in momentum, F = dp/dt, and it
was only a simplification of the concept (perhaps by
others) that lead to our using F = ma.
> The old way took that same formula, p = v * m * gamma (where m is rest
> mass), and grouped the last two terms to produce the "relativistic mass",
> which went to infinity as v approached c. But as I said that produced a
> lot of confusion. Among the problems would be the question of whether
> a sufficiently fast moving particle would become a black hole when its
> "relativistic mass" got high enough. Basically anything involving
> gravitation causes problems.
Thanks for resolving the paradox! Now indeed I understand
the danger (evidently apparent even to Newton!) of using
mass where momentum is better.
Well, at least I can hope that my "paradox" will be useful
for providing a concrete example of why you (and the more
modern textbooks) are right. Would you consider this hope
to be irrational?
Lee
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