RE: Relativity Puzzle

From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon May 26 2003 - 11:39:36 MDT

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    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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