Re: Harald V, suggestions taken

From: Jim Black (ghytrfvbnmju7654_at_mail.com)
Date: 08/13/04

  • Next message: Gerald L. O'Barr: "Re: Do Virtual Photons Exist?" 
    Date: 12 Aug 2004 20:36:47 -0700

    "Ken and Vicki" <kavs_delethis_@sysmatrix.net> wrote in message news:<GPqdnbXjQJWzO4rcRVn-tQ@sysmatrix.net>...
    > Wow! I THANK you for that meaty flavorful discourse ..definitely a keeper!
    >
    > Right -- and one would HAVE to know the masses in order to map the 4-vector
    > potential gradients about. I see how this gets thorny in a hurry.

    There are some issues with the terminology there, and then some that
    aren't just terminology. A four-vector is defined as something that
    obeys certain transformation laws; it has an existence independent of
    the coordinate system. What we have been calling the "potential" is
    an artifact of the coordinate system. It is not meaningful to speak
    of time dilation without a notion of simultaneity, which in this case
    has been defined by the coordinate system; two events with the same
    "t" coordinate could be called simultaneous. The "potential" thus
    depends on the coordinate system, and isn't technically a scalar. It
    is part of a component of the metric tensor. The derivatives of the
    metric that one might call "pseudoforces" aren't even components of
    any tensor, but of something called the "affine connection."

    The thing one usually thinks of as "real" in general relativity is the
    derivatives of the "pseudoforces" -- the differences in apparent
    acceleration between separated objects. Roughly, this is what
    space-time curvature is.

    The other, probably more meaningful issue with that is that the
    gradients of the "potential" being taken in that treatment weren't
    four-dimensional; time was left out. The approximation I was using
    back there, by assuming that c could be treated as very large, treats
    time on a different footing from space. At small velocities, the
    derivatives of what we've been calling the "potential" with respect to
    time won't cause significant forces on objects. At large velocities,
    the whole approximation breaks down.

    > In the ultra-limited case of two known-to-be equal masses in extreme
    > elliptical orbit about one another, and no other complications, could not
    > the trajectory viewed from either platform provide a good 1st order
    > approximation from which one could derive the needed g-potential differences
    > (per moment, and then integrate that) ?
    >
    > -KS

    Well, assuming the masses are the same, and velocities are small, and
    the objects are small or almost spherical, it ought to be easy to
    infer the approximate (usually a quite excellent approximation) for
    the mass from the trajectory of the objects through Newtonian
    mechanics. Given a few more objects and some reasonable assumptions,
    you should be able to calculate both masses, even if they're not
    equal. Is that what you're asking?

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