From: metares@well.sf.ca.us (Tom Van Flandern)
Subject: Re: Standard model of QSOsex
Organization: Whole Earth 'Lectronic Link
Distribution: sci
Date: Mon, 31 Aug 1992 00:59:36 GMT


[m(i), m(p), m(a) are inertial, passive gravitational, and active
gravitational masses of a body, respectively]

Earlier, I wrote:

>>>>      m(i) A = G m(p) M(a) / r^2,

>> In the Meta Model, m(i) = m(p) > m(a).  But the difference is usually too
>> small to be detectible

and mock@space.mit.edu (Patrick C. Mock) replied:

> Since the [2-body] systems is isolated:  F(total) = 0
>   _          __   __                                                 __
> { F(total) = F1 + F2  =  0 } ->  F1 = F2     (F1 is the magnitude of F1)
>
> [stuff deleted]  If the ratio varies, then F(total) is not zero and energy
> is not conserved in the Meta Model!

     In ordinary dynamics, all three mass types are considered equal, so a
lot of laws simplify.  It is safe to assume that m(i) = m(p) in all dynamics,
whether Newtonian or GR.  But in contexts where m(a) is not equal to m(i),
some of the familiar laws change.  One must be very careful before assuming a
familiar equation is still true.

     In particular, when m(a) = m(i) is not true, then "forces" which are
formed from the product of m(i) and acceleration are not equal to forces
formed from the product of m(a) and acceleration.  Of course, in a
terrestrial context, forces are always formed using m(i).  But when m(i) is
not equal to m(a), your F1 is NOT equal to F2, action is NOT equal and
opposite to reaction, and the system experiences what is called a "self
force".

     I don't recall who invented this "self-force" concept, but you can read
about it in a Newtonian context in Bartlett and Van Buren, "Equivalence of
active and passive gravitational mass using the Moon", Phys. Rev. Lett. 57,
21-24 (1986); and in a PPN context in Clifford Will's latest paper, "Is
momentum conserved?  A test in the binary system PSR 1913+16", ApJ 393, L59-
L61 (1992).

     The bottom line is that, in contexts where m(i) is unequal to m(a),
normally conserved quantities such as energy or momentum which are computed
using m(i) are no longer conserved; but if they are computed using m(a), they
are still conserved.  There is a simple explanation: if m(i) differs from
m(a), then there are two different centers of mass in the system: an inertial
and an active gravitational center of mass.  The inertial center of mass
orbits the gravitational one, while only the latter remains "inertial"
(meaning unmoving in an inertial frame).

     If all kinematics are done using active gravitational masses only, the
system has normal dynamical behavior.  The "inertial center of mass" behaves
just like an offset center of figure, and introduces primarily a libration
into the rotation of the body, with very small orbital consequences, and no
acceleration of the gravitational center of mass.  The "self-force" simply
causes the inertial center of mass to orbit around the gravitational one.

     If you apply the laws in any other way, you get unphysical accelerations
and chaos.  Examples of that are amply shown in the two papers cited.

     As this applies to the Meta Model, it means that the relationship
between m(a) and m(i) is not tightly constrained by existing experimental
results.  There is still room for a "shielding" effect.  Whenever a dense-
enough massive body comes between two others, the effect of the mass of the
outside bodies will not be able to fully pass through the shielding body and
accelerate the other outside body by a normal amount.  We will soon have the
capability to test for such an effect experimentally.

     If you wish to explore this matter further, please hold your reply until
I return in two weeks.  -|Tom|-

-- 
Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
Meta Research was founded to foster research into ideas not otherwise
supported because they conflict with mainstream theories in Astronomy.