Re: Slabinski and Mingst/Stowe disagree in Pushing Gravity
- From: Paul Stowe <ps@xxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Sat, 23 Apr 2005 16:50:03 GMT
On 22 Apr 2005 05:43:44 -0700, "TC" <tclarke@xxxxxxxxxxx> wrote:
>Paul Stowe wrote:
>> On 21 Apr 2005 07:53:16 -0700, "TC" <tclarke@xxxxxxxxxxx> wrote:
>
> Mingst/Stowe
>
> On page 191, equation (26) has form constant)x(mass)/(radius).
>
> On page 127, equation (19) has form (constant)x(mass) [Slabinksi]
>
>> ... Note however Slabinski's equation is not one of specific
>> heat (watts/m^2), as is ours, but of total heat (watts).
>
> Then if Slabinski is correct, your equation should take the form.
> (constant)x(mass)/(radius^2)
Fine, point to the specific step in the following that is either,
- mathematically wrong, or,
- logically inconsistent
We start will conservation and say, at equilibrium,
q_in = q_out
Where q is the power flux per unit area of the graviton field. Note
that q is the current, not omni-directional flux. For ease of
notation we'll set q_in = q & q_out = q'... Then for an attenuating
mass we say,
-ß -ß
q = q' = qe + q(1 - e )
The ß term is the total attenuation parameter. Clearly, if ß -> 0
then we have,
q' = q + (q - q) = q
And, if ß -> oo then,
q' = 0 + (q - 0) = q
In he first case, nothing interacts, in the second, all interacts &
is ultimately re-emitted as a secondary flux. Either way, in
equilibrium is strictly maintained!
Thus, the 'delta' or interacting component of q is (q''),
-ß
q'' = q(1 - e )
Therefore, when ß << unity the Taylor series shows us that this
can be quantified (to a very high precision) by simply writing
q'' = qß
The ß term is an expression of the departure from equilibrium of
the graviton fluence. This can be found on page 190 Eq(22) and
is given as 2GM/rc^2. Now follow this through
q'' = q(2GM/rc^2)
Regrouping this we get,
q'' = (q2G/c^2)M/r
Finally, we know that within LeSage's model,
G = ¿µ^2
and
q = ¿c/4pi
Thus,
(q2G/c^2) => ([¿µ]^2/[2pi]c) => k
q'' = kM/r
Now, to Slabinski version. ...
In our analysis above we've taken a 'big picture' or macroscopic
continuum approach to the issue. In Slabinki's work he take the
microscopic or kinetic theory type approach. You could say ours
was a top down and Slabinki's a bottom up analysis. We must also
quantify Slabinki's terms and map them to their counterparts in
our approach. Slabinki defines,
N = graviton particle density (particles per unit volume)
A = test area (length squared)
A' = absorption cross-sectional area for the smallest possible
interacting material particle... (length squared)
A''= scattering cross-sectional area for the smallest possible
interacting material particle... (length squared)
ç = Solid angle sutended by A (Radians)
K = mass absorption coefficient (length squared per unit mass)
K' = mass scattering coefficient (length squared per unit mass)
m = m, m' test particles of gravitating mass
r = distance of A from m
R = Rates (R, R', R'') net, direct, scatter
£ = net decrease in graviton flux density
c = graviton mean speed
w = graviton mass
Mapping into our version.
¿ = Nwc^2
µ = Sqrt[K(K + K'[1 - Cos æ])]
Thus mapping Slabinki's Eq 19 we get,
H = (¿2piKc)m
Dimensionally this is,
kg | m^2 | kg | m kg-m^2
-------+-----+----+--- => ------
m-sec^2| kg | |sec sec^3
Converting to a per unit area (4piL^2)we get,
(¿Kc/2)m/L^2 => kg/sec^3
Note that Slabinki is evaluating the test area of a single
interacting differential particle of matter. A, A', A''
as well as ç and æ are set by this. HE IS NOT! evaluating
a macroscopic body consisting of multiple test particles.
The 'solid' angles ç and æ are affected by size. However,
for his analysis size doesn't change. Note, area is
proportional to r^2 and density to r^3, a 1/r differential.
Paul Stowe
.
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