Natural Science Forum / Physics / Relativity / January 2005

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Part I: Historical Introduction (approx. first
1/4 of page)

This portion of "Shadows" contains a decent historical account of some of
the early discussions of gravitational physics.  The presentation is marred
by an unfortunate editorial bent.  "Shadows" seems to attempt to tar the
very idea of a physical cause of gravity with an occult or philosophical
brush (which is applied liberally at the end of the "Shadows" page).
Indeed, aside from a brief mention of the original paper citation, "Shadows"
does not discuss the history of Le Sage's theory at all! The revival of Le
Sagian gravitation by Lord Kelvin (and other leading physicists) in the 1870
's is completely bypassed.

I found only two significant errors of commission in this section.

The first is the claim that Le Sage's theory was based on ". some kind of
radiation streaming uniformly in all directions, ."  Radiation-based
theories are light-pressure theories.  This distortion is used throughout
"Shadows" - wherever Le Sage would use a physical gas of particles,
"Shadows" discusses a "radiation field."  Radiation is something that is
emitted from a matter source.  And that is the inverse of the Le Sage model.
(See also modification Note 1, in changes post.)

The second is the claim (in the last paragraph of this section) that;
"Gradually the idea of force at a distance as a primary attribute of matter
became the dominant paradigm of physics ...".  This claim is made without
any reference.  And such a viewpoint never dominated natural philosophy.
Action at a distance was considered anathema to the materialistic paradigm
of the times.  Such a view never dominated the scientific community.

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Part II: Introduction of the Physics of the Le
Sagian mechanism. (Paragraph beginning "Since the apparent size of an
object...")

"Shadows" does not even address Le Sage's model, but presents a completely
different model (Darwin's) as if it were Le Sage's.  The first paragraph is
apparently a very bad (and distorted) summary of two paragraphs from
Roseveare (page 111).  Here is the original from Roseveare:

"A novel objection to Le Sage's theory appeared in 1897 (Farr 1897).  The
theory required that absorption of gravific particles was very small, ...
because beyond a certain bulk ... attraction would become mass independent.
Farr objected that owing to a result of Nernst the molecules of liquids at
their boiling points and at atmospheric pressure occupied about 0.3 of the
total volume, a proportion so great that an unacceptable amount of screening
would occur.  This seems a strong objection so long as molecules are taken
as solid and opaque to gravific particles."

"Darwin (1905)* gave a mathematical treatment of Le Sage's theory.  He
obtained expressions for the forces due to both normal and tangential
components of the impacts ... k and k' are elasticity factors, (k' is for
the tangential component) such that k = 1 for perfectly inelastic corpuscles
and k = 2 for perfectly elastic corpuscles. This is not a rigorous inverse
square law but it may be made so if one puts k = k'. For the general law
action and reaction are not equal ... but this could be avoided if these
spheres are taken as elementary particles of matter and if all such
elementary particles of matter are of equal size. ..."

*"The analogy between Le Sage's theory of gravitation and the repulsion of
light." proc. R. Soc A 76, 387-410, 1905.

"Shadows" begins as follows:

"Since the apparent size of an object at a distance r drops in proportion to
1/r2, it's clear that fraction of the incoming radiation blocked by a given
opaque object"

Le Sage never postulated an opaque object.  This description is about
Darwin's theory.

"at a given point is also proportional to 1/r2, so we immediately get (for
spherical objects) an isotropic force that varies at least approximately as
the inverse square of the distance."

At this point, the 1/r^2 law is also true of non-spherical objects.  At
best, "Shadows" is confused because of the assumption of spherical matter
object that is made in Darwin's theory.

"However, just as immediately, we can perceive some problems with this idea.
First, in order to give a force that is proportional to mass rather than to
the size of an object, we need to posit that macroscopic bodies are almost
perfectly transparent to the ultra-mundane particles, so only a tiny
fraction of the particles passing through an object are actually
intercepted."

Since such fractional absorption is the theory of Le Sage, this is not a
problem at all for Le Sagian theory.

"This enables us to say the force is proportional to the number of particles
in a body rather than to the size of the body,"

Le Sage's mechanism is not related to the number of "particles" in a body,
but to the mass of the body.

"and it also avoids the saturation problem."

This phrase is the key that confirms "Shadows" is relying on a distorted
rendition of Roseveare's text. "Shadows" does not provide any mention of a
saturation problem at any other point . but Roseveare did.  And it did so in
just the same relation to the rest of the narrative.

(Also see Modification Note 2, in changes post.)======>

"But now we must assume the fundamental opaque particles comprising ordinary
matter are extremely tiny, spherical, with identical size and inertial mass
(or, if there are different sizes, they must be combined always in the same
proportions in macroscopic bodies), and do not align themselves in such a
way as to alter their combined gravity."

The above is merely a list of misrepresentations concerning Le Sagian
gravity. Some of these limitations may exist in Darwin's theory.  But it is
dishonest to ascribe them to Le Sage's theory.

"(Actually, a detailed analysis of the mutual force between two opaque
spherical objects given by George Darwin in 1905 shows that the force is not
actually a pure inverse-square relation unless the objects are exactly the
same size.)"

This is a flat contradiction of both Roseveare's description and of Darwin's
work. It is trivial to recover a rigorous inverse square law - even in
Darwin's theory, by setting radial and tangential elasticity to the same
value.

< =======(Also See Modification Note 2, in changes post.)

Next, "Shadows" provides a figure for what it claims is the "Fatio-Lesage
Model of Gravity."  This figure claims an "fundamental opaque particle of
normal matter."  Aside from the blatant misrepresentation of opacity in Le
Sage's model, the figure is good figure for a basic understanding of the
mechanism.

(See Modification Note 3, in Changes post)

The next paragraph in "Shadows" uses horrid logic, outright distortion, and
unsupported accusations:

"These assumptions then impose further requirements.  The inverse-square
property depends on the ability of the swarm of ultra-mundane particles to
maintain the shadowing effect in strict proportion to the angular extent of
the image of an elementary opaque particle as the distance increases.
Clearly the ultra-mundane particles must be absorbed by matter, not
reflected, because reflection would eliminate the 'Shadows', "

Reflection will not eliminate "Shadows", as the corpuscles and their
momentum vectors are removed from the prior line of travel. Corpuscles may
also lose only a fraction of their momentum to the body.

"and they must not interact with each other at all, because the slightest
interaction would smudge out the shadow effect and thereby destroy the
inverse-square relation."

This is an unsupported accusation, and also flatly untrue.  If the particles
interact with each other elastically, the vector of momentum in the fluid is
not changed.

"But even perfectly non-interacting particles must have some finite density
(particles per volume), so there is a limit to the resolution of the shadow
image that can be maintained.  At some finite distance from a fundamental
opaque particle of ordinary matter its image will become indistinguishable
from a point, by which time the inverse-square relation will have been
totally lost."

This is another travesty of logic.  An image will never be
"indistinguishable from a point;" as the latter is a mathematical ideal -
not reality.  In addition, there is no need for the "pure" Newtonian inverse
square law to hold over all distances - only over distances sufficient to
describe the Solar system.

"This characteristic distance is proportional to the size of the fundamental
opaque particles of matter, which we have already seen must be extremely
small in order to make the force of gravity proportional to the number of
particles (i.e., the mass) of macroscopic bodies and to avoid the saturation
problem.  The smaller we make the fundamental particles of matter, the
shorter becomes the distance to which the inverse-square relation will hold
for a given density of ultra-mundane particles.  In essence, the radiation
field of Lesagean particles must be dense enough (and free enough from
self-interaction) to resolve the angular radius of a particle the size of an
electron from hundreds of millions of miles away!  Thus, to maintain the
inverse square relation for any appreciable distance, we need to assume the
field of ultra-mundane particles has nearly infinite density (i.e.,
particles per unit volume), and therefore, to avoid interacting with each
other, each of these particles must have essentially zero cross-sectional
area."

"Setting aside the implausibility of all these conditions for the moment,
and accepting the combined rationalizations regarding the densities and
sizes of weighty particles ."

The rest of this is a vague, hand-waving tirade against a straw-man of
multiple distortions.  But it contains no mathematics or supporting
reasoning. The intended implication, of course, is that Le Sagian theory is
completely implausible. Thus ends the atrociously false "description" of Le
Sagian theory in "Shadows".

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Part III: Arguments on Kinetic Theories of
Gravitation (Paragraph beginning in the middle of run-on sentence that
begins "Setting Aside the Implausibility ...")

"Shadows" next attempts to address some of the properties of any kinetic
theory of gravitation.

"(T)here are still more serious problems for shadow gravity, many of which
can be traced back to the finite speed of the ultra-mundane particles."

Le Sagian theories are fundamentally mechanical.  A finite speed is a
requirement for all mechanical theories.  A finite speed of gravity provides
a modification of Newton's equation of gravitational force, to account for
the speed of transmission of the effect. Thus, Le Sagian theories share the
property of a finite speed of gravity with General Relativity (which assumes
a speed of transmission of gravity equal to 'c').

A) Laplace/Feynman Drag:

This effort begins with Feynman's drag argument - though the argument was
first wielded by Laplace. (Laplace, P.S., "Traité de Méchanique Céleste,"
T.V. Bachelier, pp. 448-452, 1825)  Once again, "Shadows" does not
acknowledge the sources of the argument.

"As a macroscopic body moves (relative to the frame with respect to which
the ultra-mundane flux is isotropic)"

The parenthetical phrase is easily replaced in Le Sagian theory by the words
"through the medium."  Apparently "Shadows" cannot tolerate Le Sagian
terminology or concepts.

"it will naturally encounter more particles on its leading face than on its
trailing face, resulting in a net drag on the body.  "

This much is true.

"Quantitatively, if a series of equally-spaced ultra-mundane particles with
speed vg are impinging on a stationary opaque object from two opposite
directions, the object will be struck by particles at the same rate on both
sides.  (How all the independent ultra-mundane particles acquired this
particular speed is not explained.)"

Le Sagian corpuscles do not need to move at any "particular speed."  Le
Sagian corpuscles would move at a range of speeds.  Only the average value
of particle speed is vg.  It is light-pressure model that has waves
traveling at single speed.  The author of "Shadows" apparently did not grasp
this distinction. There is also no reason for the corpuscles to be
equally-spaced -- even in a light-pressure model.

"However, if the object moves with speed v in one direction along this axis,
the rate of encountering particles on its leading face is increased in the
ratio (vg + v)/vg, and the rate of encountering particles on its trailing
face is decreased in the ratio (vg  - v)/vg, so the original force balance
F - F = 0 becomes (2v/vg),"

"The momentum transferred to an object by each ray of flux must be large
enough to account for gravity, which implies that F in the above equation is
not negligible.  Since we do not observe any appreciable drag on (for
example) the planets in their orbits around the Sun, we must impose some
further restriction on the model to minimize this effect."

This is a good summary of the Laplace/Feynman argument. The claim is a
common one; and has a venerable history.  However, we now know that we
cannot quantify the drag of a medium on orbiting objects from orbital
stability, because drag is not the only attribute of a physical medium.
Indeed, "Shadows" later attempts to derive a counteracting force from
gravitational aberration (Part III-C. Gravitational Aberration).
Gravitational aberration produces a counter-force to the drag force on an
orbiting body.

Usually, opponents of Le Sagian theories will advance the Feynman argument:
that the Earth would have spiraled into the Sun in about 1 million years.
Often, opponents of Le Sagian theories will advance the aberration argument:
that the Earth would have doubled it's orbital size in 1000 years.  Some
opponents even switch back and forth.  The time values above are typical;
and specifics vary - depending upon the opponent.  But "Shadows" is the
first to my knowledge that claims that the drag force always overpowers the
aberration force.

"To minimize the drag we must assume the speed vg of the ultra-mundane
particles is extremely great.  Thus, we find once again that a natural
consequence of the model must be nullified by setting one of the parameters
to an extreme value."

Because drag cannot be considered in isolation, there is no need for an
extreme value for the speed of ultra-mundane corpuscles - though some Le
Sagian proponents take this approach.  Though Tom Van Flandern postulates a
high speed of his quantum gravitons, this is partially based upon the
implicit assumption of infinite gravitational speed in actual Solar system
dynamics calculations utilizing General Relativity (GR).

One cannot use presumed orbital stability to derive the drag term in a
medium theory, because the drag term is not separable from the aberration
acceleration term in such a theory. To make the claim here is to presume the
answer.

"Shadows" now attempts to calculate the drag term on a body moving through
the Le Sagian aether medium.  In this, it is hampered by the unnecessary
inclusion of a term that it calls "Bradley aberration."  Bradley aberration
has not even a trivial affect on the calculation of drag (as "Shadows" later
admits).

The normal method of deriving Feynman drag is to first perform the
calculation for acceleration of a body (drag) travelling in a straight line.
Then one performs the calculation for the Le Sagian gravitational
acceleration of a body in orbit.  However, "Shadows" does not provide even
the elementary, classical derivations for these two terms.  Avoiding the
first allows "Shadows" to ignore the observation of Pioneer drag. (The drag
term is within a factor of 2 of the "anomalous" Pioneer drag, when vg is on
the order of c.  And has been observed over the past 20 years by
non-orbiting space probes.) Avoiding the second derivation allows "Shadows"
to avoid demonstrating how simple and obvious the Newtonian gravitational
equation becomes.

But "Shadows" does not take the simple road.  "Shadows" takes a flawed
approach that attempts to link drag (a one-body problem in the fluid) and
gravitational force (a two-body problem in the fluid) into a single
calculation, ab initio.

"To treat this more fully, let rho U dt denote a measure of the spatial
density of the ultra-mundane particles absorbed by ordinary matter, defined
such that rho U dt equals the rate of mass accretion by a sphere of a given
radius from a given direction in an increment of time dt, where U is the
relative speed between the ultra-mundane particles and the sphere along that
direction.  For a massive sphere in orbit around some center of mass with
another body we will consider just the radial and tangential flows as shown
below."

This is followed by a figure, that shows values (rho vg) vg in the left,
top, and right directions.  In the bottom direction, it shows (rho (1-k) vg)
vg.

"The radiation density from the bottom (i.e., from the direction of the
other orbiting body) is reduced by the factor (1 - k) where k is a small
number representing the fraction of the flux that was intercepted by the
neighboring body.  (Note that, since the gravitational constant does not
change appreciably with distance from the Sun, we know that k for the Sun
must be no greater than one part in a hundred million, i.e., 10^-8).  "

The fractional value is similar to that found in Le Sagian theories (i.e.
"Deriving Newton's Gravitational Law from a Le Sage Mechanism," "Pushing
Gravity", p 193). Of course this tiny value eliminates any need for
quantifying "Bradley aberration" at all! So, all those terms will be
deleted.  A simple linear interaction is all that is needed.

"Beginning with a mass m and speed v, the orbiting body will absorb in an
increment of time dt ultra-mundane particles with momentum in the horizontal
direction equal to [rho(vg-v)dt]vg and -[rho(vg+v)dt]vg.  The mass accreted
from particles in the horizontal direction is equal to the quantities in the
square brackets."

Le Sagian theories do not need to have the ultra mundane corpuscles
absorbed.  They only need a fraction of their momentum transferred.  Le Sage
himself assumed that the corpuscle was (at least temporarily) attached to
the body.  So with respect to absorption, the analysis is reasonable. But Le
Sage certainly didn't assume that all corpuscles interacted!  So the
equations above are missing an interaction parameter, mu_s.  This is an
elementary error on the part of "Shadows"' author.

But the equation above is still incorrect.  The change in momentum of the
body from absorption of a particle transfers only the momentum of the
particle relative to the body.  Which is simply rho(vg+v)dt from the front,
and -rho(vg-v)dt from the rear; or 2 rho v dt. The "extra" term of vg,
above, is erroneous.  Quite simply, the author of "Shadows" failed to
include the division by vg from his first derivation in this section.

In addition to fouling up the horizontal vector, the author also neglected
to include any unit vectors in his vector analysis.  It appears that the
author first tried to calculate a mass increase - which would not require
unit vectors.  But later in the derivation, the author attempts to determine
the relative magnitudes of the two components . even though he had already
mixed them.  Of course, to be correct, "Shadows" would have to use
calculus - not the hand-waving approach, above.

"In addition, during this same increment of time, the object will accrete
from particles in the vertical direction quantities of mass equal to
[rho(vg)dt] and [(1-k)rho(vg)dt].  Letting u denote the horizontal speed of
the object at the end of this increment of time, the conservation of
momentum requires"

Followed by an equation, which is trivially shown to be in error, because
the units aren't consistent. The LHS of the equation is:

 mv + [rho(vg+v)dt] vg  - [rho(vg+v)dt] vg

The first term has units of kg-m/sec, and the second two terms have units of
kg/m-sec.  Similarly (and for the same reason), the RHS is also mixed units:

[m + rho(vg-v)dt + rho(vg+v)dt + rho vg dt + (1-k) rho vg dt ] u

Inside the brackets, the first term has units of kg.  The rest of the terms
have units of kg/m2.

"Shadows" then follows this (erroneous) equation with the statement:

"Solving this for u, subtracting v, and dividing by the incremental time dt
gives the rate of change of speed (i.e., the acceleration) in the horizontal
direction "

{After implicitly assuming that mass m is unchanged, "Shadows" obtains the
following equation:}
dv/dt = - v (6 - k) vg rho / m

The units on the LHS are m/sec2.  The units on the RHS are m5/sec2.  Not
surprisingly, the equation is still grossly in error.

Now, the value of k is on the order of 10^-8. But, instead of simply
removing the trivial factor (k) from the above equation, "Shadows" attempts
to use it to link this to the radial acceleration.  "Shadows" does this with
a hand-wave declaration:

"We also know that the slight different in the radiation density in the
vertical direction produces the force of gravity on the object, so we have
 G m M / r2 = (k rho vg) vg  "

Once again, the units are scrambled.  The LHS has units of force
(kg-m/sec2).  The RHS has units of kg/m-sec2.  However, the derivation of
the force of gravity requires a complete, calculus derivation covering 4?
solid angle around each body.

At this point, I'm going to stop beating this particular dead horse.
Suffice it to say that the author of  "Shadows" has failed miserably to
support his claim.  Because "Shadows" whole approach is flawed - as well as
the mathematical manipulations in "Shadows" - I will simply point the reader
to the derived equations in "Pushing Gravity:"

Gravitational Force Law: p 188 (one of several ways)
  F_g = Phi_0 mu_s^2 m M / r2 = G m M / r^2

Drag from Inertial Motion: p 197
  F_d = sqrt(3) Phi_0 mu_s m v / vg

In the above equations, Phi_0 is the momentum flux of the Le Sagian aether
(kg/m-sec2), and mu_s is the mass attenuation coefficient (m2/kg).  The
ratio between the two forces is therefore given by the equation:

  Fd/Fg = [sqrt(3)/mu_s M] (v/vg)

We cannot determine the value of mu_s from purely orbital characteristics,
because G only gives us the product of Phi_0 mu_s^2.  Hence, we cannot
determine vg from orbital stability claims.

But there is a way to observationally determine the speed of gravity - in
any gravitational theory that includes a primarily inverse square force
equation.  This is phenomenon of perihelion advance of orbits.
http://www.google.com/groups?selm=vr2941i226t8a5%40corp.supernews.com

The advance of the apsides in any such theory is given by the following
equation:

  ?? = K ?3 / [ vg^2 a (1 - e^2) ]

where ?? is the advance of the apsides (perihelion or periastron) per orbit;
K is a numerical constant that depends upon the theory used (8 for "flat"
space and Entwurf GR, 24 for "modern" GR); a is the semi-major axis of the
planetary orbit; and e is the eccentricity of the orbit.  The speed of
gravity is thus determined by:
  vg = sqrt [K ?3 / ?? a (1 - e^2)]

All measurements of Mercury's perihelion advance and eclipsing binary stars
give a measure of the speed of gravity (vg) to be on the close order of the
speed of light (c) - regardless of theory used.  Hence, the primary source
of the "vaporization of the Earth" claim rests on Laplace's fundamental
error.  The speed of the ultra-mundane corpuscles is 1017 times smaller than
Laplace calculated and Poincaré used.

This takes us through the paragraph beginning "In order for the orbits of
the planets around the Sun to have persisted."  For those interested, the
argument in "Shadows" was first presented by Laplace (circa 1825) and was
cribbed by "Shadows" from Poincaré.  The whole point of the above is to lead
into the following claim with regard to the required speed of the
corpuscles.

"In order for the orbits of the planets around the Sun to have persisted for
hundreds of millions of years, the ratio of tangential to radial
acceleration can be no greater than about 10^-10,"

And here lies the problem.  "Shadows" has already admitted that
gravitational aberration is a counter-force to drag, but it has not yet
quantified the gravitational aberration.  Hence, there is no basis for
claiming that drag - alone - can be determined by such a method.

"and we've already noted that the fraction k of ultra-mundane particles
absorbed by the Sun can be no greater than 10^-8, so the above relation
implies that the speed of the ultra-mundane particles must be at least
(6)10^18 times the speed v of the planet.  The planet Mercury has an orbital
speed of about (4.8)10^4 m/sec, so the value of vg must be at least
(2.9)10^23 m/sec, which is about 10^15 times the speed of light. (Henri
Poincaré used more stringent limits on the shielding and acceleration ratios
to conclude that vg must be about 10^17 times the speed of light.) "

Actually, Laplace and Poincaré simply did the math correctly (where
"Shadows" fouled up elementary units) - even if they did set up the wrong
problem.  One can forgive Laplace for missing the effect of aberration.  One
may be able to forgive Poincaré and Feynman (for they never indicated they
were aware of the issue).  But one cannot forgive "Shadows".  For "Shadows"
explicitly knows about aberration.

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Part III, B) Claims for Mass Accretion /
Gravitational Induction Heating: (In the middle of the Paragraph beginning,
"To treat this more fully., beginning with the phrase: "Setting aside the
conflict with special relativity,")

Once again, "Shadows" cribs from a standard source.  In this case, Henri
Poincaré's "The Foundations of Science", Science Press, 1946, pp. 517-521.
A copy of, and full analysis of, Poincaré's paper is available by e-mail
(Send request to mingstb@sim-ss.com).

"Setting aside the conflict with special relativity,"

There is no conflict with special relativity.  Le Sagian theory is
unabashedly an aether-based theory.  Thus, the concerns of Special
Relativity are not relevant.

"this implies that the effective "temperature" of the flux is incredibly
high, and the flow of energy from the flux into ordinary material bodies
(like the planets) would be so great as to vaporize them in a fraction of a
second.  Maxwell had previously made a similar argument."

Maxwell's argument (1878) was based on the original stability argument of
Laplace (1825), that ignored gravitational aberration effects.  However,
that approach has been disproved, ab initio.  There is no way to determine
the speed of gravity (or corpuscles) from orbital stability claims.  In
addition, Maxwell's argument rested on the additional assumption that there
were far more molecules in a body than there were Le Sagian corpuscles to
interact with same.  See page 69 in "Pushing Gravity" for details.  Since
even neutrons are experimentally observed to gravitate, Maxwell's assumption
is the inverse of reality.

"In simple terms, the momentum of a particle of mass m is mv, whereas the
kinetic energy is mv^2/2, so the ratio of energy to momentum is v/2.
Consequently, in order for the ultra-mundane particles to impart a given
amount of momentum to an ordinary massive object (such as a planet) by being
absorbed by the object, the corresponding energy absorbed by the object
increases in direct proportion to the speed of the ultra-mundane particles."

At this point, "Shadows" launches into an involved attempt to derive the
energy deposited in the Earth by the process of Le Sagian gravitation.  But
"Shadows" does not use Le Sagian mathematics to do this.  Instead, "Shadows"
invokes a series of hand-waving assumptions that are not related to Le
Sagian gravitation at all - but is simply playing with orbital dynamics.

Just as with drag forces, it is not possible to determine the energy
deposition rate in a Le Sagian theory from orbital dynamics, alone - and for
the same reason.  Drag and heating effects are one-body problems.  Orbital
dynamics result from two-body problems.  Corpuscle heating of matter is a
function only of the mass of the heated body.  The same quantity of heat
will be generated whether the body is sitting alone in the cosmos, or in a
tight orbit around a neutron star. Yet "Shadows"' calculation depends upon
the mass of the companion star, via the orbital radius and tangential
velocity of the orbit. This dependence, alone, clearly demonstrates that
"Shadows"' calculation is again incorrect.

The primary error is that "Shadows" assumes (implicitly) that the
gravitational constant (G) is only a function of the momentum flux of the
corpuscles.  It ignores the effect of the Le Sagian attenuation parameter
completely.  If this assumption were valid, then the attenuation parameter
would always appear in every Le Sagian calculation in the same relation to
flux (Phi_0 mu_s^2).  But the squared attenuation parameter arises only in
two-body problems (like gravitation) that require a mediated interaction
between two bodies.  The attenuation parameter appears only to the first
power in one-body problems (like heat and drag).  Newtonian gravitation,
alone, cannot identify the value of the constant Phi_0 mu_s from the value
of the constant Phi_0 mu_s^2.  See page 191 of "Pushing Gravity," for
example.

"Quantitatively, Lesage's theory implies that the ultra-mundane particles
impart enough momentum to a planet of mass mp moving in a circular orbit
with speed vp to completely reverse it's direction every half revolution.
Thus its momentum changes from +mpvp to -mpvp, for a total momentum change
of 2mpvp every half revolution, or 4mpvp per revolution.  This momentum is
imparted by collisions with ultra-mundane particles with total mass mu and
speed vg such that m u vg = 4 mp vp. "

Once again, this attempt is flawed because the radius and the orbital
velocity is determined by the mass of the central body . not the mass of the
orbiting, heating body.  And it is the orbiting bodies' mass that causes
gravitational induction heating.

"The kinetic energy E = (1/2) m u vg^2 of these ultra-mundane particles is
also absorbed by the Earth."

The above is yet another fundamental error of "Shadows"' heat analysis.  The
error is the unstated assumption that the collision between the matter body
and the corpuscles are perfectly inelastic.  For a completely elastic
collision, no energy will be deposited.  The reality is contained within the
factor mu_s, and lies somewhere between these two extremes.

"Substituting from the momentum equation to eliminate mu, we get E = 2 mp vp
vg.  By Kepler's third law we also have G ms = omega^2 r^3 = v p^2 r, where
G is the gravitational constant, r is the radius of the planet's orbit,
omega is the angular speed of the planet, and ms is the mass of the Sun.
The period of the orbit and the speed of the planet are therefore given by"

  T = 2?r sqrt(r / G ms)
  vg = sqrt(ms / r)

"Substituting into the equation for the energy per revolution and dividing
by the period of one revolution gives the energy per second absorbed by the
planet"

"   2 me ve vg / T = 1/? (G ms mp / r2) vg"

"Shadows"' 2 me ve vg = E, above, and power is E/T.

"For the Earth and Sun we have {various phyiscal values} so if we assume the
speed of the ultra-mundane particles is just vg = c = (3.00)108 m/sec we
find the rate at which energy is being added to the Earth due to collisions
with the ultra-mundane particles"

"E/T = 3.4 E30 J/sec"

"For comparison, the entire energy output of the Sun is (4)10^26 J/sec, so
Lesage's theory requires us to believe that the Earth is continually
absorbing about 8500 times the Sun's energy output - and this refers not
just to the fraction of the Sun's energy that strikes the Earth, but to the
entire Sun's output!  This is based on the relatively mild assumption that
the ultra-mundane particles move at "only" the speed of light.  If, as
Laplace estimated in order to avoid aberration problems, the speed of these
particles is really a million times greater than the speed of light, the
energy flow increases by the same factor.  Even worse, if we take Poincare's
estimate that vg must be at least 10^17 times the speed of light to avoid
excessive drag, then the Earth must be absorbing energy at about 10^21 times
the Sun's total output rate."

"Shadows" comes up with an power rate that is dependent on vg to the first
power. Using the same approach, Poincaré comes up with a power rate that is
dependent on vg to the third power. "Shadows" has clearly demonstrated that
the entire approach is flawed.  The flaw is that opponents of Le Sagian
theories refuse to actually use Le Sagian theory to make their calculations!
Instead they rely upon hand-waving assumptions of some unrelated orbital
dynamical nature.

I'm going to skip the next several paragraphs of "Shadows".  They simply
repeat the prior refrain of heat death of the Earth - which I've already
shown to be invalid.

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Part III-C) Gravitational Aberration (and Drag
Again): (approx. ¾ down the page, phrase beginning "the finite speed of the
ultra-mundane particles .")

"(T)he finite speed of the ultra-mundane particles (or waves) poses
additional problems, namely, drag and aberration.  These problems are
especially acute if we set vg to "just" the speed of light.  Drag and
aberration both tend to upset the stability of planetary orbits.  Proponents
of Lesage theories sometimes argue that these two effects can compensate for
each other, but this is not the case.  To understand why, consider the
simple two-body system shown below."

    {figure for orbital aberration here}

Note:  The blue line and sphere in the above figure from "Shadows" have
nothing to do with gravitational force.  Since mass M was never "at" the
blue position, no real force (depletion of corpuscle momentum) could have
originated there. Nor is any justification provided in "Shadows" for putting
it there.  Gravitational force is a real force - not simply an appearance.

"Let m and M be the masses of the two bodies, with radial distances r and R
from the center of mass, and orbital speeds v and V respectively, and let vg
denote the finite speed of the Lesagean particles.  Clearly we have m/M =
R/r = V/v. The total "aberration" between the actual and the apparent
positions of the mass M as seen from the mass m is due to two causes.
First, there is the "Bradley effect" discussed previously."

The "Bradley effect" has no bearing whatsoever on the determination of the
gravitational aberration. "Shadows" admits, above, that the "Bradley effect"
is a factor affecting the drag force - but is less than trivial on that
force.  But the gravitational aberration angle is a factor affecting the
central gravitational force (which is 8 orders of magnitude greater than the
drag force, by "Shadows"' own calculation).  In the interest of brevity, the
rest of this irrelevancy in "Shadows" will be passed by here.

.

"The second cause of aberration is the fact that the incoming rays striking
the mass m at a given time did not originate at the mass M at that same
time, but rather at the mass M at an earlier time.  Thus the true direction
of the incoming rays is offset from the true current position of the mass M
by the angle s,"

There is no angle 's' in the above graphic.  Apparently, "Shadows" meant
angle '?'.  This is the angle between bB and bA - which is the correct
gravitational aberration angle.

"which is approximately equal to V/vg (because the sine of that angle is
roughly the distance from A to B divided by the distance from A to b, and
this is in the same ratio as the speeds)."

Instead of determining what the aberration angle is, "Shadows" simply
performs a hand-wave assertion that sigma is equal to v/vg.  But this is not
the
aberration angle . unless m = M.  A straightforward (though tedious)
geometrical evaluation of the above graphic provides:

  sigma = sqrt [2 - delta(1+m/M)+ {(m/M)2 -1}/ {delta(1+m/M)}]

where delta is the factor difference between distance Ab / Bb:

  delta = 1 / sqrt[1 + m/M (v/vg)^2]

Only where m = M does sigma resolve to v/vg for small angles.  At that
point, the aberration angle is maximum for m = M.  The aberration angle is
reduced roughly by the ratio m/M as the body masses differ.  In general, the
aberration angle is approximately (m/M) (v/vg).  While this doesn't affect
"Shadows"' calculation (because of a later, additional error), this
variation from v/vg is required for all Le Sagian theories.

"Thus we have the total aberration angle ..."

The gravitational aberration is only a function of gravitation.  There is
no "Bradley aberration" component - because (as noted earlier by "Shadows")
Bradley aberration affects only the drag force.  Whereas gravitational
aberration affects the central force.

"For the smaller of the two bodies this effect is smaller than the Bradley
aberration, which we've already seen is much too small to compensate full
for the drag, so the combined aberration cannot compensate full for the
drag."

This is a completely fallacious statement.  The reason that it is fallacious
is that "Shadows" claims that the force from "Bradley aberration" is due to
a fractional reduction of the Feynman drag force.  Whereas the gravitational
aberration force is a fraction of the central gravitational force - a factor
of 10^8 higher, by "Shadows"' own calculation.  Hence, the angle alone is
not sufficient to claim that the aberration force is less than the Bradley
force.  (Aside from the fact that "Shadows" has never shown that angle beta
is the Bradley angle, or even that it applies.)

I'm not sure where the author of "Shadows" got this particular idea.  Many
calculations exist that clearly show that aberration force based on the
speed of light transmission is usually considered far greater than the drag
force - primarily because they assume that the aberration angle is
proportional to (v/vg) instead of proportional to (m/M) (v/vg).

Once again, we may bypass the rest of the verbiage in this section of
"Shadows". "Shadows" falsely asserts that one can determine the relative
contributions from "Bradley" aberration (a reduction of drag) with
gravitational aberration (a fraction of the central force) by simply
comparing calculated angles . without considering the magnitude of the
forces that they modify.

(See Modification Note 4, in Changes post)

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Part IV: Philosophical Objections: (About 4/5 of
the way down the page, paragraph beginning: "We mentioned previously the
problem of infinite regress")

There is nothing of substance in this section of "Shadows".  This is merely
a listing of several unsupported accusations, and straw-man arguments that
have nothing to do with any Le Sagian theory.

"We mentioned previously the problem of infinite regress for the forces of
attraction holding the ultra-mundane particles together.  "

As noted above, the claim that Le Sagian corpuscles required internal
structure was completely fraudulent.

"Naturally the same problem applies to the structures of ordinary
macroscopic objects.  In fact, the very existence of stable macroscopic
objects is a problem, because one of the basic premises of a Lesagean theory
is that forces are to be understood solely in terms of inertial motions and
collisions between particles,"

This statement is an outright fabrication of "Shadows". There is no generic
"premise" in any Le Sagian theory that all forces are the results of
collisions between particles.  Le Sagian theory explains only gravitation.
It never claims to explain the other three forces of nature.

"which implies that all forces must be reducible to "pushes".  The problem
then is to account for the stability of macroscopic bodies, conceived as
extremely sparse configurations of inertial particles."

This statement is a completely fraudulent invention of "Shadows".  Le Sagian
matter models do not require "sparse configurations" of anything.

"These particles may bounce off each other, but this will just cause them to
disperse.  No combination of bouncing (i.e., repelling) interactions alone
will result in a stable coherent configuration of particles in the shape of,
say, a penny."

This is a completely unsupported claim -- also flatly untrue.

"Needless to say, we cannot claim macroscopic objects are held together by
gravity, because the forces needed to hold macroscopic bodies together and
maintain their various shapes must be vastly stronger than the force of
gravity."

Of course no Le Sagian model does such a thing.  This argument is purely
invented, irrelevant, and fraudulent.

And once again, in the interest of brevity, we skip several ranting
paragraphs that are unsupported by anything within the skipped paragraphs;
and by anything that went before in "Shadows".

....

(See Modification Note 5, in Changes post)

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Part V: Summary: (About 9/10 down the page.
Paragraph beginning "From a methodological standpoint.")

"From a methodological standpoint it's worth reflecting on the nature of the
series of rationalizations that have been required in the efforts to
maintain the viability of this model. "

What is actually amazing is the number and nature of the series of
rationalizations that have been proffered to claim disproof of any given
theory of Le Sagian nature.  Why, for example, is there no "disproof" of any
Le Sagian theory that is based on actual equations from that theory?

"The basic model consists of a flow of unseen particles in all directions
tending to push the seen particles together, but this model tends to suggest
many things (e.g., drag, saturation, aberration, heat transfer, temporal
decay, mass accretion, dependence on volume, etc.) that are contrary to
observation,"

"Shadows" lists a series of effects that it claims are contrary to
observation.  But look at the contents of the list:

Saturation was not addressed by "Shadows". Temporal decay (sic, orbital
decay) is simply a repeat of the drag claim - hence merely repetition of a
claim. Mass accretion was not addressed by "Shadows". Dependence on volume
was not addressed by "Shadows". And the ever-popular "etc."  Which is simply
a slimy way of implying that there is more - when the claimant has no idea
what this may be.

In short, "Shadows" has attempted to address only three kinematic issues:
drag, aberration and heat induction.  It has failed miserably on each one.
And each and every one of these claims was based on a flawed claim for the
value of a single parameter: the speed of the corpuscles.  Which is a far
cry from "many 'things' contrary to observations."

"so we have found it necessary to make extreme and convoluted assumptions
about both the unseen and the seen particles in order to nullify the
unwanted tendencies of the model. "

What "Shadows" attempts to do here is to continue the fiction that there is
only one "Fatio/Le Sage theory."  It is unlikely that any class of theories
that spans over 200 years will not gather some change from new data - as
both opponents and proponents become more knowledgeable.

"In fact, almost every inherent attribute of this model is inconsistent with
the facts of gravity, and therefore must be minimized or nullified by
setting some parameter of the model to near infinity or near zero."

This is another complete fabrication by "Shadows".  The only parameter that
has ever been set "near infinity" is the speed of gravity in some (not all)
models.  No parameters have been set to near zero.  And no other parameters
have been set to near infinity.  Perhaps "Shadows" is trying to imply that
purely elastic and purely inelastic collisions are not real.  But proponents
of Le Sagian theories have never argued for perfection.  Nor are such claims
needed to explain observations.

"The positing of these unseen particles has taught us nothing new about
gravity.  Instead, we are using our pre-existing knowledge of gravity to
infer things about the posited unseen particles as well as about the
constitution of ordinary matter."

Pioneer drag was predicted by Le Sage theory.  "Anomalous" heat of Neptune
was predicted by Le Sage theory.  The "mostly space" condition of normal
matter was predicted by Le Sage theory. And kinetic gravity theories are the
only causal theories of gravity available.  Perhaps the author of "Shadows"
(using the imperial "us") is simply unwilling to learn.

"Even if we overlook the fact that many of the implications are incompatible
with our current best models of elementary particles"

This is another complete fabrication by "Shadows".  Le Sagian gravity is
completely compatible with our current models of elementary particles.  The
part where the particles (whether atoms or nucleons) are mostly empty space.
It is precisely the transparency of these models that lends itself to a Le
Sagian model at the smallest levels where gravitation has been
experimentally confirmed (neutrons).

"(not to mention the fact that even if the model was correct it would not
eliminate the need for an elementary force of attraction), "

Gravitation is an elementary force of attraction.  It matters not that it is
really a "push", instead of a "pull."  Le Sagian theories do not attempt to
claim proof of the other three forces of nature.  But then, neither does GR,
Newton, or any other theory of gravitation.

"we still would have to question the value of hypothesizing an occult entity
(ultra-mundane particles) and then inferring the occult attributes of this
occult entity necessary to yield the observed phenomena."

The same slander (the word "occult" for guilt-by-association) could be
applied to the proposed existence of molecules of air - before they were
resolved in a microscope.  The value is in the scientific method.  For Le
Sagian gravity theories are the only cause-and-effect, physical model of
gravity yet proposed.  Even if they turn out to be wrong, the cause of
science is advanced by their proposal.

"Incidentally, although Lesage's model is much the same as had previously
been proposed by Nicolas Fatio, such models are almost invariably referred
to in modern literature as "Lesage theories" rather than "Fatio theories".
This may be because Lesage gave a more detailed and lucid account of it, or
it may simply be that those who discussed such theories in later years were
unaware of Fatio's priority."

The reason is that Fatio's theory was both incomplete, and did not reproduce
Newton's gravitational force equation well.  But Le Sage's theory was both
complete, and did reproduce Newton's equation.

Lastly, "Shadows" provides some historical information on Fatio - lifted and
rephrased, once again, from van Lunteren.  The only purpose appears to be to
impugn the sanity and abilities (and moral character) of Fatio.  The obvious
purpose is the tarring Le Sage with the brush of guilt-by-association.

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}

This is a continuation of the general rebuttal to "Lesage's Shadows":

This post is with regard to Substantive Changes to "Shadows" noted on
January 12th, 2005:

Modification Note 1:

In the history "section," "Shadows" has added a substantially new qualifier
to the brief mention of Le Sage's ultra-mundane corpuscles: ". and with a
nearly infinite mean free path."  This latter phrase is simply distortion.
The term used by Le Sage was "rarely collided with each other."  Obviously,
Le Sage intended a long mean free path.  But Le Sage only needed a range
equal to the solar system.  Which is hardly infinite.

Modification Note 2:

"Shadows" has removed it's overt identification of it's use of Darwin's
model.  The following sentences were removed:

"But now we must assume the fundamental opaque particles comprising ordinary
matter are extremely tiny, spherical, with identical size and inertial mass
(or, if there are different sizes, they must be combined always in the same
proportions in macroscopic bodies), and do not align themselves in such a
way as to alter their combined gravity.  (Actually, a detailed analysis of
the mutual force between two opaque spherical objects given by George Darwin
in 1905 shows that the force is not actually a pure inverse-square relation
unless the objects are exactly the same size.)"

The only problem is that "Shadows" continues to use Darwin's model, instead
of Le Sage's model.  It merely has tried to bury the evidence.

Modification Note 3:

"Shadows" has added three new paragraphs at this point:

"We now know that the atoms and molecules comprising ordinary matter
actually do consist of very tiny particles in mostly empty space (neglecting
the fields), which makes it possible for very weakly interacting particles
like neutrinos to pass through the entire Earth (for example) quite easily.
The "transparency" of matter can, with some justification, be regarded as a
prediction of Fatio-Lesage theories, since the atomic structure of matter
was unknown when the theories were first put forward. On the other hand,
according to a Lesagean theory, we can have equality between inertial and
gravitational mass only if all matter consists of identical elemental opaque
entities (i.e., entities of exactly the same size, shape, and inertial
density) in exactly the same proportion, whereas we now know that different
kinds of material substances consists of different combinations of protons,
neutrons, and electrons. Furthermore, we now know that both the inertial and
the gravitational masses of these substances depend on their binding energy
as well as the number of elementary particles they contain, and indeed we
know that even pure energy (light) is affected by gravity precisely in
accord with the equivalence principle. All these facts are inherently
incompatible with the Lesagean model of gravity. Any suggestion that we can
restore inertial and gravitation equivalence to Lesage's model by regarding
protons, neutrons, and electrons as composite bodies formed from a single
species of identical opaque particles merely introduces another layer of
structure, requiring elementary attractive forces to maintain it - the very
thing Lesagean theory is intended to obviate."

"Moreover, the structure of matter actually proposed by Lesage consisted not
of particles, but of a lattice of elemental bars forming a mesh of "cages",
which he was compelled to postulate in order to account for the structural
stability of matter with seem to appeal to any elementary attractive forces.
Needless to say, Lesage's proposed structure of matter has now been
falsified, and it's easy to see this structure was logically untenable to
begin with, because the essential tension in the bars of the cages
represents an elementary attractive force, which is inconsistent with the
categorical Lesagean rejection of such forces. (We may also mention that any
regular lattice structure would tend to exhibit non-isotropic gravity, due
to the fact that the bars would be aligned with each other more in some
directions than in others.)"

"Still, setting aside the fundamental incompatibility between Lesagean
theory and the stability of matter, we can proceed to assess the other
consequences of such a theory, based on the assumption that matter is
composed of a very sparse agregate of fundamental opaque spherical particles
with identical size and inertial mass (or, if there are different sizes,
they must be combined always in the same proportions in macroscopic bodies),
and with the assumption that these particles do not align themselves in such
a way as to alter their combined gravity. {Attaching here to the beginning
of the pre-existing paragraph}

Modification Note 4:

"Shadows" has now inserted a classic example of inverted reasoning, outright
misrepresentation, and ad hominem vitriol.

"Incidentally, some neo-Lesageans (of the crackpot variety) have suggested
that the motion of the planets through the radiation field of ultra-mundane
particles "

This is another complete fabrication.  No Le Sagian theory is based on a
"radiation field" at all. A Le Sagian theory - even a Fatio one - is based
on movement of corpuscles, not radiation.  And no such proposal for fluid
currents has ever been made by a proponent of light-pressure theory.

"imparts a "swirl" to the field, thereby reducing or eliminating the drag.
Needless to say (or so one would have thought), this suggestion is totally
incompatible with the most basic pre-requisites of Lesagean models, because
a radiation field"

This argument is an outright fraud on the part of "Shadows". Once again, a
radiation field is never part of a Le Sagian model.

"gives something like an inverse-square force only over distances comparable
to the mean-free path of the radiation particles. "

Here "Shadows" tries to twist out of the fraud by inventing the term
"radiation particles."

"Any interaction between particles destroys the inverse-square relation. "

This last statement is not supported anywhere in "Shadows", and it is
patently false.

It is interesting to note that the prediction of a "swirl" in the fluid
around a rotating body is identical to the Lenz-Thirring effect in GR.  The
same effect should manifest for two bodies orbiting a common center of mass.

Once again, we may now bypass the rest of "Shadows"' rants on the subject -
as the basis for that rant has been shown to be fraudulent.

Modification Note 5:

"Shadows" has attempted to insert some information on Le Sage's model in
this philosophical tirade:

"Lesage himself recognized this fundamental problem, and this is why he
suggested (as mentioned above) that ordinary macroscopic bodies are
constructed like "cages", i.e., a lattice network of tiny inter-connected
bars. The idea was that the lattice was sparse enough to be virtually
transparent to ultra-mundane particles, but still could maintain the
structure of macroscopic bodies. This scheme may distract some critics, but
it does nothing to actually solve the problem, because the bars of the cages
obviously must have tensile as well as compressive strength, so each of them
represents an elementary attractive force, which is precisely what the
shadow theory is supposed to do without."

Once again, a total distortion of Le Sage's work.  Le Sage did not propose
the cages as a literal model of the physics of particles.  Atoms themselves
had not yet been proven, and the structure of matter was still 150 years
away. The lie in "Shadows" is the total refusal of the author of "Shadows"
to acknowledge that the matter models in Le Sagian theories have evolved to
match the knowledge of the atom.

--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}