Ken S. Tucker wrote:
Tom's physics comes from 1905 SR (see Principle of Relativty pg 63).

Yes, of course I am using SR, that's what "Minkowski spacetime" means.


While it would be fun to use the GR
dU^i/ds = GAMMA^i _uv U^u U^v
geodesical equation,

You cannot do that, as the applied force prevents the object from
following a geodesic curve.


I'd suggest a simpler scenario.
Using a laser emitted from some fixed "inertial frame" accelerate
an object and predict it's rate of acceleration in the inertial frame.
I think that's a simple and reasonable test gedanken.

OK, we can discuss this.


My concern is a Doppler shift that does not appear in any of the
equations set forth so far.

Of course that has not been mentioned so far, because you just
introduced this gedanken.


Also does the transverse acceleration
account for aberration.

In your gedanken there is no transverse acceleration -- the laser
accelerates the object along its line-of-sight, which is necessarily the
line along which the object moves, so all motion and acceleration is
along this line -- i.e. it is longitudinal.

Your gedanken is not completely specified. and I assume the
accelerated object begins at rest in the same inertial frame
as the laser, when the laser is turned on. If you want to
do a quantitative analysis, you will also have to spcecify
the intensity of the laser, the mass of the object, and the
reflectivity of the object.


In the inertial frame of the laser, the object will accelerate along the
line-of-sight of the laser, and if the laser is powerful enough, the
object is light enough, or we wait long enough, then its speed relative
to that frame will asymptotically approach c. This is not the typical
hyperbolic motion (of an object with constant proper acceleration), as
the proper acceleration decreases as the object accelerates.


Tom Roberts

shevek wrote:
wrote:

Right, but forget the equations for a second and consider the
assumption of an ultramundane aether. In the frame where the aether is
isotropic, the missile is accelerating. Since more aether resistance
is encountered in the direction of the motion, more energy would be
needed to accelerate the object in this frame. If you were to
accelerate the object normal to the direction of motion, from the
aether frame, you would only be creating a small aether resistance as
the velocity w.r.t the aether in the normal direction is not nearly as
much as the velocity w.r.t to the aether in the original direction. In
the frame of missile, you would still find that forces were acting on
the missile, a greater force coming from one direction (the direction
in which in the aether frame the missile is moving) and a smaller force
from normal to that direction (in which in the aether frame you were
attempting to accelerate normal to the original direction). So, with
the assumption of an aether, the effect is not frame dependent, it just
changes from resistance against a moving object to an unknown force (or
an aether wind) acting on a stationary object.


Hi Vern,

That is one possible class of aether theories, the class where massive
particles are distinct from the aether, and are acted upon by the
aether. It sounds like you are envisioning here aether as only
existing -between- material bodies, rather than envisioning material
bodies as stable disturbances of the aether itself. As you may have
realized, I prefer the latter approach.

No, I think that the aether is an integral part of matter; it's just
that once the matter is of sufficient size (atomic, molecular or
bigger), then its movement through the aether at significant speeds
does cause resistance.

I'm suggesting a modification of Newton's laws to add in the effect
of aether resistance and I'm suggesting that without it there is no
explanation for the fact that it takes more force to accelerate an
object the faster you go and to also explain why it doesn't take as
much force to accelerate the object normal to its motion.


That fact becomes untrue when you measure the forces and accelerations
from within the rocket.

You mean from the frame of the rocket there's no force acting against
the rocket because we've applied the Lorentz transformation between
frames thus canceling out the force? But we only did that because we
assumed (postulated) that the speed of light is constant. And in doing
that we defacto ruled out an aether at play. The same equations work
if we do a Galilean transformation and add in aether resistance. The
math doesn't help us decide which model is right.

I see no need of -action- of the aether on material bodies in analogy
to air resistance. Rather, the effect is entirely due to the relative
motion of physical clocks and meter sticks through the aether. An
electromagnetic (physical) coordinate system ticks and extends at rates
proportional to the pressure tensor of the aether - motion through the
ether changes the pressure tensor, as described by Mach's formula of
gas pressure or the Lorentz transformation (as you pointed out below).
So in a way, it is analagous to air resistance.. but this aether
resistance manifests itself by changing the tick/extension rates of
coordinate systems in relative motion - not by providing an external
force on moving objects.

It's important to realize that these relativistic particles are not
acted upon by a force that slows them down - as happens to a projectile
in air. Relativistic particles in accelerators and cosmic rays do obey
Newton's law that an object in motion remains in motion unless acted
upon by an outside force.

I appreciate that perspective (in both paragraphs above), but I'm not
sure it's supported by the evidence (or that there is any evidence).
Let's consider that matter is stable and movement relative to the
aether does not distort it, but rather only provides a resistance to
its motion. As the motion must approach the speed of light (at least
..333) before an effect can be observed, we don't have any everyday
objects to measure. Accelerators do not have a free flight chamber
long enough and without any magnetic force present to check Newton's
1st. I'm betting that if one was designed, the particles would slow
down over time by the factor of gamma once released from any forces.

In this thread we're not talking about a wave, photon or phonon's
resistance due to motion w.r.t a medium, but instead we are considering
an object's resistance to acceleration. With the assumption of an
ultramundane aether, the effect is not due to the changes in the
coordinate system.


Let's pick an object as an example. How about an electron? In fact,
interference patterns can be observed with electrons - and they have an
associated deBroglie wavelength. Waves, wavefunctions, and solitons
are often good models of material objects.

Anyway, the effect must have something to do with changes of the
coordinate system, because some changes of coordinate system eliminate
the effect under discussion.

I think that that statement is based on QM considerations. The
equation of motion in 4-space (longitudinal vs. transverse) that Tom
gave seemed to be solely based on the gamma factor. As far as physical
explanations, isn't it either that there's more energy required or
that more resistance is encountered. I guess the equations assume more
energy, but more resistance would yield the same result.

I was trying to point out that there is a direct analogy between an
object accelerating in an ultramundane aether and an object
accelerating in the air. The Lorentz transformation formula and the
Mach formula are identical and represent a condition where the faster
you go the more resistance there is to the motion to infinity (or the
speed of light and sound respectively). If you plot both formulas on a
graph, they have identical curves.


I believe you are entirely correct that the similarity of these curves
is not a coincidence. They arise from the similar calculations,
determining the kinetic pressure in a moving reference frame. However,
a gradient in pressure in air will cause a force on e.g. an airplane
(air resistance). A gradient in 'pressure' of the aether causes no
such force on a neutral particle. It does affect charges and
electromagnetic forces in e.g. light, and therefore affects our
coordinate systems.

I'm still not convinced, because it could be either and aether
resistance makes more sense. What experiment in your opinion best
demonstrates that motion relative to the aether causes changes to
matter instead of just offering resistance to its motion?

What I find interesting is that Newton seemingly assumed a vacuum for
his laws of mechanics. That's understandable though because at the
time there wasn't any evidence that an ultramundane aether existed
and there wasn't any physical examples (like cyclotrons) to cause him
to think that there would be resistance to accelerating an object
(except from the mass of the object itself). But had Newton guessed
that we live in a medium environment even without the air, then his
laws of mechanics would have reflected resistance to motion because of
the medium. IMO, Maxwell and Lorentz both understood this.


We must be careful not to confuse resistance to acceleration with
resistance to motion. Aristotelan mechanics, and air resistance, are
examples of resistance to motion. Inertia and Newtoninan mechanics
suggest resistance to acceleration; SR suggests anisotropic (direction
& velocity dependent) resistance to acceleration, but no resistance to
motion.

I think I understand the difference between resistance to motion and
resistance to acceleration, however, I don't think I agree that
inertia and Newtonian mechanics suggest resistance to acceleration.
Newton's 1st suggests only to me that there is no aether or that if
there is an aether, it does not affect motion. Newtonian mechanics, I
believe, is based on the same premise because nowhere is there any
equation or rule for how the aether affects motion. The possibility
which was not examined is that there is an aether but because of the
rapid motion of its constituents, it doesn't affect motion until the
motion is significant wrt the isotropy of the aether. That's where
the anology with the air comes in. As long as we go this way or that
walking or running, as long as there's no wind, we don't feel any
air resistance, so we might believe there's no air; but once we start
going fast enough on a bicycle, then the resistance becomes apparent
and we can use that as evidence that a medium is present.

Vern

Tom Roberts wrote:
Ken S. Tucker wrote:
Tom's physics comes from 1905 SR (see Principle of Relativty pg 63).

Yes, of course I am using SR, that's what "Minkowski spacetime" means.


While it would be fun to use the GR
dU^i/ds = GAMMA^i _uv U^u U^v
geodesical equation,

You cannot do that, as the applied force prevents the object from
following a geodesic curve.

dU^i/ds can be non-zero. A rocket can create
GAMMA.

I'd suggest a simpler scenario.
Using a laser emitted from some fixed "inertial frame" accelerate
an object and predict it's rate of acceleration in the inertial frame.
I think that's a simple and reasonable test gedanken.

OK, we can discuss this.


My concern is a Doppler shift that does not appear in any of the
equations set forth so far.

Of course that has not been mentioned so far, because you just
introduced this gedanken.


Also does the transverse acceleration
account for aberration.

In your gedanken there is no transverse acceleration -- the laser
accelerates the object along its line-of-sight, which is necessarily the
line along which the object moves, so all motion and acceleration is
along this line -- i.e. it is longitudinal.

Your gedanken is not completely specified. and I assume the
accelerated object begins at rest in the same inertial frame
as the laser, when the laser is turned on. If you want to
do a quantitative analysis, you will also have to spcecify
the intensity of the laser, the mass of the object, and the
reflectivity of the object.


In the inertial frame of the laser, the object will accelerate along the
line-of-sight of the laser, and if the laser is powerful enough, the
object is light enough, or we wait long enough, then its speed relative
to that frame will asymptotically approach c. This is not the typical
hyperbolic motion (of an object with constant proper acceleration), as
the proper acceleration decreases as the object accelerates.

Alright. Let's consider Gedanken 2, modified from 1.
In an inertial frame (zero accelometer reading),
we place a box with a particle in the center.
Along the x,y,z axes we use laser's to maintain
the particle in the exact center of the box, 6
lasers in all. All the laser's are of the same
frequency and intensity in that inertial FoR.

Relative to a moving system, and/or accelerating
system, the laser's frequency and direction must
transform to maintain the particle fixed in the
center of the box.

Since those laser's can be simplified to EM-forces,
your equations need to be true in both gedankens,
and all FoR's, that's a GR challenge.

I think the 2nd gedanken is easier because the
center of the box is geometrically invariant and
hence is the position of the particle situated
there in all frames, by equally acting EM-forces
from the lasers attached to the box.

So I would view the problem of the transformation
of force to be one that transforms the laser's
intensities (Doppler) and directions (aberration)
together with a relativistic correction to maintain
the particle in the invariant geometric center of
the box, in ALL FoR's.

Those same equations, using GR, permit the accelerated
observer passing that box to consider themselves at
rest, and the box accelerating, otherwise one begins
to believe absolute accelaration exists, and that is
NOT GR compatible.

Regards
Ken S. Tucker

Ken S. Tucker wrote:
Tom Roberts wrote:
Ken S. Tucker wrote:
While it would be fun to use the GR
dU^i/ds = GAMMA^i _uv U^u U^v
geodesical equation,
You cannot do that, as the applied force prevents the object from
following a geodesic curve.

dU^i/ds can be non-zero. A rocket can create
GAMMA.

Ha! even polar and spherical coordinates have nonzero GAMMA.

But still, with an applied force the object will not follow a geodesic
path, and that equation does not apply. shrug


Alright. Let's consider Gedanken 2, modified from 1.
In an inertial frame (zero accelometer reading),
we place a box with a particle in the center.
Along the x,y,z axes we use laser's to maintain
the particle in the exact center of the box, 6
lasers in all. All the laser's are of the same
frequency and intensity in that inertial FoR.

OK, a new gedanken.


Relative to a moving system, and/or accelerating
system, the laser's frequency and direction must
transform to maintain the particle fixed in the
center of the box.

Sure.


Since those laser's can be simplified to EM-forces,
your equations need to be true in both gedankens,
and all FoR's, that's a GR challenge.

It happens automatically. Golly gee, invariant equations remain
invariant under a change of coordinates. shrug


I think the 2nd gedanken is easier because the
center of the box is geometrically invariant and
hence is the position of the particle situated
there in all frames, by equally acting EM-forces
from the lasers attached to the box.

So I would view the problem of the transformation
of force to be one that transforms the laser's
intensities (Doppler) and directions (aberration)
together with a relativistic correction to maintain
the particle in the invariant geometric center of
the box, in ALL FoR's.

Those same equations, using GR, permit the accelerated
observer passing that box to consider themselves at
rest, and the box accelerating, otherwise one begins
to believe absolute accelaration exists, and that is
NOT GR compatible.

Use any coordinates and you will obtain the same answer -- the particle
remains at the center of the box. How could it be otherwise?

BTW as the box is at rest in an inertial frame (which implies the
existence of such a frame), one can use SR.


Tom Roberts

Tom Roberts wrote:
Ken S. Tucker wrote:
Tom Roberts wrote:
Ken S. Tucker wrote:
While it would be fun to use the GR
dU^i/ds = -GAMMA^i _uv U^u U^v
geodesical equation,
You cannot do that, as the applied force prevents the object from
following a geodesic curve.

dU^i/ds can be non-zero. A rocket can create
GAMMA.

Ha! even polar and spherical coordinates have nonzero GAMMA.

In 4D they show up as artifacts.

But still, with an applied force the object will not follow a geodesic
path, and that equation does not apply. shrug

Sure it does, use g_01,0 as acceleration as the only
variable, (g_00,1 =0), then,

dU^1/ds = - g_01,1 ,

with the g_01,1 being inertial acceleration.

Test that using the force on your butt sitting
on your chair and find, (g_00,1 =/=0),

0 = dU^1/ds = (1/2)*g_00,1 - g_01,1 .

If you weren't restrained by your chair then
you would free-fall and

0 = dU^1/ds - (1/2)*g_00,1 ,

as you should!

The geodesic DU^u/ds = 0 contains 80 different
components of g_uv (16) and g_uv,w (64).

Alright. Let's consider Gedanken 2, modified from 1.
In an inertial frame (zero accelometer reading),
we place a box with a particle in the center.
Along the x,y,z axes we use laser's to maintain
the particle in the exact center of the box, 6
lasers in all. All the laser's are of the same
frequency and intensity in that inertial FoR.

OK, a new gedanken.


Relative to a moving system, and/or accelerating
system, the laser's frequency and direction must
transform to maintain the particle fixed in the
center of the box.

Sure.


Since those laser's can be simplified to EM-forces,
your equations need to be true in both gedankens,
and all FoR's, that's a GR challenge.

It happens automatically. Golly gee, invariant equations remain
invariant under a change of coordinates. shrug

On Aug.24 you posted on forces, Fx, Fy ... -Fz,
what you need to do is prove those equations in
the simplest gedanken.

I think the 2nd gedanken is easier because the
center of the box is geometrically invariant and
hence is the position of the particle situated
there in all frames, by equally acting EM-forces
from the lasers attached to the box.

So I would view the problem of the transformation
of force to be one that transforms the laser's
intensities (Doppler) and directions (aberration)
together with a relativistic correction to maintain
the particle in the invariant geometric center of
the box, in ALL FoR's.

Those same equations, using GR, permit the accelerated
observer passing that box to consider themselves at
rest, and the box accelerating, otherwise one begins
to believe absolute accelaration exists, and that is
NOT GR compatible.

Use any coordinates and you will obtain the same answer -- the particle
remains at the center of the box. How could it be otherwise?

BTW as the box is at rest in an inertial frame (which implies the
existence of such a frame), one can use SR.

Tom can, I can't in General. Tom may want to solve the
problem using his equations of Aug.24, with real math.
I can only use the geodesic which works fine once you
get to know you to use it.

Regards
Ken S. Tucker

wrote:
shevek wrote:
wrote:
[..]

I'm still not convinced, because it could be either and aether
resistance makes more sense. What experiment in your opinion best
demonstrates that motion relative to the aether causes changes to
matter instead of just offering resistance to its motion?


Thanks Vern, again I appreciate your thoughts here. You're right that
we need to use caution as relativistic motion is not a common
experimental possibility, at least when it comes to putting certain
laboratory equipment on board the moving platform.

You asked about what experiments could be done to discern between these
two similar aether models of SR acceleration / variable mass effects.
One thing that comes to mind is measurments of the ability of high
energy particles to retain that energy. If you are right that there is
a force provided by the aether on a moving body, the kinetic energy (of
a mass) shouldn't be conserved. The existence of high energy
(gamma1) cosmic rays reaching Earth suggests that particles have not
lost their energy despite their fast motion through the aether.
However, a mesurement of particle flux near the source as well would
make this even better experimental evidence.



[..]

I think I understand the difference between resistance to motion and
resistance to acceleration, however, I don't think I agree that
inertia and Newtonian mechanics suggest resistance to acceleration.
Newton's 1st suggests only to me that there is no aether or that if
there is an aether, it does not affect motion.

OK. It doesn't affect motion, unless it is applying a force. To me,
Newton's laws represent a well-thought definition of the words
"motion", "force", "acceleration" and "mass". If motion is changed
(acceleration exists), we say there is a force applied.

Newtonian mechanics, I
believe, is based on the same premise because nowhere is there any
equation or rule for how the aether affects motion.

Not exactly. He came up with one important rule for how the aether
affects motion - his law of gravity.

The possibility
which was not examined is that there is an aether but because of the
rapid motion of its constituents, it doesn't affect motion until the
motion is significant wrt the isotropy of the aether. That's where
the anology with the air comes in. As long as we go this way or that
walking or running, as long as there's no wind, we don't feel any
air resistance, so we might believe there's no air; but once we start
going fast enough on a bicycle, then the resistance becomes apparent
and we can use that as evidence that a medium is present.


That is cerainly worthy of consideration.. Perhaps another reader can
cite high energy experiments where a relativistic particle maintains
its energy while crossing a vacuum?

Cheers - shevek

shevek wrote:
Also, a fluid-dynamic model with point particles does not support
transverse waves. The addition of further degrees of freedom in the
particles (such as spin) will also allow transverse waves.

The æther model is obviously by inhomogeneous media. A waving string
in air is transverse or helical sound. Treat the æther as having
different states and don't assume it's a gas of field repeaters.

-Aut

shevek wrote:
wrote:

I know you like the aether sink idea, but where does the aether go?

The formula for consumption matches Newton's Law of Gravitation.

F(gravity) = G(M/R^2) (1)

F(sink) = K'(Q/R^2) (2)

Where G is the Gravitational Constant, K' is the sink-vortex constant
and Q is the rate of consumption of mass or the total number of
aethrons consumed by the sink per unit time.

There is also a circulatory pattern, so not all of the aethrons are
being consumed.


You didn't answer my question: where are they going?

Do these aethrons appear somewhere else via a wormhole or something?

The circulatory pattern looks like that of a dipole. The Earth's
magnetic field or the magnetic field of a magnet gives the general
shape of the circulatory flow. The term used in the Aethro-Kinematics
book is a donut vortex. The aether is like an ideal gas or a
superfluid. The particles themselves are simply oscillating from
random collisions with longer collision free distances towards the
sink, which is in the center of the mass around which the circulatory
pattern forms (actually, that's not totally true because it's a
sink-vortex so the longer collision free distance is both towards the
sink and in the direction of the spiral). Over time there would be
some condensation or consumption of the particles accumulating at the
core in larger masses such as the Earth which will cause the matter to
enlarge over long periods of time, but the circulatory pattern
predominates and in smaller masses (atoms, for instance), the
circulatory pattern is all that needs to be considered. The flow is
into the core in every direction, however, what results is a
circulation where the flow comes back out of the center of the mass in
linear fashion in one direction (say north/south) and then recirculates
to the other pole. This causes the mass to rotate perpendicularly to
the flow through the center (east/west). Can this type of flow
simulate gravity? It seems there would be minor fluxuations at the
poles due to the circulatory pattern. That is true for a magnet though
as there is a definite circulatory pattern, but the magnetic field is
still fairly consistent, e.g. the field strength is still the same at
the poles even through a circulatory flow is apparent.

Also, you give these particles mass.. I prefer a description of mass
density as a statistical property of their motion. Otherwise, you will
have a very massive vacuum on your hands, and still remain with the
problem of explaining what mass is. I suppose a massive vacuum does
fit in with your idea of an "aether resistance"...

The mass of each aethron is negligible; assumed to much less than the
average collision-free distance between collisions, which is estimated
to be 6 x 10^-15 cm.

It
doesn't make sense to me. I see a particle like an electron analagous
to a hurricane.. it isn't a "sink" of air, rather a stable low or high
pressure disturbance.

Kinematically, doesn't it have to either be a circular-vortex or a
sink-vortex? The sink-vortex provides the forces for elliptical
orbits, gravity, the release of energy in quanta and angular momentum;
circular-vortices don't.


Why not? A circular vortex (with conservation of particles) can
maintain a radial pressure gradient, see e.g. a hurricane or Burger's
vortex solution to the Navier-Stokes equations.

The continuity equation is the very basis of fluid mechanics, I
wouldn't abandon it until we absolutely have to.

Interestingly enough, Newton refuted Descartes' solar vortex theory
based on the mathematics of a circular vortex, while the properties of
a sink-vortex were not considered. In an ideal gas there would be no
reason for a circular vortex to form, but a sink-vortex would be a more
likely evolution.

Do you think aethrons are destroyed somehow in a
particle?

If the consumption is on a big enough scale (as in planets) then it
adds to the mass. I guess we need to play with the formula for
consumption to get an idea of what it would mean for, say, an atom.


If you are talking about destruction of aethrons then you are talking
about a sub-aether. That's getting a little ahead of the game,
hopefully we don't need to go there yet.

The circulatory flow predominates. Where the mass is large enough then
there is some consumption, not destruction, per se, but with enough
heat and pressure new material can be formed.

A charge is a divergence of electric field, a monopole
rather than a dipole (unless you have two opposite charges close
together).

But in an aether vortex model, the field is the vortex, so charge is
just the influence the medium has on a mass particle. Negative charge
is a sink and positive charge is a source.


Do you envision the aethrons going into an electron then and instantly
emerging elsewhere from a positron? And why that choice of sink/source
and not its converse?

An electron may be a single donut vortex or it may be a number of donut
vortices coupled together. Even coupled together, the basic formation
is that of a larger donut vortex. Again, the individual aethrons are
just oscillating with a different collision-free distance in relation
to the sink at the center of the donut vortex. The electron is acting
as a unit and is orbiting a nucleus because of the vortex of the
nucleus, or if a free electron, is still just a donut vortex unit. The
unit is capable of combining with other donut vortices depending on its
strength and configuration (number of units coupled). My statement
that a negative charge is a sink and a positive charge a source was
misleading as each unit functions as a linear dipole.

[...]

Particle collisions are not required for waves to propagate in a
fluid!! Remarkably, they play almost no role in affecting e.g. sounds
travelling through the air, despite the small mean free path.

Also, a fluid-dynamic model with point particles does not support
transverse waves. The addition of further degrees of freedom in the
particles (such as spin) will also allow transverse waves.

Then how does a wave travel through an ideal gas? There is nothing but
particle collisions. I seem to remember a paper by Marmanis which
modeled Maxwell's equations in an ideal gas, including transverse
waves.

If polarization is re-examined using this model, it can be explained.
An attempt was made to polarize sound waves with some success back in
the 1800's. The difference is that you don't have the interaction
of the wave with the polarizer, so the technique involved reflecting
the waves in different directions.


I guess it depends on your definition. If by "sound" you mean only
fluctuations of scalar pressure, then there's no room for polarization.
If you consider specific rotation or vibration states of the
molecules, then you could probably observe some kind of polarization.

The sound waves were made by a drum and were transmitted through an
inert gas through pipes and reflected at different angles. The article
is archived in the Aethro-Kinematics (yahoogroup) group.

Vern

wrote:
shevek wrote:
wrote:

There is also a circulatory pattern, so not all of the aethrons are
being consumed.


You didn't answer my question: where are they going?

Do these aethrons appear somewhere else via a wormhole or something?

The circulatory pattern looks like that of a dipole. The Earth's
magnetic field or the magnetic field of a magnet gives the general
shape of the circulatory flow. The term used in the Aethro-Kinematics
book is a donut vortex.

OK, no need for a "sink" then in the case of a magnetic dipole..

The aether is like an ideal gas or a
superfluid. The particles themselves are simply oscillating from
random collisions with longer collision free distances towards the
sink, which is in the center of the mass around which the circulatory
pattern forms (actually, that's not totally true because it's a
sink-vortex so the longer collision free distance is both towards the
sink and in the direction of the spiral). Over time there would be
some condensation or consumption of the particles accumulating at the
core in larger masses such as the Earth which will cause the matter to
enlarge over long periods of time,

eh? let's stick to the topic. I'm not sure what "matter enlargement"
might mean, if you are saying a meter stick grows in size then you are
addressing a philisophical argument known as "nocturnal doubling"..
such an effect might be forever unobservable to us and therefore not
worth discussing.


but the circulatory pattern
predominates and in smaller masses (atoms, for instance), the
circulatory pattern is all that needs to be considered. The flow is
into the core in every direction, however, what results is a
circulation where the flow comes back out of the center of the mass in
linear fashion in one direction (say north/south) and then recirculates
to the other pole.

Ok, well then the flow isn't into the core in -every- direction, is it.
If the particles come back out it isn't a true sink, at least the way
I understand the meaning of "sink".

I'm aware there's a paper archived on that topic in AK group as well,
but sorry I don't know much about it.

This causes the mass to rotate perpendicularly to
the flow through the center (east/west). Can this type of flow
simulate gravity? It seems there would be minor fluxuations at the
poles due to the circulatory pattern. That is true for a magnet though
as there is a definite circulatory pattern, but the magnetic field is
still fairly consistent, e.g. the field strength is still the same at
the poles even through a circulatory flow is apparent.


I think you're getting ahead of yourself here. Masses have not been
observed to receive torques in the absence of external forces, afaik.


The mass of each aethron is negligible; assumed to much less than the
average collision-free distance between collisions, which is estimated
to be 6 x 10^-15 cm.


?? First of all, negligible is very different from zero, especially
when you have on the the order of 10^100 per cubic cm. Second, a
distance is not a unit of mass. Third, your mean free path seems way
too big to me. 10^-15cm is absolutely enormous on the scale of
space-time atoms, which are closer to the Planck length, 1.5*10^-33 cm.




The continuity equation is the very basis of fluid mechanics, I
wouldn't abandon it until we absolutely have to.

Interestingly enough, Newton refuted Descartes' solar vortex theory
based on the mathematics of a circular vortex, while the properties of
a sink-vortex were not considered. In an ideal gas there would be no
reason for a circular vortex to form, but a sink-vortex would be a more
likely evolution.


?? If you are talking about a sink vortex in a fluid, you need a
mechanism for the sink. For example, your sinks have drains.


Do you envision the aethrons going into an electron then and instantly
emerging elsewhere from a positron? And why that choice of sink/source
and not its converse?

An electron may be a single donut vortex or it may be a number of donut
vortices coupled together. Even coupled together, the basic formation
is that of a larger donut vortex. Again, the individual aethrons are
just oscillating with a different collision-free distance in relation
to the sink at the center of the donut vortex.

Wait a minute.. a donut vortex is a sink? I'm not following..

[...]

Particle collisions are not required for waves to propagate in a
fluid!! Remarkably, they play almost no role in affecting e.g. sounds
travelling through the air, despite the small mean free path.

Also, a fluid-dynamic model with point particles does not support
transverse waves. The addition of further degrees of freedom in the
particles (such as spin) will also allow transverse waves.

Then how does a wave travel through an ideal gas? There is nothing but
particle collisions. I seem to remember a paper by Marmanis which
modeled Maxwell's equations in an ideal gas, including transverse
waves.


The wave travels solely due to the fact that a particle in motion
remains in motion. If you add some motion in one area, the particles
move away from the area and the region with extra motion spreads out
like a wave.

More formally, sound waves can be derived from Boltzmann's equation for
the evolution of a fluid, assuming no collisions. See e.g. Landau &
Lif****z 's Fluid Mechanics.

Marmanis' work didn't include effects of collisions afaik.

Didn't we discuss this before here?


I guess it depends on your definition. If by "sound" you mean only
fluctuations of scalar pressure, then there's no room for polarization.
If you consider specific rotation or vibration states of the
molecules, then you could probably observe some kind of polarization.

The sound waves were made by a drum and were transmitted through an
inert gas through pipes and reflected at different angles. The article
is archived in the Aethro-Kinematics (yahoogroup) group.


Thanks Vern, I'll take another look at it one of these days.

Autymn D. C.:
shevek wrote:
Also, a fluid-dynamic model with point particles does not support
transverse waves. The addition of further degrees of freedom in the
particles (such as spin) will also allow transverse waves.

The =E6ther model is obviously by inhomogeneous media. A waving string
in air is transverse or helical sound. Treat the =E6ther as having
different states and don't assume it's a gas of field repeaters.

OK, so why does that preclude exceeding the velocity of the
``ether waves?'' I can exceed the velocity of the waves on
a string.