Re: Ambiguity in the "Affine Connection"

shevek4_at_yahoo.com
Date: 02/27/05 

Date: 27 Feb 2005 14:03:04 -0800

globarr@yahoo.com wrote:
> In <1109350664.658848.196120@o13g2000cwo.googlegroups.com>
> Sheved <shevek4...@yahoo.com> wrote:
> >Gerald L. O'Barr <globarr...@yahoo.com> wrote:
> >> . . .
>
> Shevek <shevek4...@yahoo.com> wrote:
> > You might want to learn something about the kinetic
> > theory of gases before tackling aether dynamics.
> > Sound waves can exist in collisionless gases.
>
> Gerald L. O'Barr <globarr...@yahoo.com> wrote:
> And is this 'collisionless gas' a real gas, or
> just a mathematical assumption? To the best of my
> knowledge, all real gases have a very specific mean
> free path, which is to say that they collide, exactly
> as I said. And they bounce.
>

Yes, and there is a mean free path for 3 molecule collisions, and a
mean free path for 4 molecule collisions, etc. These higher orders
contribute to higher power terms in the virial equation of state. A
"collisionless gas" is one in which we can safely neglect all of these
- for example if pV=nrT.

> Shevek continues:
> > In fact,
> > assuming that gas molecules do not collide
> >allows derivation of most of acoustics. An ideal
> >gas is modeled by collisionless dynamics - a
> >maxwellian distribution of particle speeds and zero
> >collision term in the Boltzmann eqauation.
> >You only need to consider the collisions for sound
> >damping rates, and non-linear effects. Try Landau &
> >Lifshitz, "Fluid Mechanics". They have a good
> >section on sound waves, to name one. The equation
> >of state admittedly makes it a bit tricky; Newton
> >got the speed of sound wrong.
>
> Gerald L. O'Barr <globarr...@yahoo.com> wrote:
> Thanks for the update. It has been over 30 years
> since I have studied this area. But I would like to
> make a few things clear. Mathematically speaking,
> you can have a sound wave without there even being
> particles. You can mathematically handle it as a
> continuous medium.

Good point. Of course, you are giving up a lot when you give up the
kinetic theory of gases- what for example is density? What is
pressure? You must agree that the kinetic approach is superior, both
for understanding and predicting behaviors of gases.

> So what math allows, as a general rule, is not of
> much interest to me. And I am not sure exactly what
> you do to get your results. If you let loose a
> single blast of gas at a point in space, the atoms
> will all escape with very little or no collisions
> between them, but you would not have sound. You
> would have one large pressure pulse, and nothing
> more. And the velocity of this pressure pulse would
> depend upon the release conditions, not upon any
> properties of the gas as it would be as a medium.
> So I can envision situations where collisionless acts
> result in no sound (sound being defined as continuous
> self sustaining oscillations within the medium.)
> As a specific scientific point: For a real
> medium, there is a frequency cut off. That is, a
> maximum frequency at which sound can exist. Do you
> know what limits this max? And so what would be the
> maximum frequency of sound for your collisionless
> gas? Does it, therefore, have sound? I hope you
> are not talking about sloushing in a box!

Yes, diffusion is subtly different from wave propagation.
You are talking about nonlinear effects with your frequency cutoff.
Practically, the higher frequency limits are due to the difficulty of
coupling a driver (speaker) to the air at high frequencies. If it is
moving fast enough and with short enough oscillations the air is
unaffected and you are no longer creating sound. In water it is much
easier to do ultrasonics. However, there are other effects such as
dispersion that come into play and limit high frequency propagation.
For a collisionless gas there still could be nonlinear terms and a
cutoff - again, you aren't going to need to consider all collisions to
describe the behavior of a gas - even if collisions are actually quite
commonplace.

> And the most important thing of all, I am not
> doing anything in terms of ether dynamics. The
> computer handles all this.

LOL!! I recommend a graduate student, they are easier to talk to than
a x86 box. BTW, I am both a computer and a graduate student.

> So anyway, your comments
> are not very meaningful. If you really had something
> to say, I would appreciate you restating it in a more
> direct way.

My point is that kinetic theory describes galaxies as made up of
stars.. gases as made up of atoms.. it should be no surprise that
space-time and field theory can be described in the same way in terms
of statistical physics of aethrons.

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