[Physics] Discussion ‘new beginning’ in physics necessary'.

[Arend Lammertink]

Hi James,


On Mon, Dec 12, 2016 at 7:35 PM, James Rose <integrity at prodigy.net> wrote:
> Mike and Arend,
>
> Thank you for your thoughtful remarks and descriptions.
> I have three additional questions.
>
> 1)  When topological architecture reduces to zero-dimension, is there any
> way for 'information content' to remain, or does it simply vanish relative
> to all other parameters and dimensions?
>

I'm afraid you're thinking in the wrong direction here. The idea
behind considering a topological architecture in "the limit towards
zero (size)" is to *reduce* the amount of information you have to
consider, when considering the behavior of a whole lot of of these
"things" taken together.

Let's consider a truckload of marbles, let's say there's 1 million
marbles, filling up a container. Now suppose we would be interested in
the forces being exchanged between the container and the truck that's
carrying it.

In that case, we could try to describe the exact location, movement,
etc. off all these marbles, so we can describe the force each
individual marble enacts upon the bottom of the container, for
example. In such consideration, you would find that the pressure
enacted by the marbles upon the bottom of the container is not
constant. At the places where a marble is in contact with the metal of
the container, there is a pressure c.q. force. In between these
contact areas, there are relatively large areas where there is no
contact,  hence no force.

So, such consideration gives you detailed information, *but* it
requires a lot of information to be taken into account and process,
which is very complicated in case you only want to know "what are the
forces enacted upon the truck"?

In the case the container is supported by the truck at it's 4 corners,
you can compute that by adding the weight of all marbles together, and
dividing that by 4 (assuming a weightless container).

When you wish to study the dynamic behavior of the marble filled
container, one could assume the marbles are divided evenly across,
say, the lower half of the container. So, if there are n marbles per
cubic decimeter (liter) and we know the weight of each marble, we can
compute a mass density per cubic meter and assume this to be constant
across the volume occupied by the marbles. Lets call this "D".

So, then you would consider the container to be "half full" with a
"material" which has mass density D, while the other half is filled
with air.

That is essentially what is called "continuum mechanics":

https://en.wikipedia.org/wiki/Continuum_mechanics
-:-
Modeling an object as a continuum assumes that the substance of the
object completely fills the space it occupies. Modeling objects in
this way ignores the fact that matter is made of atoms, and so is not
continuous; however, on length scales much greater than that of
inter-atomic distances, such models are highly accurate. Fundamental
physical laws such as the conservation of mass, the conservation of
momentum, and the conservation of energy may be applied to such models
to derive differential equations describing the behavior of such
objects, and some information about the particular material studied is
added through constitutive relations.
-:-


So, that's what we're trying to do when we would consider a "vortex
ring topology" in the limit to zero.

Let's continue with the marble example, to illustrate this.

What would happen to our "half full" consideration, when we would have
had 10 million marbles, each with 1/10th of the size and weight of our
original 1 million bigger marbles?

Well, the mass density of the "marble material" would remain the same,
so the considerations wherein we calculate with the density in
"continuum" approximation, would remain valid as they are!

And of course, we can continue this line of thinking:

100 million marbles, 1/100th of the size/weight of our original;
1     billion marbles, 1/1000th of the size/weight of our original.

And so on, and so on.

Theoretically, one can continue this exercise indefinitely. You will
never actually reach the point where your marble has a zero size, nor
will you reach the point where you have an infinite number of marbles
in your container.

BUT in this exercise, the mass density D remains constant, regardless
of how small your marbles become, because when you divide each marble
into 2 smaller ones, the total weight remains constant.


So, when I suggest to take the limit to zero of a vortex ring
topology, the idea is to try and find out *if* we can find  continuous
parameters similar to "density" to describe the behavior of a whole
bunch of such vortex rings together, just in the example of a
container filled with marbles.


I shared a similar perspective earlier:


http://mail.tuks.nl/pipermail/physics/2016-December/000263.html
-:-
The model I made is in the form of differential equations within a
continuous fluid dynamics context. The latter means the equations do
not describe the exact movement of each "particle" within the fluid,
but rather describes the flows and the pressures within the fluid on a
more macroscopic level, where you don't "see" the individual
particles.

Using differential equations in this case means that one describes the
fluid movements and tensions/stresses over an infinitely small volume,
which means that one can consider all relationships to be linear
within such an infinitely small volume.  In computer simulations,
these infinitely small volumes are approximated with "small enough"
volumes with respect to the phenomenon one is studying. This is called
the "finite element method":

https://en.wikipedia.org/wiki/Finite_element_method

For example, if one is interested in simulating weather phenomena, one
can consider the air pressure and wind velocity to be constant across
a volume of, let's say, 10-100 meter in diameter. When one would be
interested in studying a vortex in a cup of water, one would use
volumes with a diameter in the order of 1 micrometer to 1 millimeter.

Another way of thinking of it is to consider that any non-linear
relationship/function can be approximated by a "piecewise" linear
function:

https://en.wikipedia.org/wiki/Piecewise_linear_function

The more "pieces" one uses, the better the approximation. So, when one
takes the length of each piece infinitely small mathematically, one
ends up with a 100% exact "approximation" using only linear
relationships.

In other words: differential equations allow you to use linear
equations, regardless of whether or not the "macroscopic" relations
are linear or not.
-:-



Now the problem we identified is the nature of "charge" and how the
Lorentz force works.

Obviously, the behavior of charged particles under the influence of a
magnetic field can be described in a continuous approximation. This is
what Faraday's and Ampere's laws do.

So, if our basic aether model is correct, it *must* be possible to
describe these two laws consistently by some kind of "density"-like
continuous parameters.

At this point, one can make two conclusions:

1) because our model so far does not describe these two laws properly,
our basic model must be incorrect;

2) since there is no reason to assume our basic model to be incorrect,
we should be able to find a set of continuous parameters which
describe the mentioned laws in a satisfactory manner.


I believe conclusion 2 to be applicable, because of lots of other
considerations, such as the consideration of data which suggest
longitudinal dielectric waves are indeed possible, as can be found in
this unfinished (raw) article by me:

http://www.tuks.nl/wiki/index.php/Main/LongitudinalMoonBounceChallenge

So, then the question becomes: how to find and define these
parameters, which *should* exist?

So far, it seems that the fundamental aspect we have not covered in
our model is the 90 degree angle between the two axis of rotation in a
vortex ring structure. That appears to be the missing principle in our
model, without which we cannot describe the Lorentz force nor
understand the nature of "charge". Furthermore, we note that that for
the vortex ring structure, the "rotation" or "curl" of rotation axis
1, gives you rotation axis 2.

So, if we can somehow isolate this 90 degree angle property associated
with "vortex rings" and describe this property independent of the
exact size and shape of the structure we use as our basis, our "vortex
ring" marble, we can extend our basic model with a newly defined
derived "field" with which we can describe and study "charge" and the
Lorentz force.

So, how could we do that?

Is there a "deeper" principle, which could explain or at least
describe this 90 degree angle?

Can we, or should we, refine our basic model?

At this moment, I see two options:

1) consider the use of complex math, in order to relate the two axis
of rotation by means of "complex conjugation";

2) consider to extend to basic model, such that it explicitly also
conserves rotational momentum, and work that out.

At this moment, that's where I am now. Option 2) just entered my mind,
while thinking about what I wrote just above. So, I will ponder with
this a while longer....


> 2)  Has anyone discussed or proposed entropy measures - strictly and solely
> in regard to distribution, rather than thermodynamics?
>
> 3)  When reviewing the complexity and partitioning of systems, can there be
> multiple 'entropy parameters',
>                  or, is entropy evaluated only over the entire domain as a
> single factor~parameter net~sum?
>

Well, in a completely deterministic theory, as our model, the concept
of "entropy" can be seen as exactly such a "continuous approximation"
parameter I mentioned above. Also, since there is no "randomness", we
will have to reconsider and/or redefine what we mean by "entropy".

I think one could see it as representing the energy density
distribution within the system, which could theoretically be computed
at any point within the system. In the normal meaning of the concept
"entropy", it can be seen s a measure of the amount of "randomness"
contained within the system.

In either situation, spectral (Fourier) analysis (and the variations
therein over time) could be used to study the distribution of
"entropy", albeit in the "frequency domain" rather than the spatial
domain.

Regards,

Arend.