Re: Thoughts on why space must have three dimensions

Sue... wrote:
Timothy Golden BandTechnology.com wrote:
Sue... wrote:
<snip></snip>
I think I see the reciprocal nature of what you are describing.
Introducing elasticity...

The Coulomb force is exactly 1/r^2. The reciprocal effect of the
cord, of course, is only an approximation to illustrate the delay
mechanism. A taunt (long) cord decreased the time delay.
A long Coulomb line of force increases the delay.

It would seem that the classical force equations are double sprung so
that F=kx becomes F=k1k2x1x2 gets closer to a charge phenomenon. If one
looks at force as a first plus a second derivative that could be
suggestive. Sum them and at large distance the linear one goes away. In
the near range there could be a linear component still disappearing at
zero. Then a midrange should expose it, or perhaps it should expose a
midrange. Interesting.

The magnetic component dimishes by 1/r^3.
Maxwell doesn't model things like London and Van der Waals
that can show up in near field as oscillating attractive and
repulsive and diminishing by 1/r^4 to 1/r^6..or more but
if you are working with fundamental particles they might
show up just as with Ewald sums..

By fundamental particle do you mean beneath an electron?
You come up with some pretty interesting topics.
I've just read for my first time about Ewald sums.
The use of 'reciprocal space' for them is a Fourier transform.
I use that phrase to mean just a magnitudinal distance transform of
Y = 1 / ( X + 1 )
which is quite a lot simpler. I'll have to brush up on dimensional
Fourier analysis. I'm used to it in the signal domain where it's
application is very intuitive.

So far I see Maxwells equations on the topology
0D + 1D + 2D ...
as being an operator that acts between 1D and 2D.

Time and a 2D isotropy sounds like good characteristics.
for magnets. :-)

I think you've said that before. I don't understand what you are
saying. I'm looking at magnet as sourced from the 1D in this topology.


Going from 1D to 2D (simplest first) it should be like an inverse cross
product, where the 1D is effectively yielding a 2D entity. The 2D form
may be just a simple loop so its not necessarily informationally any
greater, its just a geometric progression.

<< This way of looking at the electron puts magnet first, and
charge secondarily produced by it via this operation. >>

I boil folks in oil for that in the macro atomic world. But
subatomically we hope to find something holding electrons
together so have to allow for anything and be thankful if
it is recognisable.

Is that to say that stability ought to be a property of the particle? I
puzzle over that one some. If a particles stability is inherent then we
have to explain instability of some particles. Whether the cart is
ahead of the horse here I don't know. It's like it's going in a circle
and they are both ahead of each other. Is there a principle on this?

This is the inverse of the traditional approach of
putting the charge first and viewing its magnetic moment as a spin of
the charge, though Maxwell's equations agree that either way the
problem is the same. But where is the charge? Well this is the same as
asking where the magnet is in the standard space.

Exactly the same. The magnet in 'free space' is virtual where
no matter exist to integreate the force.

The best answer so
far is that it is inherent, or (standard space) that the spin of the
electron is inherent and hence its magnet. The interchangeability of
all of these seem to be what Maxwell's equations are about, but they
are taken and stay in a flat 3D topology.

If we consider a proton as a slow reversed version of the electron then
we could see the slow magnets joining up into a nucleus. Their lack of
speed could diminish their 2D strength via the operator that takes them
upward in dimension. The hope would be that this operator is a general
one that applies in any dimension. So going from 0D to 1D would have to
be included, and that would hopefully be where mass is exhibited, mass
being a one-signed charge whereas magnet is a two-signed charge
(dipole) would lead one to consider the next thing up to be literally a
three-signed tripole object.

Ouch! Put a crick in my neck. But are you familiar with the fractional
quantum hall effect?
"Electrons in New Guises" Horst L. Störmer and Daniel C. Tsui
http://nobelprize.org/nobel_prizes/physics/laureates/1998/press.html

The first fraction is 1/3.

Thanks for the link. I wasn't familiar with the fractional version and
really not up on the Hall effect with the exception of its use for
compasses. I'll try to learn the circular path theory. I wonder how
many accept 'quantum fluid' as a reality. To bastardize the whole thing
I'm seeing little bar magnets chaining up together to defeat the B
field by cancelling so that they can move about in the plane. Boil me
in oil.

There are so many options. But I do think that the simple minded
approach of coming up from 0D rather than coming down from highD is
worth sticking to. An argument could arise against this basic step
even. So my view of the problem is completely open, or as open as I can
be. How we can come out with charge perfectly equal and mass not at
all is probably the nicest puzzle. Perhaps we are measuring things
upon an invalid assumption. I suppose it suggests that the equality of
charge is false and that what we are getting is a balance of the entire
chain of effects that we are calling charge placed atop the others.
It's quantization and balance lead us to believe that these opposites
are identical in one regard yet nonidentical in another.

Don't fret over the gravitational/inertial mass. QM and coherent matter
seems to get by without it. The things that fly out of composite
particles are another matter. (pun intended) They have to be
accounted for.


Is this approach flawed by imposing symmetry on different species?

It probably is but we can't build an atom with a nice symetrical
collection of electrons and positrons so we have to improvise
till you get the quarks modeled. Feynman invented virtual particles
which come an go as you please. No protons required.


Particles. I think I'll just try to stick to my generic point particle
for now and see where it goes. But you bring up some good points about
keeping open to what is fundamental. I could see it going either way.
Usually I see the electron being ultimately fundamental just being
smashed up into broken parts. I don't see how you can say it is OK to
dodge the heavy proton, or is it really doging the light electron? As a
Shakespearian monkey I'll try to not see it any way at all.

-Tim



The paradigm of the invalid assumption has a lot of power. The invalid
assumption occurs often enough at an individual level. It even seems to
happen en masse as we see through the course of history and even today.
A skeptical approach will find the invalid assumption eventually. By
breaking things we can make them better. Find the weak spot and the
strong pieces will fall nicely to be reused.

I knew if I read your post all the way through I'd find something I
could understand. Next time could you put the easy paragraph
at the top?. :o)

Sue...


-Tim

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