Re: Center of Mass of the Universe?

From: EL (hemetis_at_hotmail.com)
Date: 11/12/04 

Date: 12 Nov 2004 02:06:18 -0800

"Jack Martinelli" <jack@martinelli.org> wrote in message
news:<w%Skd.24332$KJ6.14545@newsread1.news.pas.earthlink.net>...

> "EL" <hemetis@hotmail.com> wrote in message

> news:7563cb80.0411110354.1b172806@posting.google.com...

> > "Jack Martinelli" <jack@martinelli.org> wrote in message

> > news:<i2Akd.23517$KJ6.8188@newsread1.news.pas.earthlink.net>...

> >
> >> > [hanson]
> [...]
> >> > When I look at your responses in this thread, which started out
> >> > with you wanting to know whether there is a center in the
> >> > universe, I do get the feeling that you have an agenda

> >> [...]
> >> Not really, it just occurred to me that a mass of an arbitrary size &
> >> shape
> >> has a center of mass, but as the scope gets larger & larger... somewhere
> >> along the line, no more center of mass. I didn't put much effort into the
> >> notion before I posted. If I had put a little more thinking into it I
> >> probably would have realized I had the pieces to the puzzle but I lazy.
> >>
> >> One of the posters on this thread mentioned that, in an inhomogeneous
> >> space
> >> and on a local & global scale, a momentum vector or (m*l) doesn't
> >> transport
> >> in a well defined way. This pretty much satisfied me for two reasons. 1.
> >> Like Einstein, I'm convinced that particles are spatially extended
> >> objects &
> >> not point masses. I.e, how do you do a parallel transport a spatially
> >> extended object's set of vectors? And 2. If a mass were point-like,
> >> parallel transport through a massive object has got to do something to a
> >> vector's angle & magnitude. I understand the difficulty here.
> >>
> >> I think I have a solution though... but I'm still working on it. But
> >> here's a hint. You remove the curvature (I have a way -- I think), add
> >> the
> >> vectors and then you can look at the results or put the curvature back in
> >> and look at the results.
> >>
> >> Regards
> >>
> >> Jack Martinelli
> >>
> >> http://www.martinelli.org

> >
> > [EL]
> > You are fiddling with matters that demand formidable and disciplined
> > minds, Jack.
>
> Yep. I wouldn't call myself formidable, but I do have a well disiplined
> mind.

[EL]
Now that was encouraging. :-)

>
> I like tinkering with hard problems. If there's no challenge, what's the
> point?

[EL]
It should occur to you that there are those who are forced to "tinker"
as a job.
Why should "anyone" have a new theory in physics!
Why should anyone spend the time "tinkering" beyond the practical
foundations needed by average educated people!
>From my certainly very long experience on the news-groups, there are
two species other than academic scientists who enjoy to "tinker".
The "programmers" and the "inventors".
It became obvious to me that software programmers might have to deal
with complex mathematical problems and physical concepts while
modelling and/or simulating the world.
Programmers also have an easy and natural access to computers and the
Internet.
The other "species" is that of inventors (including the seekers of the
perpetual motion) who found themselves stuck with modern jargon while
educating themselves to venture into clean energy etc.
Taking the "challenge" for fun makes no sense, and you must have found
yourself here rather than planning it all the way. :-)

>
> > Usually brain-storming yields better results than fiddling.
>
> Science is iterative. With every step forward there are 100 back-tracks,
> but who documents that?
>
> I like brain-storming too. It's part of the cycle of scientific progress.
>

[EL]
There is no shame in being selfish when seeking self-education.
Brain-storming is a community activity preferred by social persons who
realize that self-advancing might demand helping others on the same
way.

> > It might be you or others who coined the expression "sub-space" but
> > does it really mean anything?
>
> Sure. Einstein never gave a word to his "spatially extended particles" so I
> did. I call them SubSpace particles. These particles are Einstein's
> invention -- not mine.

[EL]
There are about 331,000 hits on Yahoo for "subspace".
I strongly doubt that you wrote that word that number of times. :-)
It is the name of a game, a poem, and much more than you could ever
believe to exist.
Now ask yourself if it was a successful choice to choose such an
"unreserved" word.
OTOH, hyperspace is an earmarked word to indicate the same relation
but in the other direction.

>
> > I am afraid that you might have missed the definition of space being
> > founded on three dimensions of length, and that is why the expression
> > "Hyperspace" was introduced to include the time dimension as a
> > representative of a fourth dimension of length acquired by the motion
> > of solid-geometry-entities.
>
> I'm not sure I'm following your meaning. But, with my inkling of knowledge
> in this area... I'm pretty sure that differential geometry (or topology)
> only work where you have a simple continous manifold. In my model, every
> particle exists as its own space. There is no background space.

[EL]
Be careful there, as you step into the mud. :-)
Warning, you are venturing into harsh grounds of the "relativistic"
worshipers.

>
> > Each temporal escalation of translational-motion complexity adds an
> > equivalent dimension of length.
> > Naturally, each "space" is a "sub-space" of its "hyperspace".
> > Consequently, a line is a hyper-point and a plane is a hyper-line and
> > a solid-volume is a hyper-plane, and so on.
>
> I kinda get this. But aren't these kind of sub-spaces stitched together
> with knots?

[EL]
No.
Knots do exist but they serve a totally different purpose other than
"stitching" spaces.
They anchor a reference of a self-claimed space.
A dimensionless point is physically meaningless in a 3D void.
The physical meaning of a point is that it is a 2D entity created on a
plane penetrated by a third dimensional axis of rotation.
The 2D coordinates of that axis on that plane is an empirically
legitimate point.
IOW, a point is defined by the interaction of at least two other
geometric entities and it may never stand alone.
It is such a knot that materialises the axis that may move
orthogonally along a plane to describe a hyper-point which is a line
on that plane.

>
> > The consensus have arbitrated a dimension for length [L] as a
> > fundamental dimension, and consequently, an area is [L^2] and a volume
> > is [L^3] as derived dimensions.
> > Curvature, consequently is expressed as [L^-1], while the Gaussian
> > curvature is [L^-2].
>
> And these come from the metric?

[EL]
I cannot elaborate, but you may begin somewhere.

http://www.brown.edu/Students/OHJC/hm4/k.htm

http://www.ies.co.jp/math/java/calc/curve/curve.html

I was simply focussing on the dimensionality of curvature in a
relativistic sense.
Linear curvature at a point is quantified by being "over" the radius
of the circle in the plane of the line at that point.
Gaussian curvature is the product of the maximum and the minimum
linear curvatures of a point on a surface in a 3D world.

>
> (I think of curvature where a unit of length of one frame is shorter than
> another)
>
> > Arbitrating a symbol for the dimension of time as [T], the dimension
> > of velocity becomes v = [L . T^-1].
>
> makes sense.
>
> > Notice that the derived dimension of area may be expressed as a hyper
> > line as follows:
> > A = [L] . [L . T^-1] . [T], meaning that a line moved with a finite
> > velocity for a finite interval of time.
>
> I assume you mean as measured by someone's ruler & clock. Which makes
> length & time relative.

[EL]
I am not there yet, but simply exposing the foundation of the
relativistic [-ct].
The speed of light "c" is a finite velocity when direction is
considered and have the dimensions [L . T^-1].
As you may have already noticed, a line has a profound meaning when
expressed as a moving point when a time interval quantifies the
distance moved under constant speed.
The relativistic arbitrated quantification does not exchange time for
length but rather derives length from relative speed and relative time
dimensions.
That is where "someone's ruler & clock" come in.
However, the ruler is supposed to describe length, which is
relativistically expressed by the hyper-motion term.
This circular logic in the foundation of relativity is what makes it
just another arbitration yet more general and a bit sophisticated.
That problem had a solution by adopting the speed of light in vacuum
as a fundamental dimension inside which both length and time are
embedded.

>
> > As you can see, the term { [L . T^-1] . [T]} is the hyper-motion
> > multiplier of complexity.
>
> If you say so.

[EL]
Or if Einstein said so. :-)

>
> >
> > Theoretically speaking, any hypothetical subspace can be derived by
> > dividing by the hyper-motion-term { [L . T^-1] . [T]}.
> >
> > We can conclude that a relatively motionless-point is dimensionless.
> >
> > Now I do not know what exactly you had in mind, but I strongly suggest
> > that you should refrain from adding new jargon that is already
> > expressed by consensus.
>
> I agree. If only I understood the official jargon.

[EL]
The official jargon is documented in all of the theories of
relativity.

>
> > Linear Curvature is the "subspace" of a point and the Gaussian
> > (surface) curvature is the "subspace" of the linear curvature.
>
> I kind of thought that the formal definition of a subspace was the same as a
> vector space but with a couple of additional restrictions.

[EL]
There is no "formal definition" of "subspace" else than being the
opposite of a "hyperspace" in physics.
Nevertheless, a subset of a vector space is indeed a subspace by
definition within the mathematical context.
If the set is a "vector space" then its subset should have been a
"vector-subspace" to clear the ambiguity.
We might as well use the word "space" when we really mean a "gap" or a
"void".
Adding the prefix "sub" indicates an underlying independent structure
or simply a synonym for the word "under".
Philosophically, the word "sub" might indicate a cause or a
foundation.
That is why a linear curvature is expressed by the radius of the
circle to which a tangent at the point of concern intersects.
As if it was that intersection of the tangent and the radius that
caused the point to exist, hence curvature is a subspace of that point
in plane.
A point on a surface curved in 3D demands two radii in two planes
intersecting with two tangents to describe the Gaussian curvature.
Gauss realised that the inverse of the product of the maximum and the
minimum radii was the only unambiguous expression that can represent
such a curvature.

>
> > Do you have a proposal for a subspace of a Gaussian curvature?
> > Because if you do not have one, I do. :-)
>
> I wish I knew what you were talking about but I'm still learning (on my own)
> about differential geometry. It's hard to learn without an instructor to
> bug. When I hit Kronecker's delta, I couldn't believe what a kludge that
> was. It only seemed that way, however, because the book didn't prepare me
> for it. An instructor would have helped a lot!. But, I do get it now.
>
> I'm just guessing, but is Gaussian curvature related to the Gaussian curve
> (the bell shaped curve?). If so, then I think I'm headed in that direction.
> ( see:http://www.martinelli.org/fundamental/#RelativisticExpansion -- go
> down a little bit & see my "Gausian curve" )
>
> What kind of proposal do you have? And can you explain the physics so that
> a math dummy like me can understand it?
>
> Regards
>
> Jack Martinelli
>
> http://www.martinelli.org

[EL]
My proposal for a subspace of a Gaussian curvature is as simple as the
curvature of a hyper-surface.
The dimension of such a subspace is [L^-3] and it describes the
evolution of a Gaussian curvature over time as it follows the path of
a curve.
Just imagine a point on the surface of a sphere moving in a circular
orbit (for simplicity).
In that very simple example we have two identical radii (from the
sphere) multiplied by the radius of the orbit to express the
"hyper-curvature".
I stumbled into that concept while developing my "Torus Knot Topology
Of Dynamic Orbits" (AKA TKTODO).

Kind regards.

EL

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