Science > Physics > Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law
| Topic: |
Science > Physics |
| User: |
"Jay R. Yablon" |
| Date: |
04 Apr 2006 09:18:43 PM |
| Object: |
Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law |
Dear friends,
I have just posted a DRAFT paper to:
http://home.nycap.rr.com/jry/Papers/Draft%20Lorentz%20Force%20Paper.pdf
This paper is titled: "Is the Lorentz Force Law Based Upon a Relation
Between rho=mu+p Perfect Fluids and alpha=1 Kerrighan-Type Electromagnetic
Energy Tensors?"
I would appreciate your review and comment on this draft before I consider
next steps.
The abstract is as follows:
It is demonstrated how the Lorentz force law is a direct consequence of
relating a perfect fluid tensor T^uv_Euler for which the rest mass density
rho is related to the energy density me and pressure p according to
rho=mu+p, with an electromagnetic energy tensor T^uv with certain uniqueness
conditions established by Kerrighan in the early-1980s, and by in turn
relating both of these tensors with the Einstein tensor R^uv - ½ g^uvR. We
then use these relationships -- which are effectively the first integral of
the Lorentz force law -- to first establish the metric tensor g_uv using the
known general solution for a non-empty stationary axisymmetric perfect
fluid, and then, to specify the electromagnetic fields underlying the
structure of this perfect fluid for which the equation of motion is the
Lorentz force law. The key advance, is showing that a solution does exist
to the Einstein equations which is fully compatible with, and indeed is
based upon, the Lorentz force law.
I do want to emphasize that this is a work in progress. But, it is now
developed far enough that a posting seeking input is warranted at this time.
Very truly yours,
Jay R. Yablon
_____________________________
Jay R. Yablon
Email:
.
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| User: "Hexenmeister" |
|
| Title: Re: Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law |
04 Apr 2006 11:52:15 PM |
|
|
"Jay R. Yablon" <> wrote in message
news:7OFYf.40179$jf2.22180@twister.nyroc.rr.com...
| Dear friends,
|
| I have just posted a DRAFT paper to:
|
| http://home.nycap.rr.com/jry/Papers/Draft%20Lorentz%20Force%20Paper.pdf
Yeah yeah...
http://www.sciencejoywagon.com/physicszone/lesson/otherpub/wfendt/lorentzforce.htm
Squirrel cage single phase electric motors can run either counterclockwise
or clockwise.
http://en.wikipedia.org/wiki/Electric_motor
Which is the correct direction for the Lorentz force?
Androcles.
|
| This paper is titled: "Is the Lorentz Force Law Based Upon a Relation
| Between rho=mu+p Perfect Fluids and alpha=1 Kerrighan-Type Electromagnetic
| Energy Tensors?"
|
| I would appreciate your review and comment on this draft before I consider
| next steps.
|
| The abstract is as follows:
|
| It is demonstrated how the Lorentz force law is a direct consequence of
| relating a perfect fluid tensor T^uv_Euler for which the rest mass
density
| rho is related to the energy density me and pressure p according to
| rho=mu+p, with an electromagnetic energy tensor T^uv with certain
uniqueness
| conditions established by Kerrighan in the early-1980s, and by in turn
| relating both of these tensors with the Einstein tensor R^uv - = g^uvR.
We
| then use these relationships -- which are effectively the first integral
of
| the Lorentz force law -- to first establish the metric tensor g_uv using
the
| known general solution for a non-empty stationary axisymmetric perfect
| fluid, and then, to specify the electromagnetic fields underlying the
| structure of this perfect fluid for which the equation of motion is the
| Lorentz force law. The key advance, is showing that a solution does exist
| to the Einstein equations which is fully compatible with, and indeed is
| based upon, the Lorentz force law.
|
| I do want to emphasize that this is a work in progress. But, it is now
| developed far enough that a posting seeking input is warranted at this
time.
|
| Very truly yours,
|
| Jay R. Yablon
| _____________________________
| Jay R. Yablon
| Email:
|
|
.
|
|
|
|
| User: "Sue..." |
|
| Title: Re: Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law |
05 Apr 2006 01:41:10 PM |
|
|
Jay R. Yablon wrote:
Dear friends,
I have just posted a DRAFT paper to:
http://home.nycap.rr.com/jry/Papers/Draft%20Lorentz%20Force%20Paper.pdf
This paper is titled: "Is the Lorentz Force Law Based Upon a Relation
Between rho=3Dmu+p Perfect Fluids and alpha=3D1 Kerrighan-Type Electromag=
netic
Energy Tensors?"
I would appreciate your review and comment on this draft before I consider
next steps.
The abstract is as follows:
It is demonstrated how the Lorentz force law is a direct consequence of
relating a perfect fluid tensor T^uv_Euler for which the rest mass densi=
ty
rho is related to the energy density me and pressure p according to
rho=3Dmu+p, with an electromagnetic energy tensor T^uv with certain uniqu=
eness
conditions established by Kerrighan in the early-1980s, and by in turn
relating both of these tensors with the Einstein tensor R^uv - =BD g^uvR.=
We
then use these relationships -- which are effectively the first integral =
of
the Lorentz force law -- to first establish the metric tensor g_uv using =
the
known general solution for a non-empty stationary axisymmetric perfect
fluid, and then, to specify the electromagnetic fields underlying the
structure of this perfect fluid for which the equation of motion is the
Lorentz force law. The key advance, is showing that a solution does exist
to the Einstein equations which is fully compatible with, and indeed is
based upon, the Lorentz force law.
I do want to emphasize that this is a work in progress. But, it is now
developed far enough that a posting seeking input is warranted at this ti=
me.
Very truly yours,
Jay R. Yablon
Consider all the matter in the universe "illuminates"
[(8.7) or fourier transfom in Ewald]
the ball producing an induction field whose flux lines
(6.5) (6.6) (6.7) ( 6.7)
converge at a point near the balls centre of gravity.
Call it a barycentre. The couplings that define the
barycenter will minimise their energy exchange when
the centre of gravity and the barycentre are co-located
..=2E.and
the induced domains describe gaussian
surfaces. (spheres or elipsoids)
http://www.chem.purdue.edu/gchelp/liquids/inddip.html
Throwing the ball actually elongates molecular domains.
The ball then moves through the illumination 'till the
more spherically shaped domain is restored
..=2E..and
the barycentre is co-located with the centre of gravity.
http://www.research.ibm.com/grape/grape_ewald.htm
---------
Yep... you are using more of the right exponents
and they are moving closer to where they belong.
I like 6, 3 and 2. :o)
An axis of symetry helps to simplify the complexity
of the brute force Ewald but I can't convince myself
that derivatives 4,8,12,16... in (7.6) are establishing
an axis of symetry tho' they may be qualifying one.
sqrt (-g) sounds like somthing that might make
a perfect Lorentz fluid 'cause ya have to advance
and retard the potential over the path.
Checking EB orthogonal in Lorenz gauge might
catch only the induction componet. :-)
I'm not sure the thermodynamic study is helping
you any. The speed of the motion vanishes when
you transfom E to B, Eh?
Don't expect me to elaborate further. I can barely
read what I wrote and your tensors are all Greek.
Regards,
Sue...
_____________________________
Jay R. Yablon
Email:
.
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|
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|
| User: "RP" |
|
| Title: Re: Draft paper deriving a non-empty, stationary, axisymmetric solutionsolution of Einstein's Equations, based on the Lorentz Force Law |
05 Apr 2006 12:03:01 PM |
|
|
Jay R. Yablon wrote:
Dear friends,
I have just posted a DRAFT paper to:
http://home.nycap.rr.com/jry/Papers/Draft%20Lorentz%20Force%20Paper.pdf
This paper is titled: "Is the Lorentz Force Law Based Upon a Relation
Between rho=mu+p Perfect Fluids and alpha=1 Kerrighan-Type Electromagnetic
Energy Tensors?"
The temperature dependence of electromagnetic forces! Try slipping that
one past this bunch:) They weren't entirely fond of that notion 5 or 6
years ago when I hashed through the thermodynamic relationships between
charges. I, OTOH, commend you for reaching what I thought was an obvious
conclusion. Your math was beyond me, but the arguments that I
understood were refreshing. Keep up the good work.
Richard Perry
.
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| User: "Jay R. Yablon" |
|
| Title: Re: Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law |
05 Apr 2006 01:36:36 PM |
|
|
Jay R. Yablon wrote:
Dear friends,
I have just posted a DRAFT paper to:
http://home.nycap.rr.com/jry/Papers/Draft%20Lorentz%20Force%20Paper.pdf
This paper is titled: "Is the Lorentz Force Law Based Upon a Relation
Between rho=mu+p Perfect Fluids and alpha=1 Kerrighan-Type
Electromagnetic
Energy Tensors?"
The temperature dependence of electromagnetic forces! Try slipping that
one past this bunch:) They weren't entirely fond of that notion 5 or 6
years ago when I hashed through the thermodynamic relationships between
charges. I, OTOH, commend you for reaching what I thought was an obvious
conclusion. Your math was beyond me, but the arguments that I understood
were refreshing. Keep up the good work.
Richard Perry
Thanks Richard. I am waiting for my post to go up on SPR, but as you know,
there is usually a bit of lag time.
The temperature / pressure / entropy dependence actually makes sense if you
get to the bottom line question: what is the motion of a particle in ANY set
of circumstances. Not Lorentz motion, or gravitational motion, or motion
from pressure or temperature, but "motion motion." The composite result of
ALL the physical factors which play into the motion.
What I derive in section 5 is an equation of motion which includes Lorentz
motion, plus an extra term which we show in section 6 can be related to
entropy, temperature, and pressure. We can either say that the Lorentz
motion is "different" from the conventional Lorentz motion because of these
extra terms, or we can say that the Lorentz motion is the same as always,
but that is just one more contribution to the total motion and now we known
not only how Lorentz forces and gravitational forces affect the total
motion, but how the thermodynamics of the local environment also affects the
motion.
Sort of like if I am falling freely in gravitational motion and then I hit
the ground, there is more than one factor affecting my motion, and it
strains the point to say that there is a different law for gravitational
motion one I hit the ground. Rather, another set of physics principles come
into play.
If one says that there should be no thermodynamic effects on the Lorentz
motion, it is like saying that hitting the ground should not affect my
gravitational motion. Non-sequiter.
Jay.
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|
| User: "Ken S. Tucker" |
|
| Title: Re: Draft paper deriving a non-empty, stationary, axisymmetric solution solution of Einstein's Equations, based on the Lorentz Force Law |
06 Apr 2006 03:33:46 PM |
|
|
RP wrote:
Jay R. Yablon wrote:
Dear friends,
I have just posted a DRAFT paper to:
http://home.nycap.rr.com/jry/Papers/Draft%20Lorentz%20Force%20Paper.pdf
This paper is titled: "Is the Lorentz Force Law Based Upon a Relation
Between rho=mu+p Perfect Fluids and alpha=1 Kerrighan-Type Electromagnetic
Energy Tensors?"
The temperature dependence of electromagnetic forces! Try slipping that
one past this bunch:) They weren't entirely fond of that notion 5 or 6
years ago when I hashed through the thermodynamic relationships between
charges. I, OTOH, commend you for reaching what I thought was an obvious
conclusion. Your math was beyond me, but the arguments that I
understood were refreshing. Keep up the good work.
Richard Perry
Right!
Mr. Yablon reveals the creative process associated
with working with GR. My physical understanding
of Yablon's use of temperature follows...
Suppose we have an atom at absolute zero with
nucleus "+" and electrons "-" that looks like, (+,-).
Now suppose that atom absorbs a photon that
sends an electron(s) to a higher orbital that looks
like (+,,-), that I would call is a higher temperature,
energy and thus mass of that atom.
The presumption is of course the Lorentz Force
holds true in all circumstances, but what is that
Lorentz force when the mass and EM-field is
altered? The only way to know that is to carefully
apply the conservation laws as mass and EM-fields
change, and that is in accord with General Relativity
that Yablon has relied on and detailed.
There may be spectral evidence to support that
conclusion, and additionally, greater evidence
in High Energy Physics as Yablon extends his
analysis into Chromo-dynamics.
Regards
Ken S. Tucker
PS: Cheers Jay!
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