From: Amara Graps (Amara.Graps@mpi-hd.mpg.de)
Date: Mon Jun 25 2001 - 17:05:38 MDT
>http://xxx.lanl.gov/abs/astro-ph/0012345
>Magnetic tension and the geometry of the universe
>-Christos G. Tsagas (University of Portsmouth)
The implications of this paper is wild. Fascinating, really. I wish I
could follow the equations, but I never studied magnetohydrodynamics
in a general relativistic framework, so I had a lot of trouble
following it.
From: Adrian Tymes (wingcat@pacbell.net)
>John Clark wrote:
>> Adrian Tymes <wingcat@pacbell.net> Wrote:
>> >Am I reading this right as: "(massless) magnetic fields can generate gravity"?
>>
>> That looks like what he's claiming. We already knew mass is not the only thing
>> that can warp space and time, that is, create gravity, pressure can too.
I have a problem with this statement of magnetic fields generating
gravity. Unfortunately, I need to understand better, the general
relativity and the Ricci equation in that paper, to articulate my
discomfort.
>Ah, but pressure derives from mass, no? (Even magnetic pressure -
>massless by itself - only exists with regard to charged particles with
>nonzero mass.) Magnetic fields, to my understanding, can be increased
>by increasing particle velocities (current in a wire) without directly
>increasing mass (neglecting relativistic effects).
Yes, that's correct that mass is not involved in the expression of
magnetic pressure. Perhaps I can explain some things regarding
magnetohydrodynamics (as I understand it). I also feel more
comfortable treating MHD with the assumption of a plasma fluid, since
the universe is 99% plasma.
The combination of fluid theory and classical electrodynamics gives
magnetohydrodynamics (MHD). The fluid approach means that only
macroscopic variables are retained and one can write a conservation of
mass equation and a conservation of momentum equation, in terms of
macroscopic variables.
The equation that I think has relevance to this paper (in its
UNrelativistic form) is the momentum equation:
rho (dv/dt) = -nabla P + (1/c)*(J x B) + F_v + rho*g
nabla = the gradient
rho = the mass density of a fluid that combines the gas and all of the
ion species in the plasma
P = pressure of the fluid
v = the center of mass flow velocity
c = the speed of light
g = acceleration due to gravity
F_v = the change in momentum due to velocity shears in the presence
of collisions of ions in the plasma
JxB = the Maxwell force per unit volume
JxB is a term that sheds some light on the meaning of magnetic
pressure. This term (JxB) is analogous (now in a plasma context) to
the electric motor force: F=ilxB, which is the force on a length l of
a straight wire, carrying current i in a magnetic field B.
If you substitute J from Ampere's law and apply a vector identity, then
JxB = -nabla(B^2/(2mu_0)) + (1/mu_0)*(B dot nabla B)
(the constant: mu_0 = permeability of vacuum)
The first term on the right is the magnetic pressure force.
The second term on the right is the magnetic tension force, which
is the force on the plasma due to the curvature of the magnetic
field lines.
>I wonder if this could be related to the minor levitation effects,
>attributed to antigravity at the time, above spinning condutor disks.
>Likewise, I wonder if this might be a gravity-like effect on charged
>particles which is actually just known electromagnetics.
I don't see a connection between this and levitation. Levitation
doesn't require a warping of space-time, like what this paper
describes.
>...or could it be that, at high enough temperatures, where all matter
>is in a plasma state (and thus, all matter is ions), matter tends to
>form itself into plasma wires and conduct current to create magnetic
>fields, thus rendering electromagnetic force and gravity equivalent
>(with a conversion factor) at those temperatures?
It's possible, but until I understand the Ricci equation, I don't know
where the gravity fits in the picture of that paper.
The best picture I carry in my mind of the Universe's plasma with its
frozen-in magnetic field is that of molasses with wires of current
providing the molasses' thick or thin viscosity. Then gravity enters
via the MHD fluid momentum equation.
>Just a random thought.
Good thought!
Amara
--
*********************************************************************
Amara Graps | Max-Planck-Institut fuer Kernphysik
Interplanetary Dust Group | Saupfercheckweg 1
+49-6221-516-543 | 69117 Heidelberg, GERMANY
Amara.Graps@mpi-hd.mpg.de * http://galileo.mpi-hd.mpg.de/~graps
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"Never fight an inanimate object." - P. J. O'Rourke
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