Re: Introduction to the theory of gravitation
- From: PD <TheDraperFamily@xxxxxxxxx>
- Date: Wed, 14 Nov 2007 18:04:12 -0000
On Nov 14, 11:55 am, Uncle Al <Uncle...@xxxxxxxxxxxxx> wrote:
Michal Witkowski wrote:
Introduction to the theory of gravitation
1) Assumptions
2) Description
3) Experiment
4) Archive
Ad.1
a) gravitation is a dipole
TILT!
[snip 130 lines of crap]
Gravitation is isotropic by observation, e.g. the Nordtvedt effect,
astronomy. The lowest allowed multipole is quadrupole. EM is dipole
for having opposite charges. Gravitation is only attractive.
Idiot.
The experiment described by me was once performed by two Japanese scientist:
Hideo Hayasaka and Sakae Takeuchi from the Tohoku University. The experiment
was described in the Physical Review Letters, volume 63, number 25, 18
December 1989.
Polish description was published in "Wiedza and Zycie" no 8/1990 under the
tile "Ile waza baki" (How much do the gyroscopes weigh)
"New upper limit from terrestrial equivalence principle test for
extended rotating bodies"
Phys. Rev. D 66 022002 (2002)
"Null result for violation of the equivalence principle with free-fall
rotating gyroscopes"
Phys. Rev. D 65 042005 (2002)
Idiot.
Maxwell-like (vector) gravitational equations fail for a number of
reasons. Among the main ones:
1. In electromagnetism, like charges repel, while opposite charges
attract. In particular, if you have three charges, they cannot all
attract each other. (If charge 1 is positive and attracts charge 2,
then charge 2 must be negative. Then what is charge 3?) The
situation for gravity is clearly different.
You can try to alter Maxwell's equations so that like charges attract.
To do so, though, you have to change signs in such a way that the
energy of electromagnetic radiation comes out negative. This is a
disaster (and would be for gravity): it would allow a pair of charges
or masses to generate energy without limit by radiating away negative
energy.
2. Even if you ignore the sign problem, radiation in a vector theory
is emitted at a much faster rate than in a tensor theory like general
relativity. For a pair of masses in GR, radiation depends on the rate
of change of the quadrupole moment. For a pair of charges in
Maxwell's theory, or a pair of masses in a vector theory of gravity,
the radiation rate depends on the rate of change of the (much larger)
dipole moment. This leads to predictions of gravitational radiation
that disagree severely with observed decays of binary pulsar orbits.
http://arxiv.org/abs/astro-ph/0609417http://www.oakland.edu/physics/mog29/mog29.pdf
16.8995 deg/yr periastron advance PSR J0737-3039A/B
3. A general vector theory of gravitation involves three adjustable
parameters. These can be chosen, by hand, to predict the right
precession of Mercury's perihelion (though GR has the advantage that
no ad hoc choices are needed to get the right answer). But the
resulting vector theory predicts no bending of light in a
gravitational field, again disagreeing strongly with observation. See
Robertson and Noonan, _Relativity and Cosmology_, section 6.6.
4. In a vector theory of gravitation, the energy of the field itself
does not gravitate. (The electromagnetic analog is that the electric
field has no charge, and doesn't generate its own electric field.)
But we know from observation---by comparing the Earth's and the Moon's
motion toward the Sun---that gravitational binding energy *does*
contribute to the gravitational field.
Vector theories of gravity are thus strongly ruled out by observation.
The source of monopole radiation is a changing monopolemoment for a
charge q or for a mass m. Since charge and mass are conserved, there
can be neither monopole electromagnetic radiation nor monopole
gravitational radiation.
The source of dipole radiation is a changing dipole moment.
(Punctiliously, you need a second time derivative of the dipole
moment.) For a pair of charges
d = qr + q'r'
and there's nothing special about the derivatives. For a pair of
masses, the gravitational dipole moment is
d = mr + m'r'
and its time derivative is
mv + m'v' = p + p'
By conservation of momentum the second time derivative of the
gravitational dipole moment is zero, and you can go to a center of
momentum frame and set the first derivative to zero as well. There
is no gravitational "electric dipole" radiation.
Consider the analog of "magnetic dipole" radiation. The gravitational
equivalent of the magnetic dipole moment for a pair of charges is
M = mv x r + m'v' x r'
("x" is the cross product, "mv" is the "mass current")
But M is the total angular momentum, which is also conserved. There
is no gravitational "magnetic dipole" radiation.
The next moment up is quadrupole, with no relevant conservation laws,
so gravitational quadrupole radiation is permitted. You can use this
argument to advocate that gravity must be a tensorial (spin-2)
interaction. Electromagnetism is mediated by spin-1 photons.
--
Uncle Alhttp://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/lajos.htm#a2
This was a wonderful post. Well done.
.
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