Science > Physics > Gravitomagnetic field does not obey superposition, what are the implications?
| Topic: |
Science > Physics |
| User: |
"Neil Bates" |
| Date: |
15 Nov 2007 02:43:39 PM |
| Object: |
Gravitomagnetic field does not obey superposition, what are the implications? |
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Moving streams of matter should produce a "Gravitomagnetic field" =
analogous to the magnetic field from moving charges. This is orthodox =
GR, even if some details are in contention. (See for example, =
http://en.wikipedia.org/wiki/Gravitomagnetism.)
I played around with equivalent matter streams moving in opposite =
directions. That should cancel out their gravitomagnetic fields B* =
(usually just called "B" after context given), but I found an =
inconsistency. The problem was, superposition of B* from two sources as =
if a vector field did not work. (Sure, gravity is more complicated, but =
that part should approximate vector fields and emulate EM at low mass =
levels - ? - and I expect even non-linear superpositions to cancel out =
opposite fields.) For example, let's have adjacent streams going 0.5c =
in opposite directions, very low mass density to provide high expected =
linearity (albeit at relativistic speeds.) The proper value of g seen =
in our frame K is gamma squared times the value g_s at rest relative to =
either single stream (hence g =3D 2gamma^2(0.5c)g_s =3D (2*4/3)g_s =3D =
(8/3)g_s), due to the multiplied effects of Lorentz contraction and =
greater relativistic mass-energy density (thus field-producing power) =
per proper length unit in the mass flow.
We will send a unit mass M moving at 0.5c, frame K', along the streams' =
path, in either direction. We, expecting to see only "g" since the B* =
has ostensibly been canceled, expect M to experience gamma squared the =
value of proper acceleration towards the stream that we find in K =
(lateral acceleration transformation, from shorter proper time to fall.) =
Since effective mass-energy of M is gamma*M_0 (one of the cases where =
"relativistic mass" is still relevant), that is equivalent to a force in =
K increased to gamma times rest value and thus in K', gamma squared =
times the force in K (due to force transformation.) Hence by that =
consistent-seeming reckoning, the acceleration of M in K' should be =
gamma^2(0.5c)g =3D 2gamma^4(0.5c)g_s =3D (32/9)g_s.
However, in M's frame, one stream is at rest and the other one goes at =
0.8c. The combined effect is therefore [1 + gamma^2(0.8c)]g_s =3D =
(34/9)g_s =3D(17/16)*(32/9)g_s. It is easy to verify (using the =
additive gamma factor being gamma(v1 + v2) =3D gamma1*gamma2*(1 + =
v1*v2/c^2)) that the ratio in general of the second prediction to the =
first is (1 + v^4/c^4).
That is an odd contradiction, and I just don't know what to make of it. =
Sure, gravitation is not like EM and with curved space etc., but would =
anyone expect low-gravity fields of any kind not to cancel out if =
apparently of opposite sign? Has anyone found good rules for B*? Has =
this issue been talked about before, and where? Thanks.
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<DIV><FONT face=3D"Courier New" size=3D2>Moving streams of matter should =
produce a=20
<FONT face=3D"Times New Roman" size=3D1>"</FONT>Gravitomagnetic field" =
analogous to=20
the magnetic field from moving charges. This is orthodox GR, even =
if some=20
details are in contention. (See for example, <A=20
href=3D"http://en.wikipedia.org/wiki/Gravitomagnetism">http://en.wikipedi=
a.org/wiki/Gravitomagnetism</A>.)</FONT></DIV>
<DIV><FONT face=3D"Courier New" size=3D2>
<DIV> </DIV>
<DIV>I played around with equivalent matter streams moving in =
opposite=20
directions. That should cancel out their gravitomagnetic fields B* =
(usually just=20
called "B" after context given), but I found an inconsistency. The =
problem=20
was, superposition of B* from two sources as if a vector =
field did not=20
work. (Sure, gravity is more complicated, but that part should =
approximate=20
vector fields and emulate EM at low mass levels - ? - and I expect =
even=20
non-linear superpositions to cancel out opposite fields.) For =
example,=20
let's have adjacent streams going 0.5c in opposite directions, very =
low=20
mass density to provide high expected linearity (albeit at=20
relativistic speeds.) The proper value of g seen in our frame =
K is=20
gamma squared times the value g_s at rest =
relative to either=20
single stream (hence g =3D 2gamma^2(0.5c)g_s =3D (2*4/3)g_s =
=3D (8/3)g_s),=20
due to the multiplied effects of Lorentz contraction and greater=20
relativistic mass-energy density (thus field-producing power) per =
proper=20
length unit in the mass flow.</DIV>
<DIV> </DIV>
<DIV>We will send a unit mass M moving at 0.5c, frame =
K', along the=20
streams' path, in either direction. We, expecting to see only =
"g"=20
since the B* has ostensibly been canceled, expect M to experience gamma =
squared=20
the value of proper acceleration towards the stream that we =
find in K=20
(lateral acceleration transformation, from shorter proper time to=20
fall.) Since effective mass-energy of M is gamma*M_0 (one of the =
cases=20
where "relativistic mass" is still relevant), that is equivalent to =
a force=20
in K increased to gamma times rest value and thus in K', gamma =
squared=20
times the force in K (due to force transformation.) Hence by that=20
consistent-seeming reckoning, the acceleration of M in K' should be =
gamma^2(0.5c)g =3D 2gamma^4(0.5c)g_s =3D (32/9)g_s.</DIV>
<DIV> </DIV>
<DIV>However, in M's frame, one stream is at rest and the other one goes =
at=20
0.8c. The combined effect is therefore [1 + gamma^2(0.8c)]g_s =3D=20
(34/9)g_s =3D(17/16)*(32/9)g_s. It is easy to verify =
(using the=20
additive gamma factor being gamma(v1 + v2) =3D gamma1*gamma2*(1 + =
v1*v2/c^2)) that=20
the ratio in general of the second prediction to the first is =
(1 +=20
v^4/c^4).</DIV>
<DIV> </DIV>
<DIV>That is an odd contradiction, and I just don't know what to make of =
it. Sure, gravitation is not like EM and with curved space etc., =
but would=20
anyone expect low-gravity fields of any kind not to cancel out if =
apparently of=20
opposite sign? Has anyone found good rules for B*? Has this issue =
been=20
talked about before, and where? =
Thanks.</FONT></DIV></DIV></BODY></HTML>
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| User: "Neil Bates" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are the implications? |
15 Nov 2007 03:55:01 PM |
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"Neil Bates" <neil_delver@caloricmail.com> wrote in message
news:13jpbr34ls5ve63@corp.supernews.com...
"...It is easy to verify (using the additive gamma factor being gamma(v1 +
v2) = gamma1*gamma2*(1 + v1*v2/c^2)) that the ratio in general of the second
prediction to the first is (1 + v^4/c^4)."
I mean, relativistic velocity addition for gamma(v1 + v2), but don't have a
good symbol to use (the oft-used dot on top of plus is real hard to find in
fonts.)
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| User: "Sue..." |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are theimplications? |
15 Nov 2007 04:49:44 PM |
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On Nov 15, 4:55 pm, "Neil Bates" <neil_del...@caloricmail.com> wrote:
"Neil Bates" <neil_del...@caloricmail.com> wrote in message
news:13jpbr34ls5ve63@corp.supernews.com...
"...It is easy to verify (using the additive gamma factor being gamma(v1 +
v2) = gamma1*gamma2*(1 + v1*v2/c^2)) that the ratio in general of the second
prediction to the first is (1 + v^4/c^4)."
I mean, relativistic velocity addition for gamma(v1 + v2), but don't have a
good symbol to use (the oft-used dot on top of plus is real hard to find in
fonts.)
It sounds like you might be using Purcell's circular
derivation for magnetism.
http://physics.weber.edu/schroeder/mrr/MRRtalk.html
Something that actually uses superpositon would be
better.
http://en.wikipedia.org/wiki/Multiple_integral#Some_practical_applications
Time-independent Maxwell equations
Time-dependent Maxwell's equations
http://farside.ph.utexas.edu/teaching/em/lectures/lectures.html
....tho the problems with the Lorenz gauge will still exist.
Sue...
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| User: "Neil Bates" |
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| Title: What is acceleration of particles moving transverse to field of extended planar mass? |
21 Nov 2007 04:58:26 PM |
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I have heard, that the lab-frame acceleration of a mass moving transverse to
the field around an extended planar mass (with essentially uniform field
over a wide range) is not the same as what I expect from the "accelerating
elevator" (AE) and my original understanding of the equivalence principle.
In the AE, a mass dropped straight down and a bullet fired horizontally hit
the floor at the same time. That means, the same lab acceleration along g
(which looks higher to the bullet due to time dilation.) What I was told
(source not important here, but seemed credible):
g(moving transverse to g) = g(1 + v^2/c^2).
That is supposedly due to the moving body cutting planes of space time
differently than a simple falling body, etc.
But what if you accelerate a ring of vast radius R from rest to rapid
rotation, using up its own mass-energy? The total mass-energy per unit ds of
the ring, seen in the lab, stays the same (and we can use discrete points to
avoid stretching.) In my original understanding, the close to 1/r gravity
field near the ring current therefore stays the same value. That avoids free
energy tricks like raising/lowering parallel static mass rings before/after
acceleration of the first ring.
If the acceleration difference is real, then we can speed up the first ring,
get g(new) = g(rest)*(1 + v^2/c^2), lower in some sandwiching static rings,
decelerate the first ring (keeping the energy there for same mass-energy per
unit), then raise the other rings back out and keep the extra energy. It
would be worth 0.36 mg*delta h if the main ring got up to 0.6c, etc. The
other rings or sets of masses go right towards the spinning ring, there's no
way for corrections to fix energy using their own transverse velocity. Play
with it some, and maybe you'll see that differential values of g cause
problems.
Comments, anyone?
BTW, below are some references regarding this issue.
http://www.mathpages.com/home/kmath530/kmath530.htm
http://arxiv.org/pdf/gr-qc/0503092
http://arxiv.org/PS_cache/arxiv/pdf/0708/0708.2906v1.pdf
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| User: "Ian Parker" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are theimplications? |
16 Nov 2007 05:57:09 AM |
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Maxwell's equations stem from a scaler potential Quad^2=F6 =3D p Where p
is a charge density. Quad^2 is the four dimensional analogue of the
"Del" operator. =F6 is a scalar quantity.
Gravitational waves on the other hand involve tensors and NOT scalars.
This is where the confusion takes place. Gravitational waves are
quadripolar and not diploar. They have 5 planes of polarization and
gravitational fileds can be along the direction of motion.. In
elementary particle physics we say that a graviton is a boson with
spin 2. The photon has a spin of 1.
There are in fact GR codes which will give a finite element solution.
These tell us what happens when matter approached a spinning black
hole for example.
- Ian Parker
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| User: "Eric Gisse" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are the implications? |
16 Nov 2007 05:31:12 PM |
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On Fri, 16 Nov 2007 03:57:09 -0800 (PST), Ian Parker
<ianparker2@gmail.com> wrote:
Maxwell's equations stem from a scaler potential Quad^2? = p Where p
is a charge density. Quad^2 is the four dimensional analogue of the
"Del" operator. ? is a scalar quantity.
I find it infinitely better to call the D'Almbertian the "box
operator". I just like saying "box squared".
Gravitational waves on the other hand involve tensors and NOT scalars.
This is where the confusion takes place. Gravitational waves are
quadripolar and not diploar. They have 5 planes of polarization and
gravitational fileds can be along the direction of motion.. In
elementary particle physics we say that a graviton is a boson with
spin 2. The photon has a spin of 1.
*scratches head*
I thought gravitational waves only had two unique polarizations?
There are in fact GR codes which will give a finite element solution.
These tell us what happens when matter approached a spinning black
hole for example.
- Ian Parker
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| User: "Ian Parker" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are theimplications? |
17 Nov 2007 05:31:49 AM |
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On 16 Nov, 23:31, Eric Gisse <jowr.pi.nos...@gmail-nospam.com> wrote:
On Fri, 16 Nov 2007 03:57:09 -0800 (PST), Ian Parker
<ianpark...@gmail.com> wrote:
Maxwell's equations stem from a scaler potential Quad^2? = p Where p
is a charge density. Quad^2 is the four dimensional analogue of the
"Del" operator. ? is a scalar quantity.
I find it infinitely better to call the D'Almbertian the "box
operator". I just like saying "box squared".
Gravitational waves on the other hand involve tensors and NOT scalars.
This is where the confusion takes place. Gravitational waves are
quadripolar and not diploar. They have 5 planes of polarization and
gravitational fileds can be along the direction of motion.. In
elementary particle physics we say that a graviton is a boson with
spin 2. The photon has a spin of 1.
*scratches head*
I thought gravitational waves only had two unique polarizations?
There are in fact GR codes which will give a finite element solution.
These tell us what happens when matter approached a spinning black
hole for example.
http://en.wikipedia.org/wiki/Gravitational_waves
http://www.lnl.infn.it/~auriga/auriga/grav_wave.html
Cross and plus are in a plane so each one is counted twice.
These show the planes of polarization. They are totally different from
EM waves. A spin of 2 means 5 quantized states.
- Ian Parker
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| User: "RP" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are theimplications? |
17 Nov 2007 06:15:37 AM |
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On Nov 17, 5:31 am, Ian Parker <ianpark...@gmail.com> wrote:
On 16 Nov, 23:31, Eric Gisse <jowr.pi.nos...@gmail-nospam.com> wrote:
On Fri, 16 Nov 2007 03:57:09 -0800 (PST), Ian Parker
<ianpark...@gmail.com> wrote:
Maxwell's equations stem from a scaler potential Quad^2? = p Where p
is a charge density. Quad^2 is the four dimensional analogue of the
"Del" operator. ? is a scalar quantity.
I find it infinitely better to call the D'Almbertian the "box
operator". I just like saying "box squared".
Gravitational waves on the other hand involve tensors and NOT scalars.
This is where the confusion takes place. Gravitational waves are
quadripolar and not diploar. They have 5 planes of polarization and
gravitational fileds can be along the direction of motion.. In
elementary particle physics we say that a graviton is a boson with
spin 2. The photon has a spin of 1.
*scratches head*
I thought gravitational waves only had two unique polarizations?
There are in fact GR codes which will give a finite element solution.
These tell us what happens when matter approached a spinning black
hole for example.
http://en.wikipedia.org/wiki/Gravitational_waveshttp://www.lnl.infn.it/~auriga/auriga/grav_wave.html
Cross and plus are in a plane so each one is counted twice.
These show the planes of polarization. They are totally different from
EM waves. A spin of 2 means 5 quantized states.
- Ian Parker- Hide quoted text -
- Show quoted text -
Inertial mass, which is equivalent to gravitational mass by the
equivalence principle) is a measure of electromagnetic PE per
Einsteins famous argument in which he derives E = mc^2.
If a system of masses loses energy via radiation (of any sort), then
it loses inertial mass, and thus it loses either electromagnetic PE or
actual particles of matter(fermions). Gravity waves, if they exist as
described by Einstein (not being the ejection of actual massive
particles), must therefore correspond to a loss of electromagnetic PE,
that is, they must be electromagnetic waves. Thus gravitational PE is
a form of electromagnetic PE.
Also, inertial (mechanical) acceleration is always accomplished on the
microscopic level by interatomic (electromagnetic) forces. For
instance the thrust of a rocket engine is not accomplished by anti-
gravitational forces between the expanding gasses and the chamber
walls, but by electromagnetic forces acting between the atoms. The
equivalence of inertial and gravitaional acceleration is thus in
itself nothing other than a direct statement that gravity, in some
form, is analogous in an inverse way to the complex sequence of
microscopic interactions involved in inertial (mechanical)
acceleration. The zpf, which is a constant flux of vector potentials,
is produced ny the very masses that are interacting gravitationally,
and is produced by the elecromagnetic charges within the masses. The
casimir force, is one manifestation of a zpf force. It's deriation
isn't obvious until after the fact. Gravitational forces, if analogous
to the casimir force would be immensely more involved. We should
reason, as all of you have done, whether or not you are aware of it,
along the lines "because the problem of tracking em forces between all
the particles within the masses is beyond present capability, this
cannot be the correct explanation of gravity".
If OTOH, this is the correct explanation, then a gravitaitonal wave
would involve a superpostion of virtual photons of the ordinary em
sort.
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| User: "Eric Gisse" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are the implications? |
17 Nov 2007 05:45:23 AM |
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On Sat, 17 Nov 2007 03:31:49 -0800 (PST), Ian Parker
<ianparker2@gmail.com> wrote:
On 16 Nov, 23:31, Eric Gisse <jowr.pi.nos...@gmail-nospam.com> wrote:
On Fri, 16 Nov 2007 03:57:09 -0800 (PST), Ian Parker
<ianpark...@gmail.com> wrote:
Maxwell's equations stem from a scaler potential Quad^2? = p Where p
is a charge density. Quad^2 is the four dimensional analogue of the
"Del" operator. ? is a scalar quantity.
I find it infinitely better to call the D'Almbertian the "box
operator". I just like saying "box squared".
Gravitational waves on the other hand involve tensors and NOT scalars.
This is where the confusion takes place. Gravitational waves are
quadripolar and not diploar. They have 5 planes of polarization and
gravitational fileds can be along the direction of motion.. In
elementary particle physics we say that a graviton is a boson with
spin 2. The photon has a spin of 1.
*scratches head*
I thought gravitational waves only had two unique polarizations?
There are in fact GR codes which will give a finite element solution.
These tell us what happens when matter approached a spinning black
hole for example.
http://en.wikipedia.org/wiki/Gravitational_waves
http://www.lnl.infn.it/~auriga/auriga/grav_wave.html
Cross and plus are in a plane so each one is counted twice.
These show the planes of polarization. They are totally different from
EM waves. A spin of 2 means 5 quantized states.
- Ian Parker
Which means jack since the notion that the gravition is a spin 2
particle comes from trying to quantize linearized general relativity.
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| User: "Sue..." |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are theimplications? |
15 Nov 2007 03:00:47 PM |
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On Nov 15, 3:43 pm, "Neil Bates" <neil_del...@caloricmail.com> wrote:
Moving streams of matter should produce a "Gravitomagnetic field" analogou=
s to the magnetic field from moving charges. This is orthodox GR, even if so=
me details are in contention. (See for example,http://en.wikipedia.org/wiki/=
Gravitomagnetism.)
I played around with equivalent matter streams moving in opposite directio=
ns. That should cancel out their gravitomagnetic fields B* (usually just cal=
led "B" after context given), but I found an inconsistency. The problem was=
, superposition of B* from two sources as if a vector field did not work. (S=
ure, gravity is more complicated, but that part should approximate vector fi=
elds and emulate EM at low mass levels - ? - and I expect even non-linear su=
perpositions to cancel out opposite fields.) For example, let's have adjace=
nt streams going 0.5c in opposite directions, very low mass density to provi=
de high expected linearity (albeit at relativistic speeds.) The proper valu=
e of g seen in our frame K is gamma squared times the value g_s at rest rela=
tive to either single stream (hence g =3D 2gamma^2(0.5c)g_s =3D (2*4/3)g_s =
=3D (8/3)g_s), due to the multiplied effects of Lorentz contraction and grea=
ter relativistic mass-energy density (thus field-producing power) per proper=
length unit in the mass flow.
We will send a unit mass M moving at 0.5c, frame K', along the streams' pa=
th, in either direction. We, expecting to see only "g" since the B* has ost=
ensibly been canceled, expect M to experience gamma squared the value of pro=
per acceleration towards the stream that we find in K (lateral acceleration =
transformation, from shorter proper time to fall.) Since effective mass-ene=
rgy of M is gamma*M_0 (one of the cases where "relativistic mass" is still r=
elevant), that is equivalent to a force in K increased to gamma times rest v=
alue and thus in K', gamma squared times the force in K (due to force transf=
ormation.) Hence by that consistent-seeming reckoning, the acceleration of M=
in K' should be gamma^2(0.5c)g =3D 2gamma^4(0.5c)g_s =3D (32/9)g_s.
However, in M's frame, one stream is at rest and the other one goes at 0.8=
c. The combined effect is therefore [1 + gamma^2(0.8c)]g_s =3D (34/9)g_s =
=3D(17/16)*(32/9)g_s. It is easy to verify (using the additive gamma factor=
being gamma(v1 + v2) =3D gamma1*gamma2*(1 + v1*v2/c^2)) that the ratio in g=
eneral of the second prediction to the first is (1 + v^4/c^4).
That is an odd contradiction, and I just don't know what to make of it. S=
ure, gravitation is not like EM and with curved space etc., but would anyone=
expect low-gravity fields of any kind not to cancel out if apparently of op=
posite sign? Has anyone found good rules for B*? Has this issue been talked=
about before, and where? Thanks.
For simplicity, Maxwell's equations assume a axis of
symmetry that may not always exist. That is why inertial
coupling is through mass/energy equivalence in GR.
The ewald method allows the consideration of
induction components aren't symetrical
http://www.research.ibm.com/grape/grape_ewald.htm
<< Einstein published his theory of
gravitation, or general theory of relativity,
in 1916. And so a new paradigm, or set of
beliefs, was established. It was not until
1930 that Fritz London explained the weak,
attractive dipolar electric bonding force
(known as Van der Waals' dispersion force
or the 'London force') that causes gas
molecules to condense and form liquids
and solids. Like gravity, the London force
is always attractive and operates between
electrically neutral molecules
<<
What a different story might have been told
if London's insight had come a few decades
earlier? Physics could, by now, have advanced
by a century instead of being bogged in a
mire of metaphysics. >>
http://www.holoscience.com/news.php?article=3Dr4k29syp
GP-B
http://einstein.stanford.edu/
Tajmar / de Matos
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html
Sue...
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| User: "Igor" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are theimplications? |
16 Nov 2007 11:06:33 AM |
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On Nov 15, 3:43 pm, "Neil Bates" <neil_del...@caloricmail.com> wrote:
Moving streams of matter should produce a "Gravitomagnetic field" analogou=
s to the magnetic field from moving charges. This is orthodox GR, even if so=
me details are in contention. (See for example,http://en.wikipedia.org/wiki/=
Gravitomagnetism.)
I played around with equivalent matter streams moving in opposite directio=
ns. That should cancel out their gravitomagnetic fields B* (usually just cal=
led "B" after context given), but I found an inconsistency. The problem was=
, superposition of B* from two sources as if a vector field did not work. (S=
ure, gravity is more complicated, but that part should approximate vector fi=
elds and emulate EM at low mass levels - ? - and I expect even non-linear su=
perpositions to cancel out opposite fields.) For example, let's have adjace=
nt streams going 0.5c in opposite directions, very low mass density to provi=
de high expected linearity (albeit at relativistic speeds.) The proper valu=
e of g seen in our frame K is gamma squared times the value g_s at rest rela=
tive to either single stream (hence g =3D 2gamma^2(0.5c)g_s =3D (2*4/3)g_s =
=3D (8/3)g_s), due to the multiplied effects of Lorentz contraction and grea=
ter relativistic mass-energy density (thus field-producing power) per proper=
length unit in the mass flow.
We will send a unit mass M moving at 0.5c, frame K', along the streams' pa=
th, in either direction. We, expecting to see only "g" since the B* has ost=
ensibly been canceled, expect M to experience gamma squared the value of pro=
per acceleration towards the stream that we find in K (lateral acceleration =
transformation, from shorter proper time to fall.) Since effective mass-ene=
rgy of M is gamma*M_0 (one of the cases where "relativistic mass" is still r=
elevant), that is equivalent to a force in K increased to gamma times rest v=
alue and thus in K', gamma squared times the force in K (due to force transf=
ormation.) Hence by that consistent-seeming reckoning, the acceleration of M=
in K' should be gamma^2(0.5c)g =3D 2gamma^4(0.5c)g_s =3D (32/9)g_s.
However, in M's frame, one stream is at rest and the other one goes at 0.8=
c. The combined effect is therefore [1 + gamma^2(0.8c)]g_s =3D (34/9)g_s =
=3D(17/16)*(32/9)g_s. It is easy to verify (using the additive gamma factor=
being gamma(v1 + v2) =3D gamma1*gamma2*(1 + v1*v2/c^2)) that the ratio in g=
eneral of the second prediction to the first is (1 + v^4/c^4).
That is an odd contradiction, and I just don't know what to make of it. S=
ure, gravitation is not like EM and with curved space etc., but would anyone=
expect low-gravity fields of any kind not to cancel out if apparently of op=
posite sign? Has anyone found good rules for B*? Has this issue been talked=
about before, and where? Thanks.
These maxwell type equations are essentially derived from the Kerr
metric for a rotating "point" source. They won't work outside of that
particular context, since without the rotating source, you no longer
have a Kerr-type metric, and hence no gravitomagnetic field.
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| User: "Darwin123" |
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| Title: Re: Gravitomagnetic field does not obey superposition, what are theimplications? |
16 Nov 2007 12:33:29 AM |
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On Nov 15, 3:43 pm, "Neil Bates" <neil_del...@caloricmail.com> wrote:
That is an odd contradiction, and I just don't know what to make of it. Sure, gravitation is not like EM and with curved space etc., but would anyone expect low-gravity fields of any kind not to cancel out if apparently of opposite sign? Has anyone found good rules for B*? Has this issue been talked about before, and where? Thanks.
Just a word on terminology. I have in a discussion heard the
gravitomagnetic field referred to as a Thirring field. I don't know
how common that term is, but maybe it is better than the term
gravitomagnetic field.
Thirring analyzed space time curvature around a rotating mass.
This space-time curvature is analogous to the gravitomagnetic field.
So the word Thirring field may be appropriate.
I think the main difference between the Maxwell-analog gravity
and the full GR gravity is the kinematic effect of gravity on rulers
and clocks. There is no analog in a strong electric field as described
by Maxwell's equations to the slowing down of time in a strong
gravitational field predicted by GR. So Maxwell-analog gravity is not
exactly the same as GR gravity.
One difference: in Maxwell's equations, there are only two
polarizations of the free-space electromagnetic wave. So in Maxwell-
analog gravity, there are only two polarizations of gravity waves. One
can think of the two polarizations as transverse horizontal and
transverse vertical. In GR gravity, there are four polarizations of
the free-space gravitational wave. There is transverse horizontal,
transverse vertical, longitudinal, and torsional. This is true even
for small amplitude gravity waves (i.e., low gravity).
So I suspect in your case that the Thirring field is not exactly
pointing in the direction you think it is pointing. The extra two
polarizations are producing a Thirring field component which isn't
canceling out.
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