Re: Fw: Newtonian limit difficulties of General Relativity (linear regime)
Dr. Peter Enders
> Hi Peter,
>
> Please keep an eye open: Eric got away with a personal attack against
> Juan, just as he is used to do on sci.physics.relativity. :-(
>
> Thanks,
> Harald
>
> ----- Original Message ----- From: "Eric Gisse" <jow...@gmail.com>
> Newsgroups: sci.physics.foundations
> Sent: Saturday, May 10, 2008 2:18 AM
> Subject: Re: Newtonian limit difficulties of General Relativity
> (linear regime)
>
>
> [...]
>
>> Which makes him believe
> [...]
>> . Its' silly and pedantic,
>
> [...]
>
Hi Harald,
Thank you for this hint. Unfortunately, my command of English is not
sufficient to qualify these formulations as personal attack. I think, my
fellows co-moderators will judge properly and react appropriately.
Please feel free to aproach them directly via spf-...@algebra.com.
Best wishes,
Peter
Oh No
individual. The claim that acceleration is zero with the given metric is
blatantly false, and rested on confusing the covariant derivative which
leads to the geodesic equation with the partial derivative applicable in
a particular coordinate system. Geodesic motion does not imply straight
line motion.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
Juan R.
> The claim that acceleration is zero with the given metric is
> blatantly false
I have proved just the contrary in my paper "Newtonian limit
difficulties of General Relativity".
Draft which i have distributed between three expertises on
relativistic gravitation, both geometrical and non-geometrical,
including one author (Joy Christian) who is specialised [1] in
Newtonian limits of General Relativity. Nobody found error (except
minor typos, two wrong references, and similar ones).
Moreover, i have also discussed some topics with Living Review
expertise on equations of motion Eric Poisson [2], who has already
confirmed my findings about the weak field limit.
After reading your 'criticisms' here and others in
sci.physics.relativity I contacted again with Poisson the day 8 just
for curiosity and receive advice about dealing with that kind of
unsound 'criticism'. This is an extract of my mail:
(\blockquote
Hi Eric,
I have discussed with some people that the equation of motion
*rigorously*
derived when one applies linear metric to geodesic is a = 0, but they
do
not believe me, they say me i am wrong, that derivation given in
Carroll
lecture is all fine
[...]
and that I misread you. Maybe i misread you but interestingly
I also misread R. Wald when said
(\blockquote
if one stay consistently within the linear approximation, one
predicts
that test bodies are unaffected by gravity.
)
)
Poisson has *again* confirmed my findings and also confirms Wald
(\blockquote
Wald is correct.
)
Therefore Wald, Poisson, and me, the three authors claim that a = 0
(and test bodies are unaffected by gravity) in the linear regime (weak
field limit). The three claim that usual derivations in textbooks (and
websites :-) are inconsistent.
You continue making unsubstantiated claims both that here and in your
website [3] where you got certain 'weak field' equation of motion but
without any rigor
http://www.teleconnection.info/rqg/Gravitation
After proving (you may accept this or not) that General Relativity
does not reduce to Newtonian Gravity in the weak field limit i am now
working in a rigorous proof (at mathematics level of rigor) that
General Relativity does not reduce to Newtonian gravity in any limit
(quadratic, Neo-Newt NG, Max NG, Weak NCG, Strong NCG, or other).
For example, rigorous analysis of Frittelli and Reula paper [4]
disproves their approach already at eq. (9) at page 226.
I am now discussing this part with Poisson and others expert authors.
Since you and other people got strong problems with the easy part
(linear regime) of my research. Therefore probably i would not submit
to newsgroups the findings of the hard part of my research. Would I?
NOTES:
[1] He introduced the rotational holonomy constraint in NC spacetime
and proved
gauge invariance of Lagrangian in weakNC limit.
[2] See http://www.livingreviews.org/lrr-2004-6
[3] But you already were said that your website is
(\blockquote
confused throughout, often factually inaccurate, and misses too
many essential points to enumerate here.
)
in a specific thread in sci.physics.research about your website.
See
DrLundsford message.
harry
"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
news:6JuCoLBF...@charlesfrancis.wanadoo.co.uk...
> Thus spake Dr. Peter Enders <end...@dekasges.de>
>>Harald van Lintel schrieb:
>>> Hi Peter,
>>>
>>> Please keep an eye open: Eric got away with a personal attack against
>>>Juan, just as he is used to do on sci.physics.relativity. :-(
>>>
>>> Thanks,
>>> Harald
>>>
>>> ----- Original Message ----- From: "Eric Gisse" <jow...@gmail.com>
>>> Newsgroups: sci.physics.foundations
>>> Sent: Saturday, May 10, 2008 2:18 AM
>>> Subject: Re: Newtonian limit difficulties of General Relativity
>>>(linear regime)
>>>
>>>
>>> [...]
>>>
>>>> Which makes him believe
>>> [...]
>>>> . Its' silly and pedantic,
>>>
>>> [...]
>>>
>>Hi Harald,
>>
>>Thank you for this hint. Unfortunately, my command of English is not
>>sufficient to qualify these formulations as personal attack. I think,
>>my fellows co-moderators will judge properly and react appropriately.
>>Please feel free to aproach them directly via spf-...@algebra.com.
>>
> My feeling was that this was a comment on the argument, not on the
> individual.
More precisely, it referred to his belief, as quoted. But I'm surprised to
hear that. The boundary between either attacking a person, or attacking an
argument or belief of that person is sometimes very vague. I take note. In
other words Charles, your feeling was silly and pedantic.
(That last remark was of course only to make the point clear!)
Regards,
Harald
Eric Gisse
> Thus spake Dr. Peter Enders <end...@dekasges.de>
>
> >Harald van Lintel schrieb:
> >> Hi Peter,
>
> >> Please keep an eye open: Eric got away with a personal attack against
> >>Juan, just as he is used to do on sci.physics.relativity. :-(
>
> >> Thanks,
> >> Harald
>
> >> Newsgroups: sci.physics.foundations
> >> Sent: Saturday, May 10, 2008 2:18 AM
> >> Subject: Re: Newtonian limit difficulties of General Relativity
> >>(linear regime)
>
> >> [...]
>
> >>> Which makes him believe
> >> [...]
> >>> . Its' silly and pedantic,
>
> >> [...]
>
> >Hi Harald,
>
> >Thank you for this hint. Unfortunately, my command of English is not
> >sufficient to qualify these formulations as personal attack. I think,
> >my fellows co-moderators will judge properly and react appropriately.
Less of an attack and more of a shot off the bow. The problem is this
has been explored to death in sci.physics.relativity _and_ in the
literature. Now it appears here.
>
> My feeling was that this was a comment on the argument, not on the
> individual. The claim that acceleration is zero with the given metric is
> blatantly false, and rested on confusing the covariant derivative which
> leads to the geodesic equation with the partial derivative applicable in
> a particular coordinate system. Geodesic motion does not imply straight
> line motion.
Yes and no.
He does know the difference between straight line motion and geodesic
motion but isn't expressing himself clearly so I'm giving him the
benefit of the doubt here. There appears to be no confusion between
confusing the covariant and partial derivatives.
The /problem/ is ostensibly with the linearized GR itself, which is
summarized as follows:
The terms in the stress energy tensor in the Einstein equation are
already assumed to be small for the limit to apply in the first place.
Then due to the assumption that the stress tensor terms are already of
the same order as the perturbative terms, retaining the lowest order
terms gives @_a T^ab = 0. From there - strictly speaking - it is
implied that particles travel with straight line motion that is not
affected by gravitation.
If the correction terms were retained, the conservation equation would
be of higher order than the perturbation. To fix that, you have to
step up and retain corrections in the metric of order O(h^2) and then
the same problem is hit again. Lather, rinse, repeat by summing the
terms and you obtain the full nonlinear field equations again.
The argument is fleshed out in more mathematical detail in Box 7.1 on
page 186 in Misner, Thorne, Wheeler with references for how summing
the corrections gets the full field equations.
This is not as big of a deal as it is made out to be - yes the theory
is technically inconsistent if one demands consistency in the order of
terms. However...who cares? The linearized theory is still useful,
still a valid approximation, and no less messed up than other
theories. Classical electrodynamics still gives infinity for the self
energy of an electron and the radiation reaction force is still wonky
as ever, however the problems are well understood and the theory still
remains useful.
Do not fall victim to references to Eric Poisson - the article he
authored is interesting but off topic to the subject of the
inconsistency in linearized GR.
Oh No
>He does know the difference between straight line motion and geodesic
>motion but isn't expressing himself clearly so I'm giving him the
>benefit of the doubt here. There appears to be no confusion between
>confusing the covariant and partial derivatives.
>
>The /problem/ is ostensibly with the linearized GR itself, which is
>summarized as follows:
>
>The terms in the stress energy tensor in the Einstein equation are
>already assumed to be small for the limit to apply in the first place.
>Then due to the assumption that the stress tensor terms are already of
>the same order as the perturbative terms, retaining the lowest order
>terms gives @_a T^ab = 0. From there - strictly speaking - it is
>implied that particles travel with straight line motion that is not
>affected by gravitation.
>
>If the correction terms were retained, the conservation equation would
>be of higher order than the perturbation. To fix that, you have to step
>up and retain corrections in the metric of order O(h^2) and then the
>same problem is hit again. Lather, rinse, repeat by summing the terms
>and you obtain the full nonlinear field equations again.
>
>The argument is fleshed out in more mathematical detail in Box 7.1 on
>page 186 in Misner, Thorne, Wheeler with references for how summing the
>corrections gets the full field equations.
Thanks for the reference. At least this seems to clarify what is being
said.
>
>This is not as big of a deal as it is made out to be - yes the theory
>is technically inconsistent if one demands consistency in the order of
>terms. However...who cares? The linearized theory is still useful,
>still a valid approximation, and no less messed up than other theories.
I don't see a problem at all. By taking the weak field limit one is
merely finding a valid approximation to a solution of gtr. This does not
mean one has to import all the paraphanalia of a linearised theory of
gravity which is known to be inconsistent. Indeed, it is clearly wrong
to do so.
Oh No
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:6JuCoLBF...@charlesfrancis.wanadoo.co.uk...
>>>
>> individual.
>
>More precisely, it referred to his belief, as quoted. But I'm surprised to
>hear that. The boundary between either attacking a person, or attacking an
>argument or belief of that person is sometimes very vague. I take note. In
>other words Charles, your feeling was silly and pedantic.
>(That last remark was of course only to make the point clear!)
>
in the mathematical sense of the word (which is how it should be used in
physics) is subject to the objective rules of logic, and impersonal.
Oh No
>On May 15, 10:06 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
>> The claim that acceleration is zero with the given metric is
>> blatantly false
>
>I have proved just the contrary in my paper "Newtonian limit
>difficulties of General Relativity".
but you appear to be talking about a linearised theory, which is not
general relativity, hence you are not talking of the Newtonian limit of
general relativity.
>Therefore Wald, Poisson, and me, the three authors claim that a = 0
>(and test bodies are unaffected by gravity) in the linear regime (weak
>field limit). The three claim that usual derivations in textbooks (and
>websites :-) are inconsistent.
The account in MTW, refed by Eric Giese, makes quite clear that a
linearised tensor theory of gravity is inconsistent. But the linearised
theory is quite a different thing from the weak field limit, which
merely finds an approximation to the equation of motion as given by gtr,
which is not a linear theory.
>
>You continue making unsubstantiated claims both that here and in your
>website [3] where you got certain 'weak field' equation of motion but
>without any rigor
>
>http://www.teleconnection.info/rqg/Gravitation
>
The derivation there is both simple and transparent, and it is perfectly
rigorous by normal standards of the use of mathematics in physics. That
is to say it is straightforward, but tedious, to replace statements like
xdot~0 with equivalent statements in the formal language of analysis. To
do so would merely detract from clarity.
Eric Gisse
> Thus spake Juan R. <juanrgonzal...@canonicalscience.com>
>
> >On May 15, 10:06 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
> >> The claim that acceleration is zero with the given metric is
> >> blatantly false
>
> >I have proved just the contrary in my paper "Newtonian limit
> >difficulties of General Relativity".
>
> but you appear to be talking about a linearised theory, which is not
> general relativity, hence you are not talking of the Newtonian limit of
> general relativity.
Not quite.
The linearized theory is _NOT_ general relativity - it is an
_approximation_ of general relativity.
>
> >Therefore Wald, Poisson, and me, the three authors claim that a = 0
> >(and test bodies are unaffected by gravity) in the linear regime (weak
> >field limit). The three claim that usual derivations in textbooks (and
> >websites :-) are inconsistent.
>
> The account in MTW, refed by Eric Giese, makes quite clear that a
> linearised tensor theory of gravity is inconsistent. But the linearised
> theory is quite a different thing from the weak field limit, which
> merely finds an approximation to the equation of motion as given by gtr,
> which is not a linear theory.
The "weak field limit" and the "linearized theory" are different names
for the same thing - the approximation to general relativity that is a
small perturbation on top of Minkowski space.
Oh No
>> Thus spake Juan R. <juanrgonzal...@canonicalscience.com>
>>
>> >On May 15, 10:06 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>>
>> >> The claim that acceleration is zero with the given metric is
>> >> blatantly false
>>
>> >I have proved just the contrary in my paper "Newtonian limit
>> >difficulties of General Relativity".
>>
>> but you appear to be talking about a linearised theory, which is not
>> general relativity, hence you are not talking of the Newtonian limit of
>> general relativity.
>
>Not quite.
>
>The linearized theory is _NOT_ general relativity
That is what I said.
>- it is an _approximation_ of general relativity.
>
>>
>> >Therefore Wald, Poisson, and me, the three authors claim that a = 0
>> >(and test bodies are unaffected by gravity) in the linear regime (weak
>> >field limit). The three claim that usual derivations in textbooks (and
>> >websites :-) are inconsistent.
>>
>> The account in MTW, refed by Eric Giese, makes quite clear that a
>> linearised tensor theory of gravity is inconsistent. But the linearised
>> theory is quite a different thing from the weak field limit, which
>> merely finds an approximation to the equation of motion as given by gtr,
>> which is not a linear theory.
>
>The "weak field limit" and the "linearized theory" are different names
>for the same thing - the approximation to general relativity that is a
>small perturbation on top of Minkowski space.
Ok, that is how the language is used later on in MTW, but it is not
precisely what is described in box 7.1. If one is taking this as an
approximation, one is not entitled to write T^mn,n=0.
Ken S. Tucker
On May 14, 11:37 pm, "Dr. Peter Enders" <end...@dekasges.de> wrote:
> Harald van Lintel schrieb:
>
> > Hi Peter,
>
> > Please keep an eye open: Eric got away with a personal attack against
> > Juan, just as he is used to do on sci.physics.relativity. :-(
>
> > Thanks,
> > Harald
>
> > ----- Original Message ----- From: "Eric Gisse" <jowr...@gmail.com>
> > Newsgroups: sci.physics.foundations
> > Sent: Saturday, May 10, 2008 2:18 AM
> > Subject: Re: Newtonian limit difficulties of General Relativity
> > (linear regime)
>
> > [...]
>
> >> Which makes him believe
> > [...]
> >> . Its' silly and pedantic,
>
> > [...]
>
> Hi Harald,
>
> Thank you for this hint. Unfortunately, my command of English is not
> sufficient to qualify these formulations as personal attack. I think, my
> fellows co-moderators will judge properly and react appropriately.
> Please feel free to aproach them directly via spf-m...@algebra.com.
>
> Best wishes,
> Peter
IMHO, I think the moderation applied to SPF is excellent.
Myself, I ignore people I find annoying, but that's MY choice.
Of course I hope SPF does NOT degrade into a bitch fest.
Where linearizing GR is concerned, I think it's possible.
A brief and noisy discussion occurred late year in this
SPF thread, regarding Orthogonality,
"Flat/Curved SpaceTime."
How we can understand *covariant and contravariant*
geometric projections as depicted in Figure 1 in this link,
http://www.mathpages.com/rr/s5-02/5-02.htm
I find, the linear expression of GR is formally expressed by,
x_u x_u = x^u x^u , {u=0,1,2,3} , Eq.(kst1)
with the summation convention applying and is generally
true. The details are explained in "Flat/Curved SpaceTime",
that were posted last year.
Regards
Ken S. Tucker
harry
>> Thus spake harry <harald.vanlin...@epfl.ch>
[reinsert the topic:
"Which makes him believe that somehow that the weak field
limit is inconsistent & unapplicable or whatever. Its' silly and
pedantic" ]
> "Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
> news:fy67mOJR...@charlesfrancis.wanadoo.co.uk...
>> Thus spake harry <harald.vanlin...@epfl.ch>
>>>
>>>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>>>news:6JuCoLBF...@charlesfrancis.wanadoo.co.uk...
>>>>>
>>>> My feeling was that this was a comment on the argument, not on the
>>>> individual.
>>>
>>>More precisely, it referred to his belief, as quoted. But I'm surprised
>>>to
>>>hear that. The boundary between either attacking a person, or attacking
>>>an
>>>argument or belief of that person is sometimes very vague. I take note.
>>>In
>>>other words Charles, your feeling was silly and pedantic.
>>>(That last remark was of course only to make the point clear!)
>>>
>> Then you fail. A feeling is a part of myself, and personal. An argument,
>> in the mathematical sense of the word (which is how it should be used in
>> physics) is subject to the objective rules of logic, and impersonal.
Wrong: it referred to his belief, as quoted. IMHO, your belief is about as
personal as your feeling.
Thus we simply have to agree to disagree on this! :-)
Ok then, I rephrase it slightly to better mach the original:
Your feeling is that it only concerned the argument, and not the individual.
However, that's not only mistaken; it's silly and pedantic.
I have no doubt that I now made it clear and you may disagree, but it would
be useful to know what the general opinion is of the moderators.
Regards,
Harald
FrediFizzx
news:1210866...@sicinfo3.epfl.ch...
Hi Harald,
This issue is somewhat of a grey area for me. I might have rejected his
post had I caught it but might not have caught it. Some comments such
as this are bound to slip thru on occasion and ARE somewhat subject to
interpretation.
At this point I would just ask Mr. Gisse (and all) to please try to be
more polite and diplomatic in their replies. I know some issues are
likely to get "heated" during discussion. Let's have good "clean"
debates on the issues.
Best,
Fred Diether
harry
"FrediFizzx" <fredi...@hotmail.com> wrote in message
news:6946c9F...@mid.individual.net...[...]
> This issue is somewhat of a grey area for me. I might have rejected his
> post had I caught it but might not have caught it. Some comments such as
> this are bound to slip thru on occasion and ARE somewhat subject to
> interpretation.
>
> At this point I would just ask Mr. Gisse (and all) to please try to be
> more polite and diplomatic in their replies. I know some issues are
> likely to get "heated" during discussion. Let's have good "clean" debates
> on the issues.
That's what I was trying to get at. Overall the discussions are indeed very
pleasant, let's keep it that way.
Regards,
Harald
Ken S. Tucker
statement I posted. concerning Eq.(kst1) below...
On May 15, 1:19 pm, "Ken S. Tucker" <dynam...@vianet.on.ca> wrote:
> Where linearizing GR is concerned, I think it's possible.
> A brief and noisy discussion occurred late year in this
> SPF thread, regarding Orthogonality,
> "Flat/Curved SpaceTime."
>
> How we can understand *covariant and contravariant*
> geometric projections is depicted in Figure 1 in this link,
http://www.mathpages.com/rr/s5-02/5-02.htm
> I find, the linear expression of GR is formally expressed by,
>
> x_u x_u = x^u x^u , {u=0,1,2,3} , Eq.(kst1)
>
> with the summation convention applying and is generally
> true. The details are explained in "Flat/Curved SpaceTime",
> that were posted last year.
Certainly in Euclidean space, absence of matter,
and thus in a vacuum,
r^2 = (ct)^2 .
I can write that using X^i=r and X^0=ct as,
(i=1,2,3),
X^i X^i = X^0 X^0.
or equivalently,
X_i X_i =X_0 X_0
X_i X_i = X^0 X^0
X^i X^i = X_0 X_0
and it follows that
X_u X_u = X^u X^u , Eq.(KST1)
is true by definition, in Euclidean spacetime.
However let's examine and compare Eq(kst1)
in terms of a Non-Euclidean spacetime as,
x_u x_u = x^u x^u , Eq.(kst1),
that is subject to an imposed energy density,
(detailed in thread "Flat/Curved SpaceTime").
With a bit of tensor math we can do this,
g_uv x^v x_u = g^uv x_v x^u ==>
g_uv (d^v_u) x^2 = g^uv (d^u_v) x^2,
with the Kronecker delta's in brackets ( ).
Dividing off the x^2 we now obtain,
g_uv (d^v_u) = g^uv (d^u_v) , Eq(kst2),
in place of Eq.(kst1).
A simple summation applied to Eq.(kst2) over time
and space (space =radius) yields this result,
g_00 + g_11 = g^00 + g^11 ,
in accord with the Schwarzschild Solution (SS) using,
g_00 = 1-2m/r , g_11 = 1 / g_00
g^00 = 1 / g_00 , g^11 = 1 / g_11 .
(I personally use a (++++) signature as justified here,
http://physics.trak4.com/modern-spacetime.pdf)
To summarize the purpose of this essay: The EFE's
do yield the SS, in an apparent non-linear fashion,
however, using Eq.(kst1) via Eq.(kst2) is an alternative
method to arrive directly at the SS.
Regards
Ken S. Tucker
deSitter
wrote:
> On May 15, 10:06 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
> > The claim that acceleration is zero with the given metric is
> > blatantly false
>
> I have proved just the contrary in my paper "Newtonian limit
> difficulties of General Relativity".
I would like to see this paper. However the situation is simple, as
shown by Cooperstock and Tiey in their latest paper "General
Relativistic Velocity: The Alternative to Dark Matter". When one has
test particles in the field of a large central body, one can enter the
linear regime leading to the Newtonian approximation. In *any* other
case, and most particularly, in the case of an extended distribution
of matter, that is, a galaxy, globular cluster, or even a loose open
cluster, the non-linear terms are completely essential for a realistic
description of gravitating matter. The situation is precisely
analogous to that in hydrodynamics. Even very weak viscosity results
in fluid behavior that is utterly different than no viscosity
(linearized Navier-Stokes equations). "Dry matter" (linearized GR) is
as unrealistic as dry water (linearized NSE). The work of Cooperstock
shows that the rotation curves of galaxies are explained in all
details simply by retaining the non-linearity of GR. That this most
important work since Schwarzschild and Lemaitre is ignored, and even
suppressed, is a scandal that tops even the string debacle and the
inflation insanity in profoundly anti-scientific behavior on the part
of the community.
-drl
Ilja Schmelzer
> However the situation is simple, as
> shown by Cooperstock and Tiey in their latest paper "General
> Relativistic Velocity: The Alternative to Dark Matter". When one has
> test particles in the field of a large central body, one can enter the
> linear regime leading to the Newtonian approximation. In *any* other
> case, and most particularly, in the case of an extended distribution
> of matter, that is, a galaxy, globular cluster, or even a loose open
> cluster, the non-linear terms are completely essential for a realistic
> description of gravitating matter. The situation is precisely
> analogous to that in hydrodynamics. Even very weak viscosity results
> in fluid behavior that is utterly different than no viscosity
> (linearized Navier-Stokes equations). "Dry matter" (linearized GR) is
> as unrealistic as dry water (linearized NSE). The work of Cooperstock
> shows that the rotation curves of galaxies are explained in all
> details simply by retaining the non-linearity of GR. That this most
> important work since Schwarzschild and Lemaitre is ignored, and even
> suppressed, is a scandal that tops even the string debacle and the
> inflation insanity in profoundly anti-scientific behavior on the part
> of the community.
It is not ignored, but criticized in http://arxiv.org/abs/astro-ph/0508377
Juan R.
[I have recovered my usual newserver and account. Some previous postings
from mine dissapeared in the wire. I will try again.]
> I would like to see this paper. However the situation is simple, as
> shown by Cooperstock and Tiey in their latest paper "General
> Relativistic Velocity: The Alternative to Dark Matter".
They are doing that kind of claims since years ago
http://arxiv.org/abs/astro-ph/0512048
I have taken a rapid look to his new claim and i see nothing convincing,
but many unsolved questions: where is computation of a_0? and several
incorrect equations.
> When one has
> test particles in the field of a large central body, one can enter the
> linear regime leading to the Newtonian approximation.
In this short piece you did two serious mistakes.
The mistake about confusion between fields and AAAD is corrected in Phys.
Rev. E 1996: 53, 5373 for the case of electromagnetic interaction and in
[Classical Relativistic Many-Body Dynamics. 1999: Springer. Trump,
Matthew A; Schieve, William C.] and my current work for gravitational
interactions. If either the cited monograph does not introduce dual C-SR
potentials, which you only can find in my recent work for gravity and in
PRE paper for EM.
The linear regime of GR does not give Newtonian approximation (as
believed) but *absence of gravity*. This is worked with some detail in my
paper, and confirmed by experts R. Wald and Eric Poisson.
The linear regime equation usually given in literature is incorrect.
> The work of Cooperstock shows that the
> rotation curves of galaxies are explained in all details simply by
> retaining the non-linearity of GR.
In this thread i am focusing in Newtonian limits. I am interested in the
question of dark matter but i will work that in a future. But as said
before in a first reading of their recent paper i am not convinced; i
already found some equations are clearly incorrect.
--
http://canonicalscience.org/en/miscellaneouszone/guidelines.html
Juan R.
[I recovered my usual newsserver and account. Previous postings from mine
disappeared in the wire.]
> Thus spake Juan R. <juanrgo...@canonicalscience.com>
>>On May 15, 10:06 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>>
>>> The claim that acceleration is zero with the given metric is blatantly
>>> false
>>
>>I have proved just the contrary in my paper "Newtonian limit
>>difficulties of General Relativity".
>
> but you appear to be talking about a linearised theory, which is not
> general relativity, hence you are not talking of the Newtonian limit of
> general relativity.
No. I focused in the linear regime in this thread but the work also deal
with quadratic and higher order regimes.
The conclusion of the paper is that General Relativity has not, in rigor,
Newtonian limit.
>>Therefore Wald, Poisson, and me, the three authors claim that a = 0 (and
>>test bodies are unaffected by gravity) in the linear regime (weak field
>>limit). The three claim that usual derivations in textbooks (and
>>websites :-) are inconsistent.
>
> The account in MTW, refed by Eric Giese, makes quite clear that a
> linearised tensor theory of gravity is inconsistent. But the linearised
> theory is quite a different thing from the weak field limit, which
> merely finds an approximation to the equation of motion as given by gtr,
> which is not a linear theory.
Linearised GR is mathematically inconsistent. I have said a *different*
thing.
I said that the derivation of Newtonian limit in the linear regime of GR
is inconsistent. Robert Wald has expressed in next terms:
(\blockquote
if one stay consistently within the linear approximation, one predicts
that test bodies are unaffected by gravity.
)
--
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Juan R.
> Linearised GR is mathematically inconsistent.
Sorry a typo! It would say:
Linearised GR is mathematically *consistent*.
Think on the standard perturbative expansion of field equations
G_ab = (0)^G_ab + (1)^G_ab + (2)^G_ab + ...
T_ab = (0)^T_ab + (1)^T_ab + (2)^T_ab + ...
--
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Oh No
>>>Therefore Wald, Poisson, and me, the three authors claim that a = 0 (and
>>>test bodies are unaffected by gravity) in the linear regime (weak field
>>>limit). The three claim that usual derivations in textbooks (and
>>>websites :-) are inconsistent.
>>
>> The account in MTW, refed by Eric Giese, makes quite clear that a
>> linearised tensor theory of gravity is inconsistent. But the linearised
>> theory is quite a different thing from the weak field limit, which
>> merely finds an approximation to the equation of motion as given by gtr,
>> which is not a linear theory.
>
>Linearised GR is mathematically inconsistent. I have said a *different*
>thing.
>
>I said that the derivation of Newtonian limit in the linear regime of
>GR is inconsistent. Robert Wald has expressed in next terms:
>
>(\blockquote
> if one stay consistently within the linear approximation, one predicts
> that test bodies are unaffected by gravity.
>)
conclude that the Newtonian limit is not the same as the linear regime.
The clues are in things which you said earlier in the thread. The
derivation of the weak field limit I give on the website is not the same
as the linear approximation.
>Carroll is not computing the linear geodesic equation of motion but
>'inventing' a non-geometrical equation [see below].
Very true (apart from "inventing" - the equation of motion is properly
derived by Carroll). Newtonian gravity is non-geometrical, and the
equation of motion in Newtonian gravity is not geodesic.
You also said
>Indeed some derivations of Newtonian limit i revised assume that
>
>g_00 /= -1
>
>*and*
>
>g_ij = 1
>which is geometrically impossible because for the Schwarzschild metric
>
>g_00 = (-1 / g_ij)
>
But one should note the fact that Newtonian gravity uses a nonphysical
metric, Euclidean space + time, which is not the physical metric, e.g.
Schwarzschild in gtr. The object in the Newtonian limit, or weak field
limit is not to find a geometrical approximation to gtr, but to find an
approximation to the equation of motion using Euclidean space
coordinates. Whether or not some textbooks confuse this approximation
with the linear approximation which you discuss, I cannot say. All I can
say is that there is no problem with the derivation of the Newtonian
equation.
Ken S. Tucker
be helpful.
Eq.(SS)
> g^00 = 1 / g_00 , g^11 = 1 / g_11 .
>
> (I personally use a (++++) signature as justified here,http://physics.trak4.com/modern-spacetime.pdf)
>
> To summarize the purpose of this essay: The EFE's
> do yield the SS, in an apparent non-linear fashion,
> however, using Eq.(kst1) via Eq.(kst2) is an alternative
> method to arrive directly at the SS.
> Regards
> Ken S. Tucker
The Logic Progression (LP) overview of the above post is,
(r=ct)^2 => Eq.(KST1) => Eq.(kst1) => Eq.(kst2) => Eq.(SS).
I'm uncertain about the meaning of "non-linearity".
To me, it involves 1st and 2nd derivatives, that Newton
invented along with the continuum, and that causes
trouble for QGT.
The LP above does NOT depend on derivatives, and
thus is continuum free.
>From the secure definition of length and time given by,
r=ct , we proceeded to a Generally Covariant Eq.(kst2),
that yields Eq.(SS).
That permits an alternative to AE's Law Guv=Tuv with
a more generalized Eq.(kst2), independant of continuum,
to derive the Eq.(SS), which is the solution to Guv=Tuv,
in a simplistic case, that recognizes the presence of
mass "m", in juxtaposition to Eq.(KST1), wherein no mass
or density is present to affect the velocity of light.
The quantity "g_00" is entered by experimental measure.
Regards
Ken S. Tucker
Eric Gisse
> Thus spake Juan R. González-Álvarez <juanREM...@canonicalscience.com>
That isn't /strictly/ true. Cartan re-created Newtonian gravitation in
the form of geometry so that motion is geodesic. He gets around the
fact that Newton seems to operate on a constant time slice in a way
that is rather familiar from classical mechanics. He used the basic
concept between virtual work - allow a small displacement from t --->
delta t and go from there. It was rather interesting if I recall, and
there is a whole chapter dedicated to it in MTW.
>
> You also said
>
> >Indeed some derivations of Newtonian limit i revised assume that
>
> >g_00 /= -1
>
> >*and*
>
> >g_ij = 1
> >which is geometrically impossible because for the Schwarzschild metric
>
> >g_00 = (-1 / g_ij)
This is all here still hilariously wrong. No valid derivation ever
assumes anything he wrote.
>
> But one should note the fact that Newtonian gravity uses a nonphysical
> metric, Euclidean space + time, which is not the physical metric, e.g.
> Schwarzschild in gtr. The object in the Newtonian limit, or weak field
> limit is not to find a geometrical approximation to gtr, but to find an
> approximation to the equation of motion using Euclidean space
> coordinates.
Noooooooo!
The only goal is to approximate GR. There is no goal regarding /
anything/ Euclidean.
Eric Gisse
> On May 15, 10:16 am, "Juan R." <juanrgonzal...@canonicalscience.com>
> wrote:
>
> > On May 15, 10:06 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>
> > > The claim that acceleration is zero with the given metric is
> > > blatantly false
>
> > I have proved just the contrary in my paper "Newtonian limit
> > difficulties of General Relativity".
>
> I would like to see this paper. However the situation is simple, as
> shown by Cooperstock and Tiey in their latest paper "General
> Relativistic Velocity: The Alternative to Dark Matter".
Cooperstock and Tieu's paper has been shown to have unphysical sources
in their model.
Ilja already gave you the reference - but there is another version
which is more interesting and appears to be on the right side of
wrong. http://arxiv.org/abs/astro-ph/0602519v2
Why don't you read that and give comments?
>When one has
> test particles in the field of a large central body, one can enter the
> linear regime leading to the Newtonian approximation. In *any* other
> case, and most particularly, in the case of an extended distribution
> of matter, that is, a galaxy, globular cluster, or even a loose open
> cluster, the non-linear terms are completely essential for a realistic
> description of gravitating matter.
Maybe, maybe not. The papers by Cooperstock and then Balasin are
suggestive, to be sure. I find Balasin's version quite attractive and
personally do not yet see anything wrong with the idea.
> The situation is precisely
> analogous to that in hydrodynamics. Even very weak viscosity results
> in fluid behavior that is utterly different than no viscosity
> (linearized Navier-Stokes equations). "Dry matter" (linearized GR) is
> as unrealistic as dry water (linearized NSE). The work of Cooperstock
> shows that the rotation curves of galaxies are explained in all
> details simply by retaining the non-linearity of GR. That this most
> important work since Schwarzschild and Lemaitre is ignored, and even
> suppressed, is a scandal that tops even the string debacle and the
> inflation insanity in profoundly anti-scientific behavior on the part
> of the community.
This is the most common problem with people and alternative ideas on
this or any newsgroup. An interesting idea comes forth - the
Cooperstock and Tieu model - and it gets a lot of attention. Do you
remember the attention? It got on the front page of slashdot, which is
rather unusual for such a thing.
Then it goes away when the work is revealed to have some serious
flaws, like some seriously unphysical sources along the axis of the
galaxy. Oh well - it happens, but the idea was still good and I still
believe that there is something to be learned from that.
But the model is still remembered by other people folks like yourself,
but since you see it is largely ignored now you assume it is being
suppressed. That's always frustrating for everyone else because it
happens all the time - not the suppression, just the claim of
suppression - and is simply boring to see. Try to can the whining
about being suppressed or being anti-science or whatever because it is
old, played out, and always wrong.
>
> -drl
Juan R.
No. Carroll starts from an geometrical equation and finishes with a
nongeometrical linear equation, instead the correct geometrical linear
equation.
His final (wrong) equation does not verify Bianchi and other geometrical
requirements.
His inconsistent (i.e. wrong) result is the reason which Wald emphasizes
that a *consistent* linearization give a different result: (a = 0). See
Wald quote above.
The technique used by Wald is derivation of equation of motion from
'conservation' law D^a T_ab = 0. Where T_ab is EMT for matter. His is a
rigorous technique (not the incorrect ill-defined computation given in
Carroll, Weinberg, and other standard textbooks).
The technique used by Poisson is derivation of equation of motion from
'conservation' law \partial^a t_ab = 0 in body surfaces. Where t_ab is
pseudotensor for matter+field. This is another rigorous technique.
But both techniques are difficult to higher orders.
I also found (a = 0) for weak fields using a different technique. This
technique is more simple to understand why even higher order corrections
(e.g. quadratic terms) do not coincide with Newtonian gravity.
That the correct weak field result is (a = 0) has been also checked by
Eric Poisson.
I have explained in original messages that Carroll is not taking into
account an extra (\delta a) term in the LHS of original geodesic equation.
If you reintroduce that missing term the *rigorous* result is a = 0.
Wald, Poisson, and me, both the three agree at this point. I think this
part of my work is sufficiently rigorous and valid.
> Newtonian gravity is non-geometrical, and the equation of motion in
> Newtonian gravity is not geodesic.
Exactly! Newtonian gravity is not a metric theory of gravity. No limit of
a metric theory reduces to a non-metric theory.
> You also said
>
>>Indeed some derivations of Newtonian limit i revised assume that
>>
>>g_00 /= -1
>>
>>*and*
>>
>>g_ij = 1
>
>
>>which is geometrically impossible because for the Schwarzschild metric
>>
>>g_00 = (-1 / g_ij)
>>
> But one should note the fact that Newtonian gravity uses a nonphysical
> metric, Euclidean space + time, which is not the physical metric, e.g.
> Schwarzschild in gtr.
Several comments here:
i)
Time in Newtonian gravity is not dimensional and has not metric structure.
ii)
You start from assuming that Schwarzschild is physical metric but this
remains unproven. E.g. in Feynman theory of gravity (passing same current
tests that GR) the Schwarzschild metric is *unphysical*. Geodesic motion
is only an approximation in FTG.
iii)
The Schwarzschild metric in GR verifies g_00 = (-1 / g_ii). You cannot
take /by hand/
g_00 = 1 + 2\phi and g_ii = -1
as {Ivanenko & Sardanashvili 2005} do. You cannot by the simple motive
those /ad hoc/ metric coefficients are not a solution of the field
equations.
They 'invent' the metric *before* introducing in the Lagrangian
-mc (\sqrt -g_ab dx^a dx^b)
and then applying the weak field and low velocity approximations.
Why? Because if they were using the correct metric predicted by GR they
would find an extra (2\phi) term in the denominator of the kinetic term
after applying the weak field and low velocity approx to the Lagrangian.
Moreover the *spatial* element of line in the weak field approximation
would be
d\sigma^2 = (\gamma_ij = g_ij + \gamma_i\gamma_j) dx^i dx^j
= gij dx^i dx^j
= (1 - 2\phi) dx^i dx^i
But the waited result is
d\sigma^2 = 1 dx^i dx^i
Then {Ivanenko & Sardanashvili 2005} just 'invented' the metric
coefficients to its own convenience without checking if the metric is
solution of the field equations do.
A more interesting result is that can be showed that a rigorous
computation for {Ivanenko & Sardanashvili 2005} give a Lagrangian predicts
the equation of motion (a = 0). Therefore three rigorous different methods
(Lagrangian, D^aT_ab, and geodesic) give the same result: bodies
unaffected by gravity in the weak field limit.
iv)
The problem of incorrect equation of motion and wrong spatial geometry is
traced to the geometrical formulation. That is, the problem is only with
GR. Because both R-AAAD theories as
http://arxiv.org/abs/physics/0612019v9
and Feynman field theory (FTG) give non-zero accelerations and correct
spatial geometry (d\sigma^2 = 1 dx^i dx^i).
> The object in the Newtonian limit, or weak field limit is not to find a
> geometrical approximation to gtr, but to find an approximation to the
> equation of motion using Euclidean space coordinates.
Any approximation to GR may verify main principles of GR. Otherwise it is
not an approximation but a falsification.
Any Newtonian limit may verify main principles of Newtonian theory.
Otherwise it is not an "limit to" but another falsification.
{Ivanenko & Sardanashvili 2005}
see equations 4.16. on Gravitación. 2005. Editorial URSS. Ivanenko, Dmitri
Dmítrievich; Sardanashvili, Guenadi Alexándrovich.
--
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Oh No
>> >Carroll is not computing the linear geodesic equation of motion but
>> >'inventing' a non-geometrical equation [see below].
>>
>> Very true (apart from "inventing" - the equation of motion is properly
>> derived by Carroll). Newtonian gravity is non-geometrical, and the
>> equation of motion in Newtonian gravity is not geodesic.
>
>That isn't /strictly/ true. Cartan re-created Newtonian gravitation in
>the form of geometry so that motion is geodesic. He gets around the
>fact that Newton seems to operate on a constant time slice in a way
>that is rather familiar from classical mechanics. He used the basic
>concept between virtual work - allow a small displacement from t --->
>delta t and go from there. It was rather interesting if I recall, and
>there is a whole chapter dedicated to it in MTW.
I confess I had forgotten Cartan's formulation. It's many years since I
read that chapter.
>
>>
>> You also said
>>
>> >Indeed some derivations of Newtonian limit i revised assume that
>>
>> >g_00 /= -1
>>
>> >*and*
>>
>> >g_ij = 1
>> >which is geometrically impossible because for the Schwarzschild metric
>>
>> >g_00 = (-1 / g_ij)
>
>This is all here still hilariously wrong. No valid derivation ever
>assumes anything he wrote.
Allowing some latitude for ASCII & typos, I think I can guess at what
was intended.
>
>>
>> But one should note the fact that Newtonian gravity uses a nonphysical
>> metric, Euclidean space + time, which is not the physical metric, e.g.
>> Schwarzschild in gtr. The object in the Newtonian limit, or weak field
>> limit is not to find a geometrical approximation to gtr, but to find an
>> approximation to the equation of motion using Euclidean space
>> coordinates.
>
>Noooooooo!
>
>The only goal is to approximate GR. There is no goal regarding /
>anything/ Euclidean.
I don't entirely agree. I would say that, given GR, the goal is to show
that Newtonian gravity is found in approximation. Taking a standard
formulation of Newtonian gravity, that means Euclidean space. Of course,
we don't have much to show there, because we always have a Minkowski
tangent space, which we can use as a chart. All we need do is show that
geodesic motion in this chart is approximate to Newtonian gravity, which
is fairly straightforward.
Eric Gisse
Why does google groups keep spitting out a new title in the left hand
frame every time? My preference of google groups over other
newsreaders is slim, and things like this piss me off to no end...
[...]
>
> Allowing some latitude for ASCII & typos, I think I can guess at what
> was intended.
What is intended is obvious, it is just wrong. The constraint he
writes just /happens/ to be true in /certain metrics/. It is not a
general condition or even a geometric one, it is just an algebraic
condition tossed on because it seems correct.
>
>
>
> >> But one should note the fact that Newtonian gravity uses a nonphysical
> >> metric, Euclidean space + time, which is not the physical metric, e.g.
> >> Schwarzschild in gtr. The object in the Newtonian limit, or weak field
> >> limit is not to find a geometrical approximation to gtr, but to find an
> >> approximation to the equation of motion using Euclidean space
> >> coordinates.
>
> >Noooooooo!
>
> >The only goal is to approximate GR. There is no goal regarding /
> >anything/ Euclidean.
>
> I don't entirely agree. I would say that, given GR, the goal is to show
> that Newtonian gravity is found in approximation. Taking a standard
> formulation of Newtonian gravity, that means Euclidean space.
Explicit agreement here.
> Of course,
> we don't have much to show there, because we always have a Minkowski
> tangent space, which we can use as a chart. All we need do is show that
> geodesic motion in this chart is approximate to Newtonian gravity, which
> is fairly straightforward.
I see what you were trying to get at. Yes I agree with you here.
The structure of Newtonian gravitation is Euclidean, and the local
structure of general relativity is Minkowskian. However - in some
limit - the equations of motion for both theories match.
Eric Gisse
Why is this a problem? It should be obvious that covariance has been
tossed out the window the minute terms start getting dropped.
>
> His final (wrong) equation does not verify Bianchi and other geometrical
> requirements.
Which final equation - are you working from Carroll's lecture notes or
his textbook?
I'd like to see your proof that whatever was derived does not satisfy
the Bianchi and other identities, unless you'll just repeat the same
arguments that are used for the conservation law for the stress energy
tensor.
>
> His inconsistent (i.e. wrong) result is the reason which Wald emphasizes
> that a *consistent* linearization give a different result: (a = 0). See
> Wald quote above.
On the odd chance you actually read my replies I want you to explain
something.
The perturbations in the metric are already small. Furthermore, in
order for the weak field limit to apply in the first place the
components of the stress energy tensor must _also_ be small.
Why should a first derivative of something that is _small_ multiplied
against something that is also small be kept?
>
> The technique used by Wald is derivation of equation of motion from
> 'conservation' law D^a T_ab = 0. Where T_ab is EMT for matter. His is a
> rigorous technique (not the incorrect ill-defined computation given in
> Carroll, Weinberg, and other standard textbooks).
You are being dishonest.
Wald, in section 4.4, uses the _exact same derivation_ to obtain the
linearized theory as MTW and Carroll.
>
> The technique used by Poisson is derivation of equation of motion from
> 'conservation' law \partial^a t_ab = 0 in body surfaces. Where t_ab is
> pseudotensor for matter+field. This is another rigorous technique.
You cited http://www.emis.de/journals/LRG/Articles/lrr-2004-6/ as the
derivation before, but I do not actually see this derivation that you
claim is in there. Why?
>
> But both techniques are difficult to higher orders.
>
> I also found (a = 0) for weak fields using a different technique. This
> technique is more simple to understand why even higher order corrections
> (e.g. quadratic terms) do not coincide with Newtonian gravity.
>
> That the correct weak field result is (a = 0) has been also checked by
> Eric Poisson.
Where?
>
> I have explained in original messages that Carroll is not taking into
> account an extra (\delta a) term in the LHS of original geodesic equation.
But you don't actually show where these terms come from. You just
claim he is neglecting them, then move on.
>
> If you reintroduce that missing term the *rigorous* result is a = 0.
OK - let's see the proof.
Then show why it matters. Go read page 78 in Wald again.
>
> Wald, Poisson, and me, both the three agree at this point. I think this
> part of my work is sufficiently rigorous and valid.
Oh so you are in personal communication with both Wald and Poisson,
and they both explicitly agree with you on this subject? Are they OK
with you namedropping them in arguments?
>
> > Newtonian gravity is non-geometrical, and the equation of motion in
> > Newtonian gravity is not geodesic.
>
> Exactly! Newtonian gravity is not a metric theory of gravity. No limit of
> a metric theory reduces to a non-metric theory.
Go read chapter 12 in MTW. There is a metric formulation of Newtonian
gravitation.
Even if the work wasn't done - why does it matter? The only relevant
point is that the EQUATIONS OF MOTION in general relativity are
equivalent to the equations of motion in Newtonian gravitation at the
appropriate limit.
If you are to adopt this odd personal view of what correspondence
means, you'll have to then argue that quantum theory does not reduce
to classical mechanics for the same exact reason.
>
>
>
> > You also said
>
> >>Indeed some derivations of Newtonian limit i revised assume that
>
> >>g_00 /= -1
>
> >>*and*
>
> >>g_ij = 1
>
> >>which is geometrically impossible because for the Schwarzschild metric
>
> >>g_00 = (-1 / g_ij)
>
> > But one should note the fact that Newtonian gravity uses a nonphysical
> > metric, Euclidean space + time, which is not the physical metric, e.g.
> > Schwarzschild in gtr.
>
> Several comments here:
>
> i)
> Time in Newtonian gravity is not dimensional and has not metric structure.
This is not strictly true. Go read chapter 12 in MTW.
>
> ii)
> You start from assuming that Schwarzschild is physical metric but this
> remains unproven. E.g. in Feynman theory of gravity (passing same current
> tests that GR) the Schwarzschild metric is *unphysical*. Geodesic motion
> is only an approximation in FTG.
Using arguments from one theory against another theory to "prove" that
an aspect of another theory is unphysical is downright silly.
>
> iii)
> The Schwarzschild metric in GR verifies g_00 = (-1 / g_ii). You cannot
> take /by hand/
>
> g_00 = 1 + 2\phi and g_ii = -1
>
> as {Ivanenko & Sardanashvili 2005} do. You cannot by the simple motive
> those /ad hoc/ metric coefficients are not a solution of the field
> equations.
Who cares? The condition g_00 = -1 / g_ij is NOT a valid condition on
the metric, it is just something that happens to be true for certain
metrics.
Ivanenko & Sardanashvili are wrong to take that version of the metric
because that is not the actual perturbative metric. In your language,
g_00 = 1 + 2\phi and -g_ij = 1 - 2\phi. NOT g_ij = -1.
[snip remaining Ivanenko & Sardanashvili because it is irrelevant to
the overall discussion]
> A more interesting result is that can be showed that a rigorous
> computation for {Ivanenko & Sardanashvili 2005} give a Lagrangian predicts
> the equation of motion (a = 0). Therefore three rigorous different methods
> (Lagrangian, D^aT_ab, and geodesic) give the same result: bodies
> unaffected by gravity in the weak field limit.
Yea, if you are 100% rigorous in keeping only the lowest order in all
your computations. Read page 78 in Wald again.
What strikes me as odd is why this discussion is taking place at all.
You claim that the 100% rigorous computation means there is straight
line motion. Then I look at every gravitation reference I have and I
see that claim also! Then I wonder what the big deal is since this
claim is now at least 35 years old and pretty well known at this
point.
What I do not understand is why you see the associated explanations of
why this is OK and not a problem and then continue arguing anyway.
[snip other theories - irrelevant]
Juan R.
>> No. Carroll starts from an geometrical equation and finishes with a
>> nongeometrical linear equation, instead the correct geometrical linear
>> equation.
>
> Why is this a problem?
The derivation of theorems and laws has a very precise meaning in both
theoretical physics and mathematics.
>> His final (wrong) equation does not verify Bianchi and other
>> geometrical requirements.
>
> Which final equation - are you working from Carroll's lecture notes or
> his textbook?
People usually read other's posters before replying. You first reply and
then ask for info was already posted by me before in this newsgroup.
> I'd like to see your proof that whatever was derived does not satisfy
> the Bianchi and other identities, unless you'll just repeat the same
> arguments that are used for the conservation law for the stress energy
> tensor.
I confess i do not know an easy way to explain that to someone who ask
what are the units of (V / c^2) where V is a gravitational potential
http://groups.google.com/group/sci.physics.relativity/msg/6fe7633a0e8130f8
>> His inconsistent (i.e. wrong) result is the reason which Wald
>> emphasizes that a *consistent* linearization give a different result:
>> (a = 0). See Wald quote above.
>
>
(snipped stuff would not pass moderation)
> The perturbations in the metric are already small. Furthermore, in order
> for the weak field limit to apply in the first place the components of
> the stress energy tensor must _also_ be small.
>
> Why should a first derivative of something that is _small_ multiplied
> against something that is also small be kept?
Here you are just repeating something i said in one of my start messages,
except i used some explicit formulae, e.g. a mathematical definition for
'small' instead just words.
>> The technique used by Wald is derivation of equation of motion from
>> 'conservation' law D^a T_ab = 0. Where T_ab is EMT for matter. His is a
>> rigorous technique (not the incorrect ill-defined computation given in
>> Carroll, Weinberg, and other standard textbooks).
(snipped stuff would not pass moderation)
> Wald, in section 4.4, uses the _exact same derivation_ to obtain the
> linearized theory as MTW and Carroll.
That is right and i never said the contrary. But Wald recognizes that the
derivation it gives is incorrect and recognizes also that a correct
derivation gives the equation of motion (a = 0). Wald quote is
(\blockquote
if one stay consistently within the linear approximation, one predicts
that test bodies are unaffected by gravity.
)
Tricky or wrong derivations are acceptable in certain undergrad textbook
but are not acceptable at research level.
>> The technique used by Poisson is derivation of equation of motion from
>> 'conservation' law \partial^a t_ab = 0 in body surfaces. Where t_ab is
>> pseudotensor for matter+field. This is another rigorous technique.
>
> You cited http://www.emis.de/journals/LRG/Articles/lrr-2004-6/ as the
> derivation before, but I do not actually see this derivation that you
> claim is in there. Why?
That has an easy explanation. In no part of this thread i said that you
think i said.
>> That the correct weak field result is (a = 0) has been also checked by
>> Eric Poisson.
>
> Where?
Unlike you (undergrad student right?), Poisson is an expert who has some
relevant work on perturbative evaluation of equations of motion, including
derivations of Newtonian like equations.
The checks which i refer is a personal communication i maintained by him
on mail. This is is cited in my paper in a reference and Poisson correctly
aknowledged by assistance in the corresponding section.
>> I have explained in original messages that Carroll is not taking into
>> account an extra (\delta a) term in the LHS of original geodesic
>> equation.
>
> But you don't actually show where these terms come from.
I did that but you did not read or if read you did not understand.
> Then show why it matters. Go read page 78 in Wald again.
Wald is cited as reference in my paper. I know he says very well.
>> Wald, Poisson, and me, both the three agree at this point. I think this
>> part of my work is sufficiently rigorous and valid.
(off-topic stuff snipped)
>> > Newtonian gravity is non-geometrical, and the equation of motion in
>> > Newtonian gravity is not geodesic.
>>
>> Exactly! Newtonian gravity is not a metric theory of gravity. No limit
>> of a metric theory reduces to a non-metric theory.
>
> Go read chapter 12 in MTW. There is a metric formulation of Newtonian
> gravitation.
Yes, i know Cartan-like formulation and your citing of chapter in a old
undergrad textbook is of none help for this research work.
Precisely one of authors who received one of copies of my draft for
evaluation was Dr. Joy Christian, who is a recognized expertise on Newton-
Cartan formalism. He has worked the WNC formulation in detail including
gauge theory, rotational holonomy, cosmological boundaries, and quantum
gravity issues.
One of parts of my work explains why his more recent work to Newtonian
limits and quantum gravity is not correct. We maintain correspondence and
of course, he has not replied in the odd way you are doing here.
> Even if the work wasn't done - why does it matter? The only relevant
> point is that the EQUATIONS OF MOTION in general relativity are
> equivalent to the equations of motion in Newtonian gravitation at the
> appropriate limit.
This is a very superficial understanding of the whole topic.
(off-topic stuff sniped)
>> >>Indeed some derivations of Newtonian limit i revised assume that
>>
>> >>g_00 /= -1
>>
>> >>*and*
>>
>> >>g_ij = 1
>>
>> >>which is geometrically impossible because for the Schwarzschild
>> >>metric
>>
>> >>g_00 = (-1 / g_ij)
>>
>> > But one should note the fact that Newtonian gravity uses a
>> > nonphysical metric, Euclidean space + time, which is not the physical
>> > metric, e.g. Schwarzschild in gtr.
>>
>> Several comments here:
>>
>> i)
>> Time in Newtonian gravity is not dimensional and has not metric
>> structure.
>
> This is not strictly true. Go read chapter 12 in MTW.
It is wrong. By some strange reason you seem to think that all replies to
research level stuff are contained in that old undergraduate textbook.
A more adequate concept of time including non-relativistic limits are
computed in several sites in more modern literature. E.g. specialized
monograph
Classical Relativistic Many-Body Dynamics. 1999: Springer. Trump, Matthew
A; Schieve, William C.
>> ii)
>> You start from assuming that Schwarzschild is physical metric but this
>> remains unproven. E.g. in Feynman theory of gravity (passing same
>> current tests that GR) the Schwarzschild metric is *unphysical*.
>> Geodesic motion is only an approximation in FTG.
>
>
(snipped stuff would not pass moderation)
>> iii)
>> The Schwarzschild metric in GR verifies g_00 = (-1 / g_ii). You cannot
>> take /by hand/
>>
>> g_00 = 1 + 2\phi and g_ii = -1
>>
>> as {Ivanenko & Sardanashvili 2005} do. You cannot by the simple motive
>> those /ad hoc/ metric coefficients are not a solution of the field
>> equations.
>
> Who cares? The condition g_00 = -1 / g_ij is NOT a valid condition on
> the metric, it is just something that happens to be true for certain
> metrics.
If you had read i wrote you would notice that i did explicit i was talking
about "The Schwarzschild metric in GR".
> Ivanenko & Sardanashvili are wrong to take that version of the metric
> because that is not the actual perturbative metric. In your language,
> g_00 = 1 + 2\phi and -g_ij = 1 - 2\phi. NOT g_ij = -1.
Why here you just repeat that i already said?
> [snip remaining Ivanenko & Sardanashvili because it is irrelevant to the
> overall discussion]
It may be irrelevant for you but a subsection of my paper is devoted to
that issue. The reason for that section may go beyond your understanding.
>> A more interesting result is that can be showed that a rigorous
>> computation for {Ivanenko & Sardanashvili 2005} give a Lagrangian
>> predicts the equation of motion (a = 0). Therefore three rigorous
>> different methods (Lagrangian, D^aT_ab, and geodesic) give the same
>> result: bodies unaffected by gravity in the weak field limit.
>
> Yea, if you are 100% rigorous in keeping only the lowest order in all
> your computations.
Here you are confounding the lowest order (0th) with the first order
(1st).
(snipped stuff would not pass moderation)
--
http://canonicalscience.org/en/miscellaneouszone/guidelines.html
Oh No
>> Even if the work wasn't done - why does it matter? The only relevant
>> point is that the EQUATIONS OF MOTION in general relativity are
>> equivalent to the equations of motion in Newtonian gravitation at the
>> appropriate limit.
>
>This is a very superficial understanding of the whole topic.
>
claim that it is not true, but your claim is patently false. Then you
make accusations of errors in standard textbooks by misunderstanding
what this limit actually is and what is being shown in the textbooks,
and you impose some conditions which do not apply, because you say they
are part of the linear approximation. Well, if they are part of the
linear approximation, they are clearly not part of the Newtonian
correspondence. In essence your claim is equivalent to saying that the
geodesics of the surface of the earth must be represented by straight
lines in a world atlas, hence every atlas ever produced is rubbish. If
that is not what you are trying to say, then you have a great deal of
work to do to clarify what you are trying to say.
Juan R.
> Thus spake Juan R. González-Álvarez <juanR...@canonicalscience.com>
>>> Even if the work wasn't done - why does it matter? The only relevant
>>> point is that the EQUATIONS OF MOTION in general relativity are
>>> equivalent to the equations of motion in Newtonian gravitation at the
>>> appropriate limit.
>>
>>This is a very superficial understanding of the whole topic.
>>
> I should have said this was the sole point of issue or importance. You
> claim that it is not true, but your claim is patently false.
I acknowledge your interest and comments.
However at this point i may balance your personal opinion, who did not
read the paper, with opinion of authors (some with important publications
experts on Newtonian limits issue) who read a draft of the paper.
My draft may be also of some interest because i was formally invited to
participate on two recent conferences about Cosmology. That i am proving
in the paper has very important applications to cosmology. In fact i
revise Ehlers cosmological boundaries in a section of the paper.
Actually i have submitted a final draft paper to journal. Therefore i
think this thread can go to dead.
> Then you
> make accusations of errors in standard textbooks by misunderstanding
> what this limit actually is and what is being shown in the textbooks,
In this thread, i have revised the weak field derivation found in
textbooks and lecture notes. Two expertise in the topic (Wald and
Poisson) completely agree in my findings on the linear regime. Poisson
also agrees about curvature discrepancy on the quadratic regime.
> and you impose some conditions which do not apply, because you say they
> are part of the linear approximation.
As explained before i have revised the zeroth, linear, quadratic, and
higher orders. The conclusion is very rigorous and the same for the four
cases: General Relativity has not Newtonian limit.
Once proved that General Relativity has not Newtonian limit now i am
working in a dual generalization of General Relativity.
A dual generalization of field electrodynamics was already done in recent
paper:
Action at a distance as a full-value solution of Maxwell equations: The
basis and application of the separated-potentials
method. 1996: Phys. Rev. E 53, 5373. Chubykalo, Andrew E; Smirnov-Rueda,
Roman.
Erratum: Action at a distance as a full-value solution of Maxwell
equations: The basis and application of the separated-
potentials method [Phys. Rev. E 53, 5373 (1996)] 1997: Phys. Rev. E 55,
3793. Chubykalo, Andrew E; Smirnov-Rueda,
Roman.
The generalization mean that traditional LW potentials A^b(r,t)
associated to field theory are generalized as follows
A^b(r,t) --> A^b(r,t) + A^b(R(t))
Where A^b(R(t)) is a nonlocal *irreducible* component.
One of reason for this generalization of electrodynamics was that
traditional field electrodynamics has not correct Coulomb limit. This was
proved in the PRE paper cited with mathematical rigor and in other
published papers dealing with dualism. E.g:
Necessity of simultaneous co-existence of instantaneous and retarded
interactions in classical electrodynamics. 1999:
Int. J. of Mod. Phys. A 14(24), 3789. Chubykalo, Andrew E; Vlaev, Stoyan
J.
The case for gravity is more complex but something like
h^ab(r,t) --> h^ab(r,t) + h^ab(R(t))
General Relativity is the theory one recovers in the limit
h^ab(R(t)) --> 0
Actually i am collaborating with one of author of the PRE paper cited
above to give this a rigorous foundation in a Liouville space extension
of mechanics.
--
http://canonicalscience.org/en/miscellaneouszone/guidelines.html
======================================= MODERATOR'S COMMENT:
I guess it would be easier for the reader when the novel component would have another symbol than the ordinary component - PE
Juan R.
> Actually i have submitted a final draft paper to journal. Therefore i
> think this thread can go to dead.
> As explained before i have revised the zeroth, linear, quadratic, and
> higher orders. The conclusion is very rigorous and the same for the four
> cases: General Relativity has not Newtonian limit.
A final thought may be of interest for the group. I have received just a
message from Eric Poisson which i quote next:
(\blockquote
And you seem to want a Newtonian limit to GR that gives you a) the
correct field equation for phi, b) the nonzero acceleration, and c) a
flat spatial metric. This simply does not happen in GR
)
Indeed!
For 0th order GR only c) is satisfied.
For 1st order GR only a) is satisfied.
For 2nd order GR only a) and b) are satisfied.
However a), b), and c) are satisfied *at once* in other theories like
Feynman field theory of gravity. Expertise on FTG, Prof. Y. Barishev, has
revised this part of my work.
Thanks by kindly collaborations. I am in debt to Oh no (Charles Francis)
because in his message of day Thu, 08 May 2008, Francis expressed a
misunderstanding about proper acceleration (see my reply of same day).
Originally I started from perturbative geodesic equation in proper frame,
schematically,
A = -Gamma U U
and then convert it to coordinate form at each order of perturbation. I
agree with Francis this may look confusing to readers.
As a consequence, i rewrote all that section of the draft. Now i start
directly with geodesic equation in coordinate form, again in
schematically notation
a = -Gamma v v + Gamma0 v v v
and apply the perturbative technique over it.
Of course, results are the same, simply they are now more accessible.
--
http://canonicalscience.org/en/miscellaneouszone/guidelines.html
Juan R.
MODERATOR COMMENTED
(\blockquote
I guess it would be easier for the reader when the novel component would
have another symbol than the ordinary component - PE
)
Completely agree, i used a simple notation for commodity and also for
remarking that the components
A^b(r,t) and h^ab(r,t)
corresponds exactly to *standard* expressions in Maxwell electrodynamics
and General Relativity.
Chubikalo and Smirnov-Rueda use /another notation/ in the PRE paper cited
above and in other published works.
Their notation is
\phi^* = \phi^*(r,t)
A^* = A^*(r,t)
for the usual scalar and vectorial Lienard-Wiechert potentials associated
to field electrodynamics.
Above potentials generate conventional electromagnetic fields
E^* = E^*(r,t)
B^* = B^*(r,t)
Chubikalo and Smirnov-Rueda use the notation
\phi_0 = \phi_0(R(t))
A_0 = A_0(R(t))
E_0 = E_0(r,t)
B_0 = B_0(r,t)
for the nonlocal time implicit potentials and fields.
The *total* quantities in dualism electrodynamics are (again in their
notation)
\phi = \phi^* + \phi_0
A = A^* + A_0
E = E^* + E_0
B = B^* + B_0
There is similar modifications for actions, Hamiltonians...
In their notation, i would write for dualism gravity
h_ab = h^*_ab + h_0ab
where functions
h^*_ab = h^*_ab(r,t)
correspond to usual solution of GR and FTG equations
and the novel component is
h_0ab = h_0ab(R(t))
But it seemed to me a too complex notation for text newsgroup.
--
http://canonicalscience.org/en/miscellaneouszone/guidelines.html
Eric Gisse
<juanREM...@canonicalscience.com> wrote:
> Eric Gisse wrote on Mon, 19 May 2008 03:45:25 -0600:
>
> >> No. Carroll starts from an geometrical equation and finishes with a
> >> nongeometrical linear equation, instead the correct geometrical linear
> >> equation.
>
> > Why is this a problem?
>
> The derivation of theorems and laws has a very precise meaning in both
> theoretical physics and mathematics.
Yes, but that does not answer my question. _Why_ is it a problem that
the linear equation of motion is nongeometric?
I'm not in any way taking sides on whether it is or isn't because the
issue just does not strike me as being important.
>
> >> His final (wrong) equation does not verify Bianchi and other
> >> geometrical requirements.
>
> > Which final equation - are you working from Carroll's lecture notes or
> > his textbook?
>
> People usually read other's posters before replying. You first reply and
> then ask for info was already posted by me before in this newsgroup.
There was a point to the question.
The section of the lecture notes you are working from is _not_
rigorous. I do not understand why you are arguing about a simplistic -
though correct - section from a set of lecture notes when there is a
rigorous derivation in Chapter 6.
>
> > I'd like to see your proof that whatever was derived does not satisfy
> > the Bianchi and other identities, unless you'll just repeat the same
> > arguments that are used for the conservation law for the stress energy
> > tensor.
>
> I confess i do not know an easy way to explain that to someone who ask
> what are the units of (V / c^2) where V is a gravitational potential
>
> http://groups.google.com/group/sci.physics.relativity/msg/6fe7633a0e8...
Does the deflection mean you have no proof?
>
> >> His inconsistent (i.e. wrong) result is the reason which Wald
> >> emphasizes that a *consistent* linearization give a different result:
> >> (a = 0). See Wald quote above.
>
> (snipped stuff would not pass moderation)
>
> > The perturbations in the metric are already small. Furthermore, in order
> > for the weak field limit to apply in the first place the components of
> > the stress energy tensor must _also_ be small.
>
> > Why should a first derivative of something that is _small_ multiplied
> > against something that is also small be kept?
>
> Here you are just repeating something i said in one of my start messages,
> except i used some explicit formulae, e.g. a mathematical definition for
> 'small' instead just words.
The divergence condition is div.T = 0 in component notation:
div.T = @_i T^ia + Gamma ^ i_ij T^ja
Do you agree or disagree that the term Gamma ^ i_ij T^ja is quadratic
in order? Do you agree or disagree that keeping the Gamma ^ i_ij T^ja
which is quadratic in order while the rest of the theory discards
terms that are quadratic in the perturbation is inconsistent?
>
> >> The technique used by Wald is derivation of equation of motion from
> >> 'conservation' law D^a T_ab = 0. Where T_ab is EMT for matter. His is a
> >> rigorous technique (not the incorrect ill-defined computation given in
> >> Carroll, Weinberg, and other standard textbooks).
>
> (snipped stuff would not pass moderation)
>
> > Wald, in section 4.4, uses the _exact same derivation_ to obtain the
> > linearized theory as MTW and Carroll.
>
> That is right and i never said the contrary. But Wald recognizes that the
> derivation it gives is incorrect and recognizes also that a correct
> derivation gives the equation of motion (a = 0). Wald quote is
>
> (\blockquote
> if one stay consistently within the linear approximation, one predicts
> that test bodies are unaffected by gravity.
> )
>
This does not mean the derivation is wrong - just that it appears
inconsistent when one is consistent in staying within the linear
approximation.
> Tricky or wrong derivations are acceptable in certain undergrad textbook
> but are not acceptable at research level.
Except the derivations are neither tricky nor wrong when they are
_exactly similar_ to the derivation from the author you favor.
Regardless I tire of hearing arguments about Carroll's lecture notes -
I simply prefer Carroll because I like his style and the book is
substantially thinner than MTW which makes for easier reading. I'll be
happy to work from Wald & MTW since you believe Carroll's text is not
up to snuff.
>
> >> The technique used by Poisson is derivation of equation of motion from
> >> 'conservation' law \partial^a t_ab = 0 in body surfaces. Where t_ab is
> >> pseudotensor for matter+field. This is another rigorous technique.
>
> > You citedhttp://www.emis.de/journals/LRG/Articles/lrr-2004-6/as the
> > derivation before, but I do not actually see this derivation that you
> > claim is in there. Why?
>
> That has an easy explanation. In no part of this thread i said that you
> think i said.
http://groups.google.com/group/sci.physics.relativity/msg/edcad31bdb97cfb6?dmode=source
I said "before", not "this thread". All I want to see is the technique
you claim is rigorous. I don't have a particular interest in point
particles so I was hoping for a page number, rather than having to
read the whole thing in the hope of finding your point.
[snip]
> >> I have explained in original messages that Carroll is not taking into
> >> account an extra (\delta a) term in the LHS of original geodesic
> >> equation.
>
> > But you don't actually show where these terms come from.
>
> I did that but you did not read or if read you did not understand.
If I understood, I wouldn't be asking.
Carroll does not do what you claim he does. I have his textbook _right
in front of me_, and what you write in your original message has
exactly zero bearing on what is in either the textbook or the notes
the textbook is based upon.
http://groups.google.com/group/sci.physics.foundations/msg/b219b0e80c3ef10b?dmode=source
>
> > Then show why it matters. Go read page 78 in Wald again.
>
> Wald is cited as reference in my paper. I know he says very well.
Then WHAT is the problem? I ask because I honestly do not see the
problem - yes, the linearized theory is inconsistent if one stays
within the linearization but who cares? The linearized theory is an
approximation to a nonlinear theory, and theories that are
inconsistent are still useful. Classical electrodynamics is still
inconsistent but it is still a good approximation to reality - just
like linearized GR.
>
> >> Wald, Poisson, and me, both the three agree at this point. I think this
> >> part of my work is sufficiently rigorous and valid.
>
> (off-topic stuff snipped)
>
> >> > Newtonian gravity is non-geometrical, and the equation of motion in
> >> > Newtonian gravity is not geodesic.
>
> >> Exactly! Newtonian gravity is not a metric theory of gravity. No limit
> >> of a metric theory reduces to a non-metric theory.
>
> > Go read chapter 12 in MTW. There is a metric formulation of Newtonian
> > gravitation.
>
> Yes, i know Cartan-like formulation and your citing of chapter in a old
> undergrad textbook is of none help for this research work.
What are you going on about? MTW is the standard graduate level
textbook in gravitation physics.
The Cartan formulation was only brought up to counter the claim
Newtonian gravitation is "non-metric". Regardless it does not matter
since correspondence is only ever claimed for the _equations of
motion_. Nobody [should] seriously claim GR should 100% match
Newtonian gravitation in every aspect. Otherwise the theories aren't
actually different.
>
> Precisely one of authors who received one of copies of my draft for
> evaluation was Dr. Joy Christian, who is a recognized expertise on Newton-
> Cartan formalism. He has worked the WNC formulation in detail including
> gauge theory, rotational holonomy, cosmological boundaries, and quantum
> gravity issues.
>
> One of parts of my work explains why his more recent work to Newtonian
> limits and quantum gravity is not correct. We maintain correspondence and
> of course, he has not replied in the odd way you are doing here.
Why even bring him up?
>
> > Even if the work wasn't done - why does it matter? The only relevant
> > point is that the EQUATIONS OF MOTION in general relativity are
> > equivalent to the equations of motion in Newtonian gravitation at the
> > appropriate limit.
>
> This is a very superficial understanding of the whole topic.
Superficial explanation only.
What I want to hear from you is how being a metric or non-metric
formalism matters. The trajectories of particles in Newtonian
gravitation are almost exactly similar to trajectories in the weak
field limit under appropriate approximations. That's all the
correspondence there is between the two theories, and that's all
anyone is seriously concerned about.
You keep claiming that GR doesn't have a Newtonian limit, but the only
two points I see you bring up is that the linearized theory is
inconsistent and that the theories are different. I'm yet to see an
actual explanation of why the claimed Newtonian limit is wrong.
I'm tired of arguing about what's in Carroll - argue from MTW or Wald
since you refuse to take Carroll's text seriously.
>
> (off-topic stuff sniped)
>
>
>
> >> >>Indeed some derivations of Newtonian limit i revised assume that
>
> >> >>g_00 /= -1
>
> >> >>*and*
>
> >> >>g_ij = 1
>
> >> >>which is geometrically impossible because for the Schwarzschild
> >> >>metric
>
> >> >>g_00 = (-1 / g_ij)
>
> >> > But one should note the fact that Newtonian gravity uses a
> >> > nonphysical metric, Euclidean space + time, which is not the physical
> >> > metric, e.g. Schwarzschild in gtr.
>
> >> Several comments here:
>
> >> i)
> >> Time in Newtonian gravity is not dimensional and has not metric
> >> structure.
>
> > This is not strictly true. Go read chapter 12 in MTW.
>
> It is wrong. By some strange reason you seem to think that all replies to
> research level stuff are contained in that old undergraduate textbook.
For some strange reason you seem unaware that MTW is _the standard_
for studying gravitation physics, and for some even *stranger* reason
you think it is an undergraduate textbook.
The theory hasn't changed in the 35 years since the book has been
published - can you name one major advance in the theory of classical
general relativity since MTW was published?
I'd like to hear why you think the entire chapter is wrong, and
whether any of the people you namedrop agree with your conclusions.
>
> A more adequate concept of time including non-relativistic limits are
> computed in several sites in more modern literature. E.g. specialized
> monograph
>
> Classical Relativistic Many-Body Dynamics. 1999: Springer. Trump, Matthew
> A; Schieve, William C.
The text is only about dynamics - how is it a specialized monograph
about non-relativistic limits? Furthermore, how is it _relevant_ ?
>
> >> ii)
> >> You start from assuming that Schwarzschild is physical metric but this
> >> remains unproven. E.g. in Feynman theory of gravity (passing same
> >> current tests that GR) the Schwarzschild metric is *unphysical*.
> >> Geodesic motion is only an approximation in FTG.
>
> (snipped stuff would not pass moderation)
>
> >> iii)
> >> The Schwarzschild metric in GR verifies g_00 = (-1 / g_ii). You cannot
> >> take /by hand/
>
> >> g_00 = 1 + 2\phi and g_ii = -1
>
> >> as {Ivanenko & Sardanashvili 2005} do. You cannot by the simple motive
> >> those /ad hoc/ metric coefficients are not a solution of the field
> >> equations.
>
> > Who cares? The condition g_00 = -1 / g_ij is NOT a valid condition on
> > the metric, it is just something that happens to be true for certain
> > metrics.
>
> If you had read i wrote you would notice that i did explicit i was talking
> about "The Schwarzschild metric in GR".
"The Schwarzschild metric in GR verifies g_00 = (-1 / g_ii)."
The condition is not something that is true in general.
>
> > Ivanenko & Sardanashvili are wrong to take that version of the metric
> > because that is not the actual perturbative metric. In your language,
> > g_00 = 1 + 2\phi and -g_ij = 1 - 2\phi. NOT g_ij = -1.
>
> Why here you just repeat that i already said?
>
> > [snip remaining Ivanenko & Sardanashvili because it is irrelevant to the
> > overall discussion]
>
> It may be irrelevant for you but a subsection of my paper is devoted to
> that issue. The reason for that section may go beyond your understanding.
Good for you - you dedicated a subsection of your paper to slamming
two authors who use that particular form. Why is it relevant to
whether GR has a Newtonian limit or not?
>
> >> A more interesting result is that can be showed that a rigorous
> >> computation for {Ivanenko & Sardanashvili 2005} give a Lagrangian
> >> predicts the equation of motion (a = 0). Therefore three rigorous
> >> different methods (Lagrangian, D^aT_ab, and geodesic) give the same
> >> result: bodies unaffected by gravity in the weak field limit.
>
> > Yea, if you are 100% rigorous in keeping only the lowest order in all
> > your computations.
>
> Here you are confounding the lowest order (0th) with the first order
> (1st).
Lowest _nontrivial_ order. Christ.
>
> (snipped stuff would not pass moderation)
>
> --http://canonicalscience.org/en/miscellaneouszone/guidelines.html
Oh No
>> about "The Schwarzschild metric in GR".
>
>"The Schwarzschild metric in GR verifies g_00 = (-1 / g_ii)."
>
>The condition is not something that is true in general.
In fact this condition is more general than is widely known and can be
applied for geometries without expansion in appropriate coordinates,
which I show at
http://www.teleconnection.info/rqg/GeneralRelativity#StationaryObservers
This does not in any way affect the point at issue, which is that Juan
is confusing the physical metric g with the non-physical Minkowski
metric yta, on the space used to show the Newtonian correspondence. Nor
does it alter the fact that he is claiming as "research" something which
is well known and well covered in many textbooks, and saying, absurdly
imv, that this "proves" that a simple derivation, also covered in
textbooks, is wrong.
If this simple demonstration were wrong, he should show where it is
wrong. This he has singularly failed to do. Instead he concentrates on
misapplying a known result through a failure to grasp what the Newtonian
correspondence is actually saying.
Juan R.
> On May 19, 1:46 pm, "Juan R." González-Álvarez
> <juanREM...@canonicalscience.com> wrote:
>> Eric Gisse wrote on Mon, 19 May 2008 03:45:25 -0600:
>>
>> >> No. Carroll starts from an geometrical equation and finishes with a
>> >> nongeometrical linear equation, instead the correct geometrical
>> >> linear equation.
>>
>> > Why is this a problem?
>>
>> The derivation of theorems and laws has a very precise meaning in both
>> theoretical physics and mathematics.
>
> Yes, but that does not answer my question.
It did.
> The section of the lecture notes you are working from is _not_ rigorous.
Yes, i already said that before. What is the point to repeat i am saying?
> I do not understand why you are arguing about a simplistic - though
> correct - section from a set of lecture notes when there is a rigorous
> derivation in Chapter 6.
This is very easy to understand, because it is both simplistic and
incorrect.
> The divergence condition is div.T = 0 in component notation:
>
> div.T = @_i T^ia + Gamma ^ i_ij T^ja
If you decide to do strong claims about others' work first check if your
standard textbooks say you that tensors differentiate as vectors :-)
> This does not mean the derivation is wrong - just that it appears
> inconsistent when one is consistent in staying within the linear
> approximation.
A wrong interpretation of a clever statement by Wald.
>> >> The technique used by Poisson is derivation of equation of motion
>> >> from 'conservation' law \partial^a t_ab = 0 in body surfaces. Where
>> >> t_ab is pseudotensor for matter+field. This is another rigorous
>> >> technique.
>>
>> > You citedhttp://www.emis.de/journals/LRG/Articles/lrr-2004-6/as the
>> > derivation before, but I do not actually see this derivation that you
>> > claim is in there. Why?
>>
>> That has an easy explanation. In no part of this thread i said that you
>> think i said.
>
> http://groups.google.com/group/sci.physics.relativity/msg/
edcad31bdb97cfb6?dmode=source
>
> I said "before", not "this thread".
But you continue misreading. I repeat *again*, i did not say that you
think i said.
In the link that you cited i did not say that you think. In the first part
i wrote:
"During the thread on Newtonian limit difficulties of GR I have discussed
this point with an expert on curved spacetime equations of motion, Eric
Poisson [1]."
That is *all*.
>> >> I have explained in original messages that Carroll is not taking
>> >> into account an extra (\delta a) term in the LHS of original
>> >> geodesic equation.
>>
>> > But you don't actually show where these terms come from.
>>
>> I did that but you did not read or if read you did not understand.
>
> If I understood, I wouldn't be asking.
But you did not ask, you did a wrong statement.
> Carroll does not do what you claim he does. I have his textbook _right
> in front of me_, and what you write in your original message has exactly
> zero bearing on what is in either the textbook or the notes the textbook
> is based upon.
But like you recognized above: you did not understand.
> http://groups.google.com/group/sci.physics.foundations/msg/
b219b0e80c3ef10b?dmode=source
That is right.
>> > Then show why it matters. Go read page 78 in Wald again.
>>
>> Wald is cited as reference in my paper. I know he says very well.
>
> Then WHAT is the problem? I ask because I honestly do not see the
> problem - yes, the linearized theory is inconsistent if one stays within
> the linearization but who cares?
But i am saying something different. The linearized theory *is*
consistent. I also said this before in this group
http://groups.google.com/group/sci.physics.foundations/msg/
ad48b1d74e7d3735
You do not read or not understand or both.
> The Cartan formulation was only brought up to counter the claim
> Newtonian gravitation is "non-metric".
Newtonian gravitation is non-metric. The Cartan formulation (metric) does
not change that.
> You keep claiming that GR doesn't have a Newtonian limit, but the only
> two points I see you bring up is that the linearized theory is
> inconsistent
But i did not say that. You are misreading again.
http://groups.google.com/group/sci.physics.foundations/msg/
ad48b1d74e7d3735
>> A more adequate concept of time including non-relativistic limits are
>> computed in several sites in more modern literature. E.g. specialized
>> monograph
>>
>> Classical Relativistic Many-Body Dynamics. 1999: Springer. Trump,
>> Matthew A; Schieve, William C.
>
> The text is only about dynamics - how is it a specialized monograph
> about non-relativistic limits? Furthermore, how is it _relevant_ ?
But you never read it, true?
You have absolutely no idea it says about time and non-relativistic limits
still you argue.
>> > Who cares? The condition g_00 = -1 / g_ij is NOT a valid condition on
>> > the metric, it is just something that happens to be true for certain
>> > metrics.
>>
>> If you had read i wrote you would notice that i did explicit i was
>> talking about "The Schwarzschild metric in GR".
>
> "The Schwarzschild metric in GR verifies g_00 = (-1 / g_ii)."
Why do you repeat something i said? What is the point?
> The condition is not something that is true in general.
You would do comments about i say, instead about i do *not* say.
>> It may be irrelevant for you but a subsection of my paper is devoted to
>> that issue.
(snipped inadequate language would not pass moderation)
>> > Yea, if you are 100% rigorous in keeping only the lowest order in all
>> > your computations.
>>
>> Here you are confounding the lowest order (0th) with the first order
>> (1st).
>
> Lowest _nontrivial_ order. Christ.
Splitting orders into trivial and nontrivial is rather odd and very
unusual in literature. Show me a paper where it is used.
--
Center for CANONICAL |SCIENCE)
http://canonicalscience.org
======================================= MODERATOR'S COMMENT:
I have approved this with reservations. It answers no questions of physics and is becoming argumentative.
Juan R.
> Thus spake Eric Gisse <jow...@gmail.com>
> This does not in any way affect the point at issue, which is that Juan
> is confusing the physical metric g with the non-physical Minkowski
> metric yta, on the space used to show the Newtonian correspondence.
Sorry but this is another misguided comment :-)
Moreover, it is very important to remark that g is the physical metric in
geometric formulation of GR, but g is *not* the physical metric in other
theories like PDI theories
http://arxiv.org/abs/physics/0612019v9
and Feynman field theory of gravity:
http://www.amazon.com/Feynman-Lectures-Gravitation-Frontiers-Physics/
dp/0201627345
> Nor
> does it alter the fact that he is claiming as "research" something which
> is well known and well covered in many textbooks, and saying, absurdly
> imv, that this "proves" that a simple derivation, also covered in
> textbooks, is wrong.
That is a very curious attitude, four known authors with experience on
the topic disagree with you.
Of course i also disagree with you and agree with them.
I have submitted a draft to a mainstream journal of gravitation, and
initial submission was approved and assigned manuscript number a few days
ago. I am waiting by referees report and editor choice. I am not sure if
paper will get published but i *am sure* that is being considered
research :-)
Notice also I was formally invited to participate in PPC-08 conference. I
was asked to participate on the Conference with a "work on Newtonian
limits" after my work was discussed with one member of the Organizing
committe. I was also invited to 2nd Crisis Conference.
Event is explained here
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/20080516.html
But let me do you two simple and direct questions:
1) If my work get published in a journal, would you continue to say it is
not research?
2) If my work about Newtonian limits gets published would you correct
your own website?
Oh No
>Oh No wrote on Wed, 21 May 2008 03:55:06 -0600:
>
>> Thus spake Eric Gisse <jow...@gmail.com>
>
>> This does not in any way affect the point at issue, which is that Juan
>> is confusing the physical metric g with the non-physical Minkowski
>> metric yta, on the space used to show the Newtonian correspondence.
>
>Sorry but this is another misguided comment :-)
Well, apparently you are, because you want to evaluate the Newtonian
correspondence using the wrong metric.
>
>Moreover, it is very important to remark that g is the physical metric in
>geometric formulation of GR, but g is *not* the physical metric in other
>theories like PDI theories
>
This has no bearing on the Newtonian correspondence in gtr.
>
>> Nor
>> does it alter the fact that he is claiming as "research" something which
>> is well known and well covered in many textbooks, and saying, absurdly
>> imv, that this "proves" that a simple derivation, also covered in
>> textbooks, is wrong.
>
>That is a very curious attitude, four known authors with experience on
>the topic disagree with you.
You have not cited anything which shows that. You have cited stuff about
the linear approximation which does not have bearing on the point at
issue.
>I have submitted a draft to a mainstream journal of gravitation, and
>initial submission was approved and assigned manuscript number a few days
>ago. I am waiting by referees report and editor choice. I am not sure if
>paper will get published but i *am sure* that is being considered
>research :-)
>
>Notice also I was formally invited to participate in PPC-08 conference. I
>was asked to participate on the Conference with a "work on Newtonian
>limits" after my work was discussed with one member of the Organizing
>committe. I was also invited to 2nd Crisis Conference.
>
This has no bearing on your claim.
>
>But let me do you two simple and direct questions:
>
>1) If my work get published in a journal, would you continue to say it is
>not research?
Journals include much work which is not research.
>
>2) If my work about Newtonian limits gets published would you correct
>your own website?
If you can show an error in what I have written on the website, I will
correct it. At the moment you have only shown that you don't understand
what it says and made unsubstantiated accusations.
Eric Gisse
<juanREM...@canonicalscience.com> wrote:
[snip]
> > The divergence condition is div.T = 0 in component notation:
>
> > div.T = @_i T^ia + Gamma ^ i_ij T^ja
>
> If you decide to do strong claims about others' work first check if your
> standard textbooks say you that tensors differentiate as vectors :-)
They don't? A vector is a rank one contravariant tensor.
I took the covariant derivative of the stress energy tensor along one
contravariant slot and took summed on the index to form the
divergence.
Since I am so clearly wrong in your eye, I'd appreciate you writing
the _proper_ expression for taking the divergence of a rank two
tensor.
[snip]
> "During the thread on Newtonian limit difficulties of GR I have discussed
> this point with an expert on curved spacetime equations of motion, Eric
> Poisson [1]."
>
> That is *all*.
I always understood the point of a reference to be that what you are
saying is backed up by the reference.
[snip]
> >> > Then show why it matters. Go read page 78 in Wald again.
>
> >> Wald is cited as reference in my paper. I know he says very well.
>
> > Then WHAT is the problem? I ask because I honestly do not see the
> > problem - yes, the linearized theory is inconsistent if one stays within
> > the linearization but who cares?
>
> But i am saying something different. The linearized theory *is*
> consistent. I also said this before in this group
zuh? *scratches head*
Didn't we have a nice, long, and apparently meaningless discussion
about how the linearized theory is technically inconsistent if one
uses the linearized conservation law to obtain the equations of
motion? Did you have a stroke or something?
Since now the theory is consistent I now /completely/ fail to see what
you are arguing about. If you accept the consistency of the linearized
theory, it is very straightforward to show that linearized GR
replicates Newtonian gravitation.
At this point I struggle to understand what your actual point even is.
[snip]
Juan R.
>>Sorry but this is another misguided comment :-)
>
> Well, apparently you are, because you want to evaluate the Newtonian
> correspondence using the wrong metric.
But you got wrong again :-)
Maybe it is just a problem of Natural language.
Just give me *any* GR metric that you consider very important for your
own research and i will introduce in the work, with a proof it gives
wrong Newtonian limit.
>>Moreover, it is very important to remark that g is the physical metric
>>in geometric formulation of GR, but g is *not* the physical metric in
>>other theories like PDI theories
>>
> This has no bearing on the Newtonian correspondence in gtr.
Noticing difficulties of GR to give Newtonian limit is an important
point, but tracing the origin to the difficulty is more important still.
The problem is in the geometric approach to gravity. A third important
step consists on proving that non-geometrical theories give correct limit.
For instance, FTG gives the spatial element of line
d\sigma = \delta_ij dx^i dx^j.
This is not obvious, and even you can find some misunderstanding about
FTG in standard textbooks as MTW.
For instance, what is your opinion about the spatial geometry in FTG?
What is the spatial element of line in GR up to quadratic order in
perturbative series expansion of field equations?
>>But let me do you two simple and direct questions:
>>
>>1) If my work get published in a journal, would you continue to say it
>>is not research?
>
> Journals include much work which is not research.
>From the editors office manuscript info.
Title: Newtonian limit difficulties of GR
Article Type: Original Research
Keywords: Newtonian limit; dualism; Lienard-Wiechert; speed of gravity;
nonlocal gravitation, FTG; relativistic AAAD
What is your reply to my question 1?
>>2) If my work about Newtonian limits gets published would you correct
>>your own website?
>
> If you can show an error in what I have written on the website, I will
> correct it. At the moment you have only shown that you don't understand
> what it says and made unsubstantiated accusations.
Classical Relativistic Many-Body Dynamics. 1999. Springer. Trump, Matthew
A; Schieve, William C.
Phys. Rev. E 1996 53, 5373. Chubykalo, Andrew E; Smirnov-Rueda, Roman.
Phys. Rev. E 1998 57, 3683. Chubykalo, Andrew E; Smirnov-Rueda, Roman.
Int. J. of Mod. Phys. A 1999 14(24), 3789. Chubykalo, Andrew E; Vlaev,
Stoyan J.
The monograph contains several points about time, electromagnetic
interactions, and gravity are clearly wrong in your website.
The three papers point several common mistakes regarding electrodynamics
are also in your site.
I recommend to take a look and familiarize at least with the formalism
and the notation.
Oh No
>
>> is confusing the physical metric g with the non-physical Minkowski
>> metric yta, on the space used to show the Newtonian correspondence.
>>>Sorry but this is another misguided comment :-)
>>
>> Well, apparently you are, because you want to evaluate the Newtonian
>> correspondence using the wrong metric.
>
>But you got wrong again :-)
>
>Maybe it is just a problem of Natural language.
>
>Just give me *any* GR metric that you consider very important for your
>own research and i will introduce in the work, with a proof it gives
>wrong Newtonian limit.
I have restored the initial remark, which you presumably only snipped so
that you could miss the point that the metric in the Newtonian
correspondence is not the physical metric of GR. Or do you want to show
that orbits in Schwarzschild geometry are not approximately Keplerian?
>>>2) If my work about Newtonian limits gets published would you correct
>>>your own website?
>>
>> If you can show an error in what I have written on the website, I will
>> correct it. At the moment you have only shown that you don't understand
>> what it says and made unsubstantiated accusations.
>
>Classical Relativistic Many-Body Dynamics. 1999. Springer. Trump, Matthew
>A; Schieve, William C.
>
>Phys. Rev. E 1996 53, 5373. Chubykalo, Andrew E; Smirnov-Rueda, Roman.
>
>Phys. Rev. E 1998 57, 3683. Chubykalo, Andrew E; Smirnov-Rueda, Roman.
>
>Int. J. of Mod. Phys. A 1999 14(24), 3789. Chubykalo, Andrew E; Vlaev,
>Stoyan J.
>
>The monograph contains several points about time, electromagnetic
>interactions, and gravity are clearly wrong in your website.
>
>The three papers point several common mistakes regarding electrodynamics
>are also in your site.
>
>I recommend to take a look and familiarize at least with the formalism
>and the notation.
>
>
Again it seems you are unable to point to a single error, and try to
hide what you are doing by creating distraction. I am sure there are
some. I still sometimes correct proof reading errors. Perhaps if you
could find one, you would give me something to take seriously..
Juan R.
>> > The divergence condition is div.T = 0 in component notation:
>>
>> > div.T = @_i T^ia + Gamma ^ i_ij T^ja
>>
>> If you decide to do strong claims about others' work first check if
>> your standard textbooks say you that tensors differentiate as vectors
>> :-)
>
> They don't? A vector is a rank one contravariant tensor.
Using the term 'tensor' for both elements of rank two and of arbitrary
rank is an abuse of language but it would not confuse you.
Take a look to Wald section 2.3.
> I took the covariant derivative of the stress energy tensor along one
> contravariant slot and took summed on the index to form the divergence.
You took the definition that applies to vector field T^a (probably from a
textbook) and substituted for T^ab, which is an incorrect thing to do.
> Since I am so clearly wrong in your eye, I'd appreciate you writing the
> _proper_ expression for taking the divergence of a rank two tensor.
And in the eye of any author of textbook i know :-)
The number of Christoffel is *two* for EMT because its rank. The signs are
both positive because upper indices
D_j T^ik = \partial_j T^ik + \Gamma^i_mj T^mk + \Gamma^k_mj T^im
>> "During the thread on Newtonian limit difficulties of GR I have
>> discussed this point with an expert on curved spacetime equations of
>> motion, Eric Poisson [1]."
>>
>> That is *all*.
>
> I always understood the point of a reference to be that what you are
> saying is backed up by the reference.
I also, that is why i do not understand why you attributed the reference
[1] in *that* paragraph to a quotation in a *posterior* paragraph which
has *none* reference.
>> > Then WHAT is the problem? I ask because I honestly do not see the
>> > problem - yes, the linearized theory is inconsistent if one stays
>> > within the linearization but who cares?
>>
>> But i am saying something different. The linearized theory *is*
>> consistent. I also said this before in this group
>
> zuh? *scratches head*
>
> Didn't we have a nice, long, and apparently meaningless discussion about
> how the linearized theory is technically inconsistent if one uses the
> linearized conservation law to obtain the equations of motion? Did you
> have a stroke or something?
I have said in several occasions that linearized GR is consistent. I said
it in the message you are replying i did also on
http://groups.google.com/group/sci.physics.foundations/msg/
ad48b1d74e7d3735
Why you insist on changing i am *actually* saying. What is the game?
> Since now the theory is consistent I now /completely/ fail to see what
> you are arguing about. If you accept the consistency of the linearized
> theory, it is very straightforward to show that linearized GR replicates
> Newtonian gravitation.
All wrong.
Wald, Poisson, and me the three agree that if one stay consistently within
the linear approximation, one predicts that test bodies are unaffected by
gravity.
Or concisely: the geodesic equation for (4.13) is (a = 0) NOT equation
(4.19) in Carroll.
Oh No
>Eric Gisse wrote on Thu, 22 May 2008 10:01:05 -0600:
>
>>> > The divergence condition is div.T = 0 in component notation:
>>>
>>> > div.T = @_i T^ia + Gamma ^ i_ij T^ja
>>>
>>> If you decide to do strong claims about others' work first check if
>>> your standard textbooks say you that tensors differentiate as vectors
>>> :-)
>>
>> They don't? A vector is a rank one contravariant tensor.
>
>Using the term 'tensor' for both elements of rank two and of arbitrary
>rank is an abuse of language but it would not confuse you.
>
of any rank are still tensors.
>I have said in several occasions that linearized GR is consistent. I said
>it in the message you are replying i did also on
>
>http://groups.google.com/group/sci.physics.foundations/msg/
>ad48b1d74e7d3735
>
>Why you insist on changing i am *actually* saying. What is the game?
>
>> Since now the theory is consistent I now /completely/ fail to see what
>> you are arguing about. If you accept the consistency of the linearized
>> theory, it is very straightforward to show that linearized GR replicates
>> Newtonian gravitation.
>
>All wrong.
>
>Wald, Poisson, and me the three agree that if one stay consistently within
>the linear approximation, one predicts that test bodies are unaffected by
>gravity.
We all agree on that. All that means is that staying consistently within
what you call linear approximation is of limitted value, because it
restricts the form of the metric in a way which is not useful. IOW the
linear approximation is not a consistent approximation to gtr.
>Or concisely: the geodesic equation for (4.13) is (a = 0) NOT equation
>(4.19) in Carroll.
>
This is of no interest. 4.19 is an approximation to the geodesic
equation of full non-linear gtr.
Juan R.
> Thus spake Juan R. González-Álvarez <juanR...@canonicalscience.com>
>>Eric Gisse wrote on Thu, 22 May 2008 10:01:05 -0600:
>>
>>>> > The divergence condition is div.T = 0 in component notation:
>>>>
>>>> > div.T = @_i T^ia + Gamma ^ i_ij T^ja
>>>>
>>>> If you decide to do strong claims about others' work first check if
>>>> your standard textbooks say you that tensors differentiate as vectors
>>>> :-)
>>>
>>> They don't? A vector is a rank one contravariant tensor.
>>
>>Using the term 'tensor' for both elements of rank two and of arbitrary
>>rank is an abuse of language but it would not confuse you.
>>
> It's not really an abuse of language, as there is no ambiguity.
Not for you, not for me, but it had for Eric.
>>Wald, Poisson, and me the three agree that if one stay consistently
>>within the linear approximation, one predicts that test bodies are
>>unaffected by gravity.
>
> We all agree on that.
:-)
> All that means is that staying consistently within
> what you call linear approximation is of limitted value,
Sorry it is not "you call linear approximation". It is the standard
definition of linear approximation: Carroll, Wald, Weinberg...
> because it
> restricts the form of the metric in a way which is not useful. IOW the
> linear approximation is not a consistent approximation to gtr.
Could you cite a single textbook or paper supporting your *own* point the
"linear approximation is not a consistent approximation to gtr"?
First you said "we all agree" but now again you ignore i am actually
saying.
*I said that linear approximation is consistent*
>>Or concisely: the geodesic equation for (4.13) is (a = 0) NOT equation
>>(4.19) in Carroll.
>>
> This is of no interest. 4.19 is an approximation to the geodesic
> equation of full non-linear gtr.
First it was wrong, now it is of no interest. Why continue to reply then?
Oh No
>Oh No wrote on Thu, 22 May 2008 14:44:14 -0600:
>
>> Thus spake Juan R. González-Álvarez <juanR...@canonicalscience.com>
>>>Wald, Poisson, and me the three agree that if one stay consistently
>>>within the linear approximation, one predicts that test bodies are
>>>unaffected by gravity.
>>
>> We all agree on that.
>
>:-)
>
>> All that means is that staying consistently within
>> what you call linear approximation is of limitted value,
>
>> because it
>> restricts the form of the metric in a way which is not useful. IOW the
>> linear approximation is not a consistent approximation to gtr.
>
>Could you cite a single textbook or paper supporting your *own* point the
>"linear approximation is not a consistent approximation to gtr"?
Already this has been done. See box 7.1 and chapter 18 of MTW.
>
>First you said "we all agree" but now again you ignore i am actually
>saying.
>
>*I said that linear approximation is consistent*
Clearly it is trivially consistent, but as you have pointed out it does
not yield an approximation to the geodesic equation in gtr. Ergo it is
not an approximation to gtr.
>
>>>Or concisely: the geodesic equation for (4.13) is (a = 0) NOT equation
>>>(4.19) in Carroll.
>>>
>> This is of no interest. 4.19 is an approximation to the geodesic
>> equation of full non-linear gtr.
>
>First it was wrong, now it is of no interest. Why continue to reply then?
>
You made some very preposterous claims. As far as I can tell you still
do. You have not shown that 4.19 is wrong, only that it is meaningless
to stay consistently within the linear regime. Nor have you shown that
there is no Newtonian correspondence in gtr.
Juan R.
>>> because it
>>> restricts the form of the metric in a way which is not useful. IOW the
>>> linear approximation is not a consistent approximation to gtr.
>>
>>Could you cite a single textbook or paper supporting your *own* point
>>the "linear approximation is not a consistent approximation to gtr"?
>
> Already this has been done. See box 7.1 and chapter 18 of MTW.
Sorry, but linearized GR is a standard model appears in textbooks,
lectures, and papers. If you cannot take textbooks or papers take a look
to the Wiki article
http://en.wikipedia.org/wiki/Linearized_gravity
(\blockquote
This is why the conceptual approach of linearized gravity is the
canonical one in particle physics, string theory, and more generally
quantum field theory
)
It has an extra point. It remarks that the Linear approximation is also
known as the weak field approximation,
(\blockquote
This approximation is also known as the weak-field approximation as it
is only valid for tiny h's.
)
That is, also your previous claim about confusing limits does not look
solid.
>>*I said that linear approximation is consistent*
>
> Clearly it is trivially consistent, but as you have pointed out it does
> not yield an approximation to the geodesic equation in gtr.
No, I said that approximation gives the equation of motion (a = 0)
I also explained what term is missing in Carroll derivation.
> Ergo it is
> not an approximation to gtr.
What? Linearized GR is not approximation to GR?
Take a look to textbooks (Wald, Weinberg), lecture notes (Carroll),
papers [#]
http://en.wikipedia.org/wiki/Linearized_gravity
>>>>Or concisely: the geodesic equation for (4.13) is (a = 0) NOT equation
>>>>(4.19) in Carroll.
>>>>
>>> This is of no interest. 4.19 is an approximation to the geodesic
>>> equation of full non-linear gtr.
>>
>>First it was wrong, now it is of no interest. Why continue to reply
>>then?
>>
> You made some very preposterous claims. As far as I can tell you still
> do. You have not shown that 4.19 is wrong, only that it is meaningless
> to stay consistently within the linear regime.
I showed that 4.19 is not compatible with 4.13. Wald and Poisson agree
with me.
> Nor have you shown that
> there is no Newtonian correspondence in gtr.
Well but Poisson already confirmed my finding that GR cannot satisfy at
once a) Poisson equation b) nonzero acceleration c) flat space metric
gamma.
It is cited in my paper confirming that.
[#] Search papers with title "linearized general relativity" and also
"linear general relativity"
Oh No
>
>>>> because it
>>>> restricts the form of the metric in a way which is not useful. IOW the
>>>> linear approximation is not a consistent approximation to gtr.
>>>
>>>Could you cite a single textbook or paper supporting your *own* point
>>>the "linear approximation is not a consistent approximation to gtr"?
>>
>> Already this has been done. See box 7.1 and chapter 18 of MTW.
>
>Sorry, but linearized GR is a standard model appears in textbooks,
>lectures, and papers. If you cannot take textbooks or papers take a look
>to the Wiki article
>
>http://en.wikipedia.org/wiki/Linearized_gravity
>
>(\blockquote
> This is why the conceptual approach of linearized gravity is the
> canonical one in particle physics, string theory, and more generally
> quantum field theory
>)
This may be true, but I have serious reservations about using it like
this.
>
>It has an extra point. It remarks that the Linear approximation is also
>known as the weak field approximation,
>
>(\blockquote
> This approximation is also known as the weak-field approximation as it
> is only valid for tiny h's.
>)
>
>That is, also your previous claim about confusing limits does not look
>solid.
Since this is a different correspondence from the one I use as the weak
field approximation, (in which it is very clear that a!=0) it does seem
that there is a clear confusion about limits. Perhaps the confusion is
not yours alone.
>
>>>*I said that linear approximation is consistent*
>>
>> Clearly it is trivially consistent, but as you have pointed out it does
>> not yield an approximation to the geodesic equation in gtr.
>
>No, I said that approximation gives the equation of motion (a = 0)
Indeed. But that result is an obvious error, and shows only that the
linear approximation has broken down in some way.
>
>I also explained what term is missing in Carroll derivation.
>
>> Ergo it is
>> not an approximation to gtr.
>
>What? Linearized GR is not approximation to GR?
>
>Take a look to textbooks (Wald, Weinberg), lecture notes (Carroll),
>papers [#]
>
>http://en.wikipedia.org/wiki/Linearized_gravity
Clearly if you have that coordinate acceleration is 0, then geodesics
are straight lines. IOW you have imposed a condition such that the only
actual solution is flat space. Judging from MTW, this is known and
accepted. It does not mean that useful conclusions cannot be drawn, but
a=0 is not one of them.
>
>>>>>Or concisely: the geodesic equation for (4.13) is (a = 0) NOT equation
>>>>>(4.19) in Carroll.
>>>>>
>>>> This is of no interest. 4.19 is an approximation to the geodesic
>>>> equation of full non-linear gtr.
>>>
>>>First it was wrong, now it is of no interest. Why continue to reply
>>>then?
>>>
>> You made some very preposterous claims. As far as I can tell you still
>> do. You have not shown that 4.19 is wrong, only that it is meaningless
>> to stay consistently within the linear regime.
>
>I showed that 4.19 is not compatible with 4.13. Wald and Poisson agree
>with me.
You impose additional constraints, which are not intended in 4.13. If
those constraints are correctly part of the linear approximation, then
the approximation becomes incorrect and useless.
>
>> Nor have you shown that
>> there is no Newtonian correspondence in gtr.
>
>Well but Poisson already confirmed my finding that GR cannot satisfy at
>once a) Poisson equation b) nonzero acceleration c) flat space metric
>gamma.
Clearly with flat spacetime metric, GR gives zero acceleration. That is
not a finding, since it is trivial. This has no bearing on the Newtonian
correspondence because the Newtonian metric is not the physical metric
of gr.
Eric Gisse
<juanREM...@canonicalscience.com> wrote:
[...]
> > Clearly it is trivially consistent, but as you have pointed out it does
> > not yield an approximation to the geodesic equation in gtr.
>
> No, I said that approximation gives the equation of motion (a = 0)
Only when you draw clearly inappropriate conclusions from the
divergence of the stress tensor. The question is why are you ignoring
what the geodesic equation tells you?
>
> I also explained what term is missing in Carroll derivation.
First comment - of _course_ a lot is missing from the section you
continually complain about. The actual rigorous derivation is in
chapter 6 which I am yet to see you complain about.
Second comment - no, you haven't. Saying he is "missing" terms isn't
good enough. Go to chapter 6 and point out where he is leaving out
terms other than higher order terms which have to be dropped.
[...]
> > You made some very preposterous claims. As far as I can tell you still
> > do. You have not shown that 4.19 is wrong, only that it is meaningless
> > to stay consistently within the linear regime.
>
> I showed that 4.19 is not compatible with 4.13. Wald and Poisson agree
> with me.
No. You have _CLAIMED_ that the two are incompatible but you have not
backed up the claim. Why are you rejecting the straightforward
computation of the geodesic equation from the metric?
Furthemore, neither Wald nor Poisson actually agree on this point -
their agreement is strictly regarding the inconsistency in the
linearized theory. You are putting words in their mouths.
>
> > Nor have you shown that
> > there is no Newtonian correspondence in gtr.
>
> Well but Poisson already confirmed my finding that GR cannot satisfy at
> once a) Poisson equation b) nonzero acceleration c) flat space metric
> gamma.
How is this relevant to the linearized theory? The metric isn't flat
space - it is flat space plus a perturbation.
Juan R.
> The question is why are you ignoring what the geodesic equation tells
> you?
In my OP i wrote a perturbative series expansion of the geodesic and
retained terms up to linear order.
>> I also explained what term is missing in Carroll derivation.
>
> First comment - of _course_ a lot is missing from the section you
> continually complain about. The actual rigorous derivation is in chapter
> 6 which I am yet to see you complain about.
Of course that chapter does not compute the 'Newtonian' equation of
motion in any place. The own author redirect readers to section 4.
Chapter 6 starts with weak field definition (6.1), which is (4.13)
but you found nothing like (4.17) and (4.19).
And of course i also studied additional aspects such as spatial geometry d
\sigma^2, which are *absent* in both chapters.
> Why are you rejecting the straightforward computation of the geodesic
> equation from the metric?
Because the straightforward (but wrong) computation is missing \delta(a)
in the LHS of the geodesic.
Of course, the same conclusion is obtained using others methods:
D^aT_ab = 0 (Wald)
\partial^at_ab = 0 (Poisson).
> Furthemore, neither Wald nor Poisson actually agree on this point -
> their agreement is strictly regarding the inconsistency in the
> linearized theory. You are putting words in their mouths.
Interestingly, you are doing claims about quotations, works and
correspondence that you do *not* read!!
Remember a previous post where you were kindly said that normal people
evaluates the stuff after reading the stuff *not* before as is your case.
>> Well but Poisson already confirmed my finding that GR cannot satisfy at
>> once a) Poisson equation b) nonzero acceleration c) flat space metric
>> gamma.
>
> How is this relevant to the linearized theory? The metric isn't flat
> space - it is flat space plus a perturbation.
Are you able to understand you are replying?
A way to prove that you are able is if you include the general expression
for spatial metric \gamma_ij.
Juan R.
>>(\blockquote
>> This is why the conceptual approach of linearized gravity is the
>> canonical one in particle physics, string theory, and more generally
>> quantum field theory
>>)
>
> This may be true, but I have serious reservations about using it like
> this.
I would like to hear what are your serious reservations.
>>That is, also your previous claim about confusing limits does not look
>>solid.
>
> Since this is a different correspondence from the one I use as the weak
> field approximation, (in which it is very clear that a!=0) it does seem
> that there is a clear confusion about limits. Perhaps the confusion is
> not yours alone.
First, i was using the *standard* definition. See Carroll, Wald or
Weinberg. Access also to
http://en.wikipedia.org/wiki/Weak-field_approximation
Where redirects? :-)
Second, I did a mathematical statement about the definition of weak field.
Maybe you use your *own* definition. But then you are involved in a
discussion about names instead about the 'substance' behind
Third, i proved (a = 0) for weak fields pointing mistakes in standard
'textbook' derivations.
>>>>*I said that linear approximation is consistent*
>>>
>>> Clearly it is trivially consistent, but as you have pointed out it
>>> does not yield an approximation to the geodesic equation in gtr.
>>
>>No, I said that approximation gives the equation of motion (a = 0)
>
> Indeed. But that result is an obvious error, and shows only that the
> linear approximation has broken down in some way.
It is not an "obvious error", it is an consequence from General
Relativity.
The consequence follows from the Einstein equations in standard way (Wald)
The consequence follows from the Einstein equations in relaxed way
(Poisson)
The consequence follows from the perturbative geodesic equation (myself)
The three methods (authors) coincide. You pointed no serious mistake in
any of three methods and most of your 'argumentation' is about words.
> Clearly if you have that coordinate acceleration is 0, then geodesics
> are straight lines.
I said that 20 days ago, when then you still confused coordinate
accelerations with proper accelerations :-)
> IOW you have imposed a condition such that the only actual solution is
> flat space.
First, i have used a standard metric from General Relativity literature
:-)
Second, I proved that consequences from that metric are not those usually
believed and pointed to mistakes in usual derivations.
Third, h_ab is usually named the "deviation from flat metric".
> Judging from MTW, this is known and
> accepted. It does not mean that useful conclusions cannot be drawn, but
> a=0 is not one of them.
But your claim is misguided. Wald says the contrary than you and Poisson
agreed with him and me.
Their techniques are more complex and hide some fundamental aspects of the
Newtonian correspondence. That was why i did computation using a different
technique that them.
But the important point is that three techniques give the same result
a = 0
>>I showed that 4.19 is not compatible with 4.13. Wald and Poisson agree
>>with me.
>
> You impose additional constraints, which are not intended in 4.13.
Wrong. The result follows from 4.13.
>>> Nor have you shown that
>>> there is no Newtonian correspondence in gtr.
>>
>>Well but Poisson already confirmed my finding that GR cannot satisfy at
>>once a) Poisson equation b) nonzero acceleration c) flat space metric
>>gamma.
>
> Clearly with flat spacetime metric, GR gives zero acceleration.
You do not read neither me nor Wald nor Poisson :-)
You neither read Carroll lecture notes i cited. If you had read, you
would see that he obtain for linear metrics :-)
Oh No
>
>>>(\blockquote
>>> This is why the conceptual approach of linearized gravity is the
>>> canonical one in particle physics, string theory, and more generally
>>> quantum field theory
>>>)
>>
>> This may be true, but I have serious reservations about using it like
>> this.
>
>I would like to hear what are your serious reservations.
I think gtr should be treated as a geometrical theory, not as a
perturbation to a theory on flat space. Such a perturbation is an
unnecessary complication, because flat space is ultimately still
geometrical, and relies on what would be a remarkable coincidence, that
a theory of active forces can be reduced to a geometrical model without
active forces.
>
>>>That is, also your previous claim about confusing limits does not look
>>>solid.
>>
>> Since this is a different correspondence from the one I use as the weak
>> field approximation, (in which it is very clear that a!=0) it does seem
>> that there is a clear confusion about limits. Perhaps the confusion is
>> not yours alone.
>
>First, i was using the *standard* definition. See Carroll, Wald or
>Weinberg. Access also to
>
>http://en.wikipedia.org/wiki/Weak-field_approximation
>
I don't have a problem with this. Note that it says:
"The way of thinking in linearized gravity is this: the background
metric IS the metric and h is a field propagating over the spacetime
with this metric."
The effect of the field h is such as to cause accelerations in the space
with background metric. IOW this is a non-geometrical theory on flat
space. There is no problem with that. In so far as I can tell you impose
are imposing other (geometrical) conditions on h, for which the only
solution is h=0.
>Second, I did a mathematical statement about the definition of weak field.
>Maybe you use your *own* definition. But then you are involved in a
>discussion about names instead about the 'substance' behind
There is a distinction between the linearised theory described in box
7.1 of MTW, for which you do indeed find a=0 and an inconsistency, and
the linearised theory here in which h is to be regarded as a field.
>
>Third, i proved (a = 0) for weak fields pointing mistakes in standard
>'textbook' derivations.
You claim this, but have not provided a proof. Your original post does
not give a proof, as you claim, but a set of claimed results. If you
recall, I was not able to discern from this what conditions you are
imposing which lead to these claimed results.
>
>>>>>*I said that linear approximation is consistent*
>>>>
>>>> Clearly it is trivially consistent, but as you have pointed out it
>>>> does not yield an approximation to the geodesic equation in gtr.
>>>
>>>No, I said that approximation gives the equation of motion (a = 0)
>>
>> Indeed. But that result is an obvious error, and shows only that the
>> linear approximation has broken down in some way.
>
>It is not an "obvious error", it is an consequence from General
>Relativity.
Not from general relativity, because when you impose the linear
approximation you no longer have general relativity.
>
>The consequence follows from the Einstein equations in standard way (Wald)
>
>The consequence follows from the Einstein equations in relaxed way
>(Poisson)
As has been pointed out, by myself, Eric, MTW, Wald (as I understand)
and Poisson (in the quotes you have give) you cannot impose the Einstein
equations because you end up with a theory which does not exist. When
you treat the perturbation as a field you have to add a potential energy
to T. Then the theory is no longer covariant and energy is not derivable
from the stress energy tensor.
>
>The consequence follows from the perturbative geodesic equation (myself)
That is incorrect. The claims you made in your original post did not
hold.
>
>The three methods (authors) coincide. You pointed no serious mistake in
>any of three methods and most of your 'argumentation' is about words.
I have now told you what is wrong with the first two methods. You cannot
impose the Einstein equations on the weak field approximation because
they ignore the fact that h is now to be treated as a field. The third
method was not given. I cannot see mistakes in something which is not
there. Quoting claimed results is not a proof.
>
>> Clearly if you have that coordinate acceleration is 0, then geodesics
>> are straight lines.
>
>I said that 20 days ago, when then you still confused coordinate
>accelerations with proper accelerations :-)
The confusion was due to the fact that you quoted a string of results
without defining what you were saying. I was still trying to work out
what on earth you were talking about.
>
>> IOW you have imposed a condition such that the only actual solution is
>> flat space.
>
>First, i have used a standard metric from General Relativity literature
>:-)
Note again what Wikipedia says, which is also what I have been telling
you:
"The way of thinking in linearized gravity is this: the background
metric IS the metric and h is a field propagating over the spacetime
with this metric."
>
>Second, I proved that consequences from that metric are not those usually
>believed and pointed to mistakes in usual derivations.
You pointed to no mistakes, apart from making a false claim that Caroll
ignores terms which should be included on the LHS of an equation. You
did not justify that claim.
>
>Third, h_ab is usually named the "deviation from flat metric".
Note again what Wikipedia says
"The way of thinking in linearized gravity is this: the background
metric IS the metric and h is a field propagating over the spacetime
with this metric."
You cannot treat h as deviation from flat metric AND a field over
spacetime at the same time. You cannot mix views like this, or you do
indeed end up with a trivial theory in which h=0. This is well known.
>
>> Judging from MTW, this is known and
>> accepted. It does not mean that useful conclusions cannot be drawn, but
>> a=0 is not one of them.
>
>But your claim is misguided. Wald says the contrary than you and Poisson
>agreed with him and me.
>
>Their techniques are more complex and hide some fundamental aspects of the
>Newtonian correspondence. That was why i did computation using a different
>technique that them.
>
>But the important point is that three techniques give the same result
>
>a = 0
MTW also shows that if you treat things incorrectly then a=0. I cannot
find my copy of Wald, but your quotes from Poisson say the same. This is
not a result of gtr, but a result of treating things incorrectly when
you take the linear approximation.
>
>>>I showed that 4.19 is not compatible with 4.13. Wald and Poisson agree
>>>with me.
>>
>> You impose additional constraints, which are not intended in 4.13.
>
>Wrong. The result follows from 4.13.
Not on its own.
>
>>>> Nor have you shown that
>>>> there is no Newtonian correspondence in gtr.
>>>
>>>Well but Poisson already confirmed my finding that GR cannot satisfy at
>>>once a) Poisson equation b) nonzero acceleration c) flat space metric
>>>gamma.
>>
>> Clearly with flat spacetime metric, GR gives zero acceleration.
>
>You do not read neither me nor Wald nor Poisson :-)
Read again what you said. It is hardly your finding that GR gives zero
acceleration with flat metric.
The only thing clear about your quotes from Poisson is that you take him
out of context.
Eric Gisse
Juan R. González-Álvarez wrote:
> Eric Gisse wrote on Fri, 23 May 2008 16:34:00 -0600:
>
> > The question is why are you ignoring what the geodesic equation tells
> > you?
>
> In my OP i wrote a perturbative series expansion of the geodesic and
> retained terms up to linear order.
Except you did not use the perturbed metric to do it, which makes your
analysis completely irrelevant.
>
> >> I also explained what term is missing in Carroll derivation.
> >
> > First comment - of _course_ a lot is missing from the section you
> > continually complain about. The actual rigorous derivation is in chapter
> > 6 which I am yet to see you complain about.
>
> Of course that chapter does not compute the 'Newtonian' equation of
> motion in any place. The own author redirect readers to section 4.
>
> Chapter 6 starts with weak field definition (6.1), which is (4.13)
> but you found nothing like (4.17) and (4.19).
That's because he already did it in Chapter 4. The analysis in chapter
4 is just fine - it is just made more mathematically sound by the work
done in chapter 6.
Why are you fixating on this, anyway? Is there a particular reason why
you can't feed the perturbed metric into the geodesic equation? Why
the request for handholding?
There is no ground here for you to gain - the analysis here is the
same as in MTW and Wald.
>
> And of course i also studied additional aspects such as spatial geometry d
> \sigma^2, which are *absent* in both chapters.
That's because these are lecture notes, the subject is explored more
extensively in his textbook. The generalized metric under the
linearized theory is presented there, along with the Newtonian limit.
Why are you arguing about lecture notes, anyway? They are naturally
incomplete and limited - you have much better resources available to
you. Hell, if you have to argue about Carroll argue about his book.
>
> > Why are you rejecting the straightforward computation of the geodesic
> > equation from the metric?
>
> Because the straightforward (but wrong) computation is missing \delta(a)
> in the LHS of the geodesic.
There is no "\delta(a)" term as you claim. In fact, there are no delta
terms in the geodesic equation whatsoever.
You are beating on a strawman - your version of the perturbed geodesic
equation is not what MTW, Carroll, Wald, etc use.
>
> Of course, the same conclusion is obtained using others methods:
>
> D^aT_ab = 0 (Wald)
>
> \partial^at_ab = 0 (Poisson).
>
> > Furthemore, neither Wald nor Poisson actually agree on this point -
> > their agreement is strictly regarding the inconsistency in the
> > linearized theory. You are putting words in their mouths.
>
> Interestingly, you are doing claims about quotations, works and
> correspondence that you do *not* read!!
I'm sick of this - you continually namedrop people and then claim they
agree with you in private correspondence. All you have done so far is
point out where Wald and Poisson agree that the linearized theory is
inconsistent.
>
> Remember a previous post where you were kindly said that normal people
> evaluates the stuff after reading the stuff *not* before as is your case.
Why don't you post the correspondence between yourself and Wald &
Poisson? I don't see why you'd have a problem with that - you are all
too willing to claim they support you. Either that or settle for
guesses made from incomplete knowledge.
>
> >> Well but Poisson already confirmed my finding that GR cannot satisfy at
> >> once a) Poisson equation b) nonzero acceleration c) flat space metric
> >> gamma.
> >
> > How is this relevant to the linearized theory? The metric isn't flat
> > space - it is flat space plus a perturbation.
>
> Are you able to understand you are replying?
Are you?
The linearized theory assumes flat space plus a perturbation - you
_explicitly_ assume flat space. It seems much rather that you do not
actually understand what constitutes perturbation theory in the
context of general relativity.
>
> A way to prove that you are able is if you include the general expression
> for spatial metric \gamma_ij.
How about you prove one of your claims?
I really don't even see what your argument is anymore. Your original
claim was that GR doesn't have a Newtonian limit, but you have exactly
nothing to support the claim at this point.
Juan R.
> Thus spake Juan R. González-Álvarez <juanR...@canonicalscience.com>
>>Oh No wrote on Fri, 23 May 2008 14:17:11 -0600:
>>
>>>>(\blockquote
>>>> This is why the conceptual approach of linearized gravity is the
>>>> canonical one in particle physics, string theory, and more generally
>>>> quantum field theory
>>>>)
>>>
>>> This may be true, but I have serious reservations about using it like
>>> this.
>>
>>I would like to hear what are your serious reservations.
>
> I think gtr should be treated as a geometrical theory, not as a
> perturbation to a theory on flat space. Such a perturbation is an
> unnecessary complication, because flat space is ultimately still
> geometrical, and relies on what would be a remarkable coincidence, that
> a theory of active forces can be reduced to a geometrical model without
> active forces.
Here you are simply stating your beliefs about a geometrical formulation
of gravity. As Feynman stated
(\blockquote
The geometrical interpretation is not really necessary or essential to
physics.
)
Weinberg textbook devotes a chapter "The geometric analogy" to why the
geometrical formulation of gravity would not be taken seriously.
>>http://en.wikipedia.org/wiki/Weak-field_approximation
>>
> I don't have a problem with this. Note that it says:
>
> "The way of thinking in linearized gravity is this: the background
> metric IS the metric and h is a field propagating over the spacetime
> with this metric."
>
> The effect of the field h is such as to cause accelerations in the space
> with background metric. IOW this is a non-geometrical theory on flat
> space.
Plain wrong. Linearized General Relativity is still geometrical. You
simply are confused by that quote.
>>It is not an "obvious error", it is an consequence from General
>>Relativity.
>
> Not from general relativity, because when you impose the linear
> approximation you no longer have general relativity.
When one impose the linear approximation one has Linear General Relativity
also named Linearized General Relativity.
You also seems to be unaware of use of Linearized General Relativity in
practical tests as that famous of binary pulsars.
>>The consequence follows from the Einstein equations in standard way
>>(Wald)
>>
>>The consequence follows from the Einstein equations in relaxed way
>>(Poisson)
>
> As has been pointed out, by myself, Eric, MTW, Wald (as I understand)
> and Poisson (in the quotes you have give) you cannot impose the Einstein
> equations because you end up with a theory which does not exist.
Neither Wald nor Poisson nor me say this.
> When
> you treat the perturbation as a field
Neither Wald nor Poisson nor me did that.
> you have to add a potential energy
> to T.
That is also wrong, the "potential energy" is in the Linearized
Lagrangian, as would be.
> Then the theory is no longer covariant and energy is not derivable from
> the stress energy tensor.
Precisely, the famous problem of energy in GR is solved in the linear
regime, where a conservation law is recovered,
\partial t^ab = \partial T^ab = 0
When one goes beyond the linear regime the law is lost.
>>The three methods (authors) coincide. You pointed no serious mistake in
>>any of three methods and most of your 'argumentation' is about words.
>
> I have now told you what is wrong with the first two methods. You cannot
> impose the Einstein equations on the weak field approximation because
> they ignore the fact that h is now to be treated as a field.
h is not treated as a field in the geometric formulation. h only is in the
field formulation.
>>Third, h_ab is usually named the "deviation from flat metric".
>
> Note again what Wikipedia says
>
> "The way of thinking in linearized gravity is this: the background
> metric IS the metric and h is a field propagating over the spacetime
> with this metric."
>
> You cannot treat h as deviation from flat metric AND a field over
> spacetime at the same time.
Exactly, in my paper i worked both the field formulation and the geometric
formulation in linear regime.
The geometric formulation gives (a = 0)
The field formulation gives (a /= 0)
My findings about the geometric formulation were revised by expertise
Poisson.
My findings about the field formulation were revised by expertise Prof.
Barishev.
You are presenting serious misunderstandings about both formulations :-)
> You cannot mix views like this, or you do indeed end up with a trivial
> theory in which h=0. This is well known.
That is another irrelevant comment because for both the geometrical and
the field formulations I considered the case (h /= 0).
> MTW also shows that if you treat things incorrectly then a=0. I cannot
> find my copy of Wald, but your quotes from Poisson say the same. This is
> not a result of gtr, but a result of treating things incorrectly when
> you take the linear approximation.
If you take incorrectly the weak field limit on a geodesic you get the
result
a = - \grad \phi
Carroll makes this and you repeat mistakes in your website. If uou pay
more attention ot details and work a rigorous derivation you will find
that geodesic for weak field limits is
a = 0
Wald has stated this in a very simple an clear quotation
(\blockquote
if one stay *consistently* within the linear approximation, one
*predicts* that test bodies are unaffected by gravity.
)
>>You do not read neither me nor Wald nor Poisson :-)
>
> Read again what you said. It is hardly your finding that GR gives zero
> acceleration with flat metric.
You continue without reading. The metric is (g = (n + h)) with h nonzero.
> The only thing clear about your quotes from Poisson is that you take him
> out of context.
Own Poisson disagrees with you also at this point :-)
Oh No
>Oh No wrote on Mon, 26 May 2008 09:15:20 -0600:
>
>>>http://en.wikipedia.org/wiki/Weak-field_approximation
>>>
>> I don't have a problem with this. Note that it says:
>>
>> "The way of thinking in linearized gravity is this: the background
>> metric IS the metric and h is a field propagating over the spacetime
>> with this metric."
>>
>> The effect of the field h is such as to cause accelerations in the space
>> with background metric. IOW this is a non-geometrical theory on flat
>> space.
>
>Plain wrong. Linearized General Relativity is still geometrical. You
>simply are confused by that quote.
At least we have pinpointed what it is that you do not understand.
>
>> you have to add a potential energy
>> to T.
>
>That is also wrong, the "potential energy" is in the Linearized
>Lagrangian, as would be.
>From your conclusion of a clearly wrong result, viz a = 0, you should
also conclude that you are wrong about this.
>
>> Then the theory is no longer covariant and energy is not derivable from
>> the stress energy tensor.
>
>Precisely, the famous problem of energy in GR is solved in the linear
>regime, where a conservation law is recovered,
>
>\partial t^ab = \partial T^ab = 0
Clearly this is not true if you simply treat T as an approximation to T
in GR. You should again conclude that you are wrong to claim that the
potential energy in classical Newtonian gravity comes from linearising
the Lagrangian.
>
>
>h is not treated as a field in the geometric formulation. h only is in the
>field formulation.
h is part of the metric in the general relativistic formulation (it is
still a field quantity btw), but becomes a potential field in the
Newtonian approximation. If you cannot clarify this in your mind, there
is no point in continuing.
>
>>>Third, h_ab is usually named the "deviation from flat metric".
>>
>> Note again what Wikipedia says
>>
>> "The way of thinking in linearized gravity is this: the background
>> metric IS the metric and h is a field propagating over the spacetime
>> with this metric."
>>
>> You cannot treat h as deviation from flat metric AND a field over
>> spacetime at the same time.
>
>Exactly, in my paper i worked both the field formulation and the geometric
>formulation in linear regime.
>
>The geometric formulation gives (a = 0)
>
>The field formulation gives (a /= 0)
There you have it. Now get it straight.
Juan R.
>>> The effect of the field h is such as to cause accelerations in the
>>> space with background metric. IOW this is a non-geometrical theory on
>>> flat space.
>>
>>Plain wrong. Linearized General Relativity is still geometrical. You
>>simply are confused by that quote.
>
> At least we have pinpointed what it is that you do not understand.
I understand very well that you are confounding the field theoretic
approach with the geometrical approach.
>>\partial t^ab = \partial T^ab = 0
>
> Clearly this is not true
Wald devotes several paragraphs to explain this result for the Linearized
regime of GR. Take a look.
>>h is not treated as a field in the geometric formulation. h only is in
>>the field formulation.
>
> h is part of the metric in the general relativistic formulation (it is
> still a field quantity btw), but becomes a potential field in the
> Newtonian approximation. If you cannot clarify this in your mind, there
> is no point in continuing.
In despite of my efforts you continue confounding the field formulation
with the geometric one :-)
The meaning of field in the geometrical formulation is that of local
spacetime function. This is a mathematical meaning for the word field.
The meaning of field in the field formulation is that of a physical field
(with own energy) over a flat background.
The physics and the math are different for both. This is reason that
linearized field gravity gives (a /= 0) but linearized GR gives (a = 0)
Oh No
>
>
>I understand very well that you are confounding the field theoretic
>approach with the geometrical approach.
The weak field limit means knowing how to reinterpret metric
coefficients as classical potentials. Reread the Wiki quote.
"The way of thinking in linearized gravity is this: the background
metric IS the metric and h is a field propagating over the spacetime
with this metric."
>
>>>\partial t^ab = \partial T^ab = 0
>>
>> Clearly this is not true
>
>Wald devotes several paragraphs to explain this result for the Linearized
>regime of GR. Take a look.
So do MTW. I am familiar. This is why they (also) say the linearised
regime is not consistent.
To form the Newtonian correspondence you have to reinterpret the
perturbation in the metric as a classical potential. This means you must
modify T (or equivalently modify the Lagrangian) and the above equation
will not hold.
If you impose it, then you clearly have an inconsistent theory (or a
trivial one with h=0).
You have been told this enough times, but you persist in getting it
wrong. You cannot stay "consistently within the linear approximation".
Instead you must incorporate a classical potential which does not appear
in gtr.
This is the last time of telling. The thread is repetitive. Your mistake
has, at last, been clearly identified. What you are saying is a mixture
of repeating what is clearly dealt with in text books, then drawing a
false conclusion by failing to treat h correctly in the Newtonian
approximation.
Oh No
>> to T.
>
>That is also wrong, the "potential energy" is in the Linearized
>Lagrangian, as would be.
>
gravitational redshift. This is not a term in the stress energy tensor,
but appears in the weak field limit (see Pound Rebka experiment), as a
result of the differing rate of clocks wrt to each other when . It was
perhaps Einstein's first result in gtr, as it derives directly from the
equivalence principle which set him on the path toward the full theory.
The change in frequency of light shows directly that there is a change
of energy in this limit. I.e. that you cannot take the potential energy
from the linearised Lagrangian. Clearly if you do you get a wrong
answer, i.e. one which does not model reality, i.e a=0.