I am working in relationship between General Relativity and the non-
relativistic theory of Newton.

My research consists of two parts. The first part addresses the common
claim that geodesic equation of General Relativity reduces to Newton law
of motion in the linear limit, i.e. g_ab = \eta_ab + h_ab when ||h|| is
small enough to ignore quadratic and higher orders.

Take for example Carroll lecture notes available online:

http://lanl.arXiv.org/abs/gr-qc/9712019v1

Carroll starts from geodesic equation (4.9) and derives equation (4.19),
which he identifies with Newton equation (4.4) after using (4.20).

During the derivation Carroll uses the linear constraint (4.13) for the
metric tensor.

Students and general public are confused with those claims. A more
rigorous analysis does not support Carroll conclusions.

Carroll is not computing the linear geodesic equation of motion but
'inventing' a non-geometrical equation [see below].

The equation of motion in the linear limit is a = 0 and bodies are
unaffected by gravity.

A interesting conclusion is that the linearized equation of motion from
General Relativity does not coincide with that from Newtonian gravity.

For both the zeroth and the linear regimes of General Relativity bodies
have to move on straight lines.

A way to see this is expanding the geodesic equation in a perturbative
series and retaining terms up to linear order on expansion parameter,

a^\mu + \lambda \delta a^\mu

=

\lambda \delta \Gamma_{\rho\sigma}^\mu u^\rho u^\sigma

The terms in brackets correspond to zeroth order.

Carroll *assumes* that left hand side may be approximated by

a^\mu + \lambda \delta a^\mu

and the right hand side by

\lambda \delta \Gamma_{\rho\sigma}^\mu c^2

See his (4.19).

But by geometrical requirements (Carroll and textbooks are not checking
any geometrical consistency check at this point)

\delta a^\mu = \delta \Gamma_{\rho\sigma}^\mu = 0

and the result is a = 0 in the linear regime. As conclusion bodies have
to move on straight lines.

Another way to see this is deriving motion from D{T_ab} = 0.
In the linear regime, it reduces to \partial{T_ab} = 0, and like in the
special relativity case, this implies bodies move in straigth lines.

If one denotes the geodesic equation using next simplified notation

a = \Gamma vv

Then the linearized, L[], geodesic equation reads

L[a] = L[\Gamma vv] = L[\Gamma] Z[vv]

where Z[] denotes the zeroth order application.

Carroll however is computing something different

Z[a] = L[\Gamma] Z[vv]

Carroll is applying different limits to left and hand sides of the
original equation, which is a mathematically invalid procedure. Therein
my above claim he is 'inventing' the final equation rather than deriving
it by mathematical steps.

If General Relativity does not correctly reduce to Newtonian gravity then
there exists a problem with General Relativity. One cannot offer false
derivations as those in textbooks...


--
http://canonicalscience.org/en/misce...guidelines.txt

So what? If Carroll makes assumptions he's only following the path
Einstein took; you don't expect proof, do you?
--
This message is brought to you by Androcles
http://www.androcles01.pwp.blueyonder.co.uk/

"Juan R. González-Álvarez" wrote in
message news |I am working in relationship between General Relativity and the non-
| relativistic theory of Newton.
|
| My research consists of two parts. The first part addresses the common
| claim that geodesic equation of General Relativity reduces to Newton law
| of motion in the linear limit, i.e. g_ab = \eta_ab + h_ab when ||h|| is
| small enough to ignore quadratic and higher orders.
|
| Take for example Carroll lecture notes available online:
|
| http://lanl.arXiv.org/abs/gr-qc/9712019v1
|
| Carroll starts from geodesic equation (4.9) and derives equation (4.19),
| which he identifies with Newton equation (4.4) after using (4.20).
|
| During the derivation Carroll uses the linear constraint (4.13) for the
| metric tensor.
|
| Students and general public are confused with those claims. A more
| rigorous analysis does not support Carroll conclusions.
|
| Carroll is not computing the linear geodesic equation of motion but
| 'inventing' a non-geometrical equation [see below].
|
| The equation of motion in the linear limit is a = 0 and bodies are
| unaffected by gravity.
|
| A interesting conclusion is that the linearized equation of motion from
| General Relativity does not coincide with that from Newtonian gravity.
|
| For both the zeroth and the linear regimes of General Relativity bodies
| have to move on straight lines.
|
| A way to see this is expanding the geodesic equation in a perturbative
| series and retaining terms up to linear order on expansion parameter,
|
| a^\mu + \lambda \delta a^\mu
|
| =
|
| \lambda \delta \Gamma_{\rho\sigma}^\mu u^\rho u^\sigma
|
| The terms in brackets correspond to zeroth order.
|
| Carroll *assumes* that left hand side may be approximated by
|
| a^\mu + \lambda \delta a^\mu
|
| and the right hand side by
|
| \lambda \delta \Gamma_{\rho\sigma}^\mu c^2
|
| See his (4.19).
|
| But by geometrical requirements (Carroll and textbooks are not checking
| any geometrical consistency check at this point)
|
| \delta a^\mu = \delta \Gamma_{\rho\sigma}^\mu = 0
|
| and the result is a = 0 in the linear regime. As conclusion bodies have
| to move on straight lines.
|
| Another way to see this is deriving motion from D{T_ab} = 0.
| In the linear regime, it reduces to \partial{T_ab} = 0, and like in the
| special relativity case, this implies bodies move in straigth lines.
|
| If one denotes the geodesic equation using next simplified notation
|
| a = \Gamma vv
|
| Then the linearized, L[], geodesic equation reads
|
| L[a] = L[\Gamma vv] = L[\Gamma] Z[vv]
|
| where Z[] denotes the zeroth order application.
|
| Carroll however is computing something different
|
| Z[a] = L[\Gamma] Z[vv]
|
| Carroll is applying different limits to left and hand sides of the
| original equation, which is a mathematically invalid procedure. Therein
| my above claim he is 'inventing' the final equation rather than deriving
| it by mathematical steps.
|
| If General Relativity does not correctly reduce to Newtonian gravity then
| there exists a problem with General Relativity. One cannot offer false
| derivations as those in textbooks...
|
|
| --
| http://canonicalscience.org/en/misce...guidelines.txt

On May 1, 3:54*pm, "Androcles" wrote:
So what? If Carroll makes assumptions he's only following the path
Einstein took; you don't expect proof, do you?
--
This message is brought to you by Androcles
*http://www.androcles01.pwp.blueyonder.co.uk/

"Juan R. González-Álvarez" wrote in
messagenewsan.2008.05.01.18.00.56@canonicalscien ce.com...
|I am working in relationship between General Relativity and the non-
| relativistic theory of Newton.
|
| My research consists of two parts. The first part addresses the common
| claim that geodesic equation of General Relativity reduces to Newton law
| of motion in the linear limit, i.e. g_ab = \eta_ab + h_ab when ||h|| is
| small enough to ignore quadratic and higher orders.
|
| Take for example Carroll lecture notes available online:
|
|http://lanl.arXiv.org/abs/gr-qc/9712019v1
|
| Carroll starts from geodesic equation (4.9) and derives equation (4.19),
| which he identifies with Newton equation (4.4) after using (4.20).
|
| During the derivation Carroll uses the linear constraint (4.13) for the
| metric tensor.
|
| Students and general public are confused with those claims. A more
| rigorous analysis does not support Carroll conclusions.
|
| Carroll is not computing the linear geodesic equation of motion but
| 'inventing' a non-geometrical equation [see below].
|
| The equation of motion in the linear limit is a = 0 and bodies are
| unaffected by gravity.
|
| A interesting conclusion is that the linearized equation of motion from
| General Relativity does not coincide with that from Newtonian gravity.
|
| For both the zeroth and the linear regimes of General Relativity bodies
| have to move on straight lines.
|
| A way to see this is expanding the geodesic equation in a perturbative
| series and retaining terms up to linear order on expansion parameter,
|
| a^\mu + \lambda \delta a^\mu
|
| =
|
| \lambda \delta \Gamma_{\rho\sigma}^\mu u^\rho u^\sigma
|
| The terms in brackets correspond to zeroth order.
|
| Carroll *assumes* that left hand side may be approximated by
|
| a^\mu + \lambda \delta a^\mu
|
| and the right hand side by
|
| \lambda \delta \Gamma_{\rho\sigma}^\mu c^2
|
| See his (4.19).
|
| But by geometrical requirements (Carroll and textbooks are not checking
| any geometrical consistency check at this point)
|
| \delta a^\mu *= *\delta \Gamma_{\rho\sigma}^\mu *= *0
|
| and the result is a = 0 in the linear regime. As conclusion bodies have
| to move on straight lines.
|
| Another way to see this is deriving motion from D{T_ab} = 0.
| In the linear regime, it reduces to \partial{T_ab} = 0, and like in the
| special relativity case, this implies bodies move in straigth lines.


They must because any linearization will reclaim Minkowski spacetime.

Why are you sweating so much? Everyone knows that GR does not converge
to the Newtonian limit. It cannot converge. But they must say it does
otherwise it should be thrown away.

GR was a smart move but it should not have been taken seriously. It is
the gratest joke in the history of science. Even worse then epicycles.

There are better geometrical theories than GR that converge easily to
Newtonian limit.


Mike



|
| If one denotes the geodesic equation using next simplified notation
|
| a = \Gamma vv
|
| Then the linearized, L[], geodesic equation reads
|
| L[a] = L[\Gamma vv] = *L[\Gamma] Z[vv]
|
| where Z[] denotes the zeroth order application.
|
| Carroll however is computing something different
|
| Z[a] = *L[\Gamma] Z[vv]
|
| Carroll is applying different limits to left and hand sides of the
| original equation, which is a mathematically invalid procedure. Therein
| my above claim he is 'inventing' the final equation rather than deriving
| it by mathematical steps.
|
| If General Relativity does not correctly reduce to Newtonian gravity then
| there exists a problem with General Relativity. One cannot offer false
| derivations as those in textbooks...
|
|
| --
|http://canonicalscience.org/en/misce...guidelines.txt

On May 1, 10:01*am, "Juan R." González-Álvarez
wrote:
I am working in relationship between General Relativity and the non-
relativistic theory of Newton.

Oh goody.


My research consists of two parts. The first part addresses the common
claim that geodesic equation of General Relativity reduces to Newton law
of motion in the linear limit, i.e. g_ab = \eta_ab + h_ab when ||h|| is
small enough to ignore quadratic and higher orders.

Take for example Carroll lecture notes available online:

http://lanl.arXiv.org/abs/gr-qc/9712019v1

Carroll starts from geodesic equation (4.9) and derives equation (4.19),
which he identifies with Newton equation (4.4) after using (4.20).

During the derivation Carroll uses the linear constraint (4.13) for the
metric tensor.

Students and general public are confused with those claims. A more
rigorous analysis does not support Carroll conclusions.

The more rigorous analysis is /in the paper/ which you don't bother
looking at. Look at chapter 6.


Carroll is not computing the linear geodesic equation of motion but
'inventing' a non-geometrical equation [see below].

No, he is using the geodesic equation and making appropriate
approximations and using the relevant connection coefficients. Read
chapter 6 instead of the quickie in chapter 4.


The equation of motion in the linear limit is a = 0 and bodies are
unaffected by gravity.

A interesting conclusion is that the linearized equation of motion from
General Relativity does not coincide with that from Newtonian gravity.

An even more interesting conclusion is that you can't be bothered to
understand Wald, MTW, Carroll, D'Inverno...


For both the zeroth and the linear regimes of General Relativity bodies
have to move on straight lines.

A way to see this is expanding the geodesic equation in a perturbative
series and retaining terms up to linear order on expansion parameter,

a^\mu + \lambda \delta a^\mu

*=

\lambda \delta \Gamma_{\rho\sigma}^\mu u^\rho u^\sigma

The terms in brackets correspond to zeroth order.

Carroll *assumes* that left hand side may be approximated by

No he doesn't. Read Chapter 6 to see what he _actually_ does.

[snip]

Another way to see this is deriving motion from D{T_ab} = 0.
In the linear regime, it reduces to \partial{T_ab} = 0, and like in the
special relativity case, this implies bodies move in straigth lines.

No, it means that the weak field limit cannot consistently describe a
self gravitating system. There is a discussion about this in Carroll,
Wald, MTW... Go ahead and read it before raging more.

[snip rest, irrelevant]

Make claims about the actual rigorous derivation in chapter 6.

"Juan R." González-�lvarez wrote on Thu, 01 May 2008 20:01:08 +0200:

I am working in relationship between General Relativity and the non-
relativistic theory of Newton.

My research consists of two parts. The first part addresses the common
claim that geodesic equation of General Relativity reduces to Newton law
of motion in the linear limit, i.e. g_ab = \eta_ab + h_ab when ||h|| is
small enough to ignore quadratic and higher orders.

Take for example Carroll lecture notes available online:

http://lanl.arXiv.org/abs/gr-qc/9712019v1

Carroll starts from geodesic equation (4.9) and derives equation (4.19),
which he identifies with Newton equation (4.4) after using (4.20).

During the derivation Carroll uses the linear constraint (4.13) for the
metric tensor.

Students and general public are confused with those claims. A more
rigorous analysis does not support Carroll conclusions.

Carroll is not computing the linear geodesic equation of motion but
'inventing' a non-geometrical equation [see below].

The equation of motion in the linear limit is a = 0 and bodies are
unaffected by gravity.

A interesting conclusion is that the linearized equation of motion from
General Relativity does not coincide with that from Newtonian gravity.

For both the zeroth and the linear regimes of General Relativity bodies
have to move on straight lines.

A way to see this is expanding the geodesic equation in a perturbative
series and retaining terms up to linear order on expansion parameter,

a^\mu + \lambda \delta a^\mu

=

\lambda \delta \Gamma_{\rho\sigma}^\mu u^\rho u^\sigma

The terms in brackets correspond to zeroth order.

Carroll *assumes* that left hand side may be approximated by

a^\mu + \lambda \delta a^\mu

and the right hand side by

\lambda \delta \Gamma_{\rho\sigma}^\mu c^2

See his (4.19).

But by geometrical requirements (Carroll and textbooks are not checking
any geometrical consistency check at this point)

\delta a^\mu = \delta \Gamma_{\rho\sigma}^\mu = 0

and the result is a = 0 in the linear regime. As conclusion bodies have
to move on straight lines.

Another way to see this is deriving motion from D{T_ab} = 0. In the
linear regime, it reduces to \partial{T_ab} = 0, and like in the special
relativity case, this implies bodies move in straigth lines.

If one denotes the geodesic equation using next simplified notation

a = \Gamma vv

Then the linearized, L[], geodesic equation reads

L[a] = L[\Gamma vv] = L[\Gamma] Z[vv]

where Z[] denotes the zeroth order application.

Carroll however is computing something different

Z[a] = L[\Gamma] Z[vv]

Carroll is applying different limits to left and hand sides of the
original equation, which is a mathematically invalid procedure. Therein
my above claim he is 'inventing' the final equation rather than deriving
it by mathematical steps.

If General Relativity does not correctly reduce to Newtonian gravity
then there exists a problem with General Relativity. One cannot offer
false derivations as those in textbooks...

Submitted also to sci.physics.foundations and sci.physics.research.

It is already available on sci.physics.foundations.

--
http://canonicalscience.org/en/misce...guidelines.txt

On May 2, 2:31 am, "Juan R." González-Álvarez
wrote:


Submitted also to sci.physics.foundations and sci.physics.research.

It is already available on sci.physics.foundations.


...so more people can have a good laugh.

http://www.helinium.nl/trolltech.gif

On May 1, 5:24*pm, Eric Gisse wrote:



Make claims about the actual rigorous derivation in chapter 6.-


Yes, I will make claims. He writes on page 166:

"We will treat the motion of the stars in the Newtonian approximation,
where we can discuss their orbit just as Kepler would have. Circular
orbits are most easily characterized by equating the force due to
gravity to the outward “centrifugal” force"

Then he uses Newtoniam Mechanics in a somewhat wrong way and makes
referece to centrifugal forces in equations 6.86 and 6.87.

The man cannot modelk a circular orbit using GR. He must revert to
simpel Newtonian Mechanics by making first the unproved claim that GR
converges to Newtonian limit.

You think this is physics. I think it is deception.

Making about 17 assumptions to get to Newtonian limit is not physics.
It is called circus.

Mike

On May 2, 2:34*pm, Mike wrote:
On May 1, 5:24*pm, Eric Gisse wrote:



Make claims about the actual rigorous derivation in chapter 6.-

Yes, I will make claims. He writes on page 166:

"We will treat the motion of the stars in the Newtonian approximation,
where we can discuss their orbit just as Kepler would have. Circular
orbits are most easily characterized by equating the force due to
gravity to the outward “centrifugal” force"

Then he uses Newtoniam Mechanics in a somewhat wrong way and makes
referece to centrifugal forces in equations 6.86 and 6.87.

The man cannot modelk a circular orbit using GR. He must revert to
simpel Newtonian Mechanics by making first the unproved claim that GR
converges to Newtonian limit.

You think this is physics. I think it is deception.

Making about 17 assumptions to get to Newtonian limit is not physics.
It is called circus.

Mike

Why are you complaining? That was an /application/ of the Newtonian
approximation.

"Juan R." González-�lvarez wrote on Thu, 01 May 2008 20:01:08 +0200:

Carroll *assumes* that left hand side may be approximated by

a^\mu + \lambda \delta a^\mu

and the right hand side by

\lambda \delta \Gamma_{\rho\sigma}^\mu c^2

See his (4.19).

Sorry a typo. I mean that Carroll is assuming that left hand side may be
approximated by

a^\mu

This is why I said that Carroll is computing

Z[a] = L[\Gamma] Z[v v]

instead the correct

L[a] = L[\Gamma v v]


--
http://canonicalscience.org/en/misce...guidelines.txt

On May 2, 7:00*pm, Eric Gisse wrote:
On May 2, 2:34*pm, Mike wrote:





On May 1, 5:24*pm, Eric Gisse wrote:

Make claims about the actual rigorous derivation in chapter 6.-

Yes, I will make claims. He writes on page 166:

"We will treat the motion of the stars in the Newtonian approximation,
where we can discuss their orbit just as Kepler would have. Circular
orbits are most easily characterized by equating the force due to
gravity to the outward “centrifugal” force"

Then he uses Newtoniam Mechanics in a somewhat wrong way and makes
referece to centrifugal forces in equations 6.86 and 6.87.

The man cannot modelk a circular orbit using GR. He must revert to
simpel Newtonian Mechanics by making first the unproved claim that GR
converges to Newtonian limit.

You think this is physics. I think it is deception.

Making about 17 assumptions to get to Newtonian limit is not physics.
It is called circus.

Mike

Why are you complaining? That was an /application/ of the Newtonian
approximation.- Hide quoted text -

- Show quoted text -

Idiot, such "application" was never proven in the paper. It is just
assumed. Nowhere in the paper it is proved that in GR a centripetal
force must be equal to a centrifugal force in a circular orbit. This
is know only from Newtoniam Mechanics.

Furthermore, nowehere in GR the term centrifugal force comes about
unless one has read Newtonian Mechanics.

You idiot, give the GR equatiuons to a genious (not to you stupid) who
never studied Newtonian mechanics. He will never be able to write that
equation you fool. He will get nothing out of GR equations. Jusr non-
sense at the weak field limit.

http://www.albinoblacksheep.com/flash/youare

Mike