## Nonlocality of classical vacuum gravity energy & fiber bundles

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• There has been a lot of nonsense about 1. finding a local classical gravity stress-energy density tensor Pauli s 1921 classic article solves that problem
Message 1 of 7 , Sep 1, 2006
There has been a lot of nonsense about

1. finding a local classical gravity stress-energy density tensor
Pauli's 1921 classic article solves that problem adequately.

2. Newtonian interpretation of Einstein's connection field as

Einstein Connection = Non-inertial Frame Connection Non-Tensor -
Intrinsic Curvature Connection

where

Intrinsic Curvature Connection Tensor =/= 0

In fact

Intrinsic Curvature Connection = 0

and that is one aspect of the equivalence principle i.e.

The local gravity force per unit mass or "g's" felt by a non-geodesic
observer is

g^i = c^2{Einstein Connection}^i00(dx^0/ds)(dx^0/ds)

For example outside a SSS source, i = 1 is the radial direction

g^1 = GM/r^2

g^2 = g^3 = 0

for static hovering shell non-geodesic LNIF observers at fixed r

Note that g^1 is also the local frame invariant proper acceleration
because {Einstein Connection}^000 = 0.

3. Confusions about potential in GR.

If you look at the SSS metrics

g00 ~ 1 + V(Newton)/c^2

V(Newton) is the classical gravity potential energy per unit test mass.

On the other hand from the local gauge field theory fiber bundle POV

Principle bundle gives the local gauge force field.

Associated bundle gives the source field.

In the standard model, the dynamical symmetry group G is an internal
group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
that the fiber is an internal space, or possibly extra space
dimensions if you use string theory. The source fields are spinor
lepton-quarks. The spacetime symmetry group S is a non-dynamical
background.
S =/= G.

On the other hand, in 1916 GR the symmetry group G is the 10-
parameter Poincare space-time group, or possibly the 16-parameter GL
(4,R) group that includes the 15-parameter conformal group of Penrose
massless twistors as a sub-group.

However, in 1916 GR the torsion is zero, this means only the 4-
parameter T4 subgroup of the Poincare group gives dynamically
independent degrees of freedom of the geometrodynamic field that is
the fabric of 4D space-time. The Lorentz group O(1,3) generators are
redundant in that limit.

The Diff(4) GCT group is the locally-gauged T4 translation group
generated by total 4-momentum. Since total energy is only conserved
if there is time-translation invariance (Noether's theorem) and since
our accelerating expanding pocket universe in the megaverse of many
worlds is manifestly not time translation invariant in any sense, it
is obvious that the total energy of the universe is not conserved.
Our universe is not a closed system in the classical sense. Indeed,
the micro-quantum zero point vacuum dark energy density at large
scale has w = -1 therefore its energy density is constant, therefore
the total dark energy is not conserved.

Now in 1916 GR the geometrodynamic source field is the Cartan mobile

e^a, a = 0,1,2,3 in local Minkowski tangent space.

The "potential" is the Einstein connection field that is made from
gradients of Newton's potential V(Newton). That is V(Newton) is the
meta-potential of the Einstein Connection potential. This is a unique
theories where there is a qualitative separation between the
dynamical group and the space-time group, i.e. S = G is another way
to look at the equivalence principle.
• Jack, I thought you wanted to drop this subject? ... Then why did the world-class theoretical physicist and close collaborator with Einstein at Princeton,
Message 2 of 7 , Sep 1, 2006
Jack, I thought you wanted to drop this subject?

Jack Sarfatti wrote:

> There has been a lot of nonsense about
>
> 1. finding a local classical gravity stress-energy density tensor
> Pauli's 1921 classic article solves that problem adequately.

Then why did the world-class theoretical physicist and close
collaborator with Einstein at Princeton,
Nathan Rosen, propose a bimetric solution to this "non-problem" in
papers published in Physical
Review in 1940?

> 2. Newtonian interpretation of Einstein's connection field as
>
> Einstein Connection = Non-inertial Frame Connection Non-Tensor -
> Intrinsic Curvature Connection

What is the "Einstein connection"? Do you mean the Levi-Civita connection?

What is the "intrinsic curvature connection"? You can have a
non-vanishing connection field even in a flat
Minkowski spacetime so this makes no sense!

What is the "non-inertial frame connection"?

I have to presume that you actually mean

LC = GRAVITATIONAL FIELD TENSOR + INERTIAL FIELD NON-TENSOR

> where
>
> Intrinsic Curvature Connection Tensor =/= 0
>
> In fact
>
> Intrinsic Curvature Connection = 0
>
> and that is one aspect of the equivalence principle i.e.
>
> The local gravity force per unit mass or "g's" felt by a non-geodesic
> observer is
>
> g^i = c^2{Einstein Connection}^i00(dx^0/ds)(dx^0/ds)

There is no "gravity force" in GR. Only resistance to forced deviations
from motion
along geodesic trajectories.

You are confusing the external force required to *compensate* the effect
of the Einstein
g-field with the effect itself. The resistance to such forced deviations
is inertial, but the
effect (change in the objective *conditions* of unforced inertial motion
due to the presence
of matter) is *gravitational*.

> For example outside a SSS source, i = 1 is the radial direction
>
> g^1 = GM/r^2
>
> g^2 = g^3 = 0
>
> for static hovering shell non-geodesic LNIF observers at fixed r
>
> Note that g^1 is also the local frame invariant proper acceleration
> because {Einstein Connection}^000 = 0.
>
> 3. Confusions about potential in GR.
>
> If you look at the SSS metrics
>
> g00 ~ 1 + V(Newton)/c^2
>
> V(Newton) is the classical gravity potential energy per unit test mass.

This is a correspondence formula.

> On the other hand from the local gauge field theory fiber bundle POV
>
> Principle bundle gives the local gauge force field.
>
> Associated bundle gives the source field.
>
> In the standard model, the dynamical symmetry group G is an internal
> group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
> that the fiber is an internal space, or possibly extra space
> dimensions if you use string theory. The source fields are spinor
> lepton-quarks. The spacetime symmetry group S is a non-dynamical
> background.
> S =/= G.
>
> On the other hand, in 1916 GR the symmetry group G is the 10-
> parameter Poincare space-time group, or possibly the 16-parameter GL
> (4,R) group that includes the 15-parameter conformal group of Penrose
> massless twistors as a sub-group.
>
> However, in 1916 GR the torsion is zero, this means only the 4-
> parameter T4 subgroup of the Poincare group gives dynamically
> independent degrees of freedom of the geometrodynamic field that is
> the fabric of 4D space-time. The Lorentz group O(1,3) generators are
> redundant in that limit.

Coordinate invariance as a kind of gauge symmetry?

I think like many others in the field you are still confused about the
meaning of general covariance in GR.

>
> The Diff(4) GCT group is the locally-gauged T4 translation group
> generated by total 4-momentum.

Of course *mathematically* speaking coordinate transformations have
nothing at all to do with 4-momentum.
They are simply re-labeling schemes for spacetime points. They simply
permute the 4-tuple labels attached to
events.

> Since total energy is only conserved if there is time-translation
> invariance (Noether's theorem)

Right.

> and since our accelerating expanding pocket universe in the megaverse
> of many worlds is manifestly not time translation invariant in any
> sense, it is obvious that the total energy of the universe is not
> conserved. Our universe is not a closed system in the classical
> sense. Indeed, the micro-quantum zero point vacuum dark energy
> density at large scale has w = -1 therefore its energy density is
> constant, therefore the total dark energy is not conserved.
>
> Now in 1916 GR the geometrodynamic source field is the Cartan mobile
>
> e^a, a = 0,1,2,3 in local Minkowski tangent space.
>
> The "potential" is the Einstein connection field that is made from
> gradients of Newton's potential V(Newton).

Only in the correspondence model. This is only good in the Newtonian
domain, obviously.

> That is V(Newton) is the meta-potential of the Einstein Connection
> potential. This is a unique feature of the equivalence principle not
> found in the internal gauge theories where there is a qualitative
> separation between the dynamical group and the space-time group, i.e.
> S = G is another way to look at the equivalence principle.

Tolman's idea was that the metric components g_uv played the role of
"metric potential" of
Einstein's gravitational field. While the concept is analogous to a
Newtonian potential, it is not
limited to the Newtonian domain and has nothing specifically to do with
Newtonian correspondence.

Z.
• Why? Because people are stupid, that s why. You are a prime example. There is a very simple explanation why you need a pseudo-energy tensor for the gravity
Message 3 of 7 , Sep 1, 2006
Why? Because people are stupid, that's why. You are a prime example.
There is a very simple explanation why you need a pseudo-energy tensor for the gravity field.
It's because the additional energy comes from the work-done by the non-gravity forces making the non-geodesic local frames.

On Sep 1, 2006, at 3:20 PM, Paul Zielinski wrote:

Jack, I thought you wanted to drop this subject?

Jack Sarfatti wrote:

> There has been a lot of nonsense about
>
> 1. finding a local classical gravity stress-energy density tensor
> Pauli's 1921 classic article solves that problem adequately.

Then why did the world-class theoretical physicist and close
collaborator with Einstein at Princeton,
Nathan Rosen, propose a bimetric solution to this "non-problem" in
papers published in Physical
Review in 1940?

> 2. Newtonian interpretation of Einstein's connection field as
>
> Einstein Connection = Non-inertial Frame Connection Non-Tensor -
> Intrinsic Curvature Connection

What is the "Einstein connection"? Do you mean the Levi-Civita connection?

What is the "intrinsic curvature connection"? You can have a
non-vanishing connection field even in a flat
Minkowski spacetime so this makes no sense!

What is the "non-inertial frame connection"?

I have to presume that you actually mean

LC = GRAVITATIONAL FIELD TENSOR + INERTIAL FIELD NON-TENSOR

> where
>
> Intrinsic Curvature Connection Tensor =/= 0
>
> In fact
>
> Intrinsic Curvature Connection = 0
>
> and that is one aspect of the equivalence principle i.e.
>
> The local gravity force per unit mass or "g's" felt by a non-geodesic
> observer is
>
> g^i = c^2{Einstein Connection}^i00(dx^0/ds)(dx^0/ds)

There is no "gravity force" in GR. Only resistance to forced deviations
from motion
along geodesic trajectories.

You are confusing the external force required to *compensate* the effect
of the Einstein
g-field with the effect itself. The resistance to such forced deviations
is inertial, but the
effect (change in the objective *conditions* of unforced inertial motion
due to the presence
of matter) is *gravitational*.

> For example outside a SSS source, i = 1 is the radial direction
>
> g^1 = GM/r^2
>
> g^2 = g^3 = 0
>
> for static hovering shell non-geodesic LNIF observers at fixed r
>
> Note that g^1 is also the local frame invariant proper acceleration
> because {Einstein Connection}^000 = 0.
>
> 3. Confusions about potential in GR.
>
> If you look at the SSS metrics
>
> g00 ~ 1 + V(Newton)/c^2
>
> V(Newton) is the classical gravity potential energy per unit test mass.

This is a correspondence formula.

> On the other hand from the local gauge field theory fiber bundle POV
>
> Principle bundle gives the local gauge force field.
>
> Associated bundle gives the source field.
>
> In the standard model, the dynamical symmetry group G is an internal
> group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
> that the fiber is an internal space, or possibly extra space
> dimensions if you use string theory. The source fields are spinor
> lepton-quarks. The spacetime symmetry group S is a non-dynamical
> background.
> S =/= G.
>
> On the other hand, in 1916 GR the symmetry group G is the 10-
> parameter Poincare space-time group, or possibly the 16-parameter GL
> (4,R) group that includes the 15-parameter conformal group of Penrose
> massless twistors as a sub-group.
>
> However, in 1916 GR the torsion is zero, this means only the 4-
> parameter T4 subgroup of the Poincare group gives dynamically
> independent degrees of freedom of the geometrodynamic field that is
> the fabric of 4D space-time. The Lorentz group O(1,3) generators are
> redundant in that limit.

Coordinate invariance as a kind of gauge symmetry?

I think like many others in the field you are still confused about the
meaning of general covariance in GR.

>
> The Diff(4) GCT group is the locally-gauged T4 translation group
> generated by total 4-momentum.

Of course *mathematically* speaking coordinate transformations have
nothing at all to do with 4-momentum.
They are simply re-labeling schemes for spacetime points. They simply
permute the 4-tuple labels attached to
events.

> Since total energy is only conserved if there is time-translation
> invariance (Noether's theorem)

Right.

> and since our accelerating expanding pocket universe in the megaverse
> of many worlds is manifestly not time translation invariant in any
> sense, it is obvious that the total energy of the universe is not
> conserved. Our universe is not a closed system in the classical
> sense. Indeed, the micro-quantum zero point vacuum dark energy
> density at large scale has w = -1 therefore its energy density is
> constant, therefore the total dark energy is not conserved.
>
> Now in 1916 GR the geometrodynamic source field is the Cartan mobile
>
> e^a, a = 0,1,2,3 in local Minkowski tangent space.
>
> The "potential" is the Einstein connection field that is made from
> gradients of Newton's potential V(Newton).

Only in the correspondence model. This is only good in the Newtonian
domain, obviously.

> That is V(Newton) is the meta-potential of the Einstein Connection
> potential. This is a unique feature of the equivalence principle not
> found in the internal gauge theories where there is a qualitative
> separation between the dynamical group and the space-time group, i.e.
> S = G is another way to look at the equivalence principle.

Tolman's idea was that the metric components g_uv played the role of
"metric potential" of
Einstein's gravitational field. While the concept is analogous to a
Newtonian potential, it is not
limited to the Newtonian domain and has nothing specifically to do with
Newtonian correspondence.

Z.

• ... People like Nathan Rosen were stupid? I see. ... So now you re comparing me to Nathan Rosen? Are you trying to insult me here? I have to say you have an
Message 4 of 7 , Sep 1, 2006
Jack Sarfatti wrote:
Why? Because people are stupid, that's why.
People like Nathan Rosen were stupid? I see.
You are a prime example.
So now you're comparing me to Nathan Rosen? Are you trying to insult me here?

I have to say you have an interesting definition of "stupid". But then I suppose it's all
relative to one's POV, isn't it?
There is a very simple explanation why you need a pseudo-energy tensor for the gravity field.
It's because the additional energy comes from the work-done by the non-gravity forces making the non-geodesic local frames.
So if I hit the gas pedal in my rocket ship and observe the universe accelerating away from
me, the gravitational energy contained in this "inertial field" in which all the other objects of the
universe appear to be falling comes from the work done in accelerating the rocket, the pilot-
observer, and the telescope?

All other things being held equal, does the energy contained in this supposed "gravitational field"
then depend on the size of the telescope that is used to make the observation? The size of the
rocket? How FAT the observer happens to be?

And what about the equivalence principle? Isn't this supposed gravitational field supposed to be
equivalent to some homogeneous gravitational field? Could you show me a formula for the vacuum
energy density of a real homogeneous gravitational field that depends on the size of the telescope
used to observe the rest of the objects in the universe?

Interesting theory Jack. However, I have to say it sounds kind of "stupid" to me.

Z.

On Sep 1, 2006, at 3:20 PM, Paul Zielinski wrote:

Jack, I thought you wanted to drop this subject?

Jack Sarfatti wrote:

> There has been a lot of nonsense about
>
> 1. finding a local classical gravity stress-energy density tensor
> Pauli's 1921 classic article solves that problem adequately.

Then why did the world-class theoretical physicist and close
collaborator with Einstein at Princeton,
Nathan Rosen, propose a bimetric solution to this "non-problem" in
papers published in Physical
Review in 1940?

> 2. Newtonian interpretation of Einstein's connection field as
>
> Einstein Connection = Non-inertial Frame Connection Non-Tensor -
> Intrinsic Curvature Connection

What is the "Einstein connection"? Do you mean the Levi-Civita connection?

What is the "intrinsic curvature connection"? You can have a
non-vanishing connection field even in a flat
Minkowski spacetime so this makes no sense!

What is the "non-inertial frame connection"?

I have to presume that you actually mean

LC = GRAVITATIONAL FIELD TENSOR + INERTIAL FIELD NON-TENSOR

> where
>
> Intrinsic Curvature Connection Tensor =/= 0
>
> In fact
>
> Intrinsic Curvature Connection = 0
>
> and that is one aspect of the equivalence principle i.e.
>
> The local gravity force per unit mass or "g's" felt by a non-geodesic
> observer is
>
> g^i = c^2{Einstein Connection}^ i00(dx^0/ ds)(dx^0/ ds)

There is no "gravity force" in GR. Only resistance to forced deviations
from motion
along geodesic trajectories.

You are confusing the external force required to *compensate* the effect
of the Einstein
g-field with the effect itself. The resistance to such forced deviations
is inertial, but the
effect (change in the objective *conditions* of unforced inertial motion
due to the presence
of matter) is *gravitational* .

> For example outside a SSS source, i = 1 is the radial direction
>
> g^1 = GM/r^2
>
> g^2 = g^3 = 0
>
> for static hovering shell non-geodesic LNIF observers at fixed r
>
> Note that g^1 is also the local frame invariant proper acceleration
> because {Einstein Connection}^ 000 = 0.
>
> 3. Confusions about potential in GR.
>
> If you look at the SSS metrics
>
> g00 ~ 1 + V(Newton)/c^ 2
>
> V(Newton) is the classical gravity potential energy per unit test mass.

This is a correspondence formula.

> On the other hand from the local gauge field theory fiber bundle POV
>
> Principle bundle gives the local gauge force field.
>
> Associated bundle gives the source field.
>
> In the standard model, the dynamical symmetry group G is an internal
> group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
> that the fiber is an internal space, or possibly extra space
> dimensions if you use string theory. The source fields are spinor
> lepton-quarks. The spacetime symmetry group S is a non-dynamical
> background.
> S =/= G.
>
> On the other hand, in 1916 GR the symmetry group G is the 10-
> parameter Poincare space-time group, or possibly the 16-parameter GL
> (4,R) group that includes the 15-parameter conformal group of Penrose
> massless twistors as a sub-group.
>
> However, in 1916 GR the torsion is zero, this means only the 4-
> parameter T4 subgroup of the Poincare group gives dynamically
> independent degrees of freedom of the geometrodynamic field that is
> the fabric of 4D space-time. The Lorentz group O(1,3) generators are
> redundant in that limit.

Coordinate invariance as a kind of gauge symmetry?

I think like many others in the field you are still confused about the
meaning of general covariance in GR.

>
> The Diff(4) GCT group is the locally-gauged T4 translation group
> generated by total 4-momentum.

Of course *mathematically* speaking coordinate transformations have
nothing at all to do with 4-momentum.
They are simply re-labeling schemes for spacetime points. They simply
permute the 4-tuple labels attached to
events.

> Since total energy is only conserved if there is time-translation
> invariance (Noether's theorem)

Right.

> and since our accelerating expanding pocket universe in the megaverse
> of many worlds is manifestly not time translation invariant in any
> sense, it is obvious that the total energy of the universe is not
> conserved. Our universe is not a closed system in the classical
> sense. Indeed, the micro-quantum zero point vacuum dark energy
> density at large scale has w = -1 therefore its energy density is
> constant, therefore the total dark energy is not conserved.
>
> Now in 1916 GR the geometrodynamic source field is the Cartan mobile
>
> e^a, a = 0,1,2,3 in local Minkowski tangent space.
>
> The "potential" is the Einstein connection field that is made from
> gradients of Newton's potential V(Newton).

Only in the correspondence model. This is only good in the Newtonian
domain, obviously.

> That is V(Newton) is the meta-potential of the Einstein Connection
> potential. This is a unique feature of the equivalence principle not
> found in the internal gauge theories where there is a qualitative
> separation between the dynamical group and the space-time group, i.e.
> S = G is another way to look at the equivalence principle.

Tolman's idea was that the metric components g_uv played the role of
"metric potential" of
Einstein's gravitational field. While the concept is analogous to a
Newtonian potential, it is not
limited to the Newtonian domain and has nothing specifically to do with
Newtonian correspondence.

Z.

• Obviously I am insulting Rosen by comparing him to you. Your remarks on potential are stupid because you cannot follow the math. You have not the slightest
Message 5 of 7 , Sep 1, 2006
Obviously I am insulting Rosen by comparing him to you.
Your remarks on "potential" are stupid because you cannot follow the math.
You have not the slightest understanding of fiber bundles obviously.

On Sep 1, 2006, at 4:30 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

Why? Because people are stupid, that's why.
People like Nathan Rosen were stupid? I see.
You are a prime example.
So now you're comparing me to Nathan Rosen? Are you trying to insult me here?

I have to say you have an interesting definition of "stupid". But then I suppose it's all
relative to one's POV, isn't it?
There is a very simple explanation why you need a pseudo-energy tensor for the gravity field.
It's because the additional energy comes from the work-done by the non-gravity forces making the non-geodesic local frames.
So if I hit the gas pedal in my rocket ship and observe the universe accelerating away from
me, the gravitational energy contained in this "inertial field" in which all the other objects of the
universe appear to be falling comes from the work done in accelerating the rocket, the pilot-
observer, and the telescope?

All other things being held equal, does the energy contained in this supposed "gravitational field"
then depend on the size of the telescope that is used to make the observation? The size of the
rocket? How FAT the observer happens to be?

And what about the equivalence principle? Isn't this supposed gravitational field supposed to be
equivalent to some homogeneous gravitational field? Could you show me a formula for the vacuum
energy density of a real homogeneous gravitational field that depends on the size of the telescope
used to observe the rest of the objects in the universe?

Interesting theory Jack. However, I have to say it sounds kind of "stupid" to me.

Z.

On Sep 1, 2006, at 3:20 PM, Paul Zielinski wrote:

Jack, I thought you wanted to drop this subject?

Jack Sarfatti wrote:

> There has been a lot of nonsense about
>
> 1. finding a local classical gravity stress-energy density tensor
> Pauli's 1921 classic article solves that problem adequately.

Then why did the world-class theoretical physicist and close
collaborator with Einstein at Princeton,
Nathan Rosen, propose a bimetric solution to this "non-problem" in
papers published in Physical
Review in 1940?

> 2. Newtonian interpretation of Einstein's connection field as
>
> Einstein Connection = Non-inertial Frame Connection Non-Tensor -
> Intrinsic Curvature Connection

What is the "Einstein connection"? Do you mean the Levi-Civita connection?

What is the "intrinsic curvature connection"? You can have a
non-vanishing connection field even in a flat
Minkowski spacetime so this makes no sense!

What is the "non-inertial frame connection"?

I have to presume that you actually mean

LC = GRAVITATIONAL FIELD TENSOR + INERTIAL FIELD NON-TENSOR

> where
>
> Intrinsic Curvature Connection Tensor =/= 0
>
> In fact
>
> Intrinsic Curvature Connection = 0
>
> and that is one aspect of the equivalence principle i.e.
>
> The local gravity force per unit mass or "g's" felt by a non-geodesic
> observer is
>
> g^i = c^2{Einstein Connection}^i00(dx^0/ds)(dx^0/ds)

There is no "gravity force" in GR. Only resistance to forced deviations
from motion
along geodesic trajectories.

You are confusing the external force required to *compensate* the effect
of the Einstein
g-field with the effect itself. The resistance to such forced deviations
is inertial, but the
effect (change in the objective *conditions* of unforced inertial motion
due to the presence
of matter) is *gravitational*.

> For example outside a SSS source, i = 1 is the radial direction
>
> g^1 = GM/r^2
>
> g^2 = g^3 = 0
>
> for static hovering shell non-geodesic LNIF observers at fixed r
>
> Note that g^1 is also the local frame invariant proper acceleration
> because {Einstein Connection}^000 = 0.
>
> 3. Confusions about potential in GR.
>
> If you look at the SSS metrics
>
> g00 ~ 1 + V(Newton)/c^2
>
> V(Newton) is the classical gravity potential energy per unit test mass.

This is a correspondence formula.

> On the other hand from the local gauge field theory fiber bundle POV
>
> Principle bundle gives the local gauge force field.
>
> Associated bundle gives the source field.
>
> In the standard model, the dynamical symmetry group G is an internal
> group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
> that the fiber is an internal space, or possibly extra space
> dimensions if you use string theory. The source fields are spinor
> lepton-quarks. The spacetime symmetry group S is a non-dynamical
> background.
> S =/= G.
>
> On the other hand, in 1916 GR the symmetry group G is the 10-
> parameter Poincare space-time group, or possibly the 16-parameter GL
> (4,R) group that includes the 15-parameter conformal group of Penrose
> massless twistors as a sub-group.
>
> However, in 1916 GR the torsion is zero, this means only the 4-
> parameter T4 subgroup of the Poincare group gives dynamically
> independent degrees of freedom of the geometrodynamic field that is
> the fabric of 4D space-time. The Lorentz group O(1,3) generators are
> redundant in that limit.

Coordinate invariance as a kind of gauge symmetry?

I think like many others in the field you are still confused about the
meaning of general covariance in GR.

>
> The Diff(4) GCT group is the locally-gauged T4 translation group
> generated by total 4-momentum.

Of course *mathematically* speaking coordinate transformations have
nothing at all to do with 4-momentum.
They are simply re-labeling schemes for spacetime points. They simply
permute the 4-tuple labels attached to
events.

> Since total energy is only conserved if there is time-translation
> invariance (Noether's theorem)

Right.

> and since our accelerating expanding pocket universe in the megaverse
> of many worlds is manifestly not time translation invariant in any
> sense, it is obvious that the total energy of the universe is not
> conserved. Our universe is not a closed system in the classical
> sense. Indeed, the micro-quantum zero point vacuum dark energy
> density at large scale has w = -1 therefore its energy density is
> constant, therefore the total dark energy is not conserved.
>
> Now in 1916 GR the geometrodynamic source field is the Cartan mobile
>
> e^a, a = 0,1,2,3 in local Minkowski tangent space.
>
> The "potential" is the Einstein connection field that is made from
> gradients of Newton's potential V(Newton).

Only in the correspondence model. This is only good in the Newtonian
domain, obviously.

> That is V(Newton) is the meta-potential of the Einstein Connection
> potential. This is a unique feature of the equivalence principle not
> found in the internal gauge theories where there is a qualitative
> separation between the dynamical group and the space-time group, i.e.
> S = G is another way to look at the equivalence principle.

Tolman's idea was that the metric components g_uv played the role of
"metric potential" of
Einstein's gravitational field. While the concept is analogous to a
Newtonian potential, it is not
limited to the Newtonian domain and has nothing specifically to do with
Newtonian correspondence.

Z.

.
Â

• ... But Rosen also held that a tensor vacuum energy density could be defined in GR and could be extracted from Einstein s pseudotensor. And Rosen s theory also
Message 6 of 7 , Sep 2, 2006
Jack Sarfatti wrote:
Obviously I am insulting Rosen by comparing him to you.
But Rosen also held that a tensor vacuum energy density could be defined in
GR and could be extracted from Einstein's pseudotensor. And Rosen's theory
also involved a flat reference manifold. Didn't you read the abstracts I sent?

You said you thought this was a "stupid idea". You said it was "crackpot".

Like Feynman, Rosen didn't believe in "curved spacetime". He thought it was
just a geometric model for a physical field living in a flat spacetime.

Sound familiar?
Your remarks on "potential" are stupid because you cannot follow the math.
Looks like I understand the math a lot better than you ever will Jack. This mantra
is getting really old. I don't think you even understand how coordinates and coordinate
transformations are defined on curved manifolds.

Do you think Tolman couldn't follow the math? After all, this was Tolman's idea.

Your Newtonian formula is irrelevant to Tolman's idea that the metric components
g_uv are the "metric potentials" of the Einstein g-field -- although it's OK as a
*correspondence formula* good only in the Newtonian domain.
You have not the slightest understanding of fiber bundles obviously.
Jack, I know you're bluffing. Fiber bundles don't change anything here.

Z.

On Sep 1, 2006, at 4:30 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

Why? Because people are stupid, that's why.
People like Nathan Rosen were stupid? I see.
You are a prime example.
So now you're comparing me to Nathan Rosen? Are you trying to insult me here?

I have to say you have an interesting definition of "stupid". But then I suppose it's all
relative to one's POV, isn't it?
There is a very simple explanation why you need a pseudo-energy tensor for the gravity field.
It's because the additional energy comes from the work-done by the non-gravity forces making the non-geodesic local frames.
So if I hit the gas pedal in my rocket ship and observe the universe accelerating away from
me, the gravitational energy contained in this "inertial field" in which all the other objects of the
universe appear to be falling comes from the work done in accelerating the rocket, the pilot-
observer, and the telescope?

All other things being held equal, does the energy contained in this supposed "gravitational field"
then depend on the size of the telescope that is used to make the observation? The size of the
rocket? How FAT the observer happens to be?

And what about the equivalence principle? Isn't this supposed gravitational field supposed to be
equivalent to some homogeneous gravitational field? Could you show me a formula for the vacuum
energy density of a real homogeneous gravitational field that depends on the size of the telescope
used to observe the rest of the objects in the universe?

Interesting theory Jack. However, I have to say it sounds kind of "stupid" to me.

Z.

On Sep 1, 2006, at 3:20 PM, Paul Zielinski wrote:

Jack, I thought you wanted to drop this subject?

Jack Sarfatti wrote:

> There has been a lot of nonsense about
>
> 1. finding a local classical gravity stress-energy density tensor
> Pauli's 1921 classic article solves that problem adequately.

Then why did the world-class theoretical physicist and close
collaborator with Einstein at Princeton,
Nathan Rosen, propose a bimetric solution to this "non-problem" in
papers published in Physical
Review in 1940?

> 2. Newtonian interpretation of Einstein's connection field as
>
> Einstein Connection = Non-inertial Frame Connection Non-Tensor -
> Intrinsic Curvature Connection

What is the "Einstein connection"? Do you mean the Levi-Civita connection?

What is the "intrinsic curvature connection"? You can have a
non-vanishing connection field even in a flat
Minkowski spacetime so this makes no sense!

What is the "non-inertial frame connection"?

I have to presume that you actually mean

LC = GRAVITATIONAL FIELD TENSOR + INERTIAL FIELD NON-TENSOR

> where
>
> Intrinsic Curvature Connection Tensor =/= 0
>
> In fact
>
> Intrinsic Curvature Connection = 0
>
> and that is one aspect of the equivalence principle i.e.
>
> The local gravity force per unit mass or "g's" felt by a non-geodesic
> observer is
>
> g^i = c^2{Einstein Connection}^ i00(dx^0/ ds)(dx^0/ ds)

There is no "gravity force" in GR. Only resistance to forced deviations
from motion
along geodesic trajectories.

You are confusing the external force required to *compensate* the effect
of the Einstein
g-field with the effect itself. The resistance to such forced deviations
is inertial, but the
effect (change in the objective *conditions* of unforced inertial motion
due to the presence
of matter) is *gravitational* .

> For example outside a SSS source, i = 1 is the radial direction
>
> g^1 = GM/r^2
>
> g^2 = g^3 = 0
>
> for static hovering shell non-geodesic LNIF observers at fixed r
>
> Note that g^1 is also the local frame invariant proper acceleration
> because {Einstein Connection}^ 000 = 0.
>
> 3. Confusions about potential in GR.
>
> If you look at the SSS metrics
>
> g00 ~ 1 + V(Newton)/c^ 2
>
> V(Newton) is the classical gravity potential energy per unit test mass.

This is a correspondence formula.

> On the other hand from the local gauge field theory fiber bundle POV
>
> Principle bundle gives the local gauge force field.
>
> Associated bundle gives the source field.
>
> In the standard model, the dynamical symmetry group G is an internal
> group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
> that the fiber is an internal space, or possibly extra space
> dimensions if you use string theory. The source fields are spinor
> lepton-quarks. The spacetime symmetry group S is a non-dynamical
> background.
> S =/= G.
>
> On the other hand, in 1916 GR the symmetry group G is the 10-
> parameter Poincare space-time group, or possibly the 16-parameter GL
> (4,R) group that includes the 15-parameter conformal group of Penrose
> massless twistors as a sub-group.
>
> However, in 1916 GR the torsion is zero, this means only the 4-
> parameter T4 subgroup of the Poincare group gives dynamically
> independent degrees of freedom of the geometrodynamic field that is
> the fabric of 4D space-time. The Lorentz group O(1,3) generators are
> redundant in that limit.

Coordinate invariance as a kind of gauge symmetry?

I think like many others in the field you are still confused about the
meaning of general covariance in GR.

>
> The Diff(4) GCT group is the locally-gauged T4 translation group
> generated by total 4-momentum.

Of course *mathematically* speaking coordinate transformations have
nothing at all to do with 4-momentum.
They are simply re-labeling schemes for spacetime points. They simply
permute the 4-tuple labels attached to
events.

> Since total energy is only conserved if there is time-translation
> invariance (Noether's theorem)

Right.

> and since our accelerating expanding pocket universe in the megaverse
> of many worlds is manifestly not time translation invariant in any
> sense, it is obvious that the total energy of the universe is not
> conserved. Our universe is not a closed system in the classical
> sense. Indeed, the micro-quantum zero point vacuum dark energy
> density at large scale has w = -1 therefore its energy density is
> constant, therefore the total dark energy is not conserved.
>
> Now in 1916 GR the geometrodynamic source field is the Cartan mobile
>
> e^a, a = 0,1,2,3 in local Minkowski tangent space.
>
> The "potential" is the Einstein connection field that is made from
> gradients of Newton's potential V(Newton).

Only in the correspondence model. This is only good in the Newtonian
domain, obviously.

> That is V(Newton) is the meta-potential of the Einstein Connection
> potential. This is a unique feature of the equivalence principle not
> found in the internal gauge theories where there is a qualitative
> separation between the dynamical group and the space-time group, i.e.
> S = G is another way to look at the equivalence principle.

Tolman's idea was that the metric components g_uv played the role of
"metric potential" of
Einstein's gravitational field. While the concept is analogous to a
Newtonian potential, it is not
limited to the Newtonian domain and has nothing specifically to do with
Newtonian correspondence.

Z.

.

• Rosen made a mistake. Everything you say below is stupid, delusional and not even wrong. You have not once given any evidence that you understand the math
Message 7 of 7 , Sep 2, 2006
Rosen made a mistake.Â  Everything you say below is stupid, delusional and not even wrong. You have not once given any evidence that you understand the math needed. In fact you have given evidence to the contrary. What you are attempting to do is stupid and shows you do not at all understand the physics of Einstein's equivalence principle. The tidal curvature issue is a complete bogus Red Herring. If other idiots made the same mistake it only shows that even physicists can be stupid on particular issues.
On Sep 2, 2006, at 3:33 AM, Paul Zielinski wrote:

Jack Sarfatti wrote:

Obviously I am insulting Rosen by comparing him to you.
But Rosen also held that a tensor vacuum energy density could be defined in
GR and could be extracted from Einstein's pseudotensor. And Rosen's theory
also involved a flat reference manifold. Didn't you read the abstracts I sent?

You said you thought this was a "stupid idea". You said it was "crackpot".

Like Feynman, Rosen didn't believe in "curved spacetime". He thought it was
just a geometric model for a physical field living in a flat spacetime.

Sound familiar?
Your remarks on "potential" are stupid because you cannot follow the math.
Looks like I understand the math a lot better than you ever will Jack. This mantra
is getting really old. I don't think you even understand how coordinates and coordinate
transformations are defined on curved manifolds.

Do you think Tolman couldn't follow the math? After all, this was Tolman's idea.

is irrelevant to Tolman's idea that the metric components
g_uv are the "metric potentials" of the Einstein g-field -- although it's OK as a
*correspondence formula* good only in the Newtonian domain.
You have not the slightest understanding of fiber bundles obviously.
Jack, I know you're bluffing. Fiber bundles don't change anything here.

Z.

On Sep 1, 2006, at 4:30 PM, Paul Zielinski wrote:

Jack Sarfatti wrote:

Why? Because people are stupid, that's why.
People like Nathan Rosen were stupid? I see.
You are a prime example.
So now you're comparing me to Nathan Rosen? Are you trying to insult me here?

I have to say you have an interesting definition of "stupid". But then I suppose it's all
relative to one's POV, isn't it?
There is a very simple explanation why you need a pseudo-energy tensor for the gravity field.
It's because the additional energy comes from the work-done by the non-gravity forces making the non-geodesic local frames.
So if I hit the gas pedal in my rocket ship and observe the universe accelerating away from
me, the gravitational energy contained in this "inertial field" in which all the other objects of the
universe appear to be falling comes from the work done in accelerating the rocket, the pilot-
observer, and the telescope?

All other things being held equal, does the energy contained in this supposed "gravitational field"
then depend on the size of the telescope that is used to make the observation? The size of the
rocket? How FAT the observer happens to be?

And what about the equivalence principle? Isn't this supposed gravitational field supposed to be
equivalent to some homogeneous gravitational field? Could you show me a formula for the vacuum
energy density of a real homogeneous gravitational field that depends on the size of the telescope
used to observe the rest of the objects in the universe?

Interesting theory Jack. However, I have to say it sounds kind of "stupid" to me.

Z.

On Sep 1, 2006, at 3:20 PM, Paul Zielinski wrote:

Jack, I thought you wanted to drop this subject?

Jack Sarfatti wrote:

> There has been a lot of nonsense about
>
> 1. finding a local classical gravity stress-energy density tensor
> Pauli's 1921 classic article solves that problem adequately.

Then why did the world-class theoretical physicist and close
collaborator with Einstein at Princeton,
Nathan Rosen, propose a bimetric solution to this "non-problem" in
papers published in Physical
Review in 1940?

> 2. Newtonian interpretation of Einstein's connection field as
>
> Einstein Connection = Non-inertial Frame Connection Non-Tensor -
> Intrinsic Curvature Connection

What is the "Einstein connection"? Do you mean the Levi-Civita connection?

What is the "intrinsic curvature connection"? You can have a
non-vanishing connection field even in a flat
Minkowski spacetime so this makes no sense!

What is the "non-inertial frame connection"?

I have to presume that you actually mean

LC = GRAVITATIONAL FIELD TENSOR + INERTIAL FIELD NON-TENSOR

> where
>
> Intrinsic Curvature Connection Tensor =/= 0
>
> In fact
>
> Intrinsic Curvature Connection = 0
>
> and that is one aspect of the equivalence principle i.e.
>
> The local gravity force per unit mass or "g's" felt by a non-geodesic
> observer is
>
> g^i = c^2{Einstein Connection}^i00(dx^0/ds)(dx^0/ds)

There is no "gravity force" in GR. Only resistance to forced deviations
from motion
along geodesic trajectories.

You are confusing the external force required to *compensate* the effect
of the Einstein
g-field with the effect itself. The resistance to such forced deviations
is inertial, but the
effect (change in the objective *conditions* of unforced inertial motion
due to the presence
of matter) is *gravitational*.

> For example outside a SSS source, i = 1 is the radial direction
>
> g^1 = GM/r^2
>
> g^2 = g^3 = 0
>
> for static hovering shell non-geodesic LNIF observers at fixed r
>
> Note that g^1 is also the local frame invariant proper acceleration
> because {Einstein Connection}^000 = 0.
>
> 3. Confusions about potential in GR.
>
> If you look at the SSS metrics
>
> g00 ~ 1 + V(Newton)/c^2
>
> V(Newton) is the classical gravity potential energy per unit test mass.

This is a correspondence formula.

> On the other hand from the local gauge field theory fiber bundle POV
>
> Principle bundle gives the local gauge force field.
>
> Associated bundle gives the source field.
>
> In the standard model, the dynamical symmetry group G is an internal
> group like 1-parameter U(1), 3-parameter SU(2) & 8-parameter SU(3) so
> that the fiber is an internal space, or possibly extra space
> dimensions if you use string theory. The source fields are spinor
> lepton-quarks. The spacetime symmetry group S is a non-dynamical
> background.
> S =/= G.
>
> On the other hand, in 1916 GR the symmetry group G is the 10-
> parameter Poincare space-time group, or possibly the 16-parameter GL
> (4,R) group that includes the 15-parameter conformal group of Penrose
> massless twistors as a sub-group.
>
> However, in 1916 GR the torsion is zero, this means only the 4-
> parameter T4 subgroup of the Poincare group gives dynamically
> independent degrees of freedom of the geometrodynamic field that is
> the fabric of 4D space-time. The Lorentz group O(1,3) generators are
> redundant in that limit.

Coordinate invariance as a kind of gauge symmetry?

I think like many others in the field you are still confused about the
meaning of general covariance in GR.

>
> The Diff(4) GCT group is the locally-gauged T4 translation group
> generated by total 4-momentum.

Of course *mathematically* speaking coordinate transformations have
nothing at all to do with 4-momentu

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