Science > Physics > Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime
| Topic: |
Science > Physics |
| User: |
"Jay R. Yablon" |
| Date: |
05 Dec 2005 10:09:32 AM |
| Object: |
Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
Hello to all:
I thank everyone here and on SPR who has enlightened me and others about the
problems
of applying Stokes' theorem to symmetric energy tensors in curved spacetime.
I have tried to summarize my understanding of this mathematically, in the
attached 3.5 page pdf file.
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
I'd appreciate your feedback on whether I am understanding this problem
correctly, and if so, I hope this will help others to understand this
problem also.
Thanks,
Jay.
_____________________________
Jay R. Yablon
Email:
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| User: "hanson" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
05 Dec 2005 04:37:05 PM |
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"brian a m stuckless" <bastuck@nf.sympatico.ca> wrote in message
news:4394B09A.3FE2@nf.sympatico.ca...
Jay R. Yablon's symmetric energy tensors in curved spacetime.
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
and his 4-momentum conservation via Quadruple Integrals ... ascending
summation of indexes and the wedge products... ....the density of k-directed
momentum per unit of ordinary volume. ... "type II" divergence, (as opposed to
the less harsh =/= to designate two like quantities which simply are not equal).
Therefore, T::: = 0 is a) not true, b) not a conservation law, and c), because T
::: = T:: G, ... not even independent of observers and coordinates.
[Brian A M Stuckless]
$ PLANCK solar system aliens.!!
$ My GUESS iSS STANDARD = 4*pi*Moo*(MAGNETiC length lo)*
mD = m1's CAViTY DisCHARGE mass of AMBiENT
$ NATURE wants science to have coherent GUESS iSS STANDARDs.!!
$ Go-fogo-a-go-go Google GROUP SEARCH < My BiGGER bang.!! >.!!
Re: THAT IAM circumcising the FORESKiNs of your hearts.!!
[hanson]
Brian, your solution is much easier to understand then Yablon's less
harsh "type II" divergence of two like quantities which simply are not equal,
despite your, Brian's, ambient discharges from them' aliens under your foreskin .
You guys are truly pioneers of things to come. I am impressed!
ahahaha... AHAHAHAHA... ahahaha... ahahanson
.
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| User: "Ken S. Tucker" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
05 Dec 2005 08:08:14 PM |
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Yes gentleman...more below...
hanson wrote:
"brian a m stuckless" <bastuck@nf.sympatico.ca> wrote in message
news:4394B09A.3FE2@nf.sympatico.ca...
Jay R. Yablon's symmetric energy tensors in curved spacetime.
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
and his 4-momentum conservation via Quadruple Integrals ... ascending
summation of indexes and the wedge products... ....the density of k-directed
momentum per unit of ordinary volume. ... "type II" divergence, (as opposed to
the less harsh =/= to designate two like quantities which simply are not equal).
Therefore, T::: = 0 is a) not true, b) not a conservation law, and c), because T
::: = T:: G, ... not even independent of observers and coordinates.
[Brian A M Stuckless]
$ PLANCK solar system aliens.!!
$ My GUESS iSS STANDARD = 4*pi*Moo*(MAGNETiC length lo)*
mD = m1's CAViTY DisCHARGE mass of AMBiENT
$ NATURE wants science to have coherent GUESS iSS STANDARDs.!!
$ Go-fogo-a-go-go Google GROUP SEARCH < My BiGGER bang.!! >.!!
Re: THAT IAM circumcising the FORESKiNs of your hearts.!!
[hanson]
Brian, your solution is much easier to understand then Yablon's less
harsh "type II" divergence of two like quantities which simply are not equal,
Brian, Hanson, you're both right, Jay threw a curve ball
known as "tetrads". (Weinberg Eq.(12.5.3)), and when
invoking tetrads that should be specified front end exactly
because of what you guys said, and I was confused too.
That darn tetrad notation sucks.
Here's what I suggest as a standard convention, the use
of "o" for the tetrad, for example, rewrite (12.5.3) as,
V' ^o_u = (& x^v / &x' ^u) V ^o_v (K1)
I select index "o" as the index symbol, to stand for
"orthogonal" as that part of the transformaton (the
euclidean part) that flows threw the transform unaffected
by the curvilinear CS's K' and K may be fielded in.
Therefore, transforming index "o" ,(euclidean) to index
" o' " in another euclidean system is like changing
metres to yards, i.e. it is arbituary and so has no
'physical' impact and may as well be excluded,
so that o == o' , that's physics.
Regards
Ken S. Tucker
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| User: "hanson" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
05 Dec 2005 09:02:29 PM |
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"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
news:1133834894.333330.301310@o13g2000cwo.googlegroups.com...
Yes gentleman...more below...
hanson wrote:
"brian a m stuckless" <bastuck@nf.sympatico.ca> wrote in message
news:4394B09A.3FE2@nf.sympatico.ca...
Jay R. Yablon's symmetric energy tensors in curved spacetime.
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
and his 4-momentum conservation via Quadruple Integrals ... ascending
summation of indexes and the wedge products... ....the density of k-directed
momentum per unit of ordinary volume. ... "type II" divergence, (as opposed to
the less harsh =/= to designate two like quantities which simply are not
equal).
Therefore, T::: = 0 is a) not true, b) not a conservation law, and c),
because T
::: = T:: G, ... not even independent of observers and coordinates.
[Brian A M Stuckless]
$ PLANCK solar system aliens.!!
$ My GUESS iSS STANDARD = 4*pi*Moo*(MAGNETiC length lo)*
mD = m1's CAViTY DisCHARGE mass of AMBiENT
$ NATURE wants science to have coherent GUESS iSS STANDARDs.!!
$ Go-fogo-a-go-go Google GROUP SEARCH < My BiGGER bang.!! >.!!
Re: THAT IAM circumcising the FORESKiNs of your hearts.!!
[hanson]
Brian, your solution is much easier to understand then Yablon's less
harsh "type II" divergence of two like quantities which simply are not equal,
[Ken]
Brian, Hanson, you're both right, Jay threw a curve ball
known as "tetrads". (Weinberg Eq.(12.5.3)), and when
invoking tetrads that should be specified front end exactly
because of what you guys said, and I was confused too.
That darn tetrad notation sucks.
Here's what I suggest as a standard convention, the use
of "o" for the tetrad, for example, rewrite (12.5.3) as,
V' ^o_u = (& x^v / &x' ^u) V ^o_v (K1)
I select index "o" as the index symbol, to stand for
"orthogonal" as that part of the transformaton (the
euclidean part) that flows threw the transform unaffected
by the curvilinear CS's K' and K may be fielded in.
Therefore, transforming index "o" ,(euclidean) to index
" o' " in another euclidean system is like changing
metres to yards, i.e. it is arbituary and so has no
'physical' impact and may as well be excluded,
so that o == o' , that's physics.
Regards
Ken S. Tucker
[hanson]
In your o == o' notation, provided that under unambiguous conditions,
and if and only if, or iff, which is to mean that something along the
monads of o =/= o' and not o/o' then and only then will it remain in the
purely abstract state of mathematical reformations and you cannot
conclude without further assertions that anything with no physical
impact constitutes what is meant by physics. Brilliant conclusion, Ken!
However, if you introduce, ad hoc or otherwise, sufficient octionions
the then arising, but not the emerging, Kunwoo Lee 3A-6 boundary
conditions do demand that said operatives will always remain outside
the realm of ponderable reality and remain property of pure abstractions
as is seen in the conjectures when reduced to trivial algebra without
dimensional attributes. --- Bourbaki first noted that in 62, when a new
kind of Dedekind cut was attempted that is still not solved to this very day.
This is phantasic, Ken. Thanks, dude.
hanson
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| User: "Ken S. Tucker" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
06 Dec 2005 01:55:13 PM |
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hanson wrote:
"Ken S. Tucker" <dynamics@vianet.on.ca> wrote in message
[Ken]
Brian, Hanson, you're both right, Jay threw a curve ball
known as "tetrads". (Weinberg Eq.(12.5.3)), and when
invoking tetrads that should be specified front end exactly
because of what you guys said, and I was confused too.
That darn tetrad notation sucks.
Here's what I suggest as a standard convention, the use
of "o" for the tetrad, for example, rewrite (12.5.3) as,
V' ^o_u = (& x^v / &x' ^u) V ^o_v (K1)
I select index "o" as the index symbol, to stand for
"orthogonal" as that part of the transformaton (the
euclidean part) that flows threw the transform unaffected
by the curvilinear CS's K' and K may be fielded in.
Therefore, transforming index "o" ,(euclidean) to index
" o' " in another euclidean system is like changing
metres to yards, i.e. it is arbituary and so has no
'physical' impact and may as well be excluded,
so that o == o' , that's physics.
Regards
Ken S. Tucker
[hanson]
In your o == o' notation, provided that under unambiguous conditions,
and if and only if, or iff, which is to mean that something along the
monads of o =/= o' and not o/o' then and only then will it remain in the
purely abstract state of mathematical reformations and you cannot
conclude without further assertions that anything with no physical
impact constitutes what is meant by physics. Brilliant conclusion, Ken!
Let me know if this link works...
http://groups.google.com/group/sci.physics.research/browse_frm/thread/8e2e60b47346f05a/6f750af0fe08807a?q=tetrad&rnum=1#6f750af0fe08807a
Arnold mentions some notational awkwardness with "tetrads", but
it's an interesting non-technical discussion.
However, if you introduce, ad hoc or otherwise, sufficient octionions
the then arising, but not the emerging, Kunwoo Lee 3A-6 boundary
conditions do demand that said operatives will always remain outside
the realm of ponderable reality and remain property of pure abstractions
as is seen in the conjectures when reduced to trivial algebra without
dimensional attributes. --- Bourbaki first noted that in 62, when a new
kind of Dedekind cut was attempted that is still not solved to this very day.
This is phantasic, Ken. Thanks, dude.
hanson
I'm inclined to agree. If GR can support spin 1/2, 3/2 fields,
as tetrad analysis seems to suggest, then characteristics
of sub-atomic particles, and more generally the quantum
aspects of those particles can merge with GR, very likely
as seamless as GR merges with the g-field we all know
and love.
I also think tetrad analysis is simpler and more physically
intuitive than the pure tensor analysis, but you can always
switch up to pure tensors.
I was able to use tetrad analysis in High school simply
because the Christoffel has one effective index, but in
tensors it has 3 effective indexs, which is more complex.
Basically a tetrad compares a straight ruler with a rubber
ruler, while a tensor compares a rubber ruler with itself.
So tetrad analysis is an extension of simple 2D differential
calculus, but unfortunately there really is not an elementary
level introduction to tetrads that I know of. It's treated as a
sophistication of tensors.
Currently there seems to be an explosion of interest in tetrad
applications, so if they lead to some easier way to understand
GR, I'm sure that could be taught as an advanced physics
option in HS.
Regards
Ken S. Tucker
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| User: "" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
07 Dec 2005 06:17:27 PM |
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Hi, I'm sorry to pollute this thread with my presence, but I can't see
where this thread originally began. Jay can you tell me what you are
working on at present. I'm not physically minded, but find the thread
fascinating without understanding any of the maths involved. Will
understanding how stress tensor behave give you an insight into how
energy is dispersed in our universe?
Thank you in advance for indulging me.
.
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| User: "Jay R. Yablon" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
07 Dec 2005 09:57:50 PM |
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Hi Charlie,
You need to be kinder to yourself; the Al Qaeda's may be pollution, you are
not.
This thread began when I asked people to look at
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
because I want to know if I am correctly understanding a particular problem
involving the use of (or inability to use) Stokes' theorem in served
spacetime. It is interesting to ask about how energy is distributed, but my
current pursuits are in a different direction.
I really have two balls in the air. First, I do need to go back and make
some corrections to my paper at:
http://arxiv.org/abs/gr-qc/0511050
Probably not enough tine to prepare and post a good rev 2.0 before the
holidays, but I need to clean up the treatment of the gravitational pseudo
tensor, I am going to pull the quantum mechanical discussion and just focus
on the classical results, and I want to add some materials about deriving
the classical Lorentz force law as a geodesic equation. The Lorentz force
law has been derived in many different ways; I think I have a new derivation
that will reveal matter, classically, to be best represented as an Euler
fluid. In particular, for the T^uv in equation (5.3), kappa_v=0 absent
magnetic monopoles converts into the Lorentz force law, which is how, e.g.,
an electron moves. Thus, the energy tensor (5.3) is the energy tensor for a
(classical) particle such as an electron. Details of the calculation are at
http://home.nycap.rr.com/jry/Papers/Lorentz%20Force%20for%20web%20post.pdf
on my web site at http://home.nycap.rr.com/jry/FermionMass.htm.
Second, I am hunting for a connection between general relativity and
Heisenberg uncertainty. I am living, eating, and breathing angular momentum
these days, since one needs ultimately to understand why there is a
(Planck's) constant of minimal angular momentum (I believe it is a constant
of integration from a differential conservation law = 0), since Planck's
constant is in dimensions of angular momentum, and since uncertainty entails
a product relationship between energy and time or momentum and space. At
minimum, I'd like to show a GR / HUP compatibility.
A third ball in the air is to go back to
http://arxiv.org/abs/hep-ph/0509223, and do a similar analysis for weak
interaction magnetic monopoles, which a preliminary calculation shows,
together with the .003 I have already, will give the total .005 NuTeV
anomaly. While it would be good to nail this on the nose, I feel less
urgency there because I have already told people how to do that and it is
just an extension of what I have done already. Just do for the Z^u what I
already did for the A^u vis-a-vis magnetic-mediating counterparts.
Hope to see you again on this thread soon.
Jay.
_____________________________
Jay R. Yablon
Email:
<charlie12345@hotmail.com> wrote in message
news:1133998764.424528.222230@g49g2000cwa.googlegroups.com...
Hi, I'm sorry to pollute this thread with my presence, but I can't see
where this thread originally began. Jay can you tell me what you are
working on at present. I'm not physically minded, but find the thread
fascinating without understanding any of the maths involved. Will
understanding how stress tensor behave give you an insight into how
energy is dispersed in our universe?
Thank you in advance for indulging me.
.
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| User: "brian a m stuckless" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
08 Dec 2005 12:47:51 AM |
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Again ..THERE is NO *ANGULAR* momentum in the GR EQUATiON.!!
(This is because the GR EQUATiON is NOT GR, it's EUCLiDiAN.)
So-called GR EQUATiON is PYTHAGORAS THEOREM a^2 = b^2 = c^2.
( p.s. There is NO AMGULAR momentum in EUCLiDiAN geometry. )
The GR coup has: E^2 = (mass m)^2 + (LiNEAR momentum pL)^2.
(CLEARLY ..there is NO "ANGULAR momentum pA" factor ..duh.)
2. The GUESS iSS Hamiltonian ENTHALPY E = m*c^2 + pL*c + pA*f1.
(Where, m = mass; pL = LiNEAR momentum; pA = ANGULAR momentum.)
FiNALLY ..THERE is NO *ANGULAR* momentum, in the GR EQUATiON.!!
Take a SABBATiCAL, jAY.
Brian A M Stuckless
<> >><> >><> >><> >><> ^
Jay R. Yablon wrote: > > Hi Charlie, >
You need to be kinder to yourself; the Al Qaeda's may be pollution,
you are not.
This thread began when I asked people to look at
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
because I want to know if I am correctly understanding a particular
problem involving the use of (or inability to use) Stokes' theorem
in served spacetime. It is interesting to ask about how energy is
distributed, but my current pursuits are in a different direction.
I really have two balls in the air. First, I do need to go back
and make some corrections to my paper at:
http://arxiv.org/abs/gr-qc/0511050 >
Probably not enough tine to prepare and post a good rev 2.0 before
the holidays, but I need to clean up the treatment of the
gravitational pseudo tensor, I am going to pull the quantum
mechanical discussion and just focus on the classical results, and
I want to add some materials about deriving the classical Lorentz
force law as a geodesic equation. The Lorentz force law has been
derived in many different ways; I think I have a new derivation
that will reveal matter, classically, to be best represented as an
Euler fluid. In particular, for the T^uv in equation (5.3),
kappa_v=0 absent magnetic monopoles converts into the Lorentz force
law, which is how, e.g., an electron moves. Thus, the energy tensor
(5.3) is the energy tensor for a (classical) particle such as an
electron. Details of the calculation are at
http://home.nycap.rr.com/jry/Papers/Lorentz%20Force%20for%20web%20post.pdf
on my web site at http://home.nycap.rr.com/jry/FermionMass.htm.
Second, I am hunting for a connection between general relativity
and Heisenberg uncertainty. I am living, eating, and breathing
angular momentum these days, since one needs ultimately to understand
why there is a (Planck's) constant of minimal angular momentum
(I believe it is a constant of integration from a differential
conservation law = 0), since Planck's constant is in dimensions of
angular momentum, and since uncertainty entails a product
relationship between energy and time or momentum and space. At
minimum, I'd like to show a GR / HUP compatibility.
insert ..see top of PAGE, jAY.!!
A third ball in the air is to go back to
http://arxiv.org/abs/hep-ph/0509223, and do a similar analysis for
weak interaction magnetic monopoles, which a preliminary calculation
shows, together with the .003 I have already, will give the total
.005 NuTeV anomaly. While it would be good to nail this on the nose,
I feel less urgency there because I have already told people how to
do that and it is just an extension of what I have done already.
Just do for the Z^u what I already did for the A^u vis-a-vis
magnetic-mediating counterparts.
Hope to see you again on this thread soon.
Jay. > > _____________________________
Jay R. Yablon > Email:
<charlie12345@hotmail.com> wrote in message
news:1133998764.424528.222230@g49g2000cwa.googlegroups.com...
Hi, I'm sorry to pollute this thread with my presence, but I can't see
where this thread originally began. Jay can you tell me what you are
working on at present. I'm not physically minded, but find the thread
fascinating without understanding any of the maths involved. Will
understanding how stress tensor behave give you an insight into how
energy is dispersed in our universe?
Thank you in advance for indulging me. > >
.
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| User: "Jay R. Yablon" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
08 Dec 2005 06:31:24 AM |
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"brian a m stuckless" <bastuck@nf.sympatico.ca> wrote in message
news:4397D5E7.90@nf.sympatico.ca...
Again ..THERE is NO *ANGULAR* momentum in the GR EQUATiON.!!
(This is because the GR EQUATiON is NOT GR, it's EUCLiDiAN.)
So-called GR EQUATiON is PYTHAGORAS THEOREM a^2 = b^2 = c^2.
( p.s. There is NO AMGULAR momentum in EUCLiDiAN geometry. )
The GR coup has: E^2 = (mass m)^2 + (LiNEAR momentum pL)^2.
(CLEARLY ..there is NO "ANGULAR momentum pA" factor ..duh.)
2. The GUESS iSS Hamiltonian ENTHALPY E = m*c^2 + pL*c + pA*f1.
(Where, m = mass; pL = LiNEAR momentum; pA = ANGULAR momentum.)
FiNALLY ..THERE is NO *ANGULAR* momentum, in the GR EQUATiON.!!
Take a SABBATiCAL, jAY.
Brian A M Stuckless
<> >><> >><> >><> >><> ^
Well, Brian I looking forward to a nice vacation at the end of the year.
I suggest you crack open Misner, Thorne and Wheeler to page 156 where they
develop angular momentum in flat spacetime.
Jay.
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| User: "brian a m stuckless" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
08 Dec 2005 12:36:32 PM |
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$ "YOU crack open Misner, Thorne and Wheeler to page 156":
Seems Thorne & Wheeler forgot to re-adjust the GR EQUATiON.!!
(There's still NO angular momentum term, in the GR EQUATiON.)
The GR coup has: E^2 = (mass m)^2 + (LiNEAR momentum pL)^2.
(CLEARLY ..there is NO "ANGULAR momentum pA" factor ..duh.)
The GUESS iSS Hamiltonian ENTHALPY E = m*c^2 + pL*c + pA*f1.
Note, m = mass; pL = LiNEAR momentum; pA = ANGULAR momentum.
iRONiCALLY, there's no mass in GR; G_uv = T_uv isN'T equated.
Light VELOCiTY c increases iNVERSELY with PATH particle-count.
Brian A M Stuckless
<> >><> >><> >><> >><> ^
Jay R. Yablon wrote: >
"brian a m stuckless" <bastuck@nf.sympatico.ca> wrote in message
news:4397D5E7.90@nf.sympatico.ca...
Again ..THERE is NO *ANGULAR* momentum in the GR EQUATiON.!!
(This is because the GR EQUATiON is NOT GR, it's EUCLiDiAN.)
So-called GR EQUATiON is PYTHAGORAS THEOREM a^2 = b^2 + c^2.
( p.s. There is NO AMGULAR momentum in EUCLiDiAN geometry. )
The GR coup has: E^2 = (mass m)^2 + (LiNEAR momentum pL)^2.
(CLEARLY ..there is NO "ANGULAR momentum pA" factor ..duh.)
2. The GUESS iSS Hamiltonian ENTHALPY E = m*c^2 + pL*c + pA*f1.
(Where, m = mass; pL = LiNEAR momentum; pA = ANGULAR momentum.)
FiNALLY ..THERE is NO *ANGULAR* momentum, in the GR EQUATiON.!!
Take a SABBATiCAL, jAY.
Brian A M Stuckless
<> >><> >><> >><> >><> ^
Well, Brian I looking forward to a nice vacation at the end of the year.
I suggest you crack open Misner, Thorne and Wheeler to page 156
where they develop angular momentum in flat spacetime.
..dooOPs.!!
Jay.
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| User: "The TimeLord" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
04 Jan 2006 01:00:50 AM |
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On Thu, 08 Dec 2005 06:47:51 +0000, brian a m stuckless
<bastuck@nf.sympatico.ca> wrote in <4397D5E7.90@nf.sympatico.ca>:
Again ..THERE is NO *ANGULAR* momentum in the GR EQUATiON.!!
(This is because the GR EQUATiON is NOT GR, it's EUCLiDiAN.)
Have you even bothered to read the *.pdf that this part of
the discussion is based on? It's at
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
I know that I've missed the major part of the thread, but clearly
you are denegrating something that you have not bothered to find
out about.
So-called GR EQUATiON is PYTHAGORAS THEOREM a^2 = b^2 = c^2.
Not in curved space-time.
( p.s. There is NO AMGULAR momentum in EUCLiDiAN geometry. )
Could have fooled reality physics.
L = Cross[r,p] in flat space (Euclidian geometry), which is
in every basic physics text.
The GR coup has: E^2 = (mass m)^2 + (LiNEAR momentum pL)^2.
(CLEARLY ..there is NO "ANGULAR momentum pA" factor ..duh.)
That has nothing to do with the topic of energy conservation
in curved spacetime, DUH!
[...]
Jay R. Yablon wrote: > > Hi Charlie, >
[...]
This thread began when I asked people to look at
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
See, I didn't miss as much as Brian Stuckless.
[...]
To Jay Yablon:
Sounds interesting, but I'll have to review the stuff you posted.
Nevertheless, from what I have seen (preliminary), you seem to be
on the right track.
[...]
Second, I am hunting for a connection between general relativity
and Heisenberg uncertainty. I am living, eating, and breathing
Good luck! Seriously.
Most attempts at that assume that Quantum Mechanics is more
fundamental than Relativity. I think that view should be
reevaluated. Some of the stuff going on with people I hang out
with, seem to indicate that nonlinear Relativity might actually
be more fundamental than QM, ie QM might be derivable from
Relativity. However, so far nothing is set in stone.
[...]
<charlie12345@hotmail.com> wrote in message
news:1133998764.424528.222230@g49g2000cwa.googlegroups.com...
[...]
fascinating without understanding any of the maths involved.
Will
understanding how stress tensor behave give you an insight into how
energy is dispersed in our universe?
[...]
.
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| User: "brian a m stuckless" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
04 Jan 2006 02:59:48 AM |
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My GUESS iSS Hamiltonian Gibbs LaGrangian Helmoltz Stuckless analysis:
[Note pL=LiNEAR & pA=ANGULAR, momenta; And fA & fL related frequency.]
[Note nL=LiNEAR & nA=ANGULAR, NUMBERS; GUESS energy L the LaGrangian.]
m1*v1^2 m1
GUESS ENTHALPY E = m1*c^2 + {(-- - --)*(-- + 1)} + eV
2 M1
nA*{mph}*ls*c^2 m1*v1^2
= m1*c^2 + (-- -- --- -- --) - (-- - --)
rA 2
= m1*c^2 + ( pL*c ) + ( pA*fA )
= m1*c^2 + ( h*fL ) + ( nA*hbar*fA )
= m1*c^2 + ( pL*c ) + ( nA*hbar*fA )
= m1*c^2 + ( h*fL ) + ( pA*fA )
= eM + ( LaGrangian, L ) + eV
= eM + L + eV
= eM + eK
= eG + eK - eV
= eG + L.
Note:
EiTHER, energy + eV, OR energy - (m1*v1^2 / 2) ..NOT BOTH, AT ONCE.
[ This means that in any calculation you SWiTCH one to the OTHER. ]
- eV = + (m1*v1^2 / 2) = (E - eK - eG) = (L - eK) = (- E + L + eM).
Where-as:
+ eV = - (m1*v1^2 / 2) = (E - eM - L) = (eK - L) = (- E + eK + eG).
[ BOTH + eV and - (m1*v1^2 / 2) are CHARGEs, but DiFFERENT SiGNs. ]
[ BECAUSE + eV and - (m1*v1^2 / 2) are BOTH, Volt*Ampere*seconds. ]
$ Arithmetically speaking:
CLEARLY the BiGGEST DiFFERENCE, between - eV & + eV, is TWO (2) eV.
[ This is because ELECTRONs of mass leave electron HOLEs of mass. ]
[ There is NO OTHER WAY, to account for ELECTRON HOLEs phenomena. ]
[ The GUESS iSS test ELECTRON HOLE is a CAViTY of CHARGE of mass. ]
There's NO ANGULAR momentum in the General Relativity GTR equation.
There's NO CENTRAL mass QUANTiTY in the ANGULAR momentum equation.
UNanswered QUESTiON put to GR (gtr) Tivity, over, over & over..
Note: Angular momentum pA
=[(PLANET-like mass)*(orbit radius)*(velocity)];
[..with units of -> kilogram*(meter)^2/second].
Q. There is NO CENTRAL-mass quantity; WHY is that.?
There's NO mass in General Relativity, mathematically speaking.!!
PROFOUNDLY, iRONiCALLY, there's NO GR "space-time-curvature".
(The GR, G_uv = T_uv CANNOT be DEFiNED, in TERMs of "mass".!!)
possibly other factors relating to density and momentum, -=-
There is NO "mass -=- density and momentum", in GEOMETRY, duh.
G*Mp*{mph} C1*(C2a*C2b) C1
-- --- -- = -- -- -- -- = -- = 4*pi*Vu*{e}*lo = 4*pi*#*{e}*c ;
(n - 1) C2^2*c c
C1*(p1*p2)*c C1*({e}^2*c^2)*c C1(q1*q2)*c^3 C1*{e}*c
= -- --- -- -- = -- -- ---- -- -- = -- - --- - -- = -- -- --
C2^2 C2^2 C2^2 C2 ..!!
GENERAL GUESS photon mass [mph] = nA*{mph}*ls / rA = m1 = mD / n.
PARTiCULAR iSS photon mass {mph} = 2*pi*h / tp*c^2 = hbar / ls*c
= hbar / ts*c^2 = h / 2*pi*ls*c.
GRAViTY acceleration g = (g1 + g2) = G*(M1 + m2) / (n - 1)*d^2:
|G*(M1 + m2)| |4*(pi)^2*d| | 4*(pi)^2*r1 4*(pi)^2*r2 |
|-- -- -- --| = |-- -- - --| = |(-- -- -- --) + (-- -- -- --)|
|(n - 1)*d^2| | T^2 | | T^2 T^2 |
|4*(pi)^2*lbob| |4*(pi)^2*(r1 + r2)|
= |-- -- - -- --| = |-- -- --- -- -- --| = g1 + g2 = gravity g.
| (tbob)^2 | | T^2 |
$ M1*v1^2 m2*v2^2
THEN: -- - -- = -- - -- = M1*r1 = m2*r2
$ g1 g2.
NOTE: Mp*lp = {mph)*ls = me*wls = Moo*loo / 4*pi = hbar / c.
Note therefore, as radii r1 & r2 vary and/or M1 & m2 vary, etc,
then, BOTH, M1 & m2 can *TOUCH down* ON each other's SURFACE.!!
Dimension, d = r1 + r2 = centre-to-centre distance, of M1 & m2.
This isN'T fluffy-level math; This is My WHOLE-wheat arithmetic.
The GUESS iSS GR G_uv = T_uv = Ga / G = 1 / (n - 1) = G_relative.
CLOSE: Brian A M Stuckless ..over & OUT.
^
GUESS RESTmass*c^4=(iNTRiNSiC energy e)*c^2=(mol part)*K*Volt*meter.
My GUESS iSS STANDARD
< The STANDARD set. >
/\
__ _\/_ __
\_\/_/\_\/_/
/\_\/_/\ ("`-/")_.-'"``-._
_\/_/\_\/_ \. . `; -._ )-;-, `)
/_/\_\/_/\_\ \ / (v_,) _ )`-.\ ``-'
/\ - O - _ .- _..-_/ / ((.'
\/ / \ ((,.-' ((,/ By: Toe.!
$$ By deeds you know them.!! >><> >><> >><> >><> >><>
BEHOLD, IAM THAT IAM hath circumcised the FORESKiNs of your hearts.!!
$ :-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'`
$ ____ _ _ _ _
$ | _ \ | | ___ _ __ | | __ | | | |
$ | |_) | | | / _ \ | '_ \ | |/ / | | | |
$ My _ENORMOUS_ | __/ | | | (_) | | | | | | < _ |_| |_|
$ |_| |_| \___/ |_| |_| |_|\_\ (_) (_) (_)
$
$ :*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,_,.-:*'``'*:-.,_
BEHOLD, IAM THAT IAM WHOLLY WHOLLY WHOLLY He ..and no more is more.!!
PD wrote: > > Len Gaasenbeek wrote: > > > >
Actually, "relativistic mass" is an outmoded term. Instead,
physicists no longer think there is a linear relationship
between kinetic energy absorbed and linear speed (squared).
...................................................
To Eric,
So where does the additional kinetic energy of the particle
come from?
Len.
Come from? It comes from the agent that poured energy into it. How do
you describe an object's kinetic energy? It is
sqrt[(mc^2)^2 + (pc)^2] - mc^2.
In this expression, the only thing that changes
as you pour energy in is p.
[Nomen Clature] insert ..see top of PAGE.!!
This in spite of the fact that relativists agree with me, that all
relativistic particles spin around their own spin axis as they travel
along,
which contributes to their overall kinetic energy.
The problem is, the spin seems to stay the same regardless of the
amount of energy absorbed.
....................................................
To Eric,
The spin of a relativistic particle increases as it continues to absorb
energy in a particle accelerator. It is a measure of its temperature. You
are wrong again.
Len.
The temperature of particles in an acceleration is actually quite cold.
See "stochastic cooling".
The spin of particles is quite easily measurable by their coupling to
an applied magnetic field. There is no measurable increase in spin in
such magnetic fields.
PD
Re: Time dilation etc.
The TimeLord wrote:
Again ..THERE is NO *ANGULAR* momentum in the GR EQUATiON.!!
(This is because the GR EQUATiON is NOT GR, it's EUCLiDiAN.)
So-called GR EQUATiON is PYTHAGORAS THEOREM a^2 = b^2 = c^2.
( p.s. There is NO AMGULAR momentum in EUCLiDiAN geometry. )
Could have fooled reality physics.
The GR coup has: E^2 = (mass m)^2 + (LiNEAR momentum pL)^2.
(CLEARLY ..there is NO "ANGULAR momentum pA" factor ..duh.)
Jay R. Yablon wrote: > > Hi Charlie, > -=-
Second, I am hunting for a connection between general relativity
and Heisenberg uncertainty. I am living, eating, and breathing
Good luck! Seriously.
Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime.
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| User: "brian a m stuckless" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
08 Dec 2005 12:51:15 AM |
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brian a m stuckless wrote:
Again ..THERE is NO *ANGULAR* momentum in the GR EQUATiON.!!
(This is because the GR EQUATiON is NOT GR, it's EUCLiDiAN.)
So-called GR EQUATiON is PYTHAGORAS THEOREM a^2 = b^2 + c^2.
( p.s. There is NO AMGULAR momentum in EUCLiDiAN geometry. )
The GR coup has: E^2 = (mass m)^2 + (LiNEAR momentum pL)^2.
(CLEARLY ..there is NO "ANGULAR momentum pA" factor ..duh.)
2. The GUESS iSS Hamiltonian ENTHALPY E = m*c^2 + pL*c + pA*f1.
(Where, m = mass; pL = LiNEAR momentum; pA = ANGULAR momentum.)
FiNALLY ..THERE is NO *ANGULAR* momentum, in the GR EQUATiON.!!
Take a SABBATiCAL, jAY.
Brian A M Stuckless
<> >><> >><> >><> >><> ^
Jay R. Yablon wrote: > > Hi Charlie, >
You need to be kinder to yourself; the Al Qaeda's may be pollution,
you are not.
This thread began when I asked people to look at
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
because I want to know if I am correctly understanding a particular
problem involving the use of (or inability to use) Stokes' theorem
in served spacetime. It is interesting to ask about how energy is
distributed, but my current pursuits are in a different direction.
I really have two balls in the air. First, I do need to go back
and make some corrections to my paper at:
http://arxiv.org/abs/gr-qc/0511050 >
Probably not enough tine to prepare and post a good rev 2.0 before
the holidays, but I need to clean up the treatment of the
gravitational pseudo tensor, I am going to pull the quantum
mechanical discussion and just focus on the classical results, and
I want to add some materials about deriving the classical Lorentz
force law as a geodesic equation. The Lorentz force law has been
derived in many different ways; I think I have a new derivation
that will reveal matter, classically, to be best represented as an
Euler fluid. In particular, for the T^uv in equation (5.3),
kappa_v=0 absent magnetic monopoles converts into the Lorentz force
law, which is how, e.g., an electron moves. Thus, the energy tensor
(5.3) is the energy tensor for a (classical) particle such as an
electron. Details of the calculation are at
http://home.nycap.rr.com/jry/Papers/Lorentz%20Force%20for%20web%20post.pdf
on my web site at http://home.nycap.rr.com/jry/FermionMass.htm.
Second, I am hunting for a connection between general relativity
and Heisenberg uncertainty. I am living, eating, and breathing
angular momentum these days, since one needs ultimately to understand
why there is a (Planck's) constant of minimal angular momentum
(I believe it is a constant of integration from a differential
conservation law = 0), since Planck's constant is in dimensions of
angular momentum, and since uncertainty entails a product
relationship between energy and time or momentum and space. At
minimum, I'd like to show a GR / HUP compatibility.
insert ..see top of PAGE, jAY.!!
A third ball in the air is to go back to
http://arxiv.org/abs/hep-ph/0509223, and do a similar analysis for
weak interaction magnetic monopoles, which a preliminary calculation
shows, together with the .003 I have already, will give the total
.005 NuTeV anomaly. While it would be good to nail this on the nose,
I feel less urgency there because I have already told people how to
do that and it is just an extension of what I have done already.
Just do for the Z^u what I already did for the A^u vis-a-vis
magnetic-mediating counterparts.
Hope to see you again on this thread soon.
Jay. > > _____________________________
Jay R. Yablon > Email:
<charlie12345@hotmail.com> wrote in message
news:1133998764.424528.222230@g49g2000cwa.googlegroups.com...
Hi, I'm sorry to pollute this thread with my presence, but I can't see
where this thread originally began. Jay can you tell me what you are
working on at present. I'm not physically minded, but find the thread
fascinating without understanding any of the maths involved. Will
understanding how stress tensor behave give you an insight into how
energy is dispersed in our universe?
Thank you in advance for indulging me. > >
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| User: "Ken S. Tucker" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
05 Dec 2005 08:47:44 PM |
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Ken S. Tucker wrote:
Yes gentleman...more below...
hanson wrote:
"brian a m stuckless" <bastuck@nf.sympatico.ca> wrote in message
news:4394B09A.3FE2@nf.sympatico.ca...
Jay R. Yablon's symmetric energy tensors in curved spacetime.
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
and his 4-momentum conservation via Quadruple Integrals ... ascending
summation of indexes and the wedge products... ....the density of k-directed
momentum per unit of ordinary volume. ... "type II" divergence, (as opposed to
the less harsh =/= to designate two like quantities which simply are not equal).
Therefore, T::: = 0 is a) not true, b) not a conservation law, and c), because T
::: = T:: G, ... not even independent of observers and coordinates.
[Brian A M Stuckless]
$ PLANCK solar system aliens.!!
$ My GUESS iSS STANDARD = 4*pi*Moo*(MAGNETiC length lo)*
mD = m1's CAViTY DisCHARGE mass of AMBiENT
$ NATURE wants science to have coherent GUESS iSS STANDARDs.!!
$ Go-fogo-a-go-go Google GROUP SEARCH < My BiGGER bang.!! >.!!
Re: THAT IAM circumcising the FORESKiNs of your hearts.!!
[hanson]
Brian, your solution is much easier to understand then Yablon's less
harsh "type II" divergence of two like quantities which simply are not equal,
Brian, Hanson, you're both right, Jay threw a curve ball
known as "tetrads". (Weinberg Eq.(12.5.3)), and when
invoking tetrads that should be specified front end exactly
because of what you guys said, and I was confused too.
That darn tetrad notation sucks.
Here's what I suggest as a standard convention, the use
of "o" for the tetrad, for example, rewrite (12.5.3) as,
V' ^o_u = (& x^v / &x' ^u) V ^o_v (K1)
I select index "o" as the index symbol, to stand for
"orthogonal" as that part of the transformaton (the
euclidean part) that flows threw the transform unaffected
by the curvilinear CS's K' and K may be fielded in.
Therefore, transforming index "o" ,(euclidean) to index
" o' " in another euclidean system is like changing
metres to yards, i.e. it is arbituary and so has no
'physical' impact and may as well be excluded,
so that o == o' , that's physics.
Regards
Ken S. Tucker
Ps: I think Jay's (I) is a tetrad and (II) is the usual
expression, maybe Jay will clear that up later.
Ken
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| User: "Sue..." |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
06 Dec 2005 08:40:31 AM |
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Jay R. Yablon wrote:
Hello to all:
I thank everyone here and on SPR who has enlightened me and others about the
problems
of applying Stokes' theorem to symmetric energy tensors in curved spacetime.
I have tried to summarize my understanding of this mathematically, in the
attached 3.5 page pdf file.
http://home.nycap.rr.com/jry/Papers/Energy%20Tensor%20Divergence.pdf
I'd appreciate your feedback on whether I am understanding this problem
correctly, and if so, I hope this will help others to understand this
problem also.
Thanks,
Jay.
<< Is this an accurate summary of the discussion we have been having?
The maths are way over my head but you are asking the right questions.
Historically... there is some sloppy interchange of time space and
energy.
I believe your analysis with integral forms rather than differential
wrt time (dt) can clear the air about problems with the Schwartzchild
solution which has in it the absurd notion that clocks=accelerometers.
They are similar... but not equivalent.
Keep up the good work. :-)
Sue...
_____________________________
Jay R. Yablon
Email:
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| User: "Jay R. Yablon" |
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| Title: Re: Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime |
07 Dec 2005 10:46:04 PM |
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The maths are way over my head but you are asking the right questions.
Historically... there is some sloppy interchange of time space and
energy.
I believe your analysis with integral forms rather than differential
wrt time (dt) can clear the air about problems with the Schwartzchild
solution which has in it the absurd notion that clocks=accelerometers.
They are similar... but not equivalent.
Keep up the good work. :-)
Sue...
Thanks Sue. Sorry not to reply sooner; focusing on my day job these days.
Jay.
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