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Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime

Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime - Physics Forum

Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.


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  #1  
Old 12-05-2005, 04:09 PM
Jay R. Yablon
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Default 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.

[Only registered users see links. ]

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: [Only registered users see links. ]


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  #2  
Old 12-05-2005, 10:37 PM
hanson
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime

"brian a m stuckless" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
[Brian A M Stuckless]
[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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  #3  
Old 12-06-2005, 02:08 AM
Ken S. Tucker
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime

Yes gentleman...more below...

hanson wrote:

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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  #4  
Old 12-06-2005, 02:47 AM
Ken S. Tucker
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime


Ken S. Tucker wrote:

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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  #5  
Old 12-06-2005, 03:02 AM
hanson
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime

"Ken S. Tucker" <[Only registered users see links. ].ca> wrote in message
news:1133834894.333330.301310@o13g2000cwo.googlegr oups.com...
[Ken]
[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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  #6  
Old 12-06-2005, 02:40 PM
Sue...
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime


Jay R. Yablon wrote:
<< 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...


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  #7  
Old 12-06-2005, 07:55 PM
Ken S. Tucker
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime


hanson wrote:


Let me know if this link works...

[Only registered users see links. ]

Arnold mentions some notational awkwardness with "tetrads", but
it's an interesting non-technical discussion.


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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  #8  
Old 12-08-2005, 12:17 AM
charlie12345@hotmail.com
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime

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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  #9  
Old 12-08-2005, 03:57 AM
Jay R. Yablon
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime

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

[Only registered users see links. ]

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:

[Only registered users see links. ]

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
[Only registered users see links. ]
on my web site at [Only registered users see links. ].

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
[Only registered users see links. ], 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: [Only registered users see links. ]
<[Only registered users see links. ]> wrote in message
news:1133998764.424528.222230@g49g2000cwa.googlegr oups.com...


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  #10  
Old 12-08-2005, 04:46 AM
Jay R. Yablon
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Default Energy Tensor Divergences and Gauss / Stokes in Curved Spacetime

>
Thanks Sue. Sorry not to reply sooner; focusing on my day job these days.
Jay.


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