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Spoonfeeding Field Equations



 
 
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  #1  
Old February 19th 13, 08:01 PM posted to sci.physics.relativity,sci.physics,sci.astro,sci.math
Koobee Wublee
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Posts: 815
Default Spoonfeeding Field Equations

On Feb 19, 7:44 am, Giovano di Bacco wrote:
Tom Roberts wrote:


G = T


To derive it, vary the Lagrangian density, R.


thanks, it seams you forgot the cosmological term


The Cosmological constant thing can be cloned off [T] where is it none
other than a negative mass density in vacuum --- just like the
possibility of such a case within the Poisson equation. shrug

Note: [G], [T] are matrices. In this case, they are both 4-by-4.

however, i do not intend to derive them by myself, since they already are
derived, they had one hundred years to do that


Deriving the field equations is extremely easy once you have the
Lagrangian. However, the Lagrangian that derives the field equations
has never been qualified as why it is a Lagrangian in the first place
and why the action it represents must be extremized. Since everything
is so bloodily sensitive to the Lagrangian, it is very ludicrous to
say the Lagrangian that derives the field equations is thoroughly
valid. shrug

strange one cannot find the worlds most famous field equations anywhere on
internet, not even here


As shocking as it may sound, that is because there are very few
physicists out there who actually understand the field equations.
They can look up the textbook and write down ([G] = [T]), but they
never can understand what [G] and [T] represent mathematically that
allow static, spherically symmetric, and asymptotically flat solutions
(such as the Schwarzschild metric) to be solved. shrug

For all practical applications, [T] is null, and the field equations
have never been verified when [T] is not null. The only instance
where [T] comes into play is cosmology where these clowns think they
can decide the wellbeing of the universe by tweaking [T] with the
Cosmological constant as its clone. shrug

In spherically symmetric polar coordinate system with static diagonal
metric, [G] consists of only 3 unique and ordinary differential
equations. Given the following spacetime geometry,

** ds^2 = c^2 M dt^2 – P dr^2 – Q dO^2

Where

** dO^2 = cos^2(Latitude) dLongitude^2 + dLatitude^2

Two of the 3 differential equations of [G] a

** - M @^2Q@r^2 / (P Q) + M (@Q/@r)^2 / (4 P Q^2) + M @P/r @Q/@r / (2
P^2 Q) + M / Q

** (@Q/@r)^2 / (4 Q^2) + @M/r @Q/@r / (2 M Q) - P / Q

The last one is much more complex. If you are not yet bored and
twisting Koobee Wublee’s arm hard enough, He will post it. Hope this
helps. shrug
  #2  
Old February 19th 13, 09:47 PM posted to sci.physics.relativity,sci.physics,sci.astro,sci.math
Koobee Wublee
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Posts: 815
Default Spoonfeeding Field Equations

On Feb 19, 12:01 pm, Giovano di Bacco wrote:
Koobee Wublee wrote:


The Cosmological constant thing can be cloned off [T] where is it none
other than a negative mass density in vacuum --- just like the
possibility of such a case within the Poisson equation. shrug


however, the absence of it would give unnecessary unbalance


Does the absence of a negative mass density give an imbalance in the
Poisson equation? shrug

The Cosmological constant represents a negative mass in vacuum, and
the concept of a negative mass is so absurd. shrug

Note: [G], [T] are matrices. In this case, they are both 4-by-4.


perfect, i like matrices more than i like tensors


In reality, if you treat tensors as matrices, you won’t go wrong.
shrug

Deriving the field equations is extremely easy once you have the
Lagrangian. However, the Lagrangian that derives the field equations
has never been qualified as why it is a Lagrangian in the first place
and why the action it represents must be extremized. Since everything
is so bloodily sensitive to the Lagrangian, it is very ludicrous to say
the Lagrangian that derives the field equations is thoroughly valid.
shrug


what other tool would you suggest instead of Lagrangian;


None. The Lagrangian is supposed to be the density of an action.
Extemization of this action results in Euler-Lagrange equations if
certain conditions are met. The field equations are not Euler-
Lagrange equations per say, but they represent the extremization of
this Einstein-Hilbert action whatever bull**** it might be. shrug

i am not as good
at english, what does shrug means, is it for good or is it an insult?


You are on your own on this philosophical inclination. shrug

As shocking as it may sound, that is because there are very few
physicists out there who actually understand the field equations.
They can look up the textbook and write down ([G] = [T]), but they never
can understand what [G] and [T] represent mathematically that allow
static, spherically symmetric, and asymptotically flat solutions (such
as the Schwarzschild metric) to be solved. shrug


i had a suspicion that they dont know what they are talking about when
they address the public (they thing we are fools)


You are very correct. They absolutely don’t know what they are
talking about. They also believe the subject is too complex. Through
this opportunity, they have attempted to make themselves as sages.
shrug

For all practical applications, [T] is null, and the field equations
have never been verified when [T] is not null. The only instance where
[T] comes into play is cosmology where these clowns think they can
decide the wellbeing of the universe by tweaking [T] with the
Cosmological constant as its clone. shrug


if T is null, the G is also null, ahmmm???


Yes, of course. shrug

In spherically symmetric polar coordinate system with static diagonal
metric, [G] consists of only 3 unique and ordinary differential
equations. Given the following spacetime geometry,


** ds^2 = c^2 M dt^2 – P dr^2 – Q dO^2


Where


** dO^2 = cos^2(Latitude) dLongitude^2 + dLatitude^2


Two of the 3 differential equations of [G] a


** - M @^2Q@r^2 / (P Q) + M (@Q/@r)^2 / (4 P Q^2) + M @P/r @Q/@r / (2
P^2 Q) + M / Q


** (@Q/@r)^2 / (4 Q^2) + @M/r @Q/@r / (2 M Q) - P / Q


where is the equal sign? = 0 ?


If ([T] = 0), then just nullify these differential equations. shrug

The last one is much more complex. If you are not yet bored and
twisting Koobee Wublee’s arm hard enough, He will post it. Hope this
helps. shrug


okay thanks, are you telling me that the famous 10 field equations reduce
to 3 simple homogeneous differential equations?


Yes, in this case it does. shrug

In a 4x4 matrix, there are 16 elements, and each element forms a
differential equation. If you think time and space are allowed to
intertwine, then there are 16 equations. If not, there are only 10
equations. However, due to natural symmetry, they reduce down to 10
and 7 equations respectively. Furthermore, if you only allow diagonal
metric, then there are only 4 equations. Finally, if the spherically
symmetric polar coordinate system is employed, that reduces further
into just 3 equations. Solving these 3 equations is a challenging and
daunting task. Imagine doing so with 16 equations. shrug

Finally, there are infinite solutions in which the Schwarzschild
metric is one of them. The Schwarzschild metric was derived by
Hilbert. A year or two before that in early 1916, Schwarzschild
derived a solution that does not manifest black holes. shrug
  #3  
Old February 20th 13, 08:03 AM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
Koobee Wublee
external usenet poster
 
Posts: 815
Default Spoonfeeding Field Equations

On Feb 19, 1:18 pm, Giovano di Bacco wrote:
Koobee Wublee wrote:


In a 4x4 matrix, there are 16 elements, and each element forms a
differential equation. If you think time and space are allowed to
intertwine, then there are 16 equations. If not, there are only 10
equations. However, due to natural symmetry, they reduce down to 10 and
7 equations respectively. Furthermore, if you only allow diagonal
metric, then there are only 4 equations. Finally, if the spherically
symmetric polar coordinate system is employed, that reduces further into
just 3 equations. Solving these 3 equations is a challenging and
daunting task. Imagine doing so with 16 equations. shrug


i am total confuses, how do i know what to intertwine, ahmmm???


Good question. There remains no proof that time and space can be
intertwined according to the general equation describing the spacetime
geometry since all practical applications call out for the diagonal
metric which says time and space do not intertwine. shrug

what happens in nature does not depend on my intertwine;


What is that again? shrug

16 or 3 equations does not really matter, since i feed them numerically
into a computer anyway, also symbolic, let the computer do the dirty job


These solutions all predict Newtonian results when the curvature of
spacetime is weak. What separate them apart are the extreme boundary
conditions. For example, the Schwarzschild metric manifests black
holes. shrug

Finally, there are infinite solutions in which the Schwarzschild metric
is one of them. The Schwarzschild metric was derived by Hilbert. A
year or two before that in early 1916, Schwarzschild derived a solution
that does not manifest black holes. shrug


how many metrics are there anyway??


An infinite of them that satisfy Newtonian law of gravity at weak
curvature in spacetime. However, each one predicts drastically
different manifestations at extrem conditions. shrug

and i suppose the Schwarzschild solution must be right


Assumptions are mostly wrong. You need experimental verifications.
shrug

since an attempt to modelled a blackhole would
crash a computer


Either you have an outdated computer in hardware or inept programmers
that have developed the software. shrug

have you a homepage with these equations in a readable form?


Sorry no --- not yet. What Koobee Wublee has given you you can write
down these differential equations to explore if the Schwarzschild
metric is indeed a solution or not and what other solutions are out
there. Oh, @/@x means partial derivative with respect to x. shrug

Hope this helps. shrug

Oh, by the way, why are you filtering out the newsgroups when
replying? Are you one of these Einstein Dingleberries with familiar
past who is trying to learn more about GR where piles of textbooks you
are sitting on do not give any comfortable closures? Yes, they are
all written to mystify and proliferating the bull**** in order for the
self-styled physicists to maintain their elite priesthood in status
quo. shrug

However, it is comforting to see an ex-Einstein-Dingleberry able to
learn about the truth. shrug



  #4  
Old February 26th 13, 09:34 PM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
Koobee Wublee
external usenet poster
 
Posts: 815
Default Spoonfeeding Field Equations

On Feb 25, 11:53 am, Giovano di Bacco wrote:
Koobee Wublee wrote:


They are [G]_00 (time) and [G]_11 (radial displacement) where [G] is the
matrix that makes up the Einstein tensor. [G]_22 (longitude) and [G]_33
(latitude) are identical. shrug


so is only kinda scaling,


What scaling? shrug

what about translation and rotation?


In this case, [G], the Einstein tensor, is written in its spherically
symmetric polar coordinate system. So, what translation and what
rotation? shrug

The field equations are discussed quite a bit. Not too many have
brought up the subject on how the Christoffel symbols are derived
since the Christoffel symbols are the basic building blocks to the
field equations. In fact, among physicists, the Christoffel symbols
are worshipped as a divine deity. Even fewer physicists nowadays
understand how the Christoffel symbols are derived, and you cannot
find a non-circular derivation in the textbooks any more. Fcvking
sad, no? The following tells what the scientific communities are
practicing. shrug

** FAITH IS LOGIC
** LYING IS TEACHING
** DECEIT IS VALIDATION
** NITWIT IS GENIUS
** OCCULT IS SCIENCE
** FICTION IS THEORY
** FUDGING IS DERIVATION
** PARADOX IS KOSHER
** WORSHIP IS STUDY
** BULL**** IS TRUTH
** ARROGANCE IS SAGE
** BELIEVING IS LEARNING
** IGNORANCE IS KNOWLEDGE
** MYSTICISM IS WISDOM
** SCRIPTURE IS AXIOM
** CONJECTURE IS REALITY
** HANDWAVING IS REASONING
** PLAGIARISM IS CREATIVITY
** PRIESTHOOD IS TENURE
** FRAUDULENCE IS FACT
** MATHEMAGICS IS MATHEMATICS
** INCONSISTENCY IS CONSISTENCY
** INTERPRETATION IS VERIFICATION

shrug
  #5  
Old March 5th 13, 02:38 AM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
1treePetrifiedForestLane
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Posts: 974
Default Spoonfeeding Field Equations

so, please, enlighten us, them & the other guy;
you can probably encode it in shruggz ... maybe,
it already is, like;
internet on for zero, internet off for one.

In this case, [G], the Einstein tensor, is written in its spherically
symmetric polar coordinate system. *So, what translation and what
rotation? *shrug

The field equations are discussed quite a bit. *Not too many have
brought up the subject on how the Christoffel symbols are derived
since the Christoffel symbols are the basic building blocks to the
field equations. *In fact, among physicists, the Christoffel symbols
are worshipped as a divine deity. *Even fewer physicists nowadays
understand how the Christoffel symbols are derived, and you cannot
find a non-circular derivation in the textbooks any more. *Fcvking
sad, no? *The following tells what the scientific communities are
practicing. *shrug

 




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