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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
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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
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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
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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
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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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