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Re: Spoonfeeding Field Equations
Posted:
Feb 19, 2013 3:47 PM
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On Feb 19, 12:01 pm, Giovano di Bacco <gdb...@gmail.com> 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 bullshit 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] are:
>
> > ** - 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>
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