My take on dark energy, flipping the perfect fluid stress energy tensor

[JMessenger]

Avoiding the maths, I am actually doing nothing but inverting the perfect fluid tensor. This would make no different predictions than the [math]\Lambda CDM[/math] model, except you would still have to add in extra curvature to account for the dark matter. This is just mathematically consistent, whereas the current model does not seem to be mathematically, logically or physically consistent. If you happen to know whether subtracting [math]G_{\mu\nu}[/math] from [math]\Lambda[/math] has ever been historically discussed, please let me know as I cannot find it and seems to be too simple of an explanation not to have been proposed before.

 

Particles vs Waves

 

The Einstein Field Equations

Four dimensional generic functions with a constant of integration

 

[math]R_{\mu \nu}-\frac{1}{2}g_{\mu \nu}R=g_{\mu \nu}\Lambda+G_{\mu \nu}[/math]

 

The Fundamental Theorem of Calculus

 

Let [math] \frac{\partial f_{1}}{\partial x_{\mu}}= - \frac{\partial f_{2}}{\partial x_{\mu}} [/math] and [math] \int f_{1}\partial x_{\mu}=\int (C-f_{2})\partial x_{\mu} [/math]

 

 

 

 

Calculus has the limitation, in that a generic function with a constant of integration, has two possible ways in which to measure the exact same area. Any physical theory based off calculus must take this into consideration.

 

If Newton's G and speed of light c are missing, assume normalized G=c=1

 

General Relativity

Wave Theory

Particles

Waves

 

[math]R_{\mu \nu}-\frac{1}{2}g_{\mu \nu}R=G_{\mu \nu}=f_{1}[/math]

[math]R_{\mu \nu}-\frac{1}{2}g_{\mu \nu}R=g_{\mu \nu}\Lambda-G_{\mu \nu}=C-f_{2}[/math]

 

Ideal Fluid Equation

[math]T_{\mu \nu}=\left(\rho + \frac{p}{c^{2}}\right)\mu_{\mu} \mu_{\nu}+p\eta_{\mu \nu}[/math]

 

 

 

Stress energy tensor of positive energy density "particle"

Stress energy tensor of a reduced energy density "wave'

[math]T_{\mu \nu}=[-\rho,p,p,p][/math]

[math]L_{\mu \nu}=[C_\rho - \rho,-C_p +p,-C_p +p,-C_p +p][/math]

 

 

Heisenberg Uncertainty Principle and de Broglie matter waves

The more precisely the position of some particle is determined,

the less precisely its momentum can be known, and vice versa.

 

Newtonian Gradient Approximation

Pre1998

[math]\vec{g}=-\nabla\Phi=-\frac{GM}{r^{2}}\hat{\vec{r}}[/math]

Post 1998

[math]\vec{g}=-\nabla\Phi=-\frac{GM}{r^{2}}\hat{\vec{r}}+\frac{\Lambda c^{2}r}{3}\hat{\vec{r}}[/math]

[math]\vec{g}=-\nabla\Phi=-\frac{\Lambda_{\mathrm{vac}} c^{2}r}{6}\hat{\vec{r}}+\frac{G\rho_{\mathrm{res}}V}{r^{2}}\hat{\vec{r}}[/math]

 

 

The accelerating expansion is due to a "dark energy", which opposes attractive

action-at-a-distance Newtonian gravity, and is most likely the cosmological constant.

Prior to the discovery of the accelerating expansion, all matter in the universe attracted all other matter in the universe.

If one integrates the energy for the quantum vacuum down to the Planck length, the amount of energy

that should gravitate (as Einstein states that all energy and mass gravitate) could be [math]10^{120}[/math] larger

than what is empirically observed.

The majority of mass is not in the nucleus of an atom, but in the large empty spaces outside of it.

Other theory is "quintessence" (old name for the aether).

If perfect fluid stress energy tensor is flipped, gravity is more of a reduced repulsion between "masses", than an increasing attraction.

At the distance determined by [math]\Lambda[/math], the repulsion is no longer reduced,

the symmetric wave functions are no longer affected by other wave functions, and regions

that are not gravitationally bound to each other become repulsive.

The amount of gravity would probably be due to wave superposition and density, and gives the value for the gravitational field strength. Should a virtual particle pair pop into existence, and then back out, they only exhibit gravitational distortion while in existence.

 

 

No known technique provides a compelling solution for the cosmological constant problem.

It does not appear that changing the concept of [math]G_{\mu\nu}[/math] has been attempted.

My link

Edited June 25, 2012 by JMessenger

[JMessenger]

So, can [math]G_{\mu\nu}[/math] in Einstein's field equations ever be negative?

 

 

In both cases, positive or negative, a difference in the density (and pressures) of a perfect fluid is equated to the curvature tensor. This is the stress energy tensor. This difference at a point causes stress outside the immediate vicinity of it, which is reflected in a change of the coordinate system. Where the coordinate system was Euclidean (flat), it no longer is. The greater the change in the density of the perfect fluid, the greater the change away from a flat coordinate system. The equations state that the curvature away from flat would be interpreted for two regions that contain a derivative of perfect fluid density into a "force" where they tend to come together. One case would consider this as an attraction between the two regions, the other would consider that the repulsion between the two regions has decreased. The defining difference between the two is the accelerating expansion. One case considers the accelerating expansion as most likely caused by an underlying energy that opposes the attractive gravity, whereas the other case simply considers the constant of integration as the point where the repulsion is no longer reduced by the presence of a change in density of a perfect fluid in another region.

 

AFAIK, particle-wave duality is an accepted phenomenon, as is now the quantum vacuum. In addition, most of the "mass" seems to not be within the nucleus of an atom but in empty space. The density of that perfect fluid is directly tied to the density of Newtonian matter (through [math]\nabla^2 g_{00}[/math]). Therefore the majority of gravitational mass is from nothing. See starting at 19:00

I know of no way to integrate these two concepts with a positive curvature tensor, but with a negative it seems plausible. Edited July 1, 2012 by JMessenger

[JMessenger]

What, no Lorentzian Aether theory fans? In a nutshell I am saying that if Lorentz had realized that the Einstein field equations are only derivatives, then he would have seen his aether theory within it and predicted that not only is gravity not attractive but that the universe accelerates after matter achieves an average distance of [math]r=(\frac{6G\rho^{res}V}{\Lambda^{vac}c^2})^{1/3}[/math].