[math]\frac{\phi}{c^2} \cdot \int\ (\frac{\ddot{T}}{T} + \frac{kc^2}{a^2})\frac{1}{\rho_{\alpha}}\ d\log_V = \frac{3072}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2} + \Psi + (\frac{T_0}{T})\frac{P}{\rho}) = \mathbf{C}[/math]

Ok, so we spoke about [math]C[/math] being a constant, today we know it is related to energy and the main main reason why this Freidmann expansion melding into Bernoulli's principle was not a ''an assumption'' as was challenged by someone who followed the work, because he seemed to be unaware that we work with fluid dynamics when working with an expanding universe, which relies on different pressures through various complicated parameters. In other words, the two have stronger relationships to each other than most would like to agree on, or have been unaware of.

To present the laws spoken in previous posts, a general application from the last equation would be to distribute an energy, such that the constant on the right hand side, is a constant of energy. We will leave out the right hand side until I can try and simplify it further, the real equation we should concentrate will be of the form:

[math] \frac{3072}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2} + \Psi + (\frac{T_0}{T})\frac{P}{\rho})E = \mathbf{C}_{vac}[/math]

where now [math]C[/math] is no longer ''just a constant'' but is define under the units of energy defined through the vacuum contribution.

This model, finally is becoming a unified equation for the universe.... but there is one final thing to do... and that will be the last highlight of the thread, an implication no less, of a driving force which we may consider as an interpretation of the cosmological constant. To do so, we require the work of Fritz Rohrlich who demonstrated that the force on a moving system (as in opposition to one at rest) is important when considering the mass-energy equivalence.

The model he proposed considered in a frame that moves with velocity* * to the left, the driving force moving to the left is redshifted, while the driving force moving to the right is blueshifted. The blue light carries more momentum than the red light, so that the momentum of the light in the moving frame is not balanced - in other words, a cosmological constant is interpreted here-on-in as a non-balanced force since the energy is carrying some net momentum to the right.

The object has not changed its velocity before or after the emission, however, in this frame it has lost some right-momentum to the energy driving it in a particular direction. The only way it could have lost momentum is by losing mass - this may be also a statement of non-conservation and is not only quintessentially tied to Poincaré's radiation paradox, it also solves it.

So the right-moving energy carries extra momentum [math]\Delta p[/math] we then have

[math]\Delta p =\frac{v}{2c^2}E[/math]

The left-moving energy will carry a little less momentum, by the same quantity [math]\Delta p[/math] such that the total right-momentum in the energy is twice the value of [math]\Delta p[/math]. This is the right-momentum energy lost from the system (universe)

[math]2\Delta p=\frac{v}{c^2}E[/math]

The momentum of the universe moving in the directional frame after the emission is reduced by the amount of

[math]p′ = mv−2\Delta p = (m − \frac{E}{c^2})v[/math]

So the change in the universes mass is equal to the total energy lost divided by the speed of light squared - the big implication here is that any emission of energy can be carried in a two-step process in which energy used by the universe is converted to mass, while the emission of an energy is accompanied by a loss of the mass in the universe. The pressure differences will lead to a mechanical explanation without an ad hoc assumptions on what the nature of the cosmological constant comes from, or how it came into being. To do so, we require the work of Fritz Rohrlich who demonstrated that the force on a moving system (as in opposition to one at rest) is important when considering the mass-energy equivalence.

The model he proposed considered in a frame that moves with velocity* * to the left, the driving force moving to the left is redshifted, while the driving force moving to the right is blueshifted. The blue light carries more momentum than the red light, so that the momentum of the light in the moving frame is not balanced - in other words, a cosmological constant is interpreted here-on-in as a non-balanced force since the energy is carrying some net momentum to the right.

The object has not changed its velocity before or after the emission, however, in this frame it has lost some right-momentum to the energy driving it in a particular direction. The only way it could have lost momentum is by losing mass - this may be also a statement of non-conservation and is not only quintessentially tied to Poincaré's radiation paradox, it also solves it.

So the right-moving energy carries extra momentum [math]\Delta p[/math] we then have

[math]\Delta p =\frac{v}{2c^2}E[/math]

The left-moving energy will carry a little less momentum, by the same quantity [math]\Delta p[/math] such that the total right-momentum in the energy is twice the value of [math]\Delta p[/math]. This is the right-momentum energy lost from the system (universe)

[math]2\Delta p=\frac{v}{c^2}E[/math]

The momentum of the universe moving in the directional frame after the emission is reduced by the amount of

[math]p′ = mv−2\Delta p = (m − \frac{E}{c^2})v[/math]

So the change in the universes mass is equal to the total energy lost divided by the speed of light squared - the big implication here is that any emission of energy can be carried in a two-step process in which energy used by the universe is converted to mass, while the emission of an energy is accompanied by a loss of the mass in the universe. We notice then from the equation/principle provided by Bernoulli is, before we distribute through the parenthesis the energy of the universe as:

[math] \frac{3072}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2}E + \frac{\Psi}{\psi}E + (\frac{T_0}{T})\frac{P}{\rho}E) = \mathbf{C}_{vac}[/math]

Let's distribute the energy for clarity:

And it is this factor, I wish us to concentrate on [math]\frac{v^2}{2c^2}E[/math] for we will recall the importance of this term through the modified Einstein mass-equivalence as being now a momentum operator:

So the right-moving energy carries extra momentum [math]\Delta p[/math] we then have

[math]\Delta p =\frac{v}{2c^2}E[/math]

again, to keep on the same page, the left-moving energy will carry a little less momentum, by the same quantity [math]\Delta p[/math] such that the total right-momentum in the energy is twice the value of [math]\Delta p[/math]. This is the right-momentum energy lost from the system (universe)

[math]2\Delta p=\frac{v}{c^2}E[/math]

The momentum of the universe moving in the directional frame after the emission is reduced by the amount of

[math]p′ = mv−2\Delta p = (m − \frac{E}{c^2})v[/math]

But these extra equations will come later into the model. In direct replacement of the given term of interest we now have an energy equation

[math]\frac{6114}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\Delta p + \frac{\Psi}{\psi}\frac{v}{c^2}E + (\frac{T_0}{T})\frac{P}{\rho}\frac{v}{c^2}E) = \mathbf{C}_{vac}\ (\frac{1}{v})[/math]

The first modified term in the parenthesis on the left hand side, now takes into respect its full glory - it is telling which way the universe should expand based from the physics we unified throughout these posts. I'll leave it at that for now... we'll see if it takes any interest or perhaps some people will like to add their own knowledge to these thoughts.

**Edited by Dubbelosix, 05 May 2019 - 05:19 PM.**