The solution of the Cosmological constant problem ?

[Mordred]

[math]\dot{a}[/math] is velocity of the scale factor

[math]\ddot{a}[/math] is acceleration of scale factor

An interesting equation using time derivatives

[math]\dot{H}=\frac{\ddot{a}}{\dot{a}}[/math] shows that even though the Hubble parameter is decelerating ie slowing down the scale factor is accelerating.

On the repulsive gravity (lol a very inaccurate descriptive but some literature uses the term) I personally think it's misleading as one might think anti gravity which is wrong.

You can have a force term due to the negative vacuum term w=-1 but you cannot treat it from a centre or an average direction.

 Every location of spacetime the  vector will be in every direction.  Ie space expanding. Under that condition the usage of the term Planck force could apply for each discrete quantization of spacetime. The result will be the number of Planck length units will be increasing as space expands.

Edited September 15, 2019 by Mordred

[stephaneww]

26 minutes ago, Mordred said:

Every location of spacetime the  vector will be in every direction.  Ie space expanding. Under that condition the usage of the term Planck force could apply for each discrete quantization of spacetime.

This time, it's definitive. I have understood that you are right on this issue.  

Edited September 15, 2019 by stephaneww

[Mordred]

Bingo +1

[stephaneww]

 

Arf I didn't pay attention that you edited to add this:

45 minutes ago, Mordred said:

Under that condition the usage of the term Planck force could apply for each discrete quantization of spacetime.

so the consequence escapes me. I don't understand what that implies for what I propose post 2 and 3 on page 5...

Sorry I edited this after your next message

but it comforts me on this point:

On 4/27/2019 at 7:03 PM, stephaneww said:

Fp : Planck force

1 the energy density by volume of the quantum vacuum as A=Fp/lp^2 = 4.633*10^113 Joules/m^3 (formula derived from dimensional analysis in Planck units)

2 the energy density by volume of the vacuum of the cosmological constant as B= Fp* Lambda /8/ pi = 5.354*10^-10 Joules/m^3 

the ratio between the two being the number in factor of 10^122 undimensioned

the value of the adimensionless factor, X, is more precisely : A/B=X=8.654*10¹²², X is called " The cosmological constant problem ".

 

Edited September 15, 2019 by stephaneww

[Mordred]

When your applying Planck units you are quantizing spacetime into discrete units. The Planck length never changes it is always the same value. So as the volume increases the number of Planck length units must also increase without increasing the Planck length itself. 

These terms get misleading as space is just volume but in essence space is being created everywhere that is not gravitationally bound.

A better descriptive is the use of geometric expansion specifically commoving coordinates 

 

Edited September 15, 2019 by Mordred

[stephaneww]

13 minutes ago, Mordred said:

When your applying Planck units you are quantizing spacetime into discrete units. The Planck length never changes it is always the same value. So as the volume increases the number of Planck length units must also increase without increasing the Planck length itself. 

These terms get misleading as space is just volume but in essence space is being created everywhere that is not gravitationally bound.

I understand this 2 points very well

13 minutes ago, Mordred said:

A better descriptive is the use of geometric expansion

I don't know but I understand the principle for having represented it on a sheet of paper 

This is due to the fact that roughly speaking the quantity of material is conserved while for vacuum, it is the density of the vacuum that is conserved in an expanding space.

Edited September 15, 2019 by stephaneww

[Mordred]

Ok good now let's get onto surface power density.

 One of the requirements is potential difference. You don't have any potential difference between one coordinate and another. Every coordinate has the same value.

So let's look at power density and it's definition.

Power density is the amount of power (time rate of energy transfer) per unit volume.

https://en.m.wikipedia.org/wiki/Power_density

If every location has the same energy density ie potential energy then your not transferring energy from one location to another

What is a unique feature of the cosmological constant when it comes to energy conservation ? Total energy isn't conserved. As the volume increases the total energy of Lambda is increasing. It isn't being transferred 

Edited September 15, 2019 by Mordred

[stephaneww]

37 minutes ago, Mordred said:

What is a unique feature of the cosmological constant when it comes to energy conservation ? Total energy isn't conserved. As the volume increases the total energy of Lambda is increasing. It isn't being transferred 

Um, not even  transferred to vacuum temperature? (CMB's) 

for the above in your message it is being studied in detail but we agree in a first approach 

 

Edited September 15, 2019 by stephaneww

[Mordred]

The cosmological constant doesn't follow conservation of energy at any time. Total energy in essence is being created as the volume increases. (Though don't think of energy as a substance) it's always the ability to perform work ie a property.

[stephaneww]

5 minutes ago, Mordred said:

The cosmological constant doesn't follow conservation of energy at any time. Total energy in essence is being created as the volume increases. (Though don't think of energy as a substance) it's always the ability to perform work ie a property.

On this point we agree

[Mordred]

1 minute ago, stephaneww said:

On this point we agree

well the result is energy isn't being transferred so power density isn't applicable. 

[stephaneww]

13 minutes ago, Mordred said:

well the result is energy isn't being transferred so power density isn't applicable. 

Agree for my understanding currently in cosmology. Finally we have succeeded!

Edited September 15, 2019 by stephaneww

[Mordred]

+1

Oops accidentally down voted I will correct that on other posts. At least it allowed me to remove the negative reaction. However I had to apply the +1 to other posts.

Edited September 15, 2019 by Mordred

[stephaneww]

The votes are sympathetic but I prefer positive or opposition written reactions. It's clearer for me 

3 hours ago, Mordred said:

Under that condition the usage of the term Planck force could apply for each discrete quantization of spacetime. The result will be the number of Planck length units will be increasing as space expands.

In addition, it reinforces me on the validity of the formulation of [math]B[/math] in this message :

https://www.scienceforums.net/topic/118858-the-solution-of-the-cosmological-constant-problem/?do=findComment&comment=1115799

edit :

It is also a good basis for popularizing Unruh's paper

Edited September 15, 2019 by stephaneww

[stephaneww]

+1 for this of course 

On 9/14/2019 at 12:24 AM, Mordred said:

Surface power density isn't applicable in this application. The cosmological constant is a scalar field there is no force involved. A force requires a vector field. The EM field is an example as you have two charges.

The cosmological constant doesn't have a charge nor inherent vector direction.

[stephaneww]

Um, actually, there's a problem with your whole explanation:
Indeed, you are dealing with power / volume unit [math]W/m^3[/math] ( everything you say in this frame is OK)  whereas I am talking about surface power density (power /area surface unit) [math]W/m^2[/math]
cf: 

On 9/13/2019 at 10:59 PM, stephaneww said:

surface power density : [math] kg/s^3 or  W/m^2[/math]

or in French :

https://fr.wikipedia.org/wiki/Densité_surfacique_de_puissance

On 9/15/2019 at 6:38 PM, Mordred said:

Total energy in essence is being created as the volume increases

ok but what happens to the surface power density ? 

correction: read [math]\hbar[/math]

On 9/13/2019 at 10:59 PM, stephaneww said:

[math]\frac{1}{2}   \frac{h}{t^2}\frac{Λ}{8\pi}=0.50144.kg/s^3=1/1.994.kg/s^3[/math]

 

[math]\frac{1}{2}   \frac{\hbar}{t^2}\frac{Λ}{8\pi}=0.50144.kg/s^3=1/1.994.kg/s^3[/math]

Edited September 19, 2019 by stephaneww

[Mordred]

From the first link in English

As an electromagnetic wave travels through space, energy is transferred from the source to other objects (receivers). The rate of this energy transfer 

Where is the energy transfer for the cosmological constant ? 

[math] power=\frac{work}{time}[/math]

Start there however it gets more complex thermodynamically. Specifically the first law of thermodynamics. However you might want to start with the distinction between energy density and power density

https://energyeducation.ca/encyclopedia/Energy_density_vs_power_density

Edited September 19, 2019 by Mordred

[Mordred]

I know the following will probably confuse you if you haven't studies thermodynamics but here goes

First law of thermodynamics expressed for an adiabatic ( no net inflow or outflow of energy or enthalpy)

[math]0=dQ=dU=dU+PdV[/math]

Q is total heat assumed to be constant, U is internal energy of matter and radiation in the universe, P is pressure, V is the volume. One finds energy density via

[math]u=\frac{U}{V}[/math] and thus [math]du=d(\frac{U}{V})=\frac{dU}{V}-U\frac{dV}{V^2}=-(p+u)\frac{dV}{V}=-3(p+u)\frac{da}{a}[/math] if you divide this equation by [math]d\tau[/math] you get the equations of motion for the FLRW metric [math]u=\rho[/math]

now for radiation

[math]du=-4u\frac{da}{a}[/math] thus u is proportional to [math]a^{-4}[/math]

for matter

[math]du=-3\frac{da}{a}[/math] thus u is proportional to  [math]a^{-3}[/math]

now in both these cases as the universe expands the temperature decreases

now for the cosmological constant we need to employ a time derivative

[math]\dot{u}=-3(p+u)\frac{\dot{a}}{a}[/math] now a consequence is that the more negative the pressure becomes the less the energy density decreases as the universe expands however energy is created as the universe expands by Lambda so its pressure is minus its energy density

p=-u or [math]p=-\rho[/math]

the total heat is constant in all the above so there is no power in terms of work/time

in terms of the FLRW metric power density is never used as there is no transfer of heat outside of our system defined by adiabatic expansion.

https://en.wikipedia.org/wiki/Adiabatic_process

this gets complicated in terms of reversibility and a further problem of isentropic processes the work must be performed outside our system which doesn't make sense when discussing the universe when our system is the universe volume. There is no outside of the universe for a transfer of work to occur.

So how would you define power in this instance ?

 

Edited September 19, 2019 by Mordred

[stephaneww]

2 hours ago, Mordred said:

From the first link in English

As an electromagnetic wave travels through space, energy is transferred from the source to other objects (receivers). The rate of this energy transfer 

Where is the energy transfer for the cosmological constant ? 

Intuitively I would say that, over time, the transfer of energy from the cosmological constant goes into increasing the volume of the vacuum of the universe with ultimately an increase in the total energy of the vacuum.
It should be considered that the vacuum is the source and the receiver at the same time.
But I don't know if that's an acceptable answer.

I wrote this before your last post 

53 minutes ago, Mordred said:

now a consequence is that the more negative the pressure becomes the less the energy density decreases as the universe expands however energy is created as the universe expands by Lambda so its pressure is minus its energy density

Can you specify the energies involved, please, I don't understand everything

Edit, I understand 

53 minutes ago, Mordred said:

So how would you define power in this instance ?

I'll have to scratch my head for a moment.

I have a lot of notions to learn or review.

Without any guarantee of results...

 

… and thanks a lot for this link :

On 9/15/2019 at 9:26 AM, Mordred said:

Well the good news is you can find classical treatments for the equations of state.

https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.astronomy.ohio-state.edu/~dhw/A5682/notes4.pdf&ved=2ahUKEwjljPSGl9LkAhVOqp4KHbb8DtwQFjAQegQICRAB&usg=AOvVaw0xjZcR1b8OcNFbrriXGEr2

and the definition of a dot 

 

Edited September 19, 2019 by stephaneww

[Mordred]

 The thing to keep in mind is unlike say a pressure tank, a battery or a capacitor where energy can be stored and power is transferred at a rate to perform work on some external to the storage device the universe doesn't perform work outside of itself. All the energy is contained within our universe, there is no transfer of heat, energy or mass from outside our universe from inside to outside our universe. Our universe is in essence an isolated system (speaking thermodynamically) an isolated system cannot perform work outside of itself.

 To put it bluntly in every paper, textbook, article I have ever read on cosmology and the FLRW metric in terms of the universe not once have I ever encountered any usage of power density or even power being involved in any model of the universe I have ever read in 35 years.

 

[stephaneww]

You didn't see a geometric mean as a solution to the problem of the cosmological constant either.

I may have to rework the presentation (one equivalent to energy density * speed of light) to make it more obvious. But, this equality of 1/1,994 W/m^2 is not a coincidence in my opinion. The equivalence is too exact.

edit :

Um, It is very easy to show that

 

[math]\frac{\hbar\Lambda}{8\pi t_p^2}.c = \frac{c^4\Lambda}{8\pi G}[/math]

just replace [math]t_p[/math] by  [math]\sqrt{\frac{\hbar G}{c^5}}[/math]

Edited September 19, 2019 by stephaneww

[stephaneww]

In fact the 2nd and 3rd post (+ errors in the 3rd) on page 5 are most probably strictly irrelevant.....

 

At least I would have learned a lot of things

+1 to last post of Mordred

Edited September 19, 2019 by stephaneww

[Mordred]

Here is another factor to consider

Watts=voltage*current. Which doesn't make much sense for Lambda no potential difference. No current.

Edited September 19, 2019 by Mordred

[stephaneww]

If you follow me back on the subject...

Planck's force (which can be highlighted in the energy density of the cosmological constant) can be considered as a tension:

https://en.wikipedia.org/wiki/Planck_force#Planck_force_as_a_tension_constant_of_the_space_time_fabric

on French wiki we have also :

Quote

La force de Planck n'est dérivée que de la constante de gravitation universelle de Newton et de la vitesse de la lumière, qui sont constantes partout dans l’espace. Elle caractérise donc une propriété de l'espace-temps⁴.

 

translation :

Quote

Planck's force is derived only from Newton's universal gravitational constant and the speed of light, which are constant throughout space. It therefore characterizes a property of space-time⁴.

link 4 is :

https://arxiv.org/pdf/1408.1820.pdf  

where you will find an attempt to define power associated with Planck's force.

 

[math]A[/math] and [math]B[/math] on page 2 (formulation of the geometric mean) are they associable with "dipole boundaries"? 

c*pi, could it be associated with "electrical current"? 

note: the formulas and values of posts 2 and 3 on page 5 are correct contrary to what I said earlier. (post 3 use [math]h[/math] instead [math]\hbar[/math]  

the whole question for me is how to interpret W/m^2 equivalent to kg/s^3. 

...for the moment I don't have an answer

Edited September 19, 2019 by stephaneww

[Mordred]

This really isn't a very good paper in so far as it doesn't deploy any GR equations in its analysis.

Anyways its fine to employ Newton mechanics in terms of spacetime force provided you also realize that the Shell theorem also applies.

 The paper use of power applies to Dyson luminosity which is a relation velocity to luminosity relations that involves the EM field via Kaluza Klein. An EM field in this instance is coupled to the spacetime metric via a conjecture that all rotating bodies would acquire a magnetic moment thus giving a magnetic moment to velocity power ratio.

 The theory never really went anywhere you may find occasional studies on it but it's highly hypothetical. It's fundamentally a combination of the EM field to spacetime for stellar bodies so it's localized around those bodies.

Edited September 20, 2019 by Mordred