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stephaneww

The solution of the Cosmological constant problem ?

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Posted (edited)

I don't think I would have the knowledge to go as fast as you or other science professionals on the subject of quantum fields and inflation with our model. In any case, it will always go faster than with me alone if someone is interested. 

Here is what I propose for the rest of this thread:
or you let others do the research.
or you do it in a dedicated thread so that I can try to understand where it leads you.

... and you continue, in this thread or another, the lesson on the fields if you accept.

I think I understood the equality of 1.10.1

I am missing the latex writings of components and applications such as, for example, in a 3D Cartesian space

Note: I do not see any error in my proposal for the "try of conclusion" solution, so I think it is correct. You will confirm or not when you have time.

 

Edited by stephaneww

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Posted (edited)

Um, I may go too far, but I'm still going to go forward: I think this solution is a basis for unifying relativity and quantum mechanics 

 

Edited by stephaneww

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Posted (edited)

What you have is one of many potential solutions to one of the cosmological problems. There are other equally valid solutions such as the Unruh link I posted earlier.

 Inflation and unifying QM to relativity are comprised of different problems that the cosmological solution does little to nothing to solve.

They each have different criteria to be met.

That being said your solution is viable but you have to keep in mind there are numerous other potential solutions out there. I don't see any mistakes with your solution and it does get the required ratios so good job on that in so far as that goes.

 I have been searching my personal database as your solution has numerous similarities to a solution I saw in the early 90's. I know I kept a copy of it but have a lot of pdfs to go through to find it.

Edited by Mordred

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Posted (edited)
50 minutes ago, Mordred said:

There are other equally valid solutions such as the Unruh link I posted earlier.

even if I don't know how to understand it, as it is authoritative, I accept the evidence.

 

50 minutes ago, Mordred said:

 Inflation and unifying QM to relativity are comprised of different problems that the cosmological solution does little to nothing to solve.

let's put this question aside for now please, I don't have the mathematical tools to try to show somthing  (i think about the [math]\phi[/math] in particular and their use).

50 minutes ago, Mordred said:

That being said your solution is viable but you have to keep in mind there are numerous other potential solutions out there. I don't see any mistakes with your solution and it does get the required ratios so good job on that in so far as that goes.

Okay, thank you very much.

 

50 minutes ago, Mordred said:

 I have been searching my personal database as your solution has numerous similarities to a solution I saw in the early 90's. I know I kept a copy of it but have a lot of pdfs to go through to find it.

I can't imagine how many PDF you have :rolleyes:.  This not urgent

Edited by stephaneww

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Posted (edited)
5 hours ago, stephaneww said:

Um, I may go too far, but I'm still going to go forward: I think this solution is a basis for unifying relativity and quantum mechanics 

No, you're right: no connection,  I got out of line. :rolleyes:

 

On 8/29/2019 at 6:32 AM, Mordred said:

 

ϕp ϕ is typically used to represent scalar fields.

Unless I'm mistaken, the relationship between [math]\phi_p[/math] and ϕ is a multiplication with, [math]\phi_p=h/2[/math] Planck fields and ϕ, the value of Planck's force if I understood what you suggest. Both,  as scalar values, are dimensionless.  Correct please ?  

Edited by stephaneww

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Posted (edited)

[math]\phi [/math] is just any scalar function it's a standard symbol for that so it's value will vary depending on what model it's used for. It often is dimensionless but not always. Again depends on the model it's used in.

See here

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

One thing to note is a scalar quantity isn't a force. Force is always a vector quantity 

Edited by Mordred

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Posted (edited)

okay  thank you.

I searched for the value of the Planck field, in French and English, but I have only one source (so I can't cross-reference):

in this document:
http://www.spirit-science.fr/Matiere/phys4-electrodynamique.html#mozTocId491541

at the end of the paragraph "Le champ du point zéro de l'électrodynamique stochastique"

I read :
"Il reste cependant un facteur multiplicatif indéterminé, C. Nous verrons un peu plus loin que des mesures expérimentales ont permis de déterminer sa valeur. Il est égal à h/2. Avec cette valeur, on retrouve précisément le champ de la deuxième formulation de Planck."

translation into English:
"However, there is still an undetermined multiplicative factor, C. We will see a little later that experimental measurements have made it possible to determine its value. It is equal to h/2. With this value, we find precisely the field of Planck's second formulation."

so is this value correct, please:

23 hours ago, stephaneww said:

ϕp=h/2

?

Edited by stephaneww

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Posted (edited)

For a Planck field yes. However your better off using zero point energy [math]\frac{1}{2}\hbar w[/math]

Edited by Mordred

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Posted (edited)

Thank you.

Other question :

I just readed on Wikipédia :

Quote

Bill Unruh and collaborators have argued that when the energy density of the quantum vacuum is modeled more accurately as a fluctuating quantum field, the cosmological constant problem does not arise.

My proposition is equivalent, no ?

Edited by stephaneww

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Posted (edited)

what is the notation [math]\phi[/math] for Planck's force field, please?

if you give me his latex script  as well, that would be great.:-)

Edited by stephaneww

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The scalar function can be deployed in many ways, however its typical when describing a field to describe its potential energy at a given location.

so using the zero point energy of the quantum oscillator we will want to specify coordinate values.

[math]\phi(x_\mu)=\frac{\hbar w}{2}[/math] the [math] x_\mu=x^0,x^1,x^2,x^3,x^4=ct,x,y,z[/math]

A field composed of Planck units wouldn't be a Planck unit in and of itself this is why I chose the harmonic oscillator basis for this example.

Unruhs solution differs from yours in the sense that he applies QFT to show that the quantum catastrophe problem is effectively washed out on large scales. 

 

Edited by Mordred

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Here is a key line to understanding Unruhs paper.

Quote

in this paper, we make a proposal for addressing the cosmological constant problem. We treat the divergent vacuum energy density predicted by QFT seriously without trying renormalization and assume that it does gravitate to obey the equivalence principle of GR. We notice that the magnitude of the vacuum fluctuation itself also fluctuates, which leads to a constantly fluctuating and extremely inhomogeneous vacuum energy density. As a result, the quantum vacuum gravitates differently from a cosmological constant. Instead, at each spatial point, the spacetime sourced by the vacuum oscillates alternatively between expansion and contraction, and the phases of the oscillations at neighboring points are different. In this manner of vacuum gravitation, although the gravitational effect produced by the vacuum energy is still huge at sufficiently small scales (Planck scale), its effect at macroscopic scales is largely canceled.

Edited by Mordred

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2 hours ago, Mordred said:

The scalar function can be deployed in many ways, however its typical when describing a field to describe its potential energy at a given location.

so using the zero point energy of the quantum oscillator we will want to specify coordinate values.

ϕ(xμ)=w2 the xμ=x0,x1,x2,x3,x4=ct,x,y,z

A field composed of Planck units wouldn't be a Planck unit in and of itself this is why I chose the harmonic oscillator basis for this example.

Unruhs solution differs from yours in the sense that he applies QFT to show that the quantum catastrophe problem is effectively washed out on large scales. 

 

Thank you.

From then on it becomes out of my scope in terms of mathematical knowledge

Thank you for everything.

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Finally, I think that with this solution, we can, perhaps, learn something more with the domain of quantum cosmology:

we have with [math]\Lambda_{s^{-2}}=\Lambda_{m^{-2}}.c^2[/math]

[math]D=\hbar. ({\Lambda_{m^{-2}}})^2*c/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math]

[math]D=\hbar. ({\Lambda_{s^{-2}}})^2.c.c^{2}/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math]

[math]D=\hbar.(\Lambda_{s^{-2}})^2 c^{3}/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math]

[math]D=\hbar.(\Lambda_{s^{-2}})^2 c^{3}/(8*\pi)^2=6.196*10^{-133}kg*m^{-1}*s^{-2}[/math]

[math] \Lambda_{s^{-4}}=\frac{D.(8*\pi)^2}{\hbar.c^{3}}[/math]

so and if I am not mistaken in simplifying

[math]\Lambda_{s^{-2}}=( \frac {D.(8\pi)^2} { \hbar  c^{3} })^ {0.5}[/math]
assuming that there is a relationship between [math]\Lambda_{s^{-2}}[/math] and [math]H_{p,minimun}[/math] we have

[math]H_{p,minimum} = ( \frac{D.(8\pi)^2} {\hbar .c^{3} } )^{0.5*0.5}=6.2*10^{-31}s^{-1}[/math]

or about 3.04*10^24 years.

under condition of verification, we can deduce [math]\Omega_{\Lambda ,max}[/math] and consider scenarios at this age of the universe

 

Edited by stephaneww

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That is far older than the age of the universe. 

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yes, but this remains in the order of magnitude of Planck's length and time units.

Edited by stephaneww

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Wouldn't you consider that to be problematic considering your involving Hubble parameter ?

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27 minutes ago, Mordred said:

Wouldn't you consider that to be problematic considering your involving Hubble parameter ?

Probably yes. I don't actually know 

Hp,minimun is a speculative value

Quote

That is far older than the age of the universe. 

How do we get the value you're talking about please ?

Edited by stephaneww

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1 hour ago, stephaneww said:

Hp,minimun is a speculative value

I note simple that if we do the same calculation for 10^113 J/m^3 we have an age of 5.6*10^-32 s (edit : is this close to beginning or the end of the inflation period please?)

Edited by stephaneww

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Close to the beginning it's in the right ball park. I will get you the correct formula to calculate universe age though if you look at the advanced user guide to the cosmocalc that I previously linked I believe it's there.

Edited by Mordred

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Um I think you'll have to guide me once again for a new apprenticeship....

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Oh, I found a very nice numerical and literary conclusion.
As soon as I can, I do translating and formatting Latex

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Sounds good for a quick and dirty rough order age of the universe that assumes constant expansion. There is a quick calculation, to account for evolution of matter radiation and Lambda takes a considerable more work..

With the Hubble value given by Planck 2015 this will give an age of 14.4 Gyrs. However when you employ the full equation you can narrow that down. For starters lets just do the rough order calculation (initial estimate.

[math]V=frac{d}{t}[/math

[math]t=d/t[/math]

[math] H_0=v/d[/math]

[math]v=d*H_O[/math]

combine those two and substituting for velocity

[math]t=\frac{d}{v}=\frac{d}{d*H_o}=\frac{1}{H_o}[/math]

now as you know Hubble parameter isn't constant which is one reason for the discreptancy however this is a quick and dirty estimate. Practice this with the conversions first before we get into the more complex equations for the evolution of the density parameters.

a true critical flat universe would be

[math]t=\frac{2}{3}\frac{1}{H_o}[/math] were not quite a true critical flat and we have a cosmological term to deal with but practice those first.

You could use[math] 3.16*10^7 s/year[/math] its not quite accurate as your not accounting for leap years lol.

just a side note no method I show you will get precisely the Planck value for age as Planck does a best fit over several different datasets including type 1A supernova measurements.

Edited by Mordred

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what I'm preparing is more precise and leads to an interesting conclusion.


otherwise I saw on wiki: end of inflation between 10^-33 s and 10^-32 s
I can't find it right away.

Edited by stephaneww

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