stephaneww

Hello,

With M_ΛRH be the mass of dark energy included in the Hubble sphere at Hubble time t_H

We still have a  dimensional problem because :

M_ΛRH = 2/3 t_H³ ...

with kilos coming from the calculation of a cube of seconds !!!

Note also that this would imply an increase, in the Hubble sphere, of the mass of matter (dark and/or baryonic) with the age of the universe. This does not exist in the consensus cosmological models today.

In the same way one always has with a dimensional consistency problem:

at t_H,  Ω_Λ = 4/3 G/c³ t_H²

These dimensional coherence problems (always with the same ratio with respect to the measurements) may have their origin in our ignorance of what is dark energy.

Translated with www.DeepL.com/Translator (free version)

    hello

    
    I would like to know the complete formula to have a  precise value of the value of the acceleration of the expansion of the universe (m/s^2) at the Hubble radius in the Lambda-CDM model please

     ...if possible with an arXiv source, which would be a luxury

    thanks in advance

to be synthetic :

S = l_Pl² is a surface (= plate for the Casimir effect)

1/S = 1/l_Pl² in QFT or 1/S = Λ in cosmology are energies

according to their side in the equality of the Casimir effect, their physical meaning is different.

I do not see anything more convincing

of course there are no plates in cosmology

just as Λ was initially used to make the universe static to finally account for the acceleration of the expansion of the universe,

1/S = Λ changes the physical meaning of physical plates.

The fact remains that dF / dS keeps the physical meaning of an energy density (or of a pressure if you prefer)

8 hours ago, swansont said:

What does any of this have to do with the Casimir effect?

23 hours ago, stephaneww said:

We just have to pass the surface S on the other side of the equality of casimir effect with :
1/dS = Λ
and
dF = F_Pl = c⁴/G, Planck force

We have thus by the same trick as the change of side of the equality for the cosmological constant in the EINSTIEN equation to obtain the energy density of the cosmological constant.

We don't need physical plates in the cosmos anymore

once again :

in one side S is the surface of the plates, in the other side dF/dS is an energy density in Casimir effect egality

35 minutes ago, swansont said:

Once again, it sounds like you are just rearranging variables and constants without regard for any physics interactions or processes. e.g. there is no "Planck Force" as an interaction, it's just the expression of force using Planck units.

Let's see:

with :

S_Pl = l_Pl² Planck surface

1/S_Pl = 1/l_Pl² = zero point energy of the QFT

F_Pl/S_Pl = energy density of zero point energy of the QFT

the physical meaning is not in doubt here

so why would putting 1/S =Λ not make physical sense ?

On 12/23/2021 at 3:41 PM, swansont said:

The casimir effect is, more precisely, a reduction of the electromagnetic vacuum energy owing to the presence of conducting plates. 

Hello

In fact the solution is probably very simple :

We just have to pass the surface S on the other side of the equality of casimir effect with :
1/dS = Λ
and
dF = F_Pl = c⁴/G, Planck force

We have thus by the same trick as the change of side of the equality for the cosmological constant in the EINSTIEN equation to obtain the energy density of the cosmological constant.

We don't need physical plates in the cosmos anymore

1 hour ago, swansont said:

It’s your link. If you’re offering it as support you should understand it.

There was a bit of irony in my question: I don't see how one can invoke 2 plates to talk about the Casimir effect in cosmology. So it must be something else.

1 hour ago, swansont said:

Quote

this is beyond what I know and understand

1 hour ago, swansont said:

And is the crux if the issue here. You are throwing around equations without understanding the physics.

Λ and l_Pl^-2 are energies expressed in m^-2. You don't need to know complex QM terms, nor QM to understand this.

36 minutes ago, swansont said:

A single plate would feel no force

ok

36 minutes ago, swansont said:

Symmetry tells you this, but also there’s no exclusion of any of the QM modes.

 this is beyond what I know and understand

1 hour ago, swansont said:

AFAICT this is proposing to use the same calculational approach for the cosmological constant as for the casimir effect, in terms of dealing with infinities, i.e. the renormalization. 

uh, does he use two plates or a space geometry in this approach?

16 minutes ago, swansont said:

AFAICT this is proposing to use the same calculational approach for the cosmological constant as for the casimir effect, in terms of dealing with infinities, i.e. the renormalization. 

 

ok

question : do they need 2 plates for this calculational approach ? I

On 12/23/2021 at 3:34 PM, stephaneww said:

The Casimir effect having been proved experimentally as effect of the vacuum energy

41 minutes ago, Genady said:

Not proved, according to this:

"In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero-point energies of quantum fields are “real.” On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents....

 

it's not a problem. it is indeed an excessive shortcut on my part. i haven't found any sources

41 minutes ago, Genady said:

In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero-point energies of quantum fields are “real.” On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero-point energies. They are relativistic, quantum forces between charges and currents.

in my proposition, cosmologycal constant and zero-point energy of quantum fields are linked to obtain the Casimir effect

1 hour ago, swansont said:

I am not aware of this interaction. Can you point to any peer-reviewed literature that says that the cosmological constant interacts with anything?

here : https://royalsocietypublishing.org/doi/10.1098/rsta.2019.0229

Quote

The theory [47] of the Casimir stress inside inhomogeneous planar materials makes one more prediction that, when widely extrapolated to cosmological scales, explains why the Casimir effect might play a role in cosmology: the convergence of the renormalization relies on dispersion. Ordinary dielectric materials are dispersive in the sense that the refractive index n depends on frequency. The Casimir effect is a broadband electromagnetic phenomenon [15] depending on the entire frequency window of the material. For large frequencies, all materials become completely transparent, n → 1. Without this feature, the renormalized stress would contain a logarithmically diverging contribution [47]. On the other hand, the ‘material’ of general relativity—the geometry of space and time—acts on all frequencies equally, as a consequence of the equivalence principle [2]. Therefore, even the renormalized ε_vac would still diverge, although significantly weaker than the unrenormalized one. The wavelength range contributing to the forces of the quantum vacuum would go to the Planck length (1.2) where, presumably, the equivalence principle ceases to hold. So ε_vac would not grow with the inverse forth power of the Planck length as in equation (1.3) that produces the wrong 120 orders of magnitudes, but significantly weaker. The logarithmic divergence [47] is not sufficient though, for the following reason.

you can read the whole article, I didn't take the time to translate it al

1 hour ago, swansont said:

That’s what you said.

either it was badly said or it is a problem of automatic translation

1 hour ago, swansont said:

An equality that you wrote down as an assumption.

The casimir effect requires conducting plates, which force a component of the electric field to become zero, something not true in free space.

I refer you to the whole article quoted above

1 hour ago, swansont said:

I am not aware of this interaction. Can you point to any peer-reviewed literature that says that the cosmological constant interacts with anything?

here too but I haven't access : https://www.semanticscholar.org/paper/The-vacuum-energy%3A-Casimir-effect-and-the-constant-Elizalde/e0d922a743ae3c2c5ef7cb61cfb391f1fab7fcb3

55 minutes ago, swansont said:

How does that work, physics-wise?

it is simply the interaction of the cosmological constant at the quantum scale (lPl-2).

55 minutes ago, swansont said:

How does it “become” the cosmological constant? 

It does not "become" the cosmological constant. The cosmological constant is already in the equality. It is the identification of (1) to (2) that allows to say that we are in the framework of the Casimir effect

55 minutes ago, swansont said:

The casimir force can be derived by applying the conductor boundary conditions to the geometry. If L doesn’t matter then you don’t get that answer.

Quote

De plus, il est plus que probable que l'effet dépende aussi de la distance L entre les plaques.

https://fr.wikipedia.org/wiki/Effet_Casimir#Expression_de_la_force_par_unité_de_surface

traduction : Moreover, it is more than likely that the effect also depends on the distance L between the plates.

"Probable" does not prohibit another way of presenting L^-4

edit : moreover I would be curious to know what L⁴ represents in nature

12 minutes ago, exchemist said:

I'm a bit lost. Surely if S is a surface area, then dF/dS is a pressure function rather than an energy, isn't it?  

oops yes indeed it is a pressure or J/m3 i.e. an energy density

the units of (1) and (2) of the first post indicate it and are correct they

16 minutes ago, swansont said:

f it were a conductor, having a separation distance has no meaning.

the separation distance is not important in my identification of the equalities: 1/L^4 becomes the cosmological constant multiplied by the QFT quantum vacuum energy (lPl^2) to obtain the Casimir effect

33 minutes ago, swansont said:

The casimir effect is, more precisely, a reduction of the electromagnetic vacuum energy owing to the presence of conducting plates. 

Quote

On suppose de plus que les plaques sont des conducteurs parfaits de conductivité électrique infinie, et qu'elles ne sont pas chargées.

tradution : It is further assumed that the plates are perfect conductors of infinite electrical conductivity, and that they are not charged.

if I understand correctly the vacuum is conductive

33 minutes ago, swansont said:

If you are going to equate this with the cosmological constant, you need to do more than unit analysis. A force is going to have units of force, regardless of the origin of it. You can’t e.g. say an electrostatic force is gravitational, just because they have the same units.

18 minutes ago, MigL said:

Casimir effect is a local reduction of the vacuum energy ( relative to the global level ) .
The Cosmological Constant is a global reduction of the vacuum energy, which is exchanged for the expansion force/acceleration.
( similar to exchange of potential for kinetic in a gravity field )

we have to combine the cosmological constant with the QFT quantum vacuum energy (=l_Pl^-2) to obtain the Casimir effect

... and dF/dS is an energy, not a force

I identify the cosmological and quantum vacuum energy with the Casimir effect to confirm that the cosmological constant of general relativity is the cosmological vacuum energy.

https://fr.wikipedia.org/wiki/Effet_Casimir#Expression_de_la_force_par_unité_de_surface

The Casimir effect having been proved experimentally as effect of the vacuum energy

Hi

I think it's okay.

That's why I didn't post it in Speculations first.

Thanks for your opinions

casimir eng(1).pdf

.not to another day but later

5 hours ago, stephaneww said:

l_Pl^-2 is the vacuum energy from QFT in m^-2

on the right I have (kg s^-2) or1(N/m) inverse of a surface tension.

Is my problem insolvent or do you see a solution please?

and

remplace s^-2 et m² in Joules  kg m² s^-2 by Λ_s-2 and Λ_m-2

correction :

2 hours ago, swansont said:

Is that also happening for your other equation? i.e. was it from an equation with normal units, or one where they were ignored?

no, precisely I take into account the dimensions: originally I have an equality which in a form is in Joules and in a second form it gives a numerical value close to the value of Λ in m-2. I justify this difference because of a difference in degrees of freedom. 

2 hours ago, swansont said:

Since you're asking this without providing context, it's very difficult to see if this is the problem

edit :

I tried to explain the process clearly but I can't. I'll put it off for another day.

2 hours ago, swansont said:

 

IOW, Λ =  κ ρ_vac and you call it an energy density by assuming  κ is 1. But it's not actually 1

I never use this : for me ρ_{vac =} Λ F_Pl /8 pi   and  ρ_vac from QFT = l_Pl²   F_Pl 

(F_Pl =c⁴/G)

2 hours ago, swansont said:

I meant "where in standard physics literature did this equation come from"

You need to have started with mainstream physics at some point.

it is not in the standard physics. it comes from my model derived from the ΛCDM model and which approaches it under a new angle. but I find the essential of the results of the standard model. (mass at the Hubble radius and critical energy density of the universe in a certain way). other points are still speculative including this one

18 minutes ago, swansont said:

Why doesn't it have units of energy?

Uh m^-2 is the dimension of the cosmological constant.

for l_Pl^-2 of the QFT I have only one reference in French : https://www.unige.ch/communication/communiques/2019/cosmologie-une-solution-a-la-pire-prediction-en-physique/

18 minutes ago, swansont said:

Can you show where you got this equation?

This equality comes from a speculation published in French on my blog. I can't put in latex a clean way to reach  the equality that I have a problem with here.

l_Pl^-2 is the vacuum energy from QFT in m^-2

on the right I have 1(kg s^-2) or 1(N/m) inverse of a surface tension.

Is my problem insolvent or do you see a solution please?

precisions for the above diagram :
- time = 1/H , It can exist before tPl.
- the distances of the 3D flat space increase with time. l = c t and t = l / c
-each of the 3 axes of the 3D flat space merges with the time axis and vice versa  

let's try to go forward with the correspondence of the critical density of my model with the one of the standard cosmological model :

Well no, this scheme is not consistent either.

Let's see if the next one gives satisfaction or permit to progress:

corrected diagram