stephaneww

What is the IOW, please?

Otherwise, very quickly, I didn't really deal with the problem of the cosmological constant but another point that shows a ratio in 10^122

11 hours ago, swansont said:

The paper linked to on that site for "limiting density of matter" is in Russian, so I don't know what the actual argument is for density.

file attached , the English version. I can't get the translation: the PDF is an image file.

source : https://ui.adsabs.harvard.edu/

I'll get back to you on the rest later.

article_20160.pdf

1 hour ago, swansont said:

What is the justification that that particular energy density has physical significance?

Which one?

1 hour ago, swansont said:

1. AFAIK Zero-point energy gets contributions from all frequencies. That’s what the Casimir force shows. That’s a reason I have been begging you to look into the actual QM analysis.

Thank you, I did my best but I didn't realize the importance of the contribution of all frequencies. I will try to go deeper with what I find on the web. 

1 hour ago, swansont said:

2. If 1 is wrong, 2 is irrelevant,...

Of course !

1 hour ago, swansont said:

but why use that volume ?

Because it was the one who was consistent with [math]t_p[/math]. 
-1.- being wrong I don't know if it's still relevant.

1 hour ago, swansont said:

Is that what they are? They aren’t derived from QM

Indeed, they are'nt derived from the QM, but by dimensional analysis (which I have sometimes been reproached for using in this thread, unless I'm mistaken) and in their formula, [math]\hbar[/math], the minimum energy value of a quanta appears each time. 

But that doesn't take away from the fact that they are conceptually linked to a fundamental physical level :

edit : that's why I thought that the energy density of Planck could be used to make an approach to the problem of the cosmological constant as in the document I used as a reference. But this is not going to stop my research with the zero point energy approach. 

Quote

Planck units have little anthropocentric arbitrariness, but do still involve some arbitrary choices in terms of the defining constants. Unlike the metre and second, which exist as base units in the SI system for historical reasons, the Planck length and Planck time are conceptually linked at a fundamental physical level. Consequently, natural units help physicists to reframe questions. Frank Wilczek puts it succinctly:

https://en.wikipedia.org/wiki/Planck_units#Significance

edit 2 : click on "show" of Table 5: Interpretations of the Planck units [21] and take a look at the interpretation of "density". It does seem to have a physical meaning, doesn't it? 

1 hour ago, swansont said:

Is vacuum energy a constant? Forgive me if I don’t take your word for it. How do you arrive at that conclusion?

Now that you have put your finger on the question of the contribution of all frequencies to zero-point energy, this constancy becomes much less obvious now for me

As far as the constancy of the energy density of the cosmological constant you will find plenty of references that assert this within the framework of the standard cosmological model.

7 hours ago, swansont said:

It’s a unit. You can put it in terms of fortnights squared, too. Minutes, years, etc. 

Until you connect it to something with physical significance, it’s numerology.... There’s a reason why physicists look at unitless physical constants - they don’t depend on the units you pick.

The numerical value of the vacuum catastrphe X is dimensionless and must be a ratio in SI units, for example :
[math]X=\frac{t_p^{-2}}{\Lambda_{s^{-2}}}=\frac{l_p^{-2}}{\Lambda_{m^{-2}}}=\frac{\text{quantum energy density} (J/m^3)}{\text{cosmological constant energy density} (J/m^3)}[/math]

I have sketched in this jumble of thread a physical meaning with the meaning of a square root of an energy density. I put it back if necessary if what follows makes sense, otherwise there's no point in looking at it.

7 hours ago, swansont said:

It looks like you’re shopping for a unit system that you want, and you found it.

Question : 

1. Is [math]1/t_p[/math] the value of [math]\nu[/math] for calculating zero-point energy?
2. And divide it by [math]l_p^3[/math] to get its energy density?

- If yes, my solution remains valid to within one constant and not only with numbers but with formulas. 
- If it is not the case, I remain in the unknown for the moment.

The values [math]t_p[/math] and [math]l_p[/math] are not only a system of units in my approach but minimum physical values that make sense (smallest possible time value for known physics, smallest possible length value in QM). That's why I don't understand the criticism about the unit system.

7 hours ago, swansont said:

The wikipedia link labels this as a coincidence. Is that what this is?

Not at all; I hadn't paid attention to it. Vacuum energy (quantum and cosmological) is a constant. The problem is that we expect a ratio of 1 and that it is in 10^122 or 10^123.

Moreover the energy density of the cosmological constant is fixed while the age of the universe varies. The link made and the two seem more than suspicious

I wonder if you're not looking for lice in my head :

Here (https://en.wikipedia.org/wiki/Planck_units#In_cosmology) we have: 

Cosmological constant 5.6 × 10^-122 tp^ -2
 
which is just another way of presenting the cosmological constant problem with a numerical factor (which depends among other things on the precision of the data) and a factor pi close to my presentation of the problem

44 minutes ago, swansont said:

I don’t know what “smallest possible quantum oscillation that applies to zero-point energy” means

I was trying to express that there "existed" a frequency [math]\nu[/math] associated with [math]t_p[/math] in the Big Bang model (value of MQ and not just as a unit). i.e. below [math]t_p[/math], we would need to have a new physics other than the QM  (but this is not my point).

44 minutes ago, swansont said:

Also saying that the Planck time is “smallest” is not correct, I think. The Big Bang model does not apply before a certain time, but that’s not the same as saying time increments that are smaller can’t exist.

I also don't know if after this minimum value in the Big Bang model ([math]t_p[/math]), which has a physical meaning, time should be considered as a continuous function or if it is and should be considered by quantas.

1 hour ago, swansont said:

The Casimir effect is something that tells you zero-point energy is a real phenomenon. The Casimir effect itself is not the vacuum energy, it’s one result of it.

I understand better. Thank you

And how about this, what do you think, please ?
Nonsense or not ?

23 hours ago, stephaneww said:

Let's try to get back to the physical sense:
- Planck's time is the smallest possible value in the Big Bang model.
Is it acceptable to say that between t=0 and t_p it is the smallest possible quantum oscillation that applies to zero-point energy ?
... or is it again nonsense ?

10 hours ago, swansont said:

The Casimir effect is more specifically about excluded photon modes, because of the boundary conditions in place from having conducting surfaces. I’m not aware of a connection to a false vacuum.

 

read on french wikipedia :

Raison

Quote

 

The energy of the "vacuum" between two plates is calculated by taking into account only photons (including virtual photons) whose wavelengths exactly divide the distance between the two plates ({\displaystyle n\lambda =L}, where {\displaystyle n}n is a positive integer, λ the wavelength of a photon, and L the distance between the two plates). This implies that the energy density of the vacuum (between these two plates) is a function of the number of photons that can exist between these two plates.

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

 

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

but I'm not quite sure what that means.

edit :

and we need "two parallel, conductive, uncharged plates"... so matter. It's not exactly a vacuum..

On 6/11/2020 at 10:24 PM, swansont said:

Yes. Have you read those pages? They talk about the Casimir effect and a particle in a box zero-point energy. 

... moreover, if I'm not mistaken, the Casimir effect involves photons, and, if I understood correctly, this is also partly the case for the QED. It seems to me that this is a vacuum with a minimum of radiations, a "false vacuum"?

So I wonder if the "theoretical vacuum" in QM can be treated with Planck's time for the frequency of zero-point energy since the theory (the Big Bang model) cannot go below Planck's time.

On 6/11/2020 at 11:58 PM, swansont said:

You aren’t deriving the value from any physics. You’re just manipulating constants to get a number.

No response to my request at this time.

Let's try to get back to the physical sense:
- Planck's time is the smallest possible value in the Big Bang model.
Is it acceptable to say that between t=0 and t_p it is the smallest possible quantum oscillation that applies to zero-point energy ?
... or is it again nonsense ?

I may have a reference on the French web : a deterministic approach of quantum mechanics recovers the formula of zero-point energy for n=1. I will contact the author to try to know what would be its value in J/m^3 from his work. Who tries nothing has nothing.

6 minutes ago, swansont said:

That’s for you to investigate. The Wikipedia article has a reference

Sobs, references 3 and 4 are books. 

7 minutes ago, swansont said:

 

Quote

 

If I don't make a mistake : 

E=12htp=6.1∗109J  is, in Joules the energy of the theoretical vacuum of the QED for example. It's the vacuum energy theoretically expected.

The number might be. But the QED example comes from QED, not manipulating physical constants. Where is the QED analysis?

How else than dividing E= 6,1 *10^9 J by lp^3 to get 10^114 J/m^3 then ?

4 hours ago, swansont said:

“However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant suggest a much larger value of 10^113 joules per cubic “

1 hour ago, swansont said:

Yes. Have you read those pages? They talk about the Casimir effect and a particle in a box zero-point energy. 

For the Casimir effect, I vaguely know that it's a force of attraction of two plates very close together in a vacuum. It's experimentally observed.

1 hour ago, swansont said:

You know what those links don’t have? Planck units.

I confess I don't understand what you're asking.. When I want to compare values, I put them in the same system of units, the SI. I don't understand what the problem is with that.

1 hour ago, swansont said:

What is your physical justification for these calculations?

If I don't make a mistake : 

[math]E=\frac{1}{2}\frac{h}{t_p}=6.1 * 10^9 J[/math]  is, in Joules the  theoretical vacuum   of the Quantum field theory . It's the vacuum energy theoretically expected.

[math]E_p=E/\pi=1,96* 10^9 J [/math] is, in Joules the Planck energy

[math]E_p/l_p^3 = 4.6* 10^{113 }J/m^3[/math] is Planck's density energy.

1 hour ago, swansont said:

What phenomenon has such a frequency?

I don't know,.

2 hours ago, swansont said:

My point is that you do not appear to be using electrodynamics. You are using Planck units, without making the connection to QED or SED. Planck units predate both GR and QM, so it’s dubious make too strong of a connection to them.

Please, look for my supposed numerical error in SI units.

Here :

https://en.wikipedia.org/wiki/Vacuum_energy#Origin     ( https://en.wikipedia.org/wiki/Zero-point_energy#Quantum_field_theory )

[math]E=\frac{1}{2}h\nu=\frac{1}{2}\frac{h}{t_p ?}=\frac{1}{2}\frac{6,626070 *10{-34} \text{ }  kg. m^2/ s}{5,391247* 10^{-44} s}=6,1452116 * 10^9 \text{ }kg .m^2/s^2=E_p*\pi=m_p*c^2*\pi=m_p\frac{l_p^2}{t_p^2}*\pi[/math] unit :  [math]J = kg .m^2/s^2[/math]

to have something around 10^133 J/m^3 = kg / (m s^2) you have to take the value  [math]l_p^3[/math]  with  [math]m_p\frac{l_p^2}{t_p^2}\frac{1}{l_p^3}=\frac{m_p}{l_p t_p^2}[/math] = 4.6*10^113 J/m^3 

[math]E\frac{1}{l_p^3}=\frac{1}{2}h\nu\frac{1}{l_p^3}=\frac{1}{2}\frac{h}{t_p ?}\frac{1}{l_p^3}[/math] = 1.5*10^114 J/m^3 near 10^114, (not 10^113)

2 hours ago, swansont said:

“However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant suggest a much larger value of 10^113 joules per cubic “

2 hours ago, swansont said:

My point is that you do not appear to be using electrodynamics. You are using Planck units, without making the connection to QED or SED. Planck units predate both GR and QM, so it’s dubious make too strong of a connection to them.

if [math]\nu=1/t_p[/math] I have a connection to QED within a Pi factor ?

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

4 hours ago, swansont said:

The problem I see is that Planck units are a unit system 

The problem goes beyond that for all I understand.

But first of all, there may be a Pi factor missing from my proposal, or it needs to be added for it to be correct:

[math]E_\text{Vacuum Energy}=1/2 h\nu=???? =E_p=m_pc^2[/math] I think so, but I have a doubt about the value of [math]\nu[/math] that I don't know. Can you tell me the value, formula,  and unit of [math]\nu[/math] please?

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

In wikipedia link you also find the definition of the problem :

Quote

However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant suggest a much larger value of 10^113 joules per cubic                                                                                                                                                                      noted by me : (I)

and :

Quote

 Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10^−9 joules per cubic meter.                                                                          noted by me : (II)

Quote

This huge discrepancy is known as the cosmological constant problem.

____________________________________

You can change the value of [math]h[/math] and [math]\nu[/math] if you want, you'll have always a spread (that you'll call cosmologycal constant problem with another value) between (I) and (II), excepted in rare cases.

The problem is that (I) don't match (II)

I have checked, indeed, my proposal works in all cases as long as the values given to Planck's units are consistent with the formulas that govern them.

It makes sense when my proposal is formulated in terms of fundamental constants as I do in this quote below :

On 6/10/2020 at 1:09 AM, stephaneww said:

I have a begining of idea :

in A=mplp.t2p=c7G2.ℏ  we have G2 ,  a QM approach of energy density with value of gravitation ?

in B=ℏ.Λ2m−2.c(8π)2  we have Λ2 , a QM approach of energy density with value of  dark energy ?

B came from the same message where I suggest a mathematic solution of the cosmological constant problem  https://www.scienceforums.net/topic/118858-the-solution-of-the-cosmological-constant-problem/?do=findComment&comment=1115799

or is ot only a circular raisonnement ?

[math]C=\sqrt{A}\sqrt{B}[/math] =  value of density energy of cosmological constant. (note hbar disappears with the multiplication A B square root)

3 hours ago, Mordred said:

I agree with Swansont on needing the SI units to delve into the cosmological problem.

it's what I've always done.

1 hour ago, Mordred said:

Well your going to have to be clearer on which cosmological problem your addressing.

 The cosmological constant has several problems associated with it. The problem you have been working on in the past is the problem of why the observed values are so small. Much smaller than the 10^120 originally predicted value.

It is indeed this latter question that I am trying to answer. 
 I don't know what DM and DE is (edit: Dark Matter and Dark Ernergy ?), probably, it doesn't matter in the context of what I'm trying to address.

The paper I have linked is not trying to solve it, he's just stating it in simple terms  with equality (1). That's what I thought.

Can the problem be approached in this way, which also poses the terms of the problem:

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

with [math]E =\frac{1}{2} h \nu = E_p=m_p c^2[/math] if I don't make a mistake (I'm not sure about these equalities)

and [math] E_p/l_p^3=m_p c^2/l_p^3[/math] to obtain the value of [math]10^{113} J/m^3[/math]

That's what I was trying to say before. I hope it will be clearer

which article are you referring to, please?

https://arxiv.org/ftp/physics/papers/0611/0611115.pdf

https://royalsocietypublishing.org/doi/full/10.1098/rspa.2007.0370

are the same paper

I understand the definition of  mathematical coincidence. It's not the question of numbers in 10^120 wich  interrested me but the way to calculate the cosmolgical constant problem do by the equalty (1)

The definition of wikipedia being too vague, I looked for a more precise definition.

Besides, I couldn't find any scientific discussion on the rest of the paper. (the coincidence between these numbers) a priori this is probably not relevant while the subject of the cosmological constant problem remains open

13 hours ago, swansont said:

That does not follow. Planck units are not a QM prediction. 

Same answer as for Mordred : 

22 hours ago, stephaneww said:

I relied on the equality (1) of this document:

https://arxiv.org/ftp/physics/papers/0611/0611115.pdf

https://royalsocietypublishing.org/doi/full/10.1098/rspa.2007.0370

is that a nonsense?

(Ep=mp c^2)

sorry DeepL gave me a mistranslation for  "Uh-huh:", I meant "Uh... (Clears throat)"

Uh-huh:
ε_p=m_p c^2/l_p^3

c^2=l_p^2/t_p^2

so

m_p c^2/lp^3 = m_p/ (l_p t_p^2) , right?

thank you for your requests, it obliges me to bring clarifications that should have been made from the start

1 hour ago, Mordred said:

PS I'm assuming your using the ⋅ for the multiply operand rather than the cross product. As I am aware your not familiar with inner and cross products in vector notation though that wouldn't make a difference in this case. The logic in either case escapes me.

It makes zero sense to take mass and divide or even multiply by length even with time as part of the operation.

Yes, I use multiplication. Sorry I didn't say it before.

I'll avoid the "." in the future so there won't be any confusion.

I relied on the equality (1) of this document:

https://arxiv.org/ftp/physics/papers/0611/0611115.pdf

https://royalsocietypublishing.org/doi/full/10.1098/rspa.2007.0370

is that a nonsense?

Hi Mordred,

Apart from the dimensional problems encountered and  attempts to introduce the notions of force or electromagnetism (I'll come back to that later) , we can be satisfied with this reminder:

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

[math]c^7[/math] appears naturally when we rewrite mp/(lp.tp^2) with the fundamental constants

______________________________________________

[math]l_p^2=\frac{G\hbar}{c^3}[/math]

[math]m_p^2=\frac{c\hbar}{G}[/math]

[math]t_p^2=\frac{G\hbar}{c^5}[/math]

( mp/(lp.tp^2) )^2 = [math]\frac{c^{14}}{G^4.\hbar^2}[/math]

_______________________________________________

I have a begining of idea :

in [math] A=\frac{ m_p}{l_p.t_p^2}=\frac{c^7}{G^2.\hbar}[/math] we have [math]G^2[/math],  a QM approch of energy density with value of gravitation ?

in [math]B=\frac{\hbar.\Lambda_{m^{-2}}^2.c}{(8\pi)^2}[/math] we have [math]\Lambda^2[/math], a QM approch of energy density with value of  dark energy ?

[math]B[/math] came from the same message where I suggest a mathematic solution of the cosmological constant problem  https://www.scienceforums.net/topic/118858-the-solution-of-the-cosmological-constant-problem/?do=findComment&comment=1115799

or is ot only a circular raisonnement ?

25 minutes ago, swansont said:

You have mass/length*time^2

What is that supposed to represent? What physics equation does that come from?

It is the energy density per volume in Planck units (Ep/lp^3 ,  J/m^3) in the QM 

This is a theoretical vacuum energy in QM

[math]\frac{c^4 \Lambda}{8\pi .G}[/math] is the observed value, The cosmological constant problem  is the mismatch between the two with a ratio of 10^122.

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

52 minutes ago, swansont said:

As a general rule, if G shows up in an equation, that equation has something to do with gravity. If h-bar shows up, it’s related to quantum mechanics. G and h-bar are not “just data”

 

Quote

You mean it's not important ?

Since you say it doesn’t exist, I’d guess the answer is that it’s not.

 

Okay, but what is your point of view about :

[math]\frac{m_p}{l_p t_p^2}=\frac{c^7}{G^2 \hbar}[/math] in this case ?

specifically what is G^2 or c^7 physically ?

.. then the cosmological constant problem can be write as :

[math]\frac{8\pi.c^3.G}{\Lambda. \hbar}=8.73*10^{122}[/math]

Thank you for questioning me. It stimulates me.