The solution of the Cosmological constant problem ?

[swansont]

“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 “

 

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.

 

For example: “The Planck time is the unique combination of the gravitational constant G, the relativity constant c, and the quantum constant h, to produce a constant with units of time.”

https://www.universetoday.com/79418/planck-time/

Combining constants to get units right is not something you can take as physically meaningful. 

 

When talking about a factor of 10^122, a missing factor of pi is not a big deal.

[stephaneww]

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

 

Edited June 11, 2020 by stephaneww

[swansont]

49 minutes ago, stephaneww said:

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

I didn’t say you made a numerical error

 

Quote

Here :

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

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

 

Quote

[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 :  J=kg.m2/s2

to have something around 10^133 J/m^3 = kg / (m s^2) you have to take the value  l3p   with  mpl2pt2p1l3p=mplpt2p = 4.6*10^113 J/m^3 

E1l3p=12hν1l3p=12htp?1l3p = 1.5*10^114 J/m^3 near 10^114, (not 10^113)

You know what those links don’t have? Planck units. What is your physical justification for these calculations? (i.e. something in physics, not derived from Planck units)

 

Quote

 

if ν=1/tp I have a connection to QED within a Pi factor ?

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

 

What phenomenon has such a frequency?  (i.e. something in physics, not derived from Planck units)

 

[stephaneww]

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,.

 

 

Edited June 11, 2020 by stephaneww

[swansont]

29 minutes ago, stephaneww said:

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.

Yes. It has to do with vacuum states having zero-point energy.

29 minutes ago, stephaneww said:

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.

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

Why not multiply the energy by the fine structure constant, raised to the ~60th power? It’s unitless, so you’ll still have units of energy. Then the problem goes away.

 

29 minutes ago, stephaneww said:

 

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?

 

[stephaneww]

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 “

 

[swansont]

14 minutes ago, stephaneww said:

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

 

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

[stephaneww]

6 minutes ago, swansont said:

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

Sobs, references 3 and 4 are books. 

[swansont]

1 hour ago, stephaneww said:

Sobs, references 3 and 4 are books. 

Library.

[stephaneww]

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.

[stephaneww]

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 ?

Edited June 20, 2020 by stephaneww

[stephaneww]

 

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.

 

Edited June 20, 2020 by stephaneww

[swansont]

6 hours ago, stephaneww said:

 

... 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.

 

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.

 

[stephaneww]

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..

Edited June 20, 2020 by stephaneww

[swansont]

37 minutes ago, stephaneww said:

read on french wikipedia :

Raison

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

but I'm not quite sure what that means.

Photons between conductors have to form a standing wave, so not all wavelengths are allowed, unlike free space.

 

Quote

edit :

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

So? The “vacuum” label is there to tell you it’s there even when you have nothing. You generally don’t care about the walls of a vacuum, anyway. 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.

[stephaneww]

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 ?

 

Edited June 21, 2020 by stephaneww

[swansont]

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

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.

[stephaneww]

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.

Edited June 21, 2020 by stephaneww

[stephaneww]

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

[swansont]

2 hours ago, stephaneww said:

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

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. It looks like you’re shopping for a unit system that you want, and you found it. There’s a reason why physicists look at unitless physical constants - they don’t depend on the units you pick. The fine structure constant, for example, is always the same value, regardless of your unit system. And it shows up in EM interactions.

What interaction, and formula that predicts it, gives rise to the Planck time, to connect it to this? The wikipedia link labels this as a coincidence. Is that what this is?

[stephaneww]

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

 

Edited June 21, 2020 by stephaneww

[swansont]

27 minutes ago, stephaneww said:

The numerical value of the vacuum catastrphe X is dimensionless and must be a ratio in SI units, for example :
X=t−2pΛs−2=l−2pΛm−2=quantum energy density(J/m3)cosmological constant energy density(J/m3)

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.

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

Quote

Question : 

1. Is 1/tp the value of ν for calculating zero-point energy?
2. And divide it by l3p to get its energy density?

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.

2. If 1 is wrong, 2 is irrelevant, but why use that volume?

 

Quote

 

The values tp and lp 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.

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

 

Quote

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

 

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

[stephaneww]

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.

Edited June 21, 2020 by stephaneww

[swansont]

3 hours ago, stephaneww said:

Which one?

The one I keep objecting to. Your energy density using planck energy and planck length

 

Quote

 

Because it was the one who was consistent with tp . 
-1.- being wrong I don't know if it's still relevant.

I'm not sure how "consistent with" applies here.  The Planck energy is almost 2 x 10^9 J. That's huge on the quantum scale. If you're insisting that the Planck length and time are the smallest increments, isn't it more "consistent" to find a minimum energy? Or at least an energy that makes sense on the quantum scale, for a quantum phenomenon?

 

Quote

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, ℏ , the minimum energy value of a quanta appears each time. 

ℏ is not a minimum energy value, though, since the frequency of quanta can approach zero.

Quote

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. 

What is the "fundamental physics level" of ~2 Gigajoules?

 

Quote

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? 

I guess that's something for you to investigate. But "limiting density of matter" sounds very much like it's not a vacuum phenomenon

If you go to the link in the citation (number 21) the author says "The Planck units have no practical application" and points out that the Planck mass is 17 orders of magnitude larger than the top quark mass, an so makes a conjecture that it's an upper limit. 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.

 

 

 

[stephaneww]

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

Edited June 22, 2020 by stephaneww