The solution of the Cosmological constant problem ?

[Mordred]

After 10 pages of modification and corrections over nearly a year. Easily done. 

To be honest I lost track and I am one of your most active guide as well as participant.

[stephaneww]

On 5/13/2020 at 12:08 AM, stephaneww said:

I confess I've lost track a little over the time...

 

 

Me too Mordred 😉

[Mordred]

Then I suggest you go through this lengthy thread and plan a finalized form to debate in a separate thread. 

 This would cut short a lot of the training steps for other readers.

[stephaneww]

This proposal suits me. 

What title do you propose for the new thread ?

[Mordred]

Work on your finalized form and I will get approval from the other moderator staff. Then PM you once approval is gained.

 

[stephaneww]

ok

 

 

Edited May 23, 2020 by stephaneww

[Mordred]

Recommendation on steps apply the FLRW metric without the cosmological constant.

Then apply the changes to the expansion rate due to the constant.

Specifically describe which of the cosmological constant problems you are describing.

Show previous other person solutions to the problem  as reference such as the Unruh paper for comparison 

Then describe your solution in comparison to the solutions you discussed in this thread.

Treat this as a full paper.

!

Moderator Note

Request has been sent.

 

[stephaneww]

2 hours ago, swansont said:

Does that help?

Like I said, it looks like you have roundoff error, and you've shown that 1 = 1

yes, that help me, thank you 👍

after simplication the equality is correct

 

and ...

2 hours ago, swansont said:

I’m not sure why Fp made an appearance, but yes.

...about of the doubt of the interest of the physical meaning of equality :

I had note before that Fp = Coulomb's force with Planck's units  ([math]q_1=q_2=q_p[/math] and [math]r=l_p[/math])

 

But I don't know if that equality can make physical sense with the problem of the cosmological constant with or whitout an electromagnetic framework .

Do you have any idea ?

4 hours ago, stephaneww said:

note 2 : possible link with the problem of the cosmological constant ?

About the Coulomb's force, there was a particular problem with the sign of the charges. . Can this "equality" help solve or am I going to fall back on circular reasoning...  ? 

 

 

Edited June 8, 2020 by stephaneww

[stephaneww]

...

1 hour ago, stephaneww said:

About the Coulomb's force, there was a particular problem with the sign of the charges. . Can this "equality" help solve or am I going to fall back on circular reasoning...  ? 

The signs of the charges are opposite (electrically neutral universe), the Coulomb force is negative but its square is positive for example

Edited June 8, 2020 by stephaneww

[swansont]

I am unaware of any connection to the cosmological constant. There are no gravitational terms in the simplified formulas

[stephaneww]

The simplicity of your argument had eluded me. Thank you.

Edit :

 

12 hours ago, stephaneww said:

But I don't know if that equality can make physical sense with the problem of the cosmological constant with or whitout an electromagnetic framework .

Do you have any idea ?

In the cosmological constant problem, there are no gravitational terms in the simplified formulas either, right ?

Edited June 8, 2020 by stephaneww

[Mordred]

Nope the cosmological constant has no gravitational force or Coulomb force term.

A force is a vector it has a magnitude and direction. 

The cosmological constant is a scalar quantity. It's value only has a magnitude.

 This is one critical detail you have to learn to seperate. The two types of fields will have different dynamics.

Edited June 8, 2020 by Mordred

[stephaneww]

1 minute ago, Mordred said:

A force is a vector it has a magnitude and direction. 

 

Yes, we've already talked about it, but for a force squared, what about it?

[Mordred]

Let's take an example.

Take two stars at some distance apart 

Now surround those stars with a uniform mass/energy density. The pressure is uniform so there is no pressure gradient.

On all sides of those stars equal pressure is exerted.  So no net force exists to give the star movement into a particular direction.

Yet the stars do seperate due to expansion. The cosmological constant affects the uniform distribution contributing to added volume. Yet it does not exert a force or pressure term.

[swansont]

1 hour ago, stephaneww said:

The simplicity of your argument had eluded me. Thank you.

Edit :

 

In the cosmological constant problem, there are no gravitational terms in the simplified formulas either, right ?

If you were to determine the cosmological constant from experiment, what formula(s) would you use?

[swansont]

26 minutes ago, Mordred said:

Nope the cosmological constant has no gravitational force or Coulomb force term.

A force is a vector it has a magnitude and direction. 

The cosmological constant is a scalar quantity. It's value only has a magnitude.

 

The fine structure constant is a scalar as well, and yet it depends on other terms. 

[stephaneww]

22 minutes ago, Mordred said:

Let's take an example.

Take two stars at some distance apart 

Now surround those stars with a uniform mass/energy density. The pressure is uniform so there is no pressure gradient.

On all sides of those stars equal pressure is exerted.  So no net force exists to give the star movement into a particular direction.

Yet the stars do seperate due to expansion. The cosmological constant affects the uniform distribution contributing to added volume. Yet it does not exert a force or pressure term.

Yes, okay, but the pressure should decrease as the volume increases. But the pressure of the cosmological constant is constant as the volume increases.

And I don't know what a square force is physically speaking to know if my "equality" can have a physical meaning

[swansont]

36 minutes ago, stephaneww said:

Yes, we've already talked about it, but for a force squared, what about it?

If this is in reference to Fp, you need to realize the planck units are those of scale. The Planck force is not an actual force. It simply a value of force under certain assumptions. 

It’s no different than saying 1 Newton is the force exerted on 1 kg that makes it accelerate at 1 m/s^2. It’s not a new category of force.

[stephaneww]

3 hours ago, swansont said:

If you were to determine the cosmological constant from experiment, what formula(s) would you use?

I don't know if it's really from an experiment, but I use and datas from the Planck satellite from Wikipedia :

[math] \Lambda=1,1056*10^{-52}.m^{-2}[/math]
[math]\rho_{\Lambda}c^2=\frac{c^4 \Lambda}{8 \pi G}[/math] (2)

and :

[math]\frac{m_p.l_p^2}{t_p^2}[/math] (1)

vaccum catastrophe = (1)/(2)

 

3 hours ago, swansont said:

If this is in reference to Fp, you need to realize the planck units are those of scale. The Planck force is not an actual force. It simply a value of force under certain assumptions. 

It’s no different than saying 1 Newton is the force exerted on 1 kg that makes it accelerate at 1 m/s^2. It’s not a new category of force.

Thank you, it was about Fp indeed.
So a priori there's no physical sense of force squared... right ?

In the same vein: does a squared pulse have a physical meaning in QM ? I ask the question because I've already seen it in an unpublished research work.

 

 

Edit : 

The origin of the last messages after May comes from this thread: : https://www.scienceforums.net/topic/122287-puzzle-for-the-week-mystery-and-gum-ball-around-a-fine-structure-constant-in-planck-units-dimensioned-with-the-coulomb/

 

..  where I try to propose a link between the fine structure constant and the cosmological constant problem with this formula:  : 

[math]\Large{\alpha=\frac {F_p^2}{e^2}. \frac {t_p^3}{m_p.2.\pi} . \frac {8.\pi^2}{c} .\frac {1}{\mu_0} }[/math]

 

- [math]\alpha[/math]: fine constant structure

- Fp: Planck's force  

- e : elementary charge

- t_p³/(mp.2.pi) : inverse of Planck's surface power density * 1/(2pi) 

note 1 : units of surface power density = W/m^2 = kg/s^3

note 2 : possible link with the problem of the cosmological constant ?

- c : speed of light

- μ0 : vacuum permeability

Edited June 8, 2020 by stephaneww

[stephaneww]

1 hour ago, stephaneww said:

I don't know if it's really from an experiment, but I use and datas from the Planck satellite from Wikipedia :

and of course mission Planck is an experiment  (shame on me  ):

https://en.wikipedia.org/wiki/Planck_(spacecraft)

[joigus]

Sorry. If it's not too much trouble, I really want to understand your argument. The way I see it, there are two problems related to the cosmological constant. Or, if you wish, a problem in two steps. One is: 1) Why is it that QFT predicts such a large value (about 10¹²⁰ times its measured value.)? And then: 2) Why is it that its actual value is so small and why that particular value?

[stephaneww]

I suggest that QM is not of the same nature as relativity:
I put the comological constant in a context of MQ by dimensional analysis. Here we find an extremely low energy density by volume
 

The multiplication of the two square roots of the energy volume densities of the QM gives the value of the cosmological constant in relativity

To my knowledge, there is no theory that includes square roots of energy volume density in QM, relativity or cosmology. (I know very little about QM and relativity)

The only context in which I could find this dimension (J/m^3)^^1/2 is with the Hildebrand solubility parameter

41 minutes ago, joigus said:

1) Why is it that QFT predicts such a large value (about 10¹²⁰ times its measured value.)?

I suggest that QM is not of the same nature as relativity:
I put the comological constant in a context of MQ by dimensional analysis. Here we find an extremely low energy density by volume
 

The multiplication of the two square roots of the energy volume densities of the QM gives the value of the cosmological constant in relativity

To my knowledge, there is no theory that includes square roots of energy volume density in QM, relativity or cosmology. (I know very little about QM and relativity)

The only context in which I could find this dimension (J/m^3)^^1/2 is with the Hildebrand solubility parameter

 

42 minutes ago, joigus said:

2) Why is it that its actual value is so small and why that particular value?

I don't know

ooops error

2 hours ago, stephaneww said:

[math]\frac{m_p.l_p^2}{t^3}[/math]   (1)

vaccum catastrophe = (1)/(2)

(1)=[math]\frac{m_p}{l_p.t^2}[/math] is right

Edited June 8, 2020 by stephaneww

[Mordred]

1 hour ago, joigus said:

Sorry. If it's not too much trouble, I really want to understand your argument. The way I see it, there are two problems related to the cosmological constant. Or, if you wish, a problem in two steps. One is: 1) Why is it that QFT predicts such a large value (about 10¹²⁰ times its measured value.)? And then: 2) Why is it that its actual value is so small and why that particular value?

This link is earlier in this thread.

Unruh came up with an interesting solution. Just thought I would post here for you Joigus.

https://arxiv.org/pdf/1703.00543.pdf

[joigus]

3 minutes ago, Mordred said:

This link is earlier in this thread.

Unruh came up with an interesting solution. Just thought I would post here for you Joigus.

https://arxiv.org/pdf/1703.00543.pdf

Thanks a lot, Mordred.

[swansont]

4 hours ago, stephaneww said:

I don't know if it's really from an experiment, but I use and datas from the Planck satellite from Wikipedia :

Λ=1,1056∗10−52.m−2
ρΛc2=c4Λ8πG (2)

and :

mp.l2pt2p (1)

 

And there’s G, in equation 2. It’s related to gravity.

Equation 1 has no physical significance, AFAIK

Quote

 

 Thank you, it was about Fp indeed.
So a priori there's no physical sense of force squared... right ?

Show an equation that has F^2 in it, and include the derivation.

 

4 hours ago, stephaneww said:

I

The origin of the last messages after May comes from this thread: : https://www.scienceforums.net/topic/122287-puzzle-for-the-week-mystery-and-gum-ball-around-a-fine-structure-constant-in-planck-units-dimensioned-with-the-coulomb/

 

..  where I try to propose a link between the fine structure constant and the cosmological constant problem with this formula:  : 

α=F2pe2.t3pmp.2.π.8.π2c.1μ0

 

Where did the equation come from?

 

You have to be careful assigning physical relevance when all you’re doing is rewriting constants.

If you replace all terms of c with the airspeed velocity of an unladen swallow (times some unitless number, of course), it does not mean your equation suddenly  has a connection to bird flight.