exact value of vaccum catastroph ?

[stephaneww]

hello

 

can somebody give the exact value of vaccum catastroph with 1 decimal and the calculation please ?

 

thank you in advance.

 

stéphane

Edited April 26, 2016 by stephaneww

[swansont]

hello

 

can somebody give the exact value of vaccum catastroph with 1 decimal and the calculation please ?

 

thank you in advance.

 

stéphane

 

 

I'm not sure the number exists with that level of precision. The quantum vacuum value depends in part on what assumptions you use rather than empirical data inputs.

[stephaneww]

with current data mission planck, cosmological constant is arround 1,1*10^-52 m^-2. the rest is planck values and c so i think it's possible...

Edited April 26, 2016 by stephaneww

[stephaneww]

I'm not sure the number exists with that level of precision. The quantum vacuum value depends in part on what assumptions you use rather than empirical data inputs.

 

I try an exact value with 3 decimal, in using defintion (1) of this document, the last values of Plank mission and codata values, then I engage a discussion about it. If the moderation think it's necessary, thanks to move the thread in "speculation" section.

 

Cosmological constant = [LaTex]\Lambda = 1,111*10^{-52}* m^{-2}[/LaTex] = [LaTex]9,992*10^{-36}s^{-2}[/LaTex]

 

Vaccum energy density of cosmological constant = [LaTex]5,354**10^{-10} Joules*m^{-3}[/LaTex]

 

Density of quantum vacuum = [LaTex]\frac{m_p}{l_p^3}[/LaTex] = [LaTex]5,155 * 10^{96}*Kg*m^{-3}[/LaTex]

 

"Planck energy density" = [LaTex]4,633**10^{113}Joules*m^{-3}[/LaTex]

 

"Planck energy density" / Vaccum energy density of cosmological constant = [LaTex]8,654*10^{122}[/LaTex] adimensionless

___________________________________________________________________________________________

 

I have also found that if we exprim the units with s^-2 we have :

 

(2) [LaTex]\frac{2*\pi*4}{t_p^2*\Lambda}[/LaTex] exactly egals to :

 

"Planck energy density" / "Vaccum energy density of cosmological constant" = [LaTex]8,654*10^{122}[/LaTex] adimensionless

 

___________________________________________________________________________________________

 

Now, if we use [LaTex]\Lambda = 1,111*10^{-52}* m^{-2}[/LaTex]

 

square racine of (2) = [LaTex]8,8*10^{69}*\frac{m}{s}[/LaTex] : is "very" above of the ligth speed so this seems to be an absurd value and seems to mean that the vaccum catastroph is an absurd problem

 

 

 

(except perhaps if it's linked to cosmic inflation)

Edited November 22, 2016 by stephaneww

[Mordred]

The major problem here is that the Planck energy density is roughly 120 orders of magnitude too high.

 

This is a known problem in QM.

 

"However, most Planck units are many orders of magnitude too large or too small to be of practical use, so that Planck units as a system are really only relevant to theoretical physics. In fact, 1 Planck unit is often the largest or smallest value of a physical quantity that makes sense according to our current understanding."

 

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

[stephaneww]

 

 

I have also found that if we exprim the units with s^-2 we have :

 

(2) [LaTex]\frac{2*\pi*4}{t_p^2*\Lambda}[/LaTex] exactly egals to :

 

"Planck energy density" / "Vaccum energy density of cosmological constant" = [LaTex]8,654*10^{122}[/LaTex] adimensionless

 

hello

 

I have a new question :

 

(2) is also exactly egals to

 

(3)[LaTex]\frac{2*\pi*4}{l_p^2*\Lambda}[/LaTex] when [LaTex]\Lambda[/LaTex] is in [LaTex]m^{-2}[/LaTex]

 

My question :

 

If (3) is mathematically dimensionless, it seems to have a different "meaning physically".

 

Indeed : .

 

[LaTex]l_p^2\Lambda[/LaTex] (4) is a length multiplied by an energy.

 

So can we say that (4) is "physically dimensionless" and, if no, is it a possible explanation of the vacuum catastrophe?

Edited January 15, 2017 by stephaneww

[Mordred]

I will have to post my reply later. vacuum is to say the least difficult to describe. You seem to have some skill but looks like you need a proper direction which will take considerable time to latex in.

 

The first step is to understand the very term vacuum which is not straightforward. Prior to different vacuum expectation values.

hello

 

can somebody give the exact value of vaccum catastroph with 1 decimal and the calculation please ?

 

thank you in advance.

 

stéphane

I hope your ready for some very complex mathematics. Once I post how a vacuum is defined you will see just how complex answering this question really is. At the very best I can only generalize the principles and mathematics involved to give a direction for you to further research in the proper direction.

 

It will simply be impossible to cover everything you will need to understand on a forum.

Edited January 15, 2017 by Mordred

[stephaneww]

hello Mordred

 

if you think it's necessary, I can post the demonstration of the equivalences

I will have to post my reply later. vacuum is to say the least difficult to describe. You seem to have some skill but looks like you need a proper direction which will take considerable time to latex in.

The first step is to understand the very term vacuum which is not straightforward. Prior to different vacuum expectation values.

I hope your ready for some very complex mathematics. Once I post how a vacuum is defined you will see just how complex answering this question really is.

Ooops I'm not sure to have the level...

 

I try an exact value with 3 decimal, in using defintion (1) of this document, the last values of Plank mission and codata values, then I engage a discussion about it. If the moderation think it's necessary, thanks to move the thread in "speculation" section

 

.

 

I have use the definitions of the document arxiv

Edited January 15, 2017 by stephaneww

[Mordred]

I will have to take it step by step. Particularly since it involves QFT. Simply no shorter way I can think of and be accurate. The first field I will have to detail is the Higgs field.

Edited January 15, 2017 by Mordred

[stephaneww]

I don't understand the QFT

Edited January 15, 2017 by stephaneww

[Mordred]

The last post isn't much use unless you know how a vacuum is defined mathematically. Thats why I need to first cover that step. Then I can better detail the different types of vacuum

I don't understand the QFT

I know I figured that much out so will try as best as possible to simplify it for you

I don't understand the QFT

I know I figured that much out so will try as best as possible to simplify it for you

Edited January 15, 2017 by Mordred

[stephaneww]

Ok, but, again, I think I do not have the level to understand.

[Mordred]

Ok, but, again, I think I do not have the level to understand.

Not yet but its better to start at the beginning than jump to the end. There is a key formula involved that requires explaining. It a formula that involves all types of vacuum

Edited January 15, 2017 by Mordred

[stephaneww]

Not yet but its better to start at the beginning than jump to the end. There is a key formula involved that requires explaining. It a formula that involves all types of vaooppps

oops I have not the time to answer after your edit

 

I will try to understand if it's simplified ,)

Edited January 15, 2017 by stephaneww

[Mordred]

I will do the best I can lol. It is a good question just not easy to answer

Edited January 15, 2017 by Mordred

[stephaneww]

I will have to take it step by step. Particularly since it involves QFT. Simply no shorter way I can think of and be accurate. The first field I will have to detail is the Higgs field.

Uh, I do not use the Higgs field, but the definition that raised the question for the first time. After that, if we do not find an explanation for this "first error", we will look elsewhere with the Higgs field or something else.

 

But I'm ready for your explanations, I will do my best

Edited January 15, 2017 by stephaneww

[Mordred]

First step we must define a field, a field is an abstract device. Fields are a way of describing a behavior of some physical nature. For example a magnetic field is not some mysterious substance filling space but a statement that objects placed near a magnetic field placed near a magnet move in a certain way. This is is the first misnomer to hurdle., I specified particular treatment.

In essence fields is a way to to describe the behavior of a physical system. In order to describe a physical system you must first define the system itself. In the case of vacuum the system we must describe is its dimensions. One can arbitrarily define a system of coordinates but the preferred methodology is a coordinate independent system primary example being tensors as per GR.

While fields are fundamental, they are still strictly an abstract methodology. One of the most important concepts to understand in physics is that any system described or state of a system depends upon the methodology or property being examined. At the very best more often or not this is a set of reasonable/best approximations depending upon the dynamic in question. In essence we describe any application of any collection of events/action in terms of a field.

 

A field being heuristically treated as a collection of dynamics being examined. For example of primary importance's a collection of events as per GR

 

Now the intuitive definition of a vacuum is that which we take away all particles, including field fluctuations ie virtual particles/fluctuations and real particles/excitation's. The primary distinction being individual fluctuations being of insufficient energy/momentum to cause "action" ie observable or individually measurable. However a group of individual VP can cause effective action under boundary confinement.

I have been avoiding numerous key terminology but under careful study any dynamic under careful study, any effective action is classified as an operator, whilst a contributor to quantify as a virtual particle is a propagator. An operator adds or subtracts an effective action whilst it requires a group of propagators under a restricted confinement to cause effective action.as all real particles depends on its effective action. A virtual particle has insufficient momentum and mass to perform a quanta of action. Indeed the very term particle is a historical misnomer as all particles are field excitation's. They are not little balls colliding with one another but discrete quantities that exhibit point-like and wavelike characteristics. This equates to boundary confinement.

Action equates to kinematic motion, ie scattering/interference etc. In the principle of of least action it equates to motion itself.

In essence particles are just localized dynamics of a field or localized clumped dynamics. This is the rudimentary core of defining any particle. Every quantum number is under specific property treatment..

 

Now onto vacuum itself . A vacuum itself is what system we could take from it all particles from above.

 

edit::ran out of time will have to post further next post, far too late to accurately describe the above in terms of vacuum lol brain is getting fried and this is by far too an important topic to make stupid mistakes. However I needed to first clarify numerous key aspects

Edited January 15, 2017 by Mordred

[stephaneww]

lol, thanks you

...

 

Now the intuitive definition of a vacuum is that which we take away all particles, including field fluctuations ie virtual particles/fluctuations and real particles/excitation's. The primary distinction being individual fluctuations being of insufficient energy/momentum to cause "action" ie observable or individually measurable. However a group of individual VP can cause effective action under boundary confinement....

 

edit::ran out of time will have to post further next post, far too late to accurately describe describe the above in terms of vacuum lol brain is getting fried and this is too a key topic to make stupid mistakes

lol good night

 

what is "VP" please ?

virtual particles ?.

Edited January 15, 2017 by stephaneww

[Mordred]

Yes shorthand for virtual particles. I will type in the rest later.

 

as your OK with the above we can move on. First a vacuum is ideally a state void of all particles however due to the Heisenburg uncertainty principle the field energy can never be exactly zero. The best we can ever hope for is a minimal value. This minimal value is the true vacuum. Any higher value is a false vacuum state. See image here https://en.wikipedia.org/wiki/False_vacuum#/media/File:Falsevacuum.svg

 

Now first we require a metric that conforms to GR to describe our universe. The FLRW metric is handy for that.

 

[latex]d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{r^2}d\Omega^2][/latex]

[latex]S\kappa r= \begin{cases} R sin r/R &k=+1\\ r &k=0\\ R sin r/R &k=-1 \end {cases}[/latex]

 

Our universe is extremely close to flat so the curvature constant k which is also dimensionless as is r as r is a commoving volume. It is a(t) that carries the dimensions of length above.

 

to get better details you can read an article I wrote on this topic

http://cosmology101.wikidot.com/universe-geometry

page two is

http://cosmology101.wikidot.com/geometry-flrw-metric/

 

Now a vacuum is a scalar field we can describe this with an equation of state

https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

 

see scalar modelling at the last link however a missing key detail on that link is how energy density and pressure defined under that equation.

 

[latex]\rho=\frac{1}{2}\dot{\phi}^2+V(\phi)[/latex]

[latex]p=\frac{1}{2}\dot{\phi}^2-V(\phi)[/latex]

 

now if our field varies slowly as it does the interesting consequence is that [latex]p=-\rho[/latex] so it behaves like a cosmological constant term in the Einstein field equations

 

[latex]R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}+\Lambda g_{\mu\nu}=0[/latex]

 

for a flat universe [latex]\Lambda=G_nV \phi[/latex] the Einstein field equations reduce to the FLRW equation

 

[latex]H^2=\frac{8\pi G_n}{3}\rho\rightarrow \frac{\dot{a}}{a}=\sqrt{\frac{8\pi G_nV(\phi)}{3}}[/latex]

 

now we can further set a function of time [latex]\phi=\phi(t)[/latex] where the resulting stress tensor becomes

[latex]T_{\mu\nu}=\nabla_{\mu\phi}\nabla_{v\phi}-1/2g_{\mu\nu}\nabla_{\rho\phi}\nabla^\rho_\phi-g_{\mu\nu}V(\phi)[/latex]

 

The Hamiltonian- density for a scalar field is given by

 

[latex] H=\frac{\dot{\phi}^2}{2}+\frac{1}{2}(\nabla\phi)^2+V(\phi)[/latex]

 

 

 

Anyways now you have some of the more useful tools to model a scalar field without getting too intense in QFT treatment. This should significantly improve your understanding.

 

The above can be applied to any scalar field. I figure this is a better approach than detailing the Higg's field.

 

To assist you further

 

http://www.google.ca/url?sa=t&source=web&cd=3&ved=0ahUKEwibsrjQxMXRAhVH-mMKHYvcDY0QFgglMAI&url=http%3A%2F%2Fcatarina.udlap.mx%2Fu_dl_a%2Ftales%2Fdocumentos%2Flfa%2Fjuarez_a_ba%2Fcapitulo2.pdf&usg=AFQjCNFQ5u_jG9kbZx7L1RVgSnqzikYRsw&sig2=-w0qYSDm0D6ZcSZGl00E_g

 

http://www.google.ca/url?sa=t&source=web&cd=5&ved=0ahUKEwibsrjQxMXRAhVH-mMKHYvcDY0QFggqMAQ&url=http%3A%2F%2Fweb.mit.edu%2Fviz%2FEM%2Fvisualizations%2Fcoursenotes%2Fmodules%2Fguide01.pdf&usg=AFQjCNGhjsnbi1o5pMP9SUbZvRly1MO7cw&sig2=lDXjZMU4ZC-XiuQHUkkEwg

 

http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

 

Hope that helps

Edited January 16, 2017 by Mordred

[Mordred]

hello

 

can somebody give the exact value of vaccum catastroph with 1 decimal and the calculation please ?

 

thank you in advance.

 

stéphane

Now the reason why this is so difficult to answer is that all the above doesn't include quantum corrections.

 

[latex]V(\phi_o)=1/2m^2\phi^2_o+\frac{\lambda}{4!}\phi^4_o[/latex] this is the 0 loop correction the 1-loop correction is

[latex]+\frac{M^4}{64\pi^2}(ln\frac{m^2}{u^2})-\frac{3}{2})-\frac{\tilde{m}^4}{16\pi^2}(ln(\frac{\tilde{m}^2}{\mu^2})-\frac{3}{2}[/latex]

 

it is the quantum corrections which is the real issue specific to the vacuum catastrophe. However even this is an approximation

 

 

I'm not sure the number exists with that level of precision. The quantum vacuum value depends in part on what assumptions you use rather than empirical data inputs.

which is what Swansont referred to here.

 

In order to explain the above would literally require a course in QFT.

 

Edit my apologies these are the corrections on the Higgs field itself. I thought something was off so had to recheck. It was [latex]\tilde{m}^4[/latex] that clued me in as the Higgs field has a quartic dependence on mass

Edited January 16, 2017 by Mordred

[stephaneww]

Hello Mordred

As I said, I do not know the QFT, so I did not understand anything sorry.

The only thing I know is that QFT as the string theory are currently speculative.

Thank you very much for your efforts of explanation, I hope that other people will understand.

Have a good day

[Mordred]

Actually very little of this is in QFT format. I did this using the FLRW metric with some GR. Its far easier to learn the FLRW metric than QFT. These are your classical field equations

 

If you look at the last two links they are literally free textbooks.

 

Also QFT isn't string theory.

Edited January 16, 2017 by Mordred

[stephaneww]

Actually very little of this is in QFT format. I did this using the FLRW metric with some GR. Its far easier to learn the FLRW metric than QFT. These are your classical field equations

 

If you look at the last two links they are literally free textbooks.

 

 

uh, I have a lot of work to learn FLRW metric.

 

Also QFT isn't string theory.

 

I know that, they are competing

Edited January 17, 2017 by stephaneww

[stephaneww]

 

hello

 

I have a new question :

 

(2) is also exactly egals to

 

(3)[LaTex]\frac{2*\pi*4}{l_p^2*\Lambda}[/LaTex] when [LaTex]\Lambda[/LaTex] is in [LaTex]m^{-2}[/LaTex]

 

My question :

 

If (3) is mathematically dimensionless, it seems to have a different "meaning physically".

 

Indeed : .

 

[LaTex]l_p^2\Lambda[/LaTex] (4) is a length multiplied by an energy.

 

So can we say that (4) is "physically dimensionless" and, if no, is it a possible explanation of the vacuum catastrophe?

oops ... read :

 

Indeed : .

 

[LaTex]l_p^2\Lambda[/LaTex] (4) is a surface multiplied by an energy.

 

So can we say that (4) is "physically dimensionless" and, if no, is it a possible explanation of the vacuum catastrophe?

 

please Mordred what is your answer for this question (a surface multiplied by an energy) ?

 

I have ask a french physical Dr. and he anwsers me that a surface multiplied by an energy is unknow and a nosense in physics.

[swansont]

I have ask a french physical Dr. and he anwsers me that a surface multiplied by an energy is unknow and a nosense in physics.

And I agree, it's nonsense. A surface does not have units.

 

But an area multiplied by an energy would be perfectly acceptable, if that's what you had.