The vacuum energy v. Higgs field - discrepancy

[chron44]

Hi,

The average vacuum energy is estimated to about 3 GeV/m^3 (the observed). If relying on this value (when
the calculated in extremely much higher). -And the Higgs field energy VEV, the vacuum expectation value, is
both observed in the LHC experiment and fairly calculated to about 246 GeV. How are these differences
explained in QM physics?

3 GeV versus 246 GeV?

I understand that the VEV amount is presented without any special volume in mind. But surely the VEV
isn't correlated to the cubic meter volume, though must be estimated to the Planck scale. Far minor
than the m^3 which the vacuum is given with. The VEV is a universal constant thought to fill all
universe with neither any much higher nor any lower energy content. This issue is raised with the
condition of both the vacuum energy volume and the Higgs field are without any elementary particles,
though being absolutely empty of any visible "matter". -Without even one single photon or neutrino
or whatever. The only content is the absolute vacuum itself (3 GeV).

The VEV can be regarded for proven with the Higgs boson discovery in 2012. And the vacuum content
have with the Planck Collaboration project also been verified.

/chron44

[Mordred]

11 minutes ago, chron44 said:

Hi,

The average vacuum energy is estimated to about 3 GeV/m^3 (the observed). If relying on this value (when
the calculated in extremely much higher). -And the Higgs field energy VEV, the vacuum expectation value, is
both observed in the LHC experiment and fairly calculated to about 246 GeV. How are these differences
explained in QM physics?

3 GeV versus 246 GeV?

I understand that the VEV amount is presented without any special volume in mind. But surely the VEV
isn't correlated to the cubic meter volume, though must be estimated to the Planck scale. Far minor
than the m^3 which the vacuum is given with. The VEV is a universal constant thought to fill all
universe with neither any much higher nor any lower energy content. This issue is raised with the
condition of both the vacuum energy volume and the Higgs field are without any elementary particles,
though being absolutely empty of any visible "matter". -Without even one single photon or neutrino
or whatever. The only content is the absolute vacuum itself (3 GeV).

The VEV can be regarded for proven with the Higgs boson discovery in 2012. And the vacuum content
have with the Planck Collaboration project also been verified.

/chron44

This evening when I get home I will be able to run the formulas for you. Yes you can calculate the vacuum energy density per cubic metre. For that one can get a decent estimate using the critical density formula. (Assuming Lambda is the result of the Higfs field) one line of research. The calculations differ for the quantum harmonic oscillator contributions however that results in the vacuum catastrophe but I also have the related calculations for that as well.

[Mordred]

8 hours ago, chron44 said:

Hi,

The average vacuum energy is estimated to about 3 GeV/m^3 (the observed). If relying on this value (when
the calculated in extremely much higher). -And the Higgs field energy VEV, the vacuum expectation value, is
both observed in the LHC experiment and fairly calculated to about 246 GeV. How are these differences
explained in QM physics?

3 GeV versus 246 GeV?

 

ok First off you have vacuum energy and vacuum energy density confused.  The first case though not a useful form for energy density. The VeV is the vacuum expectation value VeV this isn't the density. This is a term describing the effective action

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

for Higgs the effective action is defined by the equation

\[v-\frac{1}{\sqrt{\sqrt{2}G^0_W}}=\frac{2M_W}{g}\]

here \(M_W\) is the mass of the W boson and \( G^0_W\) is the reduced Fermi constant.

These are used primarily when dealing with Feymann path integrals in scatterings or other particle to particle interactions involving Higgs in particular dealing with the CKMS mass mixing matrix. So its not your energy density 

more specifically they describe CKMS mixing angles or Weinberg mixing angles. 

for the above without going into too much detail the mixing angles are

\[M_W=\frac{1}{2}gv\]

\[M_Z=\frac{1}{COS\Theta_W}\frac{1}{2}gv=\frac{1}{Cos\theta_W}M_W\]

more details can be found here. Page three I'm starting to compile the previous pages

now if you want the vacuum energy density the FLRW has a useful equation.

\[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\]

 

if you take the value of the Hubble constant today and plug it into that formula you will get approximately \(5.5\times 10^{-10} joules/m^3\)

if you convert that over you will find your  fairly close to 3.4 GeV/m^3 which matches depending on the dataset used for the Hubble constant.

The confusion you had was simply not realizing the VeV isn't the energy density. hope that helps. I won't get into too many details of the quantum harmonic oscillator via zero point energy but if you take the zero point energy formula and integrate over momentum space d^3x you will end up with infinite energy. So you must renormalize by applying constraints on momentum space. However even following the renormalization procedure you still end up 120 orders of magnitude too high. There has been resolutions presented to this problem however nothing conclusive enough.

Quantum field theory demystified by David Mcmahon has a decent coverage of the vacuum catastrophe

edit forgot to add calculating the energy density for the cosmological constant uses the same procedure as per the critical density formula.

 

Edited April 25 by Mordred

[MigL]

Here is a simple to follow calculation of the expected vacuum energy, and comparison to the observationally estimated vacuum energy which results in the 124 orders of magnitude 'vacuum catastrophe'.

It also provides clarification about Cosmology, universal expansion and the Cosmological Principle.

 

[MigL]

And a more, shall we say, controversial ( as always ) interpretation of vacuum energy

 

Edited April 25 by MigL

[chron44]

Hi,

I understand that the VEV is the (lowest) "strength" at which mass comes to existence or is revealed (where the intrinsic mass is activated for all massive particles). And Higgs field is an energy field that permeates all the universe. Also that the vacuum energy or the vacuum energy density (is there a difference?) have been measured or observed. (If so, then I mean the vacuum energy density.)

Though to my knowledge VEV is although discovered (LHC) and calculated via some of the formulas Mordred is providing giving the amount of about 246 GeV. Although, if using the ChatGPT3.5, it says that VEV quote "It represents the minimum energy configuration of the Higgs field and is a fundamental property of the vacuum." -That Higgs field energy never is going under this value in entire universe.

So one of you (or both) are separating on the lowest energy associated for manifesting mass, VEV. -And the ChatGPT..?? which is declaring that VEV - also - is "a fundamental property of the vacuum". I.e. not only being a strength or an "effective_action" applied on intrinsic masses.

I believe that my quest remains.

(Though the ChatGPT may lure or confuse me when it says that VEV is a "fundamental property of the vacuum" when it really only is meaning that VEV is the lowest universal/ vacuum energy constant at which mass is manifested at.)

/chron44

[chron44]

58 minutes ago, chron44 said:

Also that the vacuum energy or the vacuum energy density (is there a difference?) have been measured or observed. (If so, then I mean the vacuum energy density.)

 

There may be a way around this issue if we - as indicated by Mordred - if we really differ on the vacuum energy and the vacuum energy density. Where the vacuum energy is the total amount including virtual particles/ fields and so that any cosmic stray volume may hold. (Doesn't this view end with the vacuum catastrophe?) -Where the vacuum energy density represents any stray universal volume free from all the known elementary particles. I.e. calculating only with the absence of visible matter and the seemingly "empty" space.

 

1 hour ago, chron44 said:

Although, if using the ChatGPT3.5, it says that VEV quote "It represents the minimum energy configuration of the Higgs field and is a fundamental property of the vacuum."

 

The vacuum energy (density or not) still remains confusing for me. And adding the VEV of the Higgs field the universal vacuum situation becomes even more enigmatic. It really looks like we should have use for some physics theory updates.

/chron44

[exchemist]

5 hours ago, MigL said:

And a more, shall we say, controversial ( as always ) interpretation of vacuum energy

 

Well I must say that video seemed to make perfect sense to me, as a total non-expert in this area. Sabine's key point seemed to be that there is a  vacuum energy inherent in GR that is just a constant of nature, arising purely from GR in a self-contained way, with no connection at all to the energy of vacuum fluctuations in QFT.

Is that controversial? 

[chron44]

 

If I got it right, vacuum energy is the overall fluctuating energy calculated from QFT in universe. -And the vacuum energy density is the various values one gets from QFT depending on the timeframe and varying fluctuations in a specific volume. And the (observed) cosmological constant describes the homogeneous, average vacuum energy per volume in universe?

 

Λobs ∼3 GeV/m^3

If I (we) got at least this right, then only the issue of the VEV, the vacuum expectation value, or the vacuum state, remains. Which is used in the Higgs mechanism calculus. For me it not only correlates to the lowest energy_action at which mass becomes visible in the Higgs field. To me it also resembles of some type of constant energy amount present in the Higgs field which permeates entire universe. And when the observed cosmological constant (vacuum energy density) is expressed within the cubic meter of only about 3 GeV. How come that the Higgs field holding the minimum and constant energy amount, of about 246 GeV, at which mass is expressed in the Higgs mechanism is far more than the observed vacuum energy?

It's like adding 3 to a very large amount (per m^3) and still get 3. 

/chron44

[Mordred]

Might be easier to understand that in statistical mechanics, QM and QFT the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement.

What that statement tells us is that it includes all possible outcomes. It is a probability function.

Expectational values is used regularly in statistical mechanics, QM and QFT.

Path integrals also have probability weighted sums 

Edited April 25 by Mordred

[MigL]

Mordred is much more qualified to answer, but there is a difference between vacuum energy , and vacuum expectation value.
My ( limited ) understanding is that while the concept of the VEV is a property of the vacuum which in Quantum field theory ( QED, QCD, Higgs ) governs virtual particles and condensation of fundamental masses, vacuum energy ( zero point or false zero ) is a property of the universe, and encompasses contributions made by virtual particles.
The one place where the two 'meet up' is in regards to spontaneous symmetry breaking.

2 hours ago, exchemist said:

Is that controversial? 

Physicists are not like chemists ( no offence meant ).
We are much more anal, and hate plugging numbers ( constants, fundamental or otherwise ) into equations.
These numbers have to have a 'reason', otherwise we ask "Why that number ?", or have to invoke the observation selection effect ( anthropic principle ).
So we try to derive these such numbers from 'first principles'.
The usual method for vacuum energy is treating each point in space as a harmonic oscillator, summing over all such points and renormalizing the resultant infinity, usually with a suitable cut off, or ( as Sabine mentions ) that energy is a gauge condition where only differences are measurable.
I believe there has been some research into using vacuum energy as 'effective mass' of the vacuum, or a field strength that 'resists' global curvature ( in GR ), to derive G from first principles ( like I said, we are anal 😄 ).
 

[Mordred]

We cross posted Migl but I included a primary missing detail in terms of VEV being a probability value much like a weighted sum in statistics.

[chron44]

1 hour ago, Mordred said:

Might be easier to understand that in statistical mechanics, QM and QFT the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement.

 

1 hour ago, Mordred said:

We cross posted Migl but I included a primary missing detail in terms of VEV being a probability value much like a weighted sum in statistics.

 

Okay, in simple terms explained VEV is not like G, the gravitational constant, applicable almost in every astro physical formula. VEV has different amounts in different theories' framework. Or as Mordred says - being a probabilistic value.

A necessary note is that the observed value of the VEV being around 246 GeV is specific to the Standard Model framework and the experimental results obtained at the LHC.

So according to (using) the Standard Model and QFT..?? we still have the discrepancy not totally explained.

/chron44

[chron44]

 

So, here we have noticed at least two Standard Model (QFT) anomalies. First the cosmological catastrophe. And secondly an unexplained and unexpected large discrepancy between the VEV (even if being a probabilistic amount) and the observed cosmological constant.

Thus, being the cornerstone in modern physics it is, it obviously can be shaken and giving strong divergences. If so, can we trust the 2012 LHC result at all? Is there a parallel theory and explanation for maybe the Higgs boson? The LHC did though confirm theories sprung from mid 1960's. -Finally, we have to trust the main parts in the Standard Model when proven right so many times.

/chron44

 

[Mordred]

30 minutes ago, chron44 said:

 

So, here we have noticed at least two Standard Model (QFT) anomalies. First the cosmological catastrophe. And secondly an unexplained and unexpected large discrepancy between the VEV (even if being a probabilistic amount) and the observed cosmological constant.

Thus, being the cornerstone in modern physics it is, it obviously can be shaken and giving strong divergences. If so, can we trust the 2012 LHC result at all? Is there a parallel theory and explanation for maybe the Higgs boson? The LHC did though confirm theories sprung from mid 1960's. -Finally, we have to trust the main parts in the Standard Model when proven right so many times.

/chron44

 

The VeV isn't an issue it's something you observe only during scatterrings via say a particle accelerator it's a local property at each particle such as the W boson simply put a coupling term. The probabilities are much the same as the probabilities associated with Feymann path integrals.

It isn't the vacuum energy density itself so it's not anywhere near Like the vacuum catastrophe from QM. 

[chron44]

7 minutes ago, Mordred said:

The VeV isn't an issue it's something you observe only during scatterrings via say a particle accelerator it's a local property at each particle such as the W boson simply put a coupling term. The probabilities are much the same as the probabilities associated with Feymann path integrals.

It isn't the vacuum energy density itself so it's not anywhere near Like the vacuum catastrophe from QM. 

 

Okay, thanks for the correction. Appreciates fair and relevant explanations.

If I finally got it right, the vacuum fluctuations are the probabilistic function which govern the VEV amount. Resulting in the vacuum expectation value. Which furthermore is expressed as approximately 246 GeV, if the Standard Model being used.

Have to add that I never intended to mix the vacuum energy density with VEV, I fairly understand the differences. This issue although have been raised for to enlighten both physicals' functions. Similarities and differences. I try to learn from ChatGPT, which seemingly is a bit insecure at this level of physics.

Thanks, again, for your answers.

/chron44

[Mordred]

In essence that's correct without going too indepth on the differences between operators and propogators of QFT. You can accurately treat it as a fundamental constant of the Higgs field with regards to how the field couples to other particles for the mass term

I really wouldn't trust Chatgp your far better off in this regard studying the standard model via the Lanqrangian equations. For the W boson it's the SU(2) group and U(1) groups for the relevant details with Higgs.

It's also why I recommended starting with Quantum field theory Demystified as it's reasonably well explained for the laymen to grasp.

Edited April 25 by Mordred

[chron44]

Hi, again

I still have some remaining issues; can one notice the Higgs field only "visible" through the QFT fluctuations which are delectated as the VEV amount? I.e. Higgs field is hiding behind the VEV and only theoretically confirmed via this stance? There is no other way we can confirm Higgs field, for the moment? (Only at the LHC and ATLAS studies?)

/chron44

Edited April 26 by chron44
correction

[chron44]

1 hour ago, chron44 said:

I still have some remaining issues; can one notice the Higgs field only "visible" through the QFT fluctuations which are delectated as the VEV amount? I.e. Higgs field is hiding behind the VEV and only theoretically confirmed via this stance? There is no other way we can confirm Higgs field, for the moment? (Only at the LHC and ATLAS studies?)

 

Of course, we also have the Higgs boson revealed from the proposed Higgs field so these two results, the boson and the VEV at about 246 GeV "hints" Higgs field. But isn't Higgs field an energy field which permeates all universe, yes it is. And all this was already theorized in mid 1960. And if reading the Wiki it tells you that Higgs field still is under potent physics investigation. -Still not totally confirmed and the theory itself not fully understood. And the LHC is just enlarging its power for to get more data.

So, are there any fresh ideas applicable for to examine the datas to come?

/chron44

 

[Mordred]

2 hours ago, chron44 said:

Hi, again

I still have some remaining issues; can one notice the Higgs field only "visible" through the QFT fluctuations which are delectated as the VEV amount? I.e. Higgs field is hiding behind the VEV and only theoretically confirmed via this stance? There is no other way we can confirm Higgs field, for the moment? (Only at the LHC and ATLAS studies?)

/chron44

Correct the only direct confirmation is via LHC and Atlas etc. 

3 minutes ago, chron44 said:

 

Of course, we also have the Higgs boson revealed from the proposed Higgs field so these two results, the boson and the VEV at about 246 GeV "hints" Higgs field. But isn't Higgs field an energy field which permeates all universe, yes it is. And all this was already theorized in mid 1960. And if reading the Wiki it tells you that Higgs field still is under potent physics investigation. -Still not totally confirmed and the theory itself not fully understood. And the LHC is just enlarging its power for to get more data.

So, are there any fresh ideas applicable for to examine the datas to come?

/chron44

 

Studies are continually improving at each CERN LHC etc upgrade. We barely hit the required energy levels in 2012 so yes research is continually improving.

[joigus]

On 4/25/2024 at 3:02 AM, Mordred said:

ok First off you have vacuum energy and vacuum energy density confused. 

(My emphasis). I think the importance of this comment cannot be overstated.

How can there be a discrepancy between an energy density and an energy?

It's like stating that there is a discrepancy between the speed of light and the radius of the proton.

[chron44]

 

Well, one serious issue is if the research versus the ideas and the theory mainly using the Standard Model and QFT are "synchronized". In early LHC study epoch about 2010-2012 I was a bit concerned about the "black hole" spooky rumor. And to my knowledge the LHC team have been prosecuted in the US from this fright.

Even the LHC team does admin the possibility of micro black holes may occur, though the Hawking radiation immediately should vaporize these.

So, the theory involved in the LHC should be declared in some layman manner for to calm ppl, maybe. Have in mind the QFT related cosmic constant problem. And the Standard Model used in the LHC project is mostly built on the QFT.

There exists a somewhat relevant issue when asking for some new or updated ideas concerning the LHC.

/chron44

 

9 minutes ago, joigus said:

On 4/25/2024 at 3:02 AM, Mordred said:

ok First off you have vacuum energy and vacuum energy density confused. 

(My emphasis). I think the importance of this comment cannot be overstated.

How can there be a discrepancy between an energy density and an energy?

It's like stating that there is a discrepancy between the speed of light and the radius of the proton.

 

It's about how one uses the language in combination with me being a somewhat layman orientated individual, though being most interested in physics. I wouldn't be the first mixing these entities, either. Have some indulgence with an advanced issue.

/chron44

 

[Mordred]

Ok let's make it easier for when your looking at Higgs related papers

E is energy , \(\rho\) is energy density, v is used for VeV. Think of VeV as a coupling constant for Higgs interactions a lot of the equations apply it in that manner.

Energy is the ability to perform work.

Energy density is the mean average over some field volume.

Three distinct properties with distinctions in the mathematics

Hope that helps

 

Edited April 26 by Mordred

[Mordred]

Here is the association of VeV to Fermi-constant

Fermi's interaction - Wikipedia

[chron44]

1 hour ago, Mordred said:

Here is the association of VeV to Fermi-constant

Fermi's interaction - Wikipedia

 

Hmm.. yeah, right. Somewhat above my novel understanding.

The Fermi-constant should be used in calculations involving decay rates, cross-sections, and
other properties related to weak interactions. (Is what ChatGPT informs.)

It was proven right in the finding of Higgs boson. I.e. the Fermi-constant was also more or less
proven at the success of the LHC in 2012? (Besides the Higgs theory.)

14 minutes ago, chron44 said:

 

 

Much more to learn about such subjects.

/chron44

 

Edited April 27 by chron44