The Higgs field is such a strange beast. No wonder we mere mortals cannot understand it!
To integrate with the Standard Model:
The Higgs field is non-zero because its equation of motion is like that of a ball at the bottom of a wine bottle. The solution at H=0 (red ball) is a position of unstable equilibrium. The green balls represent two non-zero points of stable equilibrium. A ball in an ordinary bowl shape (shown on the right) has only one point of stable equilibrium. By the way, the fact that there are + and - values for H doesn't seem to matter as it's always H^2 that appears in equations.
Reference: https://profmattstrassler.com/artic...2-why-the-higgs-field-is-non-zero-on-average/
Learning and being bemused all the time! 😎
To integrate with the Standard Model:
- The Higgs field has to exist at all points in the Universe.
- Its intensity can not decrease with distance as is the case with other fields such as electromagnetism
- Since it is a scalar (spin-0) field it does not point anywhere so does not have a preferred direction, unlike the vector (spin-1) electric field.
- All observers are at rest relative to the Higgs field since, as a relativistic field, it produces no preferred frame of reference.
- During collisions at the LHC waves appear in the Higgs field, the quanta of these waves is what we call the Higgs particles.
- The Higgs field has a non-zero value of 246 GeV. It can not be zero because the solution at H=0 is unstable (see diagram & explanation below).
The Higgs field is non-zero because its equation of motion is like that of a ball at the bottom of a wine bottle. The solution at H=0 (red ball) is a position of unstable equilibrium. The green balls represent two non-zero points of stable equilibrium. A ball in an ordinary bowl shape (shown on the right) has only one point of stable equilibrium. By the way, the fact that there are + and - values for H doesn't seem to matter as it's always H^2 that appears in equations.
Reference: https://profmattstrassler.com/artic...2-why-the-higgs-field-is-non-zero-on-average/
Learning and being bemused all the time! 😎
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Sorry for the self quoting, but I should have written "Higgs field".
The Higgs boson itself, like any other elementary particle, gets its mass by interacting with the Higgs field.
I do not get the bit about it existing at all points in the universe. Clearly that’s linked to point 2 since I imagine the Higgs field just permeates the cosmos. Is this part of quantum foam aka vacuum energy ephemeral fermions?
I would say that points 1 and 2 are linked together with point 6 in that the Higgs field has a non-zero value so can be said to permeate (exist at all points in) the Universe, whereas an electric field can not be said to permeate space since it can have a zero value.
I see no connection with "quantum foam" which is a prediction of quantum gravity models of quantum fluctuations of spacetime on the Planck level.
A reminder that "ephemeral fermions" are postulated quantum fluctuations invoked to explain the propagation of photons through 'empty' space.
I see no connection with "quantum foam" which is a prediction of quantum gravity models of quantum fluctuations of spacetime on the Planck level.
A reminder that "ephemeral fermions" are postulated quantum fluctuations invoked to explain the propagation of photons through 'empty' space.
I am currently focussed on @Galu's De Broglie matter waves and their relation to (wavelike) photons of the same energy, but this is on hold whilst I refresh myself on differentiation.
I have forgotten how to do it. 🙁
Hopefully it is mere forgetfulness, not early-onset dementia.
"A" Level Pure Mathematics textbook on its way from one of my mathematical pals! Progress is assured, one feels. 🙂
Since y'all must talk about the Higgs, it seems, here is a video from Arvin Ash that a child of ten can understand:
https://eightify.app/summary/mathem...nation-of-higgs-field-s-mass-giving-mechanism
Salient points:
The Mexican Hat
The LHC mass of the Higgs particle is 125GeV, but this is not what we are talking about. Actually, I would expect the 246 GeV (or -246GeV...) point to be on the y axis, but maybe I am looking at it the wrong way? 😕
Interaction between Fields
I was curious how Arvin managed to get a haircut mid-video. But he is certainly on a roll here, as usual. 😎
I have forgotten how to do it. 🙁
Hopefully it is mere forgetfulness, not early-onset dementia.
"A" Level Pure Mathematics textbook on its way from one of my mathematical pals! Progress is assured, one feels. 🙂
Since y'all must talk about the Higgs, it seems, here is a video from Arvin Ash that a child of ten can understand:
https://eightify.app/summary/mathem...nation-of-higgs-field-s-mass-giving-mechanism
Salient points:
The Mexican Hat
The LHC mass of the Higgs particle is 125GeV, but this is not what we are talking about. Actually, I would expect the 246 GeV (or -246GeV...) point to be on the y axis, but maybe I am looking at it the wrong way? 😕
Interaction between Fields
I was curious how Arvin managed to get a haircut mid-video. But he is certainly on a roll here, as usual. 😎
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Good stuff, Steve!
The final image looks like an attempt to illustrate the 'vibration coupling' I waffled on about earlier.
And to think I found the "Mexican Hat" at the bottom of a wine bottle! 😀
The final image looks like an attempt to illustrate the 'vibration coupling' I waffled on about earlier.
And to think I found the "Mexican Hat" at the bottom of a wine bottle! 😀
One of the "Key Insights" given in your link is as follows:
To explain why the Higgs field is critical to the basic structure of an atom (a tiny nucleus surrounded by a hugely larger volume of space occupied by the electrons) we must consider that atoms are made up of three elementary particles - the electron and the up and down quarks.
An electron can be considered as a quantum wave packet that obtains its relatively small mass by interacting weakly with the Higgs field. The small mass/energy translates to a long wavelength, so the electron wave packet is spread out in space. This results in the atom having a large size overall.
The up and down quarks which make up the nucleons of the atom obtain a relatively larger mass by interacting strongly with the Higgs field. This large mass/energy translates to a short wavelength, so the quark wave packets are less spread out in space. This results in the nucleus being much smaller than the overall size of the atom.
Fair enough, but if these are particles and they exist across the entire cosmos (permeate it), where do they reside? Are they just sitting out there, densely packed? I suggested they were part of the quantum foam simply because that is said to permeate the whole cosmos, so assumed the Higgs was something similar or part of it.
When we talk of a particle having a certain energy field, I am led to understand it as the amount of energy required to excite the particle, not necessarily that the said particle has that energy level. This is not always the case, because there are high-energy particles out there that are moving at tremendous velocities, so do have these energy levels - eg the 'god particle'. I probably need to be schooled on this, but that's my 'The First Three Minutes' understanding.
🙂
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It's just one 18 minute long video. You'll be interested to know it mentions the virtual particles that pop up out of the energetic vacuum, and to which you alluded earlier.
The Higgs field is said to break symmetries, and Ash's follow up video on "Symmetry Breaking" will be the one for me to watch later.
I don't foresee me gaining much understanding from the video as the ideas of symmetry and symmetry-breaking are not easily explained.
I think Ash's video goes a long way towards clarifying the points you make.
I now have much greater understanding of symmetry breaking!
If I'm wrong, I'll eat my Sombrero! 😊
If I'm wrong, I'll eat my Sombrero! 😊
I've been looking again at the mathematical description of the Standard Model of particle physics (see attachment) that I mentioned earlier in the thread.
Section 1 is specific to gluons, Section 2 is dedicated to the interactions between bosons, Section 3 involves the weak force plus interactions with the Higgs field, and Sections 4 & 5 clear up some mathematical redundancies by referring to virtual particles called ghosts.
I've been wondering - what are these "ghosts" and exactly what role do they play in the Standard Model?
From what I read, ghosts are unphysical - meaning contrary to the laws of physics - but are necessary to maintain the integrity of the Standard Model.
Apparently, "good ghosts" remove unwanted infinities from the model, while "bad ghosts" permit the existence of undesired states.
In a Feynman diagram a ghost looks a bit like a corkscrew, as shown in green in the diagram below. 🤓
Wikipedia goes into the detail, but most of it is pretty much undecipherable to me! https://en.wikipedia.org/wiki/Ghost_(physics)
To conclude, I perceive ghosts to be "fudge factors" which serve only to cover up our basic lack of knowledge of physics.
Section 1 is specific to gluons, Section 2 is dedicated to the interactions between bosons, Section 3 involves the weak force plus interactions with the Higgs field, and Sections 4 & 5 clear up some mathematical redundancies by referring to virtual particles called ghosts.
I've been wondering - what are these "ghosts" and exactly what role do they play in the Standard Model?
From what I read, ghosts are unphysical - meaning contrary to the laws of physics - but are necessary to maintain the integrity of the Standard Model.
Apparently, "good ghosts" remove unwanted infinities from the model, while "bad ghosts" permit the existence of undesired states.
In a Feynman diagram a ghost looks a bit like a corkscrew, as shown in green in the diagram below. 🤓
Wikipedia goes into the detail, but most of it is pretty much undecipherable to me! https://en.wikipedia.org/wiki/Ghost_(physics)
To conclude, I perceive ghosts to be "fudge factors" which serve only to cover up our basic lack of knowledge of physics.
Attachments
The Mexican Hat potential with the Higgs Field is not a graph of Energy and Physical Space, but a graph of Energy and the Expectation Value, it seems.
Any Competent Mathematician recognises this shape, it is a quartic:
https://en.wikipedia.org/wiki/Quartic_function
To make further progress, I would be looking to take that 246 GeV value and see what sort of solution and numbers that leads to. Maybe a "Golden Quartic"?
Perhaps one of you might find time? I have other projects.
I have given up on my maths pal producing the goods. Clearly not a person who feels the urgency of these things. Portsmouth Central Library has thrown up this very heavy Tinker & Lambourne gem:
The whole book is a treasure. Full of Graphs, Integrals, Differentials, Hyperbolic functions, Physical Constants and even Schrodinger's Equation!
A sample:
My new "Take Everywhere" book! 🙂
Any Competent Mathematician recognises this shape, it is a quartic:
https://en.wikipedia.org/wiki/Quartic_function
To make further progress, I would be looking to take that 246 GeV value and see what sort of solution and numbers that leads to. Maybe a "Golden Quartic"?
Perhaps one of you might find time? I have other projects.
I have given up on my maths pal producing the goods. Clearly not a person who feels the urgency of these things. Portsmouth Central Library has thrown up this very heavy Tinker & Lambourne gem:
The whole book is a treasure. Full of Graphs, Integrals, Differentials, Hyperbolic functions, Physical Constants and even Schrodinger's Equation!
A sample:
My new "Take Everywhere" book! 🙂
Any competent mathematician will know that "the expectation value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes".
The random variable in the Higgs case is the vacuum energy, so the sombrero is a graph of Potential Energy against Vacuum Expectation Value.
Someone like you, Steve, who is revising the process of differentiation, may struggle with expectation value as it's arrived at by integration! 😉
You might be interested to learn that expectation value originated from the Problem of Points, aka Division of the Stakes, that so energised the minds of Pascal and Fermat and motivated the beginnings of modern probability theory. https://www.wikiwand.com/en/Problem_of_points
