Hypothesis about the formation of particles from fields

[joigus]

The KG equation does not represent electron clouds. It represents the dynamics of creation/annihilation of charged/neutral, as the case may be, spin-zero particles, as @Markus Hanke told you.

2 minutes ago, computer said:

And an electron in an atom has no reason to move at speeds close to of light.

Very internal electrons might. I'm not sure about that now, but I'd expect them to have a sizable fraction of the speed of light as expected value.

[computer]

4 minutes ago, joigus said:

Microscopic version of Maxwell's equations can be expressed either in terms of B , E , or in terms of φ and A --the scalar and vector potentials.

From this more canonical investigation without "alternative" velocity field V we get, that even for description of electric dipole radiation three "separate" fundamental field required, not two. Original Maxwell's equations anyway have to be extended, and this is not a religious dogma but a reason to think.

[joigus]

1 minute ago, computer said:

From this more canonical investigation without "alternative" velocity field V we get, that even for description of electric dipole radiation three "separate" fundamental field required, not two. Original Maxwell's equations anyway have to be extended, and this is not a religious dogma but a reason to think.

What do you mean "more canonical"? Something is either canonical or it isn't. You can't be more presidential than being a president.

50 minutes ago, joigus said:

Very internal electrons might. I'm not sure about that now, but I'd expect them to have a sizable fraction of the speed of light as expected value.

Here it is. I seem to be right about this:

Quote

One thus finds that for uranium (𝑍=92Z=92) the speeds for the inner-most shell are of the order of the speed of light. This makes this atom a useful test-bed for relativistic quantum theory. More widely, from caesium (𝑍=55)(Z=55) on up the inner electrons have speeds of the order of half the speed of light, and from francium (𝑍=87)(Z=87) about half the electrons have speeds above a third of 𝑐c.

https://physics.stackexchange.com/questions/20187/how-fast-do-electrons-travel-in-an-atomic-orbital

According to Andrew Steane, Oxford Physics professor.

[joigus]

More comments: You can't solve the dynamics, energy splittings, etc. of internal electrons with the non-relativistic Schrödinger equation. You have to use the Dirac equation and do an expansion series with different relativistic corrections, like the Darwin term, mass-velocity term, etc. If it has many electrons, you really have to go to a whole different level, with the Slater method, etc. So it's more complicated than you want it to be.

[joigus]

19 hours ago, computer said:

And an electron in an atom has no reason to move at speeds close to of light.

Wrong! Did you read what I wrote? I hate to write the same thing 100 times.

Sorry. Your comment was previous to my comments.

[computer]

joigus,

You gave good link to Arxiv article, confirming than on electric and magnetic field only, with zero divergences, we cannot build something realistic (except magnetic dipole spheric radiation), with behaviour like photon or electron for example. Only some kinds of exotic math games. Thanks for reference.

In any case, electrons do not fly along "orbits" at almost constant speed. Rather they abruptly change their speed and direction of motion. If You try to simulate movement of electrons in an atom, soon there will be complete chaos. Only after great time possibly it can be noticed that in some places an electron is more frequent, others do not visit at all. But it is impossible to wait so long to gather good statistics. Only Schrödinger equation helps.

[joigus]

On 10/7/2022 at 7:30 PM, computer said:

"Very wide range" does mean if field intensity decreases with distance as 1 / r, 1 / r², 1 / r³ and so on.

Multipolar expansions of the field:

1/r: radiation, as wide-range as you can get, without getting into GR.

1/r²: monopolar, narrower-range

1/r³: dipolar, even narrower

...

Van der Waals (Casimir effect,) etc.

On 10/7/2022 at 7:30 PM, computer said:

I have not found any word "classic" or "classical" in my last article about objects moving at the speed of light.

You said "spin." Don't look now, but that's quantum, in a way that cannot even be thought of as classical.

[computer]

3 hours ago, joigus said:

1/r²: monopolar, narrower-range

1/r³: dipolar, even narrower

It is very interesting if this might have anything to do with neutrinos. I think the nonlinearity of equations is also important, since neutrino types clearly correspond to leptons (electron, muon, tauon). For photons maybe it is possible that nonlinear effects have almost no influence.

3 hours ago, joigus said:

You said "spin." Don't look now, but that's quantum, in a way that cannot even be thought of as classical.

I only wished to say photon-like objects can be of two types with opposite fields orientation. How it correlates with "spin", additional investigations are required. Probably it is relation between magnetic moments and mechanical ones, created by energy flux or velocity vector V. In a photon all fields are transferred synchronously in one direction at the speed of light, so spin is recognized as +1 or -1. In an electron maybe other picture, magnetic moment is generated twice more effective than mechanical, after all-space integration of densities.

[joigus]

7 minutes ago, computer said:

It is very interesting if this might have anything to do with neutrinos. I think the nonlinearity of equations is also important, since neutrino types clearly correspond to leptons (electron, muon, tauon). For photons maybe it is possible that nonlinear effects have almost no influence.

Not exactly. It has to do with an expansion of the classical EM field away from the sources that are not point-like (charges and currents.)

Look, eg, at the field from a dipole antenna: https://en.wikipedia.org/wiki/Dipole_antenna

It falls off as 1/r with the distance.

Neutrinos are a completely different matter. There is no way that you can study neutrinos with a classical approximation, as you can do with EM field. They have spin 1/2. They are always highly relativistic. They're always left-handed. They change flavour ever so slightly. So, as you get away from their source, an electron neutrino mutates into a muon neutrino, and so on...

They're very quirky on a series of levels. Anomalous deviations from predictions of the standard model being one of them. Here's a quick but high-quality low-down of the whole thing:

And there certainly isn't a multipolar expansion for the neutrino field, as it has no sources. It sources itself, so to speak.

You can have quantum wave functions --I suppose-- serve as analogues of radiation from a source point by, eg, having them diffract from a narrow window...

Non-linearity may be very important in many, many contexts. GR is certainly non-linear. It's important from the start in the strong interactions. Even in QED you have non-linear effects of sorts, because at very high energies, photons can scatter off each other. But one has to be very careful stating in what precise sense one's talking about non-linear effects.

[computer]

It seems neutrino sequence is not limited of 3 types (e, mu, tau). Japanese scientist had proposed the law, how to calculate mass of next lepton via masses of previous ones. And there is no evident limit, after lepton-3 (tau) can be lepton-4 and so on. But masses become so great, that it is practically impossible to get such particles in experiment. And heavier leptons may have corresponding neutrinos.

If neutrinos are left-handed, I think antineutrinos are right-handed. Obviously, it can be related to electric and magnetic field orientation.

[swansont]

4 hours ago, computer said:

If neutrinos are left-handed, I think antineutrinos are right-handed. Obviously, it can be related to electric and magnetic field orientation.

What electric and magnetic field? Right- and left-handed refer to the spin relation to the momentum vector. There’s no charge or charge distribution.

[computer]

21 hours ago, swansont said:

There’s no charge or charge distribution.

Only with zero divergence electric field is impossible to construct something realistic, like particle. Except electric or magnetic dipole spheric radiation. Example of plain 1-dimensional wave, often encountered in books, does not exist in real world, it is infinite in space and has infinite energy.

[swansont]

1 hour ago, computer said:

Only with zero divergence electric field is impossible to construct something realistic, like particle. Except electric or magnetic dipole spheric radiation. Example of plain 1-dimensional wave, often encountered in books, does not exist in real world, it is infinite in space and has infinite energy.

What does this have to with neutrinos?

[computer]

19 hours ago, swansont said:

What does this have to with neutrinos?

If neutrinos have magnetic dipole moment, evidently, they "partially" consist of magnetic field also. But there can be other fields like "weak", still never described and explained well in theories. And that's right, even to explain photon structure and behaviour non-linearity of equations is required.

[exchemist]

On 10/7/2022 at 7:32 PM, joigus said:

The KG equation does not represent electron clouds. It represents the dynamics of creation/annihilation of charged/neutral, as the case may be, spin-zero particles, as @Markus Hanke told you.

Very internal electrons might. I'm not sure about that now, but I'd expect them to have a sizable fraction of the speed of light as expected value.

The undergraduate explanation for the colour of gold is based on electrons in atoms with very high nuclear charge moving at such speeds and thus, in terms of non-relativistic QM, having a greater effective mass than they would otherwise: 

https://math.ucr.edu/home/baez/physics/Relativity/SR/gold_color.html

 

 

[swansont]

6 hours ago, computer said:

If neutrinos have magnetic dipole moment

Do they have one? Can you cite any evidence?

 

1 hour ago, exchemist said:

The undergraduate explanation for the colour of gold is based on electrons in atoms with very high nuclear charge moving at such speeds and thus, in terms of non-relativistic QM, having a greater effective mass than they would otherwise: 

https://math.ucr.edu/home/baez/physics/Relativity/SR/gold_color.html

 

Most treatments of this that I’ve seen are careful to note that this is a relativistic correction to the energy level, and make no claim regarding either the speed or mass.

[exchemist]

7 hours ago, swansont said:

Do they have one? Can you cite any evidence?

 

Most treatments of this that I’ve seen are careful to note that this is a relativistic correction to the energy level, and make no claim regarding either the speed or mass.

No doubt that would be the more rigorous way to treat it, the concept of speed being a bit dodgy in such a context. But it was used to explain at undergrad level why these corrections are only required for atoms with vey high nuclear charge. How does this arise in the more rigorous treatments you have in mind?

Edited October 13, 2022 by exchemist

[swansont]

6 hours ago, exchemist said:

No doubt that would be the more rigorous way to treat it, the concept of speed being a bit dodgy in such a context. But it was used to explain at undergrad level why these corrections are only required for atoms with vey high nuclear charge. How does this arise in the more rigorous treatments you have in mind?

As I said, it's a relativistic correction to the energy levels. That's it. There's no Bohr-atom extrapolation to the speed (which is an overused crutch, common in undergrad explanations), or relativistic mass invocation.

[joigus]

My intuition is that it would have to do with a kinematic (Doppler-like) effect, rather than a dynamical one (energy-momentum.)

Quote

Color of gold and caesium[edit]

 

Spectral reflectance curves for aluminum (Al), silver (Ag), and gold (Au) metal mirrors

 

Alkali-metal coloration: rubidium (silvery) versus caesium (golden)

The reflectivity of aluminium (Al), silver (Ag), and gold (Au) is shown in the graph to the right. The human eye sees electromagnetic radiation with a wavelength near 600 nm as yellow. Gold appears yellow because it absorbs blue light more than it absorbs other visible wavelengths of light; the reflected light reaching the eye is therefore lacking in blue compared with the incident light. Since yellow is complementary to blue, this makes a piece of gold under white light appear yellow to human eyes.

The electronic transition from the 5d orbital to the 6s orbital is responsible for this absorption. An analogous transition occurs in silver, but the relativistic effects are smaller than in gold. While silver's 4d orbital experiences some relativistic expansion and the 5s orbital some contraction, the 4d–5s distance in silver is much greater than the 5d–6s distance in gold. The relativistic effects increase the 5d orbital's distance from the atom's nucleus and decrease the 6s orbital's distance.^[15]

From: https://en.wikipedia.org/wiki/Relativistic_quantum_chemistry#:~:text=Gold appears yellow because it,compared with the incident light.

(My emphasis in boldface.)

Clarification: By Doppler-like I don't mean that reflected light gets Doppler shifted, but that it's kinematic (like Doppler effect), in this case because orbitals appear compressed, which affects the absorption properties.

I hate being vague, but I hope it makes sense and is intelligible.

[exchemist]

1 hour ago, swansont said:

As I said, it's a relativistic correction to the energy levels. That's it. There's no Bohr-atom extrapolation to the speed (which is an overused crutch, common in undergrad explanations), or relativistic mass invocation.

OK but can you provide some insight into what is it that makes the correction significant for atoms with a high nuclear charge? Because that seems to be the point the undergrad explanation tries to address. 

[joigus]

By the way, @computer. Your idea is a noble one, and I want to pay respect to it. It's such a pity it doesn't work, at least not directly, because... Well, because you need quantum mechanics at some point.

To prove to you how intelligent an idea it is, I'll let Einstein do the talking.

Quote

It was the great merit of H. A. Lorentz that he brought about a change here in a convincing fashion. In principle a field exists, according to him, only in empty space. Matter —considered as atoms— is the only seat of electric charges; between the material particles there is empty space, the seat of the electromagnetic field, which is created by the position and velocity of the point charges which are located on the material particles. Dielectricity, conductivity, etc., are determined exclusively by the type of mechanical tie connecting the particles, of which the bodies consist. The particle-charges create the field, which, on the other hand, exerts forces upon the charges of the particles, thus determining the motion of the latter according to Newton's law of motion. If one compares this with Newton's system, the change consists in this: action at a distance is replaced by the field, which also describes the radiation. Gravitation is usually not taken into account because of its relative smallness; its consideration, however, was always possible by means of the enrichment of the structure of the field, i.e., expansion of Maxwell's law of the field. The physicist of the present generation regards the point of view achieved by Lorentz as the only possible one; at that time, however, it was a surprising and audacious step, without which the later development would not have been possible.

If one views this phase of the development of theory critically, one is struck by the dualism which lies in the fact that the material point in Newton's sense and the field as continuum are used as elementary concepts side by side. Kinetic energy and field-energy appear as essentially different things. This appears all the more unsatisfactory inasmuch as, according to Maxwell's theory, the magnetic field of a moving electric charge represents inertia. Why not then total inertia? Then only field-energy would be left, and the particle would be merely an area of special density of field-energy. In that case one could hope to deduce the concept of the mass-point together with the equations of the motion of the particles from the field equations—the disturbing dualism would have been removed.

H. A. Lorentz knew this very well. However, Maxwell's equations did not permit the derivations of the equilibrium of the electricity which constitutes a particle. Only other, nonlinear field equations could possibly accomplish such a thing. But no method existed by which this kind of field equations could be discovered without deteriorating into adventurous arbitrariness. In any case one could believe it possible by and by to find a new and secure foundation for all of physics upon the path so successfully begun by Faraday and Maxwell.

(My boldface emphasis.)

From: Autobiographical and Scientific Reflections; A. Einstein

https://ebin.pub/einstein-on-einstein-autobiographical-and-scientific-reflections-0691183600-9780691183602.html

I read this little book about 41 years ago. Many of the comments went over my head those many years ago. But that observation, and a couple of other ones, deeply impressed me, and have always stuck with me.

 

Edited October 13, 2022 by joigus
minor correction

[swansont]

25 minutes ago, exchemist said:

OK but can you provide some insight into what is it that makes the correction significant for atoms with a high nuclear charge? Because that seems to be the point the undergrad explanation tries to address. 

The kinetic energy of the inner state electrons is a reasonable fraction of the mass energy. p^2/2m is no longer a reasonable approximation. The energy level (where KE = 1/2 |PE|) depends on Z^2

 

[computer]

20 hours ago, exchemist said:

The undergraduate explanation for the colour of gold is based on electrons in atoms with very high nuclear charge moving at such speeds and thus, in terms of non-relativistic QM, having a greater effective mass than they would otherwise: 

https://math.ucr.edu/home/baez/physics/Relativity/SR/gold_color.html

In this article is written:

"delocalised electron sea"

The same thing as "cloud". It behaves as distributed in the space object, not very small flying electron-particle.

"The 3d, filled in copper, is less shielded by the s and p subshells than you might relativistic effects you get reasonably good agreement with reality"

3d-level in a copper atom is not too "inner'. It's not told about 1s-cloud.

18 hours ago, swansont said:

Do they have one? Can you cite any evidence?

I have doubts. But if neutrino has very little "mass", it can have some littlest moment also. Really this suggestion is inspired by joigus, and I think he will explain better if neutrino has magnetic moment.

2 hours ago, joigus said:

It's such a pity it doesn't work, at least not directly, because

My suggestions are only the rudiments of possible theories. To explain something better, we need nonlinear equations. And I want to emphasize that my assumptions relate rather to the internal structure of elementary particles and have nothing to do with electron clouds in atoms built on the principles of long-action and statistics.

Edited October 13, 2022 by computer

[joigus]

25 minutes ago, computer said:

I have doubts. But if neutrino has very little "mass", it can have some littlest moment also. Really this suggestion is inspired by joigus, and I think he will explain better if neutrino has magnetic moment.

It was you who started talking about neutrinos. From a classical POV, neutrinos would have zero magnetic moment. Magnetic moment doesn't come from mass, but from circulating currents. In the context of the Standard Model, they're expected to have a very small magnetic moment, no doubt due to radiative corrections.

AFAIK, only upper bounds to magnetic moment of neutrinos have been experimentally determined.

32 minutes ago, computer said:

These suggestions are only the rudiments of possible theories. To explain something better, we need nonlinear equations. And I want to emphasize that my assumptions relate rather to the internal structure of elementary particles and have nothing to do with electron clouds in atoms built on the principles of long-action and statistics.

It would be a good idea to read what I posted above.