[compuAI (OP)]

Let us consider what field " blobs" can be, moving at the speed of light in a certain direction while maintaining their shape. That is, compact formations capable of traveling long distances compared to their size without significant changes in structure. Unlike dipole radiation, which propagates spherically in all directions. Perhaps such structure have emissions of atoms during the transitions of electron clouds to less energetic levels.

Let us take as basis the equations, existence of which in the real world is justified in the topic on dipole radiation: https://www.thenakedscientists.com/forum/index.php?topic=85518

The following symbols are used:
Scalar potential = a
Vector potential = A
Electrical field = E
Speed of light in vacuum = c
Time derivatives are denoted by singlequote '

a' = - c² · div A
A' = - E - grad a
E' = c² · rot rot A

The formulas are given in cylindrical coordinate system (ρ,φ,z),
associated with the point of space where the geometric center of field blob is located at the time of observation.
Let us put r² = ρ² + z²
Motion occurs along z-axis at the speed of light and structure of field object remains unchanged,
that is, ∂/∂t = - c · ∂/∂z for all physical quantities.
Also, integral of internal energy throughout all the space must be finite, density of which is expressed by the law:
u = ε0/2 · E² + μ0/2 · H²
where E² = Eρ² + Eφ² + Ez², H² = Hρ² + Hφ² + Hz²
H = 1/μ0 · rot A, B = rot A = μ0 · H
Let us put J = rot B = rot rot A

Let us start with the mathematically simplest descriptions possible from the point of view of field laws mentioned above. In cylindrically symmetric case, when ∂/∂φ = 0 for all physical quantities.

Basic equations are divided into two independent systems:

1. With circular electric field.

Aφ' = - c · ∂Aφ/∂z = - Eφ
→ Eφ = c · ∂Aφ/∂z
→  ∂Eφ/∂z = c · ∂²Aφ/∂z²
Eφ' = - c · ∂Eφ/∂z = c² · Jφ
= c² · (- ∂²Aφ/∂z² - ∂²Aφ/∂ρ² - ∂Aφ/∂ρ / ρ + Aφ / ρ²)
→ ∂Eφ/∂z = c · (∂²Aφ/∂z² + ∂²Aφ/∂ρ² + ∂Aφ/∂ρ / ρ - Aφ / ρ²)
Equating ∂Eφ/∂z from two equations, we get
∂²Aφ/∂ρ² + ∂Aφ/∂ρ / ρ - Aφ / ρ² = 0
→ ∂/∂ρ (∂Aφ/∂ρ + Aφ / ρ) = 0
If Aφ is not zero in all the space,
so ∂Aφ/∂ρ + Aφ / ρ = 0, and Aφ is proportional to 1 / ρ, that gives infinite energy integral. Hence, such non-zero components of compact radiations can not exist. After artificial creation or computer modeling such structures will diverge in waves in all directions, instead of moving in one direction at the speed of light.

2. With circular magnetic field.

a' = - c · ∂a/∂z = - c² · (∂Aρ/∂ρ + Aρ / ρ + ∂Az/∂z)
→ ∂a/∂z = c · (∂Aρ/∂ρ + Aρ / ρ + ∂Az/∂z)
Aρ' = - c · ∂Aρ/∂z  = - Eρ - ∂a/∂ρ
→ Eρ = c · ∂Aρ/∂z - ∂a/∂ρ
∂Eρ/∂z = c · ∂²Aρ/∂z² - ∂2a/∂ρ/∂z
Az' = - c · ∂Az/∂z = - Ez - ∂a/∂z
→ Ez = c · ∂Az/∂z - ∂a/∂z
∂Ez/∂z = c · ∂²Az/∂z² - ∂²a/∂z²
Eρ' = - c · ∂Eρ/∂z = c² · Jρ
→ ∂Eρ/∂z = c · (∂²Aρ/∂z² - ∂²Az/∂ρ/∂z)
Ez' = - c · ∂Ez/∂z = c² · Jz
→ ∂Ez/∂z = c · (∂²Az/∂ρ² - ∂²Aρ/∂ρ/∂z - ∂Aρ/∂z / ρ + ∂Az/∂ρ / ρ)
Equating ∂Eρ/∂z from the equations for Aρ' и Eρ', we get
c · ∂²Aρ/∂z² - ∂²a/∂ρ/∂z = c · (∂²Aρ/∂z² - ∂²Az/∂ρ/∂z)
and conclude that a = c · Az if we are talking about quantities decreasing to zero with distance from the center goes to infinity.
From the equation for a' then follows ∂Aρ/∂ρ + Aρ / ρ = 0,
which means Aρ = 0 if Aρ is not proportional to 1 / ρ with infinite energy integral.
From the equation for Az' follows Ez = 0 at a = c · Az
The following equations remain valid:
Eρ = - ∂a/∂ρ = - c · ∂Az/∂ρ
whereas from ∂Ez/∂z = c · (∂²Az/∂ρ² + ∂Az/∂ρ / ρ) = 0
it follows that with non-zero Az must be Az proportional to ln(ρ) and energy integral is infinite.

Thus, no valid expressions for field formations were found. The situation changes if we assume that div E ≠ 0 (non-zero charge density) and introduce additional terms into formulas for E' using the velocity field:
E′ = c² · J - grad (E · V) - V · div E
where div E = ∂Eρ/∂ρ + Eρ / ρ + ∂Ez/∂z
in case of circular magnetic field, whereas case of circular electric field remains within previous calculations, since there div E = 0
Assuming that Vz = c is in the entire space around isolated field object, whereas Vρ = 0 and Vφ = 0,
and since E · V = Ez · c, we get
Eρ' = - c · ∂Eρ/∂z = c² · Jρ - c · ∂Ez/∂ρ - 0 · div E
→ ∂Eρ/∂z = ∂Ez/∂ρ - c · Jρ
→ ∂Eρ/∂z = ∂Ez/∂ρ - c · (∂²Az/∂ρ/∂z - ∂²Aρ/∂z²)
Ez' = - c · ∂Ez/∂z = c² · Jz - c · ∂Ez/∂z - c · div E
→ ∂Ez/∂z = - c · Jz + ∂Ez/∂z + div E
→ c · Jz = div E
→ c · (∂²Aρ/∂ρ/∂z - ∂²Az/∂ρ² + ∂Aρ/∂z / ρ - ∂Az/∂ρ / ρ) = div E
The following equations remain true
∂a/∂z = c · (∂Aρ/∂ρ + Aρ / ρ + ∂Az/∂z)
Eρ = c · ∂Aρ/∂z - ∂a/∂ρ
Ez = c · ∂Az/∂z - ∂a/∂z
From the expression for Ez' after substitutions it follows:
c · (∂²Aρ/∂ρ/∂z - ∂²Az/∂ρ² + ∂Aρ/∂z / ρ - ∂Az/∂ρ / ρ)
= ∂Eρ/∂ρ + Eρ / ρ + ∂Ez/∂z = c · ∂²Aρ/∂ρ/∂z - ∂²a/∂ρ²
+ c · ∂Aρ/∂z / ρ - ∂a/∂ρ / ρ + c · ∂²Az/∂z² - ∂²a/∂z²
→ ∂²a/∂ρ² + ∂a/∂ρ / ρ + ∂²a/∂z² = c · (∂²Az/∂ρ² + ∂Az/∂ρ / ρ + ∂²Az/∂z²)
Which leads to the conclusion a = c · Az
Then Ez = 0, also ∂Aρ/∂ρ + Aρ / ρ = 0, hence Aρ = 0 to avoid infinity of energy integral.
As result we get:
a = c · Az, Aρ = 0, Ez = 0
Eρ = - ∂a/∂ρ = - c · ∂Az/∂ρ
Which corresponds to the equation derived earlier from Eρ'
∂Eρ/∂z = ∂Ez/∂ρ - c · (∂²Az/∂ρ/∂z - ∂²Aρ/∂z²)
Herewith Bφ = - ∂Az/∂ρ = Eρ/c

Charge, spin and polarization

If one looks in the direction of movement of field object, it is easy to notice that in the above version with annular magnetic field it is possible to orient this field clockwise or counterclockwise. Accordingly, radial electric field will be directed from z-axis outward or inward to this axis. To one type of field formations can be attributed conditional positive "spin", to the second negative.

Let us try to find out how intensity of fields can decrease at distance from the geometric center of object.
Let a = A0 / s, где A0 = amplitude constant,
and s²  = R² + ρ² + z², where R = object's scaling constant, possibly having an indirect relation to conditional "wavelength" in experiments. Note that ∂s/∂ρ = ρ / s, ∂s/∂z = z / s
Then Az = A0 / c / s, Aρ = 0, Eρ = A0 · ρ / s³, Ez = 0
div E = ∂Eρ/∂ρ + Eρ / ρ = A0 · (2 / s³ - 3 · ρ² / s⁵)
The integral of charge density (divided by dielectric constant) over the entire space will be equal to
∫-∞,+∞∫0,2·π∫0,∞ (2 / s³ - 3 · ρ² / s⁵) · ρ ∂ρ ∂φ ∂z = 0
That is, although charge density is not locally zero, the object as a whole is charged neutrally. This is natural, for example, for radiation arising from atoms and molecules, taking into account laws of conservation, since the particles located there will not give up part of their charge.

In general, when E = Eρ = - ∂a/∂ρ, the subintegral expression
ρ · div E = ρ · (∂Eρ/∂ρ + Eρ / ρ) = ρ · (- ∂²a/∂ρ² - ∂a/∂ρ / ρ)
= - ρ · ∂²a/∂ρ² - ∂a/∂ρ = ∂/∂ρ (- ρ · ∂a/∂ρ)
Computing the integral ∫0∞ ρ · div E ∂ρ we get
for ρ = 0 the function - ρ · ∂a/∂ρ = 0,
for ρ = ∞ the function - ρ · ∂a/∂ρ = 0
if ∂a/∂ρ decreases by absolute value with a distance faster than 1 / s
Further computation of integrals by φ and z will not change zero result. The author of this article tested using MathCAD zero equality of the triple integral for a = A0 · ρ² / s³ with Eρ = A0 · (2 · ρ / s³ - 3 · ρ³ / s⁵), also for a = A0 · ρ⁴ / s⁵ with Eρ = A0 · (4 · ρ³ / s⁵ - 5 · ρ⁵ / s⁷), for a = A0 · ρ / s², a = A0 · z / s², a = A0 / s²

Very wide range of such objects is neutrally charged in general, although it is likely that field formations are statistically inclined to take simplest geometric shapes, with minimum number of spatial extrema.
It should be noted that when a = A0 / s² or s appears with even higher degrees, field formation receives significantly greater ability to penetrate matter than with a = A0 / s or a = A0 · ρ² / s³
Accordingly, the probability of registration of field object by measuring instruments is reduced. Which may be similar to the behavior of neutrinos in experiments.

Polarized field object can be described as follows:
s² = R² + X · x² + Y · y² + Z · z²
where R, X, Y, Z are scaling constants
∂s/∂x = X · x / s, ∂s/∂y = Y · y / s, ∂s/∂z = Z · z / s
If a = A0 / s, where A0 is amplitude
Az = A0 / c / s, Ax = 0, Ay = 0
Ex = A0 · X · x / s³, Ey = A0 · Y · y / s³, Ez =  0
Bx = - A0 / c · Y · y / s³, By = A0 / c · X · x / s³, Bz = 0
div E = ∂Ex/∂x + ∂Ey/∂y + ∂Ez/∂z
= A0 · (X / s³ - 3 · X · x² / s⁵ + Y / s³ - 3 · Y · y² / s⁵)
At the same time, all the above formulas for case of circular magnetic field remain true,
E′ = c² · J - grad (E · V) - V · div E
Ex' = c² · (∂Bz/∂y - ∂By/∂z) - 0 - 0 = 3 · A0 · c · X · Z · x · z / s⁵
Ey' = c² · (∂Bx/∂z - ∂Bz/∂x) - 0 - 0 = 3 · A0 · c · Y · Z · y · z / s⁵
Ez' = c² · (∂By/∂x - ∂Bx/∂y) - 0 - c · div E = 0

That is, there may be no cylindrical symmetry, with different X and Y, the field object will be stretched or extended along x- axis or y-axis. Compression or extension along z-axis is determined by multiplier Z. With significant differences between coordinate multipliers, structures arise with predominant orientation of fields in one direction (and the opposite also) in areas with high field energy density.

This topic can be considered as a continuation:
https://www.thenakedscientists.com/forum/index.php?topic=85274

[Origin]

Let us consider what field " blobs" can be, moving at the speed of light in a certain direction while maintaining their shape.

What is a field blob?

[paul cotter]

In "new theories" word salad is a common occurrence, is this a case of mathematical salad?

[compuAI (OP)]

What is a field blob

An object with bigger energy density at the centre and much more sparce with a distance.

[evan_au]

moving at the speed of light

That narrows it down a lot.
The only things that can move at exactly the speed of light are massless particles: The Photon, Gluon and the (hypothetical) Graviton.
But Gluons are never observed by themselves, as they are confined with the massive quarks (eg inside protons and neutrons).
https://en.wikipedia.org/wiki/Massless_particle

Neutrinos have a very small mass (nobody is exactly sure how much mass), and so travel slightly slower than light.
https://en.wikipedia.org/wiki/Neutrino#Flavor,_mass,_and_their_mixing

"blobs"...moving in a certain direction while maintaining their shape

For an object to maintain its shape, there must be some force holding it together.
- Familiar objects around us in our house are held together by the electromagnetic force (photons)
- If we look bigger, the Earth is held in shape by the Gravitational force (hypothetical gravitons)
- If we look much smaller, the atomic nucleus is held in shape by the Strong Nuclear Force (Gluons)

However, Houses, Planets and Atomic Nuclei are not massless, and cannot travel at the speed of light.
- And photons and gravitons do not interact strongly with each other, so will not hold the shape with which they were emitted - they will tend to spread out. (I'm not so familiar with the behaviour of Gluons....)

There is one way that particles can hang out together, and that is in a soliton wave.
- If the passage of light interacts with the media (eg an optical fiber) so that an optical pulse retains its shape, that could produce long-distance optical fibers, resistant to dispersion.
- However, photons only travel at the speed of light in a vacuum, and travel at around 2/3 of that speed in an optical fiber.
https://en.wikipedia.org/wiki/Soliton

Field objects moving at the speed of light?

In Summary: None that I know of...

[Kartazion]

An object with bigger energy density at the centre and much more sparce with a distance.

Probability of the particle following a distance.

[Kartazion]

Perhaps such structure have emissions of atoms during the transitions of electron clouds to less energetic levels.

I find this part very interesting in that the density blossoms as the distance grows. It is true that the luminous density of a bulb fades from its source of emission to a low density spread out in space. With regard to the atom it is already true that the probability density is also of the same principle because the more one moves away from the nucleus, the more the density decreases while the probability of finding the particle is defined by its peaks.

[compuAI (OP)]

The only things that can move at exactly the speed of light are massless particles

"Field object" is not surely a particle. For example, spheric radiation of electric or magnetic dipole also moves at speed of light.

[Eternal Student]

Hi.

   I've tried to look through what you've written but I am a little puzzled about what is happening.

1.   This looks like electric and magnetic field stuff using Maxwell's equations.

You mention this:

The following symbols are used:
Scalar potential = a

    You don't make it clear what that scalar potential is but the only sensible thing seems to be the Elelctric potential field.   This is usually dentoted as  φ   instead of a.

Later on you do then use the symbol  φ :

1. With circular electric field.

Aφ' = - c · ∂Aφ/∂z = - Eφ
→ Eφ = c · ∂Aφ/∂z
→  ∂Eφ/∂z = c · ∂2Aφ/∂z2
  .........  etc......

   Although the symbol φ was never explained in the introduction it does look like this is the electric potential scalar field again - the thing you were calling a.    To say this another way:  You seem to be changing between using the symbol  a  and φ to represent the same thing. 


2.   There's no obvious question here.   That's OK, maybe you were just presenting something you've noticed or discovered.  However, I'm not really clear on what the final conclusion is supposed to be and hence what it is you might have shown.    The opening paragraph is suggesting we will find out what these "field blobs" might be.   The closing section just tells us something about how some fields might behave.


3.    This early sentence seems odd: 

Perhaps such structure have emissions of atoms during the transitions of electron clouds to less energetic levels.

    Did you really mean they emit entire whole atoms   or just that they (these "field blobs") have emissions that are similar to the sort of emissions you get from atoms?

4.   People have already commented on the uncertainty about what a "field blob" is   -  but I think that's the main point of the post.   You seem to be examining some unusual blip  in the Electric and Magnetic fields that may propagate a certain way and have just temporarily described these as field blobs   (I really don't know).

5.   Overall,  bits of the algebra and the use of what appears to be Maxwells equations does look perfectly sensible in places.   That's great.  However, it looks like bits of work thrown together without a consistent use of symbols and without a coherent purpose.   It's very difficult to follow.   If I was going to make a guess then I'd think you might have copy-and-pasted different things from various places and mashed them together for some purpose.   However, maybe that's not the case - perhaps you worked on different sections at different times and used different symbols in each session.   

    ----------
None of this matters too much.   It might just help everyone if you explained what it was you were trying to do here:   Were you trying to present some new work,    or   asking a question,    or something else?

Best Wishes.

[paul cotter]

Mathematical salad.

[compuAI (OP)]

This is usually dentoted as  φ   instead of a.
Later on you do then use the symbol  φ

φ is the angle in cylindrical coordinate system. Letter "a" here denotes only scalar potential and used to avoid confusion with angle.

[compuAI (OP)]

There's no obvious question here

The most controversial issue is the existence of fundamental velocity field. More details are described in the topic:
https://www.thenakedscientists.com/forum/index.php?topic=85274.0
and I would wish to know your opinion.

[compuAI (OP)]

Did you really mean they emit entire whole atoms   or just that they (these "field blobs") have emissions that are similar to the sort of emissions you get from atoms

Fields are emitted by atoms, not vice versa. And maybe that's what we perceive as "light".

Electric field (in my article is denoted E and is not the same as scalar potential gradient) and magnetic field (curl of vector potential) are "carriers" of conservative energy. So transverse waves, based on them, are usually called electromagnetic. But they are not the only fields, existing in the real world, and magnetic is not fundamental (but A).

[Eternal Student]

Hi.

More details are described in the topic:
https://www.thenakedscientists.com/forum/index.php?topic=85274.0

   Sorry, I have a new computer and haven't set up much anti-virus protection or any other security measures yet.   It will be quite a while before I download any files attached to a post.

Best Wishes.

[paul cotter]

You say "E is not the scalar potential gradient". The definition of E is E=∇V. Your use of "E" is meaningless.

[compuAI (OP)]

You say "E is not the scalar potential gradient". The definition of E is E=∇V. Your use of "E" is meaningless.

The law:
A' = - E - grad a
is not my invention, you can find it elsewhere, usually as:
E  = - A' - grad a
where sequence cause-consequence is distorted for some practical goals.
E and grad a are separate things, although in schoolbooks this issue is not clarified enough.

[paul cotter]

In the absence of time varying fields, E=-∇V. with a time varying magnetic field E=-∇V-∂A/∂t. Part of the confusion arises from incorrect symbols. I do apologise for the missing minus sign in E=∇V.

[compuAI (OP)]

In the absence of time varying fields, E=-∇V

Not always, even numerically. Constant electric field can exist as closed lines with zero divergence, represented mathematically as a curl of some vector instead of a scalar gradient.

[paul cotter]

"constant electric field can exist as closed lines with zero divergence represented mathematically as a curl of some vector instead of a scalar gradient". That's just a vague and inaccurate description, it is not mathematics.

[paul cotter]

Since E=-∇V-∂A/∂t, ∇ΧE=∇Χ(-∇V-∂A/∂t),  thus ∇ΧE=∇Χ(-∂A/∂t), since the curl of a gradient is zero. ∇ΧE=-μ ∂H/∂t.