Field objects moving at the speed of light

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. Discussion of how justified use of the term "photon" in relation to such objects is beyond the scope of this article.

Let us take as basis the equations, existence of which in the real world is justified in the topic on dipole radiation: ?

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 putJ = 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
wherediv 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
∫-∞+∞∫02·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
forρ = 0 the function- ρ ·∂a/∂ρ = 0,
forρ = ∞ 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 / s3with Eρ = A0 · (2 · ρ / s3 - 3 · ρ3 / s5), also for a = A0 · ρ4 / s5withEρ = A0 · (4 · ρ3 / s5- 5 · ρ5 / s7), fora = 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.

 

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This is gibberish. How can electron transitions emit atoms?

More fundamentally, how can an object with electrons, i.e. with a non-zero rest mass, travel at c?

 

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I was talking about photons and neutrinos only. As a probability, I am not sure.
Atoms emit photons, atoms travel not by themselves.

 

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Of course. Does behaviouг of such field objects coincide with properties of real emissions of atoms and molecules?
Exist some mathematical models that describe them using electric fields with zero divergence?
Or real atomic emissions are like spheric waves from dipole emitters?

 

No.

 

Asked and answered. Thread closed?

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"No" it's an incomprehensible answer. I would like to understand your version of what fundamental fields and how "light radiation" is arranged.

 

"My" version is just the standard model of light, as expressed in terms of the EM field and QM. I don't need to recite that for you. If you have studied physics you will be familiar with it already.

 

I never saw visualization or program code for computer simulation. In my humble opinion, I we cannot simulate or visualize something, it is doubtful to be some physical reality. Officially accepted quantum physics, for example, at all does not concern arrangement of elementary particles, considering them as infinitely small "material points".

 

Your opinion is wrong based on quantum mechanics which is an extremely successful theory, so it is not looking good.

Correct, elementary particles do not have a size or structure. Whether you can visualize this or not is irrelevant.

 

Then your opinion is wrong. QM requires mathematical concepts that don't correspond to 3D visualisation. Look up Hilbert space, for instance.

 

Is this simulation at all relevant?
(Both this discussion and the simulation are above my head but I came upon it a few months back and wonder if it might be the sort of thing you are talking about)


I hope to be able to understand it better in the medium term....

 

It feels very unintuitive to me that any object should have no internal structure and be described as a "point particle" with no diameter at all.

But does it become easier to understand this if particles are understood as moving excitations in their particular field?

To me ,if (and I understand this is now mainstream science) we have to ditch the old idea of particles and see these phenomena as aspects of a field ,does it become easier to understand them as having no extent and just occupying a region where only one thing is happening -almost like a point where lines cross?

Or are we ,if we had the technology (which may not exist in the universe) eventually going to find some internal structure in objects or phenomena that, according to the ongoing model we describe as dimensionless points?

 

Only from the viewpoint of official quantum physics, representing some level of approximation. All canonical quantum equations are linear, but this gives no answer why particles have strictly defined charges and masses. If we multiply basic values (wavefunction, electric and magnetic field) by some constant number, and probabilities or energy densities by its square, we also get valid object. To explain properties of particles non-linear equations are required.

 

It is good video for purposes of physics popularization. But "probability" to encounter a particle appears, for example, when electron is moving chaotically with some statistics near atomic nucleus. Schrödinger and Pauli equations are very useful in the simulation of atoms and molecules. But they work only if there is center of attraction with electrostatic potential. The remaining terms of the equations, probably except less-significant magnetic corrections, disperse electron cloud. We cannot represent in similar way "single" electron without nucleus. Some historical attempts, like Klein-Gordon equation, really explain nothing. Although maybe useful for other goals, like description of 2-dimensional currents in frozen conductors.

 

Correct.

This is a strange statement. The term 'canonical' is a religious term, not a scientific term so I have no idea why you are using it. Equations used in QM are not all linear. Even in basic mechanics the equations are mostly nonlinear. The equations are just simplified to linear equations by ignoring the nonlinear aspects like friction.

 

I have seen the term "canonical" used quite a lot on science forums recently.

I don't know yet what it means in a scientific context but a quick Google seems to answer the question


https://en.m.wikipedia.org/wiki/Canonical