quiet

Thanks to all the people who have made themselves present. Each written note contributes to the reflection and that helps me.

Let's leave the word function, because we have other less confusing. And let's leave the microwave background to think about electromagnetic waves of astronomical length, which really have been detected. If it is also a residue of previous stages of cosmic evolution, we would have a scenario for our thinking. And a very different scenario if it is part of something astronomical objects do normally all the time.

5 hours ago, swansont said:

"fulfill any known function" is kind of awkward wording.

Hello swansont. I asked for some function because I remembered the case of such an isotropic microwave noise, detected by Penzias and Wilson, wich was there without explanation until the cosmologists recognized the function of that radiation. If cosmology, or any branch of physics, has recognized that these electromagnetic waves of astronomical length fulfill a specific function, I would like to receive the news.
 

Hi. I have put in the internet search engine the following:

longest wavelength electromagnetic waves in space

The following appeared in the list of the findings:

https://hypertextbook.com/facts/2001/RachelShapiro.shtml

Electromagnetic waves as long as the distances between astronomical objects. Do those waves fulfill any known function?
 

Thanks for point out that.

I put in this note what I really tried to express before.

- Classical electrodynamics in a vacuum.

- Propagation in a vacuum includes the waves of the fields [math]\vec{E}[/math] and [math]\vec{H}[/math]. It also includes waves from other fields, such as the vector potential [math]\vec{A}[/math] and the electric displacement [math]\vec{D}[/math].

- In the simplest case, flat wave without circular or elliptical polarization, [math]\vec{D}[/math] has a property that all other fields do not have. The wave equation of [math]\vec{D}[/math] in the vacuum admits a complex solution of exponential type.

[math]D = \hat{D} \ e^{i \left( \omega t - kx  \right)}[/math]

 [math]\hat{D} \ \ \ \rightarrow[/math] module of [math] \vec{D} [/math]

Let's write the identity of De Moivre for the case that concerns us.

[math]e^{i \left(\omega t - kx \right)} = cos\left(\omega t - kx \right) + i \ sin\left(\omega t - kx \right)[/math]

Applying that identity we have the following.

[math]D = \hat{D} \ \left[ cos\left(\omega t - kx \right) + i \ sin\left(\omega t - kx \right) \right] [/math]

8. The vector field [math] \vec{D} [/math], which has two components and module [math] \hat{D} [/math], corresponds to a plane electromagnetic wave propagating in the direction of the axis [math] x [/math]. If those components were not mutually perpendicular, they could not correspond to a complex number. They are mutually perpendicular and correspond to different axes of the coordinate system. Which axes?

9. Let's write the vector expression of the electric displacement.

[math]\vec{D}= \vec{P} + \varepsilon \vec{E} [/math]

In the vacuum is [math] \varepsilon = \varepsilon_o [/math]. We apply it.

[math]\vec{D}= \vec{P} + \varepsilon_o \vec{E} [/math]

The components [math] \vec{P} [/math] and [math] \varepsilon_o \vec{E} [/math] are mutually perpendicular. Can they be both cross-sectional? Let's reason. In terms of local results, polarization is a field with colinear symmetry that does not alter the electrical neutrality. That means that, within a finite length segment, there is a pair of equal and opposite vectors, resulting from all local contributions. In the case we are dealing with, could polarization be transversal? Impossible, because two transverse vectors that correspond to different values of [math] x [/math] are not collinear. Two longitudinal vectors corresponding to different [math] x [/math] values are collinear, because both vectors have the [math] x [/math] axis  direction.

10. What does the vacuum do when a wave propagates? Is it inert or participate in any way? The velocity of propagation is determined only by two properties of the vacuum, which are the permeability [math] \mu_o [/math] and the permitivity [math] \varepsilon_o [/math]. That leaves no doubt. The vacuum participates. How do it participate? The expression of displacement leaves no doubt. Participate polarizing. In that way it set the speed [math] C [/math] of propagation. That means that the displacement has a transversal component [math] \varepsilon_o \vec{E} [/math] and a longitudinal component [math] \vec{P} [/math].

[math]\vec{D}= \vec{x} P + \vec{y} \varepsilon_o E[/math]

In terms of the wave function we have the following.

[math] \vec{D} = \vec{x} \hat{D} \ cos\left(\omega t - kx \right) + \vec{y} \hat{D} \ sin\left(\omega t - kx \right) [/math]

[math] \vec{D} [/math] has finite divergence, corresponding to the charge density of the polarization. That divergence has the form of a wave function.

[math]\nabla \cdot \vec{D} = \hat{D} \ k \ sin\left( \omega t - kx \right)[/math]

Does that mean that some charge travels in a vacuum when the wave propagates? No charge needs to travel to produce that divergence. In the cities there are giant illuminated signs, which are panels populated by thousands of luminous cells, controlled by a programmable device. A program can achieve that the brightness of each cell varies sinusoidally, in the form corresponding to a wave function. You can program two colors, say blue and red. The first cell is initially dark. Then the blue light grows sinusoidally, reaches the maximum and decreases sinusoidally, until the cell becomes dark. Follow the sinusoidal stage of the red light, which does the same. All the cells are immobile on the board, but the program manages to see alternate blue and red areas traveling along the board. The effect is equivalent to colors in movement. At each point of the vacuum, the charge density varies sinusoidally. The signs of the charge do the same as the colors. The effect is equivalent to alternating zones with opposite charges traveling in the direction of propagation, although no infinitesimal or finite charge is actually moving.

- Although the charge does not really move, the effect is equivalent to moving charge, as happens with colors that look like moving sections with [math]\tfrac{1}{2} \ \lambda[/math] in blue and [math]\tfrac{1}{2} \ \lambda[/math] in red.

- The effects of the virtual movement of the charge density are equivalent to a virtual density of current in the direction of propagation, equal and opposite to the longitudinal component of [math]\dfrac{\partial \vec{D}}{\partial t}[/math] . This derivative is part of the Ampere-Maxwell law.

Ampere-Maxwell law [math]\rightarrow \ \ \ \vec{\nabla} \times \vec{H}=\vec{j}+ \dfrac{\partial \vec{D}}{\partial t}[/math] .

Finally [math]\vec{\nabla} \times \vec{H}[/math] it remains, in a net form, identical to the result obtained for the real solutions of the wave equation, which lack a longitudinal component.

- The law of Ampere-Maxwell allows to calculate the inductance of the propagation in a vacuum. Then the energy of the magnetic field is calculable by two methods. One is to integrate the energy density, as we usually do. Another is based on the inductance and the currents involved. Equating the results of both methods all the geometrical measurements and the shape of the autonomous configuration that has the inductance and capacity calculated. It is a cylinder whose length is equal to [math]\lambda [/math] and its diameter is

[math]\dfrac{\lambda}{2 \pi}[/math]

The inductance and the capacitance have the following values.

[math]\mathcal{L}= \mu_o \ \dfrac{\lambda}{2 \pi}[/math]

[math]\mathcal{C}= \varepsilon_o \ \dfrac{\lambda}{2 \pi}[/math]

So it turns out that the total energy of the stunned configuration is

[math]E=2 \ \pi \mu_o \ C \ Q_o^2 \ \ \nu[/math]

[math]Q_o \ \ \ \rightarrow[/math]   elemental charge of vacuum polarization

The development shows that [math]Q_o[/math] It is a universal constant. Then the energy of the autonomous configuration is directly proportional to the frequency and the Planck law of quantum energy is proved. There is also the Planck constant expressed in electrodynamic constants melting.

[math]h=2 \ \pi \mu_o \ C \ Q_o^2[/math]

If in the formal definition of the fine structure constant you express h in that way, you get

[math]\alpha=\dfrac{1}{4 \ \pi} \ \left( \dfrac{e}{Q_o} \right)^2[/math]

That is, alpha is given by the quotient between the charge of the electron and the elementary charge of the polarization of the vacuum, that same charge that appears in the Spanish article of the electromagnetic knots.

The next stage of the development is to analyze the mutual frontal collision of two autonomous configurations, that is, of two photons having the cylindrical shape and the calculated measurements. Photons do not pass through one another like ghosts. They interpenetrate, but not totally. Mutual penetration only reaches a certain depth, because the impulse gradually decreases. The partially interpenetrated photons form a larger object for a moment, which ends up breaking in one of the two sections that delimit the penetration zone. The large object is fragmented. One of the fragments takes the fraction of charge that the other contributed to the penetration zone. That fraction is equal to [math] e [/math]. One of the fragments, the electron, remains with charges [math]-(Q_o+e),+Q_o [/math] and its net charge is [math]-e[/math]. The other fragment, positron, remains with [math]-(Q_o-e),+Q_o[/math] and its net charge is [math]+e[/math].
By proposing the wave functions and the energy balance, the theoretical value of the quotient between the net charge [math]e[/math] and the elemental charge of vacuum polarization [math]Q_O[/math] is obtained as a result, without using a single empirical data, that is, without involving physical constants. The result is

[math]\dfrac{e}{Q_o}=\dfrac{-3+\sqrt{13}}{2}[/math]

In decimal numeration is

[math]\dfrac{e}{Q_o}=0,30277563773199...[/math]

The inverse is the factor that appears in the Spanish article of electromagnetic knots.

[math]\dfrac{Q_o}{e}=3,30277563773199...[/math]

As that article points out, [math]Q_o[/math] It is about 3.3 times greater than the electron charge.

- The force between a pair of charges [math]Q_o[/math] It has the same properties as the force between the plates of a capacitor, that is, it is a force independent of the distance between charges. And in relative terms it's [math](3,30277563773199...)^2[/math] , about 11 times greater than the force between two charges [math]e[/math]. Do those characteristics remind us of something? Strong force has the same characteristics.

- Let's formulate [math]\alpha[/math]

[math]\alpha=\dfrac{1}{4 \ \pi} \ \left( \dfrac{e}{Q_o} \right)^2[/math]

[math]\alpha=\dfrac{1}{4 \ \pi} \ \left( \dfrac{-3+\sqrt{13}}{2} \right)^2[/math]

In decimal numeration is

[math]\alpha=0,0072951124566757786721625768237...[/math]

It differs 0.03% with respect to the empirical value published by CODATA. As far as I can analyze, the calculation of [math]\alpha[/math] in this context, it does not allow retouching that equals the value given by CODATA. If the empirical value is fully reliable, the development based on classical electrodynamics should be understood as a first approximation.

- That development includes more details. For example, it shows that the electron and the positron are constituted by cylindrical rotating waves, electromagnetic waves obviously. And determined what proportion of the constituent energy of each particle is in the electric field and what proportion in the magnetic field of the wave. 65.1% of the energy [math]m_o \ C^2[/math] of the electron is in the electric field. And 34.9% in the magnetic field. That means that the magnetic field can not overcome the potential barrier of the electric field and, for that reason, the electron does not decompose. In the positron the percentages are identical, but the greatest proposal corresponds to the magnetic field. That is why the positron decomposes easily. Many more issues appear in the development, but exposing them to all coherently demands 130 pages of writing, a space that we do not have here. We do not even have space to adequately expose the details shown in this note.
 

I will express my conviction. The charge radiates only in the conditions that break the object. In cases that do not cause breakage, the charge not radiate. Why ? Because to break and to radiate, a contribution of energy is necessary. And only the own acceleration corresponds to an energy received by the object that is broken or by the load that radiates.

Thanks MigL, thanks Markus for what you have exposed.

Perfectly understood. I suppose I can think without confusing the proper acceleration with the acceleration that is detected only from some reference systems.

Radiating is not the only phenomenon caused by acceleration. Think of an object designed to break when it suffers a proper acceleration. The charge and the fragile object are on board the same vehicle. If we say that the charge is seen radiating from some reference systems and from others not, none of our claims destroys the charge. But we must be more careful in what we say about the fragile object. If a rupture is observed from a reference system can, from another reference system, be observed that the object has not been broken?

My surprise was great, because you get to the same elemental charge of vacuum polarization developing the consequences of the displacement wave. I wrote the beginning of that topic in the thread initiated by Achilles, entitled: Is there anything left to discover in electromagnetism?
The full development is interesting. Did you know, for example, that this elementary charge is a universal constant, property demonstrated in development? Did you know that the fine structure constant is given only by the quotient between the charge of the electron and the polarization elememtal charge? And that this quotient is an intrinsic property of the system of 4 Maxwell-Heavside equations, so that the quotient is calculated in a purely theoretical way, without using a single empirical data? Thus a purely theoretical alpha value is obtained. The development contains much more, as you imagine. That's why the Spanish publication caused me great surprise.

Is acceleration absolute? I ask for what is observed, for example in a car that travels occupied by 3 people. We admit ideal conditions to simplify. When braking intensely, all people suffer the shaking without seeing relative acceleration between people. At the same time, between a person standing on the sidewalk and a car accelerating, there is relative acceleration. But only the occupants of the car feel the effect. That is, the relative acceleration is physically irrelevant. Only own acceleration causes effects and, judging the evidence, I am forced to understand that it is absolute. Errors in my interpretation of those examples?

10 hours ago, MigL said:

The problem specified two detectors

9 hours ago, Markus Hanke said:

the earth-bound detector will detect radiation.

Hi. Surely it is a mistake to use classical mechanics in this problem. Please also allow me to raise a doubt in those terms.

In classical mechanics the mass of a body links acceleration with force. For example, the resultant force is equal to zero in a system of two equal and opposite forces. Is that equivalent to two equal and opposite accelerations, which give a resultant acceleration equal to zero? If that equivalence were coherent, then in condition A a force is the weight of the set formed by the charged body and the detector that accompanies it. Another force is the sustentation, opposed to the weight. In case of reasoning well, in classical terms, in condition A the net acceleration is equal to zero and the charge does not radiate.

In condition B there is only the weight and there is no sustaining force. Then the net acceleration is nonzero and the charge radiates.

In case of being the previous erroneous thing, a didactic explanation would be very useful for me, that allows to easily understand the error.

14 hours ago, Markus Hanke said:

What exactly do you mean by “topological difference”?

I tried to look for something that I had seen before and, instead, I found something surprising. It is a study of the topological properties of electrodynamics, done in two Spanish universities. It is written in English. It comes to establish the quantization of the charge and relates that to the polarization of the vacuum. It is not based on the breaking of spacetime. It is based on knots. On page 85 you can read a synthesis of the result. It is at the following address.

http://cdn.intechopen.com/pdfs/33435/InTech-Topological_electromagnetism_knots_and_quantization_rules.pdf

30 minutes ago, Strange said:

One of the requirements of the mathematics used to model the curvature of spacetime is that it is continuous. Therefore discontinuities, such as cracks, are not supported. 

Thanks for pointing that out. Let me now replace the idea of splitting by the idea of topological change that happens inside a finite three-dimensional region. I think of a change that produces some kind of symmetry, limited to a finite region. Please allow a rude analogy. Take putty, of that used to put glasses. Without breaking it, in a place of putty you mold something topologically different from the rest of the putty piece. There will be a boundary between both topological conditions, so that a Gaussian surface can wrap around the region where the topology has changed and symmetry has been created. That boundary does not delimit a break, but it delimits a clear topological difference.

27 minutes ago, MigL said:

No,  scientific jargon says that the model ( GR ), involving curvature of the co-ordinate system, matches observation/experiment to a very high degree.
That is the model, whether space or space-time is curved ( or can be curved ) is immaterial.

Thank you MigL for providing a response. I need now to think a little.

1 hour ago, MigL said:

This is all 'frame of reference' related...

Thank you MigL for providing a response. I need now to think a little.

Current physics explains that the state of a portion of space depends on the phenomena, local and / or distant. It also explains that states can and do evolve, change depending on events.

The mathematics that expresses some states is similar to the mathematics that describes the curvature in geometry. In short, in scientific jargon it is said that space can be curved. This abbreviated language also includes contraction, elongation, torsion ...

Does it include excision? That is, the possibility of something whose mathematics is similar to the mathematics of a crack?

I mean the vacuum. In a region where there is no break initially, could one happen? If yes, does something appear as a product of that break? If yes, is that product something known for a long time?

Hi. First of all I beg to be apologized, in case of creating the thread in the wrong section. Maybe you can help in a question that causes me doubts.

- Ideal conditions, all theoretical, as simple as possible, mental experiment, everything happens in a vacuum.

- Device formed by an electrically charged spherical body and a radiation detector, rigidly connected by an insulating connection.

- Fixed to the planet there is another radiation detector.

- Condition A: Initially the device is at a distance from the ground and there is no relative movement between the device and the planet.

- Condition B: The device is in free fall towards the planet.

- The planet is electrically neutral.

- What does each detector record in condition A?

- What does each detector record in condition B?

Agradezco a todas las personas que han colaborado para cambiar mi apodo. Me alegra mucho el apodo que realmente deseo. Saludo cordial.

4 minutes ago, neuerwind said:

Please e-mail me.

I recently joined the forum and I do not know where to find your email.

7 minutes ago, neuerwind said:

I have gathered certain evidence that proves the incompleteness of our current EM field theory.

I would like to have access to the evidence you have gathered.

12 minutes ago, neuerwind said:

Bring back quaternions into the original Maxwell theory, and you will see a whole new world opening.

Yes, I read some of that out of the mainstream. Some articles of that kind have been written by scientifically prepared people, even by university professors. All agree in denouncing the interested suppression of an essential part of the first publication made by Maxwell. They also reject the compact form Heavside gave to the theory, replacing the original 20 quaternion equations with 4 vector equations. I've only read out of curiosity. I have not delved into the subject. You do?

Hello Markus. I deeply respect your opinion, I admire your capacity to unite coherently what the theories contribute and, in the same measure, I admire your honesty and your firmness.

On the first page of the Discourse on Method, Descartes wrote the following. Intelligence is the best distributed thing in the world, because no one complains about having little and all people consider that they have enough.

We believe that this phrase exudes irony. But in a universe where something elementary, like the photon, exhibits conduct that deserves to be qualified as intelligent, where there are signs of intelligence in plants, in minerals and in all animal organisms, we can write without irony the same phrase.

Some people harbor in their minds the idea of a god and other people do not. In my life I met people in enough variety and quantity to have a statistical sample. We assume that I form a function of two variables. The dependent variable is the degree of mental adherence to the belief in a god. The independent variable is the amount of intelligence of the person. In the statistical sample of my experience, a Gauss bell would appear when plotting that function. That is, my less intelligent acquaintances and my more intelligent acquaintances do not adhere to the idea of a god. My acquaintances who have intermediate intelligences adhere to that idea. I do not take into account what people say to be good to those who listen. I keep in mind the behaviors. The behavior sample is represented by a Gaussian bell.

Why is the lack of intelligence and maximum intelligence inadequate to believe in a god? Politics is another issue where those two extremes of intelligence fail. The same applies to surgery and other manual health services, such as kinesiology, nursing, etc.

Obviously there are privileges reserved for intermediate intelligence, completely inaccessible for low and maximum intelligence. If I wanted to gather, for my personal purposes, most of the population, I would create an institution whose distinctive flag was the idea of a god. And I would create it by pure pragmatism, regardless of my personal stance on that idea.

To analyze from science and from philosophy the idea of a cosmic being, the first step is to get rid of everything that the pragmatic institutions teach, that congregate people under a flag to lead the masses more easily, with the same ease of the shepherd leading a flock.

To analyze from science and from philosophy the idea of a cosmic being, equanimity is essential, a faculty that is at the antipodes of pragmatism.

Can I achieve equanimity? In my personal case, that is impossible. Can I achieve a condition that imperfectly substitutes for equanimity, even if it partially serves to analyze the idea of a god? I guess so. And I suppose that sometimes I have reached that condition, which helped me to make the idea of a god pass through the scientific-philosophical filter. At the exit of the filter there are no reasons that guarantee the existence of a universal being. But when I do not demand guarantees, I find in science and philosophy indications of an appreciable probability with respect to the existence of that being.

15 hours ago, Markus Hanke said:

Maxwell‘s electrodynamics is the purely classical limit of quantum electrodynamics - hence it does not and cannot account for any quantum effects.

Hello Markus. 

Do you think that classical electrodynamics is fully developed, to the limit of its exhaustion? Some people felt that in the second half of the 18th century about mechanics, founded by Newton a century earlier. Euler and Laplace, with amazing advances, had drawn from the Newtonian bases consequences that extended the application to the entire universe.

Was there anything left to extract? Impossible, everything has been extracted !, said those people with admiration. Several decades later, Lagrange and Hamilton managed to extract from the Newtonian bases much more than everything extracted in the previous history. 

Hamilton went on to show that classical mechanics involves a wave formulation of the motion of a particle. He called phase wave to that formulation. He showed that the action is the governing parameter of the phase wave. Obviously, Hamilton did not quantize the parameter. If he had, he would have laid the foundations of quantum mechanics. Those who rushed to believe that the Newtonian bases were exhausted, received a blunt surprise when Lagrange and Hamilton arrived.

Do you think it's a good idea to rush to believe that everything has been exhausted in classical electrodynamics? Or maybe something similar to what happened in mechanics can appear, so that quantum properties are deduced from classical electrodynamics?

On 3/8/2018 at 3:01 AM, Achilles said:

Is there anything left to discover in electromagnetism?

Somethig more here:

https://arxiv.org/abs/1005.0131

Thanks anyway. Best regards.