View source for Mathematical Model of Independent Radiation Field

{{Infobox paper
| title = Mathematical Model of Independent Radiation Field
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5916.pdf Link to paper]
| author = [[Qing Zeng]]
| keywords = [[radiation of electric wave]], [[reception principle]], [[inverse distance square theorem]]
| published = 2010
| num_pages = 16
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_5916.pdf here]

==Abstract==

We can think that Michelson-Morley experiment negates ether medium, so, there is no medium for electromagnetic wave to transmit. So, the motion of electromagnetic wave is not transmission, but radiation, it radiates to the outside like ray flux. Now that it is radiation, time variable electric field is supposed to be the vector field with independent radiation, and it does not need time variable magnetic field to "bridge". In other words, in the vacuum, because electric wave or light wave does not have the medium of oscillation-transmission, and the mass of the field is zero, the motion of the field does not need the force, so the motion of the field is a kind of radiation, it does not need another field to be "bridge". According to this, time variable magnetic field can radiate independently, time variable electric field can also radiate independently. The more important thing is, we benefit from the great Hertz experimental logic. Initiating from LC oscillation circuit, and gradually extends into half-wave dipole antenna, the oscillation of the current on the half-wave dipole antenna generates time variable current and time variable charges. Its electric field wave is the radiation of the time variable charges on the oscillator, its magnetic field wave is the radiation of the time variable current on the oscillator. The exchange between electric field and magnetic field is through the flow of the time variable current on the half-wave dipole. In other words, time variable electric field and time variable magnetic field are generated by the time variable motion of the metal electrons on the transmitting antenna. Furthermore, this article proves the principle of radiation model and antenna receiving signal which satisfies the inverse distance square theorem.

==Overview==

Zeng Qingping, a professor at the Air Force Radar Academy in Wuhan, wrote this paper as one instalment of a long series attacking what he calls Maxwell's "mutual generation" theory — the doctrine that a changing electric field creates a magnetic field and vice versa, the two leapfrogging each other through space. His starting point is an engineering complaint rather than a philosophical one: the standard dipole radiation formula, integrated over a sphere centred on the source, does not conserve the radiated vector field, and does not reproduce the inverse-square dependence that radar and communications practice actually observe. "It is neither the conservation of transmitting wave energy, nor the conservation of radiation vector field."

His alternative is that the two fields never generate each other at all. Since the Michelson–Morley result removes the [[Aether|ether]], there is no medium to transmit anything; what happens instead is ''radiation'' — the field is emitted outward like a ray flux, has zero mass, and therefore needs no force and no intermediary to move. On this view a time-varying electric field radiates independently, produced by the time-varying ''charge'' on the antenna, and a time-varying magnetic field radiates independently, produced by the time-varying ''current''. The only place the two exchange is inside the conductor, through the flow of charge in the half-wave dipole. Everything else in the paper is the working-out of that claim with [[Coulomb's Law]] and the Biot–Savart–Laplace law in place of [[Maxwell's Equations]].

==The argument==

===The spherically symmetric charge===

The paper's foundational construction is a screened tube that fires charge onto a metal sphere ''a'', so that the charge changes at a rate ''Q''(''t'') and the resulting field is spherically symmetric. Because of the symmetry, ∂''B''/∂''t'' = 0 and ''H'' = 0: there is ''no'' magnetic field anywhere around the sphere. Yet the time-varying electric field is present throughout free space. Zeng's conclusion is that it must have radiated independently, since there was no magnetic field available to generate it.

From Coulomb's law he writes the field at distance ''r'' with a propagation delay ''r''/''c''<sub>0</sub>:

: '''E'''(''r'', ''t'') = [''Q''(''t'' − ''r''/''c''<sub>0</sub>) / 4πε<sub>0</sub>''r''<sup>2</sup>] '''e'''<sub>''r''</sub>

where ''c''<sub>0</sub> is "the radiation speed of the electric field lines". Taking a spherical surface ''S'' about the centre, the flux out of ''S'' is conserved — and this, he says, is "the important conclusion of inverse distance square theorem". The field is irrotational and falls as 1/''r''<sup>2</sup>. He takes the discovery of the positron as licence to make the sphere's charge sinusoidal, ''Q''(''t'') = ''Q''<sub>0</sub> sin ω''t'', so that a genuine sine wave radiates with '''H''' = 0 throughout.

He then attacks the symmetry argument in Einstein's 1905 paper directly: if Maxwell's asymmetric treatment of the moving magnet and the moving coil rests on a defective equation, and if the magnetic field wave in fact radiates independently, "then it needs to reconsider Einstein's relativity principle."

===The electric dipole===

For a real antenna the source is not a point but a pair of charges ±''Q'' separated by ''l''. Zeng computes the retarded potential, expands ''r''<sub>1</sub> and ''r''<sub>2</sub> binomially for ''r'' ≫ ''l'', drops higher terms, and obtains

: Φ = ''Q''(''t'')''l'' cos θ / 4πε<sub>0</sub>''r''<sup>2</sup>

Taking the gradient gives the independently radiated dipole field

: '''E'''(''r'', θ, ''t'') = [''Q''<sub>m</sub>''l'' cos θ sin ω(''t'' − ''r''/''c''<sub>0</sub>) / 2πε<sub>0</sub>''r''<sup>3</sup>]'''e'''<sub>''r''</sub> + [''Q''<sub>m</sub>''l'' sin θ sin ω(''t'' − ''r''/''c''<sub>0</sub>) / 4πε<sub>0</sub>''r''<sup>3</sup>]'''e'''<sub>θ</sub>

with no '''e'''<sub>''φ''</sub> component. Zeng anticipates the obvious objection — this falls as 1/''r''<sup>3</sup>, while measured received current falls as 1/''r''<sup>2</sup> — calls it "a good question", and defers the answer to his reception analysis. He explains the 1/''r''<sup>3</sup> as arising because the positive and negative fields partly cancel. He also gives a physical account of transverse waves: the field lines radiate ''vertically'' from each charge, but the vector superposition of the positive and negative sets makes the composite lines curve, and "the farther distance is, the power lines after being composited quite resemble the horizontal power lines, which is so called transversal wave."

===The magnetic dipole===

The magnetic side runs in parallel. A solenoid carrying ''i'' = ''I''<sub>m</sub> sin ω''t'' contains '''B'''(''t'') = μ<sub>0</sub>''n i''(''t''): the time-varying magnetic field is generated by the time-varying current, "such conclusion is obviously correct." Zeng argues from a sawtooth-current example that a linearly varying magnetic field radiates independently, then that a triangular wave does, then — fitting the two halves of a triangle with a smooth curve — that a sinusoid does.

Applying Biot–Savart–Laplace to a finite magnetic dipole in cylindrical coordinates he obtains

: '''B''' = (μ<sub>0</sub>''I'' / 4π''r'')(sin α<sub>1</sub> − sin α<sub>2</sub>)'''e'''<sub>φ</sub>

and notes that when ''z'' ≫ ''r'' — at the two ends of the dipole — sin α → 0 and '''B''' → 0, so "there is almost no magnetic field at the two ends of the magnetic dipole. It also indicates that magnetic dipole has very strong direction character." In the broadside far field, ''r'' ≫ ''z'', this reduces to the ''inverse-square'' form

: '''B'''(''r'', ''t'') = [μ<sub>0</sub>ω''I''<sub>m</sub>''l'' sin ω(''t'' − ''r''/''c''<sub>0</sub>) / 4π''r''<sup>2</sup>]'''e'''<sub>φ</sub>

This is the paper's key asymmetry: the radiated magnetic field goes as 1/''r''<sup>2</sup> while the radiated electric field goes as 1/''r''<sup>3</sup>.

===Opening the LC circuit===

Section 4 retraces Hertz's construction. In a closed ''LC'' circuit the electric field is confined to the capacitor and the magnetic field to the inductor, so nothing radiates. Opening the capacitor plates and the inductor winding stage by stage yields the dipole antenna, at which point "time variable electric field is open in the whole free space" and likewise for the magnetic field. Zeng insists this is Hertz's own experimental logic and "not the particular creation of this article, only the conclusion."

The exchange between electric and magnetic energy, he stresses repeatedly, happens through the motion of charges in the circuit and takes time — the capacitor discharges through the coil, the coil then recharges the capacitor — and "not the direct exchange between electric field and magnetic field." Resonance is what makes the half-wave dipole efficient. The 90° phase difference between the two radiated fields is inherited from the 90° phase difference between ''i''(''t'') and ''Q''<sub>C</sub>(''t'') on the antenna, not from any field-generating-field mechanism.

===Reception and the inverse-square law===

The last section is where the deferred question is answered. Zeng asks how the received signal is produced — by a wave striking the antenna? by an ''E''×''H'' energy density entering it? — and answers: neither, and "even less likely the action of Maxwell's curl theory."

The metal electrons in the receiving antenna feel two forces: the electric force ''e'''''E''', and what he calls the General Lorentz magnetic force ''e''(−'''c'''<sub>0</sub>×'''B'''), the magnetic field moving right at ''c''<sub>0</sub> being equivalent to electrons moving left. The radial component ''E''<sub>''r''</sub> is perpendicular to the antenna and generates nothing; only the components parallel to the wire count, and their resultant is

: ''F'' = √(''F''<sub>''E''</sub><sup>2</sup> + ''F''<sub>''B''</sub><sup>2</sup> + 2''F''<sub>''E''</sub>''F''<sub>''B''</sub> cos φ) · sin(ω''t'' + ψ)

with amplitudes

: ''F''<sub>''E''</sub> = ''eQ''<sub>m</sub>''l'' sin θ / 4πε<sub>0</sub>''r''<sup>3</sup>  and  ''F''<sub>''B''</sub> = ''e c''<sub>0</sub> μ<sub>0</sub>ω''Q''<sub>m</sub>''l'' / 4π''r''<sup>2</sup>

Evaluating both at ν = 10<sup>8</sup> Hz (metre-wave band) with sin θ = 1, Zeng finds ''F''<sub>''B''</sub> is about twice ''F''<sub>''E''</sub> at unit distance; at a receiving station one kilometre away, because of the differing powers of ''r'', ''F''<sub>''B''</sub> is "two thousand times" ''F''<sub>''E''</sub>. The received signal is therefore essentially entirely magnetic, and since ''F''<sub>''B''</sub> ∝ 1/''r''<sup>2</sup>, "its signal intensity is inversely proportional to distance square… which coincides with the engineering practice."

Two corollaries follow. "The whole free space is mainly filled with magnetic wave", the electric part dying away quickly because the positive and negative time-varying charges partly cancel. And since ''F''<sub>''B''</sub> is proportional to ω, "the effect when magnetic wave acts on the object is proportional to the frequency, which coincides with the frequency relationship of Planck's quantum hypothesis of the blackbody radiation experiment."

==Assessment==

The paper has a genuine virtue that is easy to miss behind its polemics: it insists that a radiation theory should be answerable to what antenna engineers actually measure, and it treats the received signal — not an abstract field — as the thing to be calculated. The physical picture of the exchange between electric and magnetic energy taking place ''in the conductor'', through the motion of charge, rather than between the fields in empty space, is a coherent and arguably more concrete way to describe a resonant dipole than the leapfrogging-fields cartoon of the textbooks, and Zeng is right that the cartoon is a cartoon. The observation that the ends of a magnetic dipole radiate almost nothing is correct, and the derivation of the dipole potential by binomial expansion is done properly. He is also candid: he raises the 1/''r''<sup>3</sup> objection against himself rather than hiding it.

The difficulties, however, go to the foundation. The paper's central deduction — that because a spherically symmetric charge distribution produces no magnetic field, the electric field must "radiate independently" — mistakes a well-known null result for a discovery. Maxwell's equations give exactly the same answer: a spherically symmetric time-varying charge distribution radiates ''nothing at all''. The monopole term has no radiative content; the field outside is the quasi-static Coulomb field of the enclosed charge, which changes as charge accumulates but carries no energy away. Zeng's construction is not an independently radiating electric wave; it is the standard result that there is no monopole radiation, redescribed. His screened tube, moreover, must carry a current to deliver charge to the sphere, and that current is precisely the source of the magnetic field the symmetry argument sets to zero.

The dipole result is the decisive point. Zeng obtains '''E''' ∝ 1/''r''<sup>3</sup> and '''B''' ∝ 1/''r''<sup>2</sup>, whereas the standard theory gives both radiation fields falling as 1/''r'', in phase, with the ratio ''E''/''B'' = ''c''. His 1/''r''<sup>3</sup> is the ''near-field'' static dipole term; the radiation term, which comes from differentiating the retarded potential with respect to time as well as position, is absent because he expanded the geometry but never took the time derivative that produces it. This is not a small discrepancy: fields falling as 1/''r''<sup>3</sup> and 1/''r''<sup>2</sup> carry a Poynting flux falling as 1/''r''<sup>5</sup>, whose surface integral over a sphere vanishes as ''r'' → ∞, so on Zeng's own equations a transmitter radiates no power at all into the far field. The engineering fact he set out to explain — that received ''power'' falls as 1/''r''<sup>2</sup>, which is what conservation of radiated energy through a growing sphere requires — is exactly the fact his field expressions cannot deliver. The Friis transmission equation, on which every link budget in radar and telecommunications is computed, follows from 1/''r'' fields and is verified daily to a fraction of a decibel.

The 90°-phase claim is likewise contradicted by direct measurement. Zeng requires the radiated '''E''' and '''B''' to be in quadrature, inherited from the phase relation between charge and current on the antenna. In the far field they are measured to be ''in phase'' — this is precisely why a receiving antenna extracts net power rather than only reactive power, and it is confirmed by every measurement of radiated power density. Quadrature fields transport zero time-averaged energy, which is another statement of the same failure.

Two further steps are asserted rather than argued. The claim that the received signal is "two thousand times" more magnetic than electric at one kilometre rests on comparing two amplitudes with different ''r'' dependences, and so is an artefact of the erroneous 1/''r''<sup>3</sup> electric term rather than a physical result; in the correct far field the two contributions to the force on a conduction electron are of comparable size, since ''E'' = ''cB''. And the appeal to Planck's blackbody relation, on the grounds that ''F''<sub>''B''</sub> ∝ ω, is a coincidence of proportionality, not a derivation: Planck's law concerns the energy per quantum, ''E'' = ''hν'', not the force on a conductor, and no value of ''h'' or of the spectral distribution follows from anything in the paper.

Finally, the framing argument is weaker than Zeng needs. He takes the Michelson–Morley null result to abolish the medium and therefore to abolish "transmission", leaving only "radiation" as the alternative. But nothing in that inference bears on whether the two fields are coupled: fields in vacuum obeying [[Maxwell's Equations]] require no medium either, and the coupling of '''E''' and '''B''' is a statement about the equations, not about a substance. The paper's motivating problem — an alleged failure of energy conservation in the standard dipole solution — is stated but never demonstrated here, being referred to the author's earlier books and conference papers.

==See also==

* [[Qing Zeng]]
* [[Maxwell's Equations]]
* [[Coulomb's Law]]
* [[Lorentz Force]]
* [[Michelson-Morley Experiment]]
* [[Aether]]
* [[Speed of Light]]
* [[Planck Constant]]

[[Category:Scientific Paper|mathematical model independent radiation field]]

[[Category:Aether|mathematical model independent radiation field]]

[[Category:Electrodynamics]]

[[Category:Electromagnetism]]

[[Category:Light]]