Maxwell's vacuum
The early hours of the theory ... and after

The initial document

ISBN… 024-3 / EAN … 0243 (annex 02), extern link.

Analyzing the initial document

-           Generalizing the Poynting’s vector (proposition)

-           Analyzing the initial result with a constant wave vector

ISBN … 141-7 / EAN … 1417, extern link, 13 pages, version: 15 October 2018.

Comments

In writing Maxwell’s equation (EM) for empty regions of our universe (no mass and no electrical charge) in the dual space E*(3, C), and in introducing then the trivial decomposition for each cross product appearing there, I got an expression for a volumetric density of force.

The mathematical demonstration exhibits seemingly no peculiar difficulty and, in some way, is developed in a totally classical world (17th century) which would be today identified with a universe “à la ADM”; i.e.: as one of the plausible 3 + 1 slices of the full four-dimensional world. Therefore, the result may wake up the attention: “Why is there a force where nothing should happen?”

Thinking more deeply about the circumstances, we can identify two acceptable explanations: (i) We intuitively and experimentally know that an observer which is flying in vacuum (for example inside the ISS) will “feel” the influence of relatively far situated sources; recently detected gravitational waves reinforce this knowledge. (ii) The mathematics has replaced the supposedly physical space E(3, C) by its mathematical dual representation E*(3, C). Even if mathematics tells us that both spaces are isomorphic to each other: “Is the dual space really the same than the original one, or is it -for example- orthogonal to it?” With different words: “Has the use of this mathematical isomorphism discretely replaced Maxwell’s context where his equations were supposed to act and where the discussion was supposed to be developed by another?” The first explanation is no scoop and makes it acceptable to think that empty regions of our universe may be crossed by energetic streams. The second one is the starting point for quite subtler discussions.

Let me leave the questioning open for a while and go a step further in that analysis. The result itself contains three parts: (i) a first part can be interpreted as a description of the natural polarization of Maxwell’s empty regions (These regions have an electrical permittivity, e0, and a magnetic permeability: m0); (ii) a second one can be understood as being a natural resistance depending on the spatial gradient of the local volumetric density of EM energy against the progression of the wave; (iii) and the third one had, until now, no clear interpretation.

I am continuing the analysis of my initial document (Maxwell’s vacuum; the early hours of the theory) and doing all calculations in much details for a supposedly unique plane wave. A term proportional to E x B which is nothing but the Poynting’s vector appears effectively… but not exactly at the same place than the one which has been proposed in [01] and [02]. That means that the initial result is effectively a differential equation of the first order depending on that vector. I think that it is an undisputable result. This, until now, unfortunately doesn’t bring much light on the meaning of the third term. So, I am working further. There is a French version of that quest showing another side of my research on the same item (notion de chiralité).  

Bibliography (suggestion)

[01] Realizing optical pulling force using chirality ; arXiv: 1307.3074v1 [physics.optics], license.

[02] Lateral optical force on chiral particles near a surface; arXiv: Nature Communications 5, Article number 3307 (2014).

© Thierry PERIAT, 14 October 2018.