Maxwell's vacuum
The early hours of the theory ... and after
The initial document
ISBN… 0243 / 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 … 1417 / 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 (17^{th} 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 fourdimensional 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, e_{0}, and a magnetic permeability: m_{0}); (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.