# Maxwell's-vacuum.

**Author**: PERIAT, T.

**Title**: The Theory of the (E) Question - Annex 02.

**Matriculation**: EAN 978-2-36923-024-3, EAN 9782369230243.

**Language**: GB/USA.

**Published**: 29 July 2014.

**Number of pages**: 7.

**The document**: Ean 978236923024 annex02 (370.08 Ko).

**Comments**

In writing Maxwell’s equations (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 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:

- We intuitively and experimentally know that an observer who is “flying” in vacuum (for example inside the ISS) “feels” the influence of far situated sources (e.g.: Earth gravitation, gravitational waves, …). Hence, an empty space only is a theoretical concept and, whatever we do, (what I have called) the Maxwell’s vacuum is equivalent to a volume that is fulfilled with a tiny polarized electromagnetic field. That weak polarization is enough to induce small forces.

- The mathematical demonstration is realized in E*(3, C), supposedly thought as isomorphic to the physical space. But: “Is the dual space
*really*the same than the original one, or does the passage from one space to the other one introduces some not immediately visible transformation which is at the end corrupting the analysis?”

The first explanation is known 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 mathematical discussions that I leave for later, preferring to go a step further in that analysis.

The resulting equation itself contains three parts:

- (i) a first part effectively represents the electromagnetic (EM-)polarization of Maxwell’s empty regions (These regions have a non-zero electrical permittivity, e
_{0}, and a non-zero magnetic permeability: m_{0}). - (ii) a second one can be interpreted as being a component acting against the progression of the energetic flow. It depends on the spatial gradient of the local volumetric density of EM energy.
- (iii) and the third one has at this stage, no clear interpretation but is related to the existence of a whirl tensor, the presence of which will be understood later when I shall explore that topic in a full four-dimensional context.

© Thierry PERIAT.

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Date de dernière mise à jour : 31/03/2022