Cosmic strings - The theory of the (E) question
A website exposing an attempt to connect general relativity and quantum mechanics

The Quantum Gravity Project in four-dimensional spaces

A personal vision: Vacuum-and-Strings

Since I can observe the sky and read books about astronomy, I am totally fascinated by the omnipresence of empty regions and the partition of observable matter in the universe: it is obviously forming a net of strings and, in between, giant empty bubbles. 

This fact, together with the actual enigma concerning the dark energy and the expansion of our universe, is for me the proof that we don't yet have reached a good understanding of basic stones. 

My intuitive vision is that these seemingly empty regions (which are containing huge quantities of energy) are corresponding to a strange kind of (perfect) fluid where the matter, exceptionally, granulates. Although presumably omnipresent and supposedly acting on very long distances, the gravitation should be perhaps understood as a "by side product" appearing when the ad hoc conditions are realized.

Presentation: Foundations

I can say that my vision concerning our universe, more precisely the empty regions of our universe, is based on a statement: "Why so many volumes containing nothing?" The similitude with an iceberg immediately invades the brain: the visible part of the ice is only a small part of the cube.

This statement can be made by everybody and it has been made a long time ago, long before the discovery of dark energy in our universe. The latter is in some way just reinforcing the comparison with the iceberg (why so much energy in ... nothing?) and suggesting a link "empty volumes - dark energy". Unfortunately, for now the link doesn't give us any element increasing our understanding on what is really happening in front of our telescopes/eyes.

As I was yet a child, some pictures were already available and suggesting that the matter was distributed in the cosmos in such a manner that it was forming filaments drawing huge empty volumes. Recent and better images are showing a kind of spider web. More or less regular matter-made tubes are delimiting regions where nothing is detected. These pictures have been my inspiration for the document "vacuum and strings"(077-9; available on www.researchgate.net).

Actually, when I attentively read my document again, I must say that it is not only demonstrating that elastic extending strings may sometimes be characterized by an equation of state which presumably is the one of the actual expanding vacuum. It also tells us that any region which we actually consider as an expanding one may be compared to an elastic string.

Now, if because of that first document, we accept the idea that any region is equipped with:

(a) a touch of elasticity (this hypothesis is not really a scoop: see the theory of relativity and two predicted effects: gravitational waves and the Thirring-Lense effect), or

(b) with a touch of instability (an hypothesis which may hurt the point of view of researchers focusing attention on thermodynamic because the empty regions occupy the majority of all volumes in our universe*),

we then also may consider that the Heisenberg's uncertainty principle (HUP) is our next door neighbor.

With different words: the volume of our universe can mentally be separated in a set of infinitesimal volumes in which the HUP applies for the pair (energy, time). If that hypothesis holds true, I would not say that any infinitesimal volume can be the region where a universe might be born. I would just ask:

"What are the reasons why -despite of that theoretical liberty in the interplay between a local variation of energy and a local lapse of time- each infinitesimal volume stays obviously connected to the next ones?"

"What explain that (a) an infinitesimal volume, here and now, exhibits the characteristics specifying the presence of a given particle and that (b) a little bit later in space and time, the next infinitesimal volume exhibits the same characteristics specifying the presence of that given particle as long as no interaction happens?"

The first question spontaneously arises from the statement that we never have observed topological failures in space-time, except if we consider that the most elementary particles are themselves such failures.

The second question is justified by the oldest known law in physics (due to Newton): the kinetic momentum is invariant as long as the particle at hand doesn't interact. This invariance would never occur if some glue would not be there and act to insure the continuity, despite of the fundamental uncertainty ("Will the next instant exist?").

Since we know that an interaction with another particle can modify the "trajectories" of all particles involved in the interaction, we may say that any interaction generates a curvature in the trajectory of each particle. If that procedure is transposed to the interaction between a particle and the geometry (a Gedanken Experiment which the verification of the Thirring-Lense effect makes meaningful), then we come to the conclusion that the gravitation field must be the field which is insuring the continuity/glue between two successive "states" of these empty regions. Fortunately, that heuristic deduction can be mathematically proved (The document exists and has already been published in the past years on my different blogs or websites).

I have examined that scenario and, because of it, revisited the HUP (096-0) with the point of view of someone focusing on the mathematical theory concerning deformed tensor products. This has been made with the help of the Lorentz-Einstein law (LEL) of motion and the maneuver was possible because of a natural coherence concerning the units involved in the HUP. The LEL is not only a direct product of the principle of equivalence introduced within the theory of relativity; it also contains a "gravitational term" which fortunately is de facto a deformed tensor product.

These statements allow the development of a toy scenario in which, per convention, the Planckian limit is preserved for each infinitesimal volume. That way of thinking allows not only the recovery of the solutions of the theory of relativity (the ds) in a short and elegant way but the writing of a specific formalism for the tensor representations of the EM fields. These fields have peculiar characteristics (031-1) which sometimes allow comparing them with an infinitesimal variation of the geometry (085-4; available on www.researchgate.net).

At the end of the day, we have a scenario:

- linking Einstein's theory of relativity and Heisenberg's principle;

- "working" in a four dimensional space;

- yielding the ds again in a pleasant and natural manner;

- producing sometimes specific EM fields mimicking infinitesimal variations of the metric.

*The meta-stability of the empty regions which may a priori chock the opinion of specialists working on the thermodynamics can be addressed if one accept the following idea. These regions are always living in a stable equilibrium between EM forces and gravitational forces (the gravitational term of the LEL). Any modification of that equilibrium generates a manifestation which we call a particle.

10 May 2018