The state of the art.

This page in the French language.

The context.

A century ago, A. Einstein’s theory of gravitation introduced the idea that the geometry is not always and everywhere Euclidean because it can be deformed by the presence of matter or, more generally, by any form of energy.

In our rationalistic world, any hypothesis, any idea must be:

  • formulated with a coherent mathematical machinery;
  • proved (the experiences confirm the propositions).

Former works due to Gauss, Riemann, E. B. Christoffel, and Hilbert had brought the basic stones for a renewed formulation of geometry. Einstein and the few people who have helped him did the rest.

Very recent experiments (Gravity Probe B measuring the Thirring-Lense effect and LIGO revealing the presence of gravitational waves) have convinced the public that that predictive idea was right.

The actual paradigm and its difficulties.

This theory and its consequences in cosmology put our society into a new era; why?

Because we must now accept the counterintuitive fact that our everyday geometry, the three-dimensional Euclidean one, is far to be unique and that it can be deformed.

This statement contains important and implicit information that are not easy to understand.

In the usual Euclidean environment, the forms of the objects surrounding us can be classified (topology) and these objects can be referred to simple static or rotating rigid frames.

We know since a long time that the objects can have changing forms and move; there no scoop here.

The new information is that the frames to which we are referring these objects can also be deformed by the presence of these objects or by any sort of energy. In such circumstances, how can we correctly describe the motions of these objects?

This newly discovered property (spacetime can be deformed) is adding technical difficulties in the mathematical formalism which is supposed to be involved in the description of the effective reality.

Anyway, the permanently renewed confrontation between the actualized understanding of our theories (gravitation, measurements) and successive experiments has led to results giving the sensation of living in a universe in expansion; furthermore, with an increasing acceleration.

Since, up today, no rationalistic argument can explain these unexpected results, we are forced to reexamine the foundations of the theories and we are constrained to ask the correctness of the measurements: not only their precision but the methods which have been involved to get them, as well. The recent discussion around the cosmological constant illustrates what I mean.

We are forced to reexamine the foundations of the theories too; for example: the cosmological constant problem: “What is its origin?”, “Is its presence in the equations an absolutely necessity?”, “Which physical reality is it describing?” (For more information on this topic: see the French part of this website).

Another embarrassing fact is that Einstein’s theory of gravitation considers the measurement of the energy in the empty regions of our universe from a totally different viewpoint than the quantum theory does it.

© Thierry PERIAT.

To go further, please visit the page: “Involution”.

Otherwise, you can go back to the: “Homepage”.

  • Maxwell's-vacuum. NEW

    In writing Maxwell’s equations (EM) for empty regions in introducing the trivial decomposition for each cross product, I got a volumetric density of force.
  • Koide-formula

    A discussion on the preservation of the speed of light in vacuum allows the discovery of a ratio mimicking the Koide's formula.
  • Bowen-York-Black-Holes

    The non-trivial decomposition of a deformed angular momentum can be related to a Bowen-York Black Hole.
  • Involution

    The behavior of light in the vicinity of black holes motivates the study of involutive deformed tensor products.