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Pressure influence on space – time structure and interactions between bodies


1. Introduction.

Einstein's relativity theories gave a new vision of universe different from Newton approach. It is common to represent the four dimensions Einstein's space time by a membrane deformed by heavy bodies like planets and stars. In this theory, interactions between bodies are not explained by forces (like in the Newtonian approach) but by deformations of space – time membrane giving hollows and bumps and also trajectories corresponding to space – time geometry. (Science et Vie n° 1079, august 2007, p 68-72). From Einstein's vision, gravitational interactions apply on large distances and their intensity is low compared to electrostatic interactions found between two atomic particles like proton and electron (ratio in the order of 1038).

If the structure of macroscopic world is well described by Einstein theory, what is the situation at the atomic scale ? At this time gravitation theories can not be applied to the microscopic scale. Even if atom description given by N. Bohr had a planetary structure, the only way found to explain interactions between protons and electrons was electrostatic theory. His mathematical form is close to the equation of Newton for gravitation. Finally, strong nuclear forces were introduced in order to explain nucleus cohesion and probabilities theories were used to describe atom phenomena.

In this paper, we tried to find the link between infinitely small (atoms) and infinitely large (planets and stars). To achieve this goal, we first compared physical properties of bodies at these two scales and we calculate pressures applied on space – time membrane. From this approach we propose a possible structure of our world and we deduced a new vision of the nature of light coming from a break of space – time membrane.

2. Physical properties of bodies at atomic and cosmologic scales.

Physical properties of macroscopic bodies are mainly density (kg/m3), specific heat (J/kg.°K), thermal conductivity (W/m.°K) and dynamic viscosity (Pa.s). In this first approach, we considered density as the fundamental physical property governing behaviours at both microscopic and macroscopic scales. This approach is not new in astrophysics, evolution of stars in neutrons stars and finally black holes give a huge increase in density and finally a break of space – time membrane. But density was not studied and used at the atomic scale.

2.1 Density at the astronomic scale.

In our approach, stars are considered as perfect spheres. This assumption is acceptable for densities calculations.

- Earth case : mass of our planet is 5.976 1024 kg, average radius is 6 378 140 m. These values give a density Mvt of approximately 5 500 kg/m3. This value agree with density commonly found around us.

- Sun case : sun mass is 1.9891 1030 kg, average radius is 6.96 108 m. Sun density Mvs = 1408.4 kg/m3.
- Sun evolution as dwarf star : sun radius is then in the order of 5 106 m. Density Mvnb = 3.8 109 kg/m3.

- Neutrons star : radius is in the order of 5 000 m. Density Mven = 3.8 1018 kg/m3.

For densities greater than this last value, i.e. for radius in the order of Schwartzschild value, gravity reach extremely high values giving rise to black hole formation.

We can analyse densities values we found as follows :

- For planets and stars, densities are in the order of 103 kg/m3.

- For dwarf stars, first step of stars death, densities are in the order of 109 kg/m3.

- For neutrons stars, densities magnitudes reaches 1018 kg/m3. For greater densities values, black holes formation occurs and space – time membrane deformations are so high that we obtain an often called singularity.

2.2 Densities at the atomic scale.

For the following calculations we considered atomic particles as perfect spheres.

- Electron : electrons mass is 9.1095 10-31 kg and radius is 2.8179 10-15 m; then density Mve = 9.72 1012 kg/m3.

- Protons : protons mass is 1,6726 10-27 kg and radius is 0.805 10-15 m; then density Mvp = 6.23 1017 kg/m3.

2.3 Comparison between densities values at these two scales.

It clearly appeared that atomic particles have huge densities values compared to planets and stars. It is then not surprising that classical gravitation laws can not be applied. Considering lower scale problems encountered in physics : heat and mass transfers, fluid mechanics…; dimensionless numbers are used in order to overcome scaling problems (Reynolds number, Prandtl number…).

At this level of our approach, we can observe that densities values found at both atomic and astrologic scales are logical. But they can not explain simple phenomena like attraction and repulsion of atomic particles.


3. Pressures on space – time membrane calculations.

Let just remember that pressure is the simple ratio between force and surface :

P = F/S

International units being Pascals for pressure (Pa), Newtons for forces (N) and square meters for surface (m2).

For calculations, we considered each body as a perfect sphere and we took the surface of discus having the sphere radius for contact surface with the space – time membrane.

Calculation of gravity force F applied to space – time membrane needs a value of gravity acceleration "g" in m.s-2. For earth, we used the average value of "g" : 9.81 m.s-2. For the sun, value of "g" is about 120 time the value of earth. We took then 1200 m.s-2. For atomic particles, we used the well known Einstein formula : E = m.c2. Dividing then "E" by electron or proton volume gave then a pressure value.

3.1 Pressure values at cosmological scale.

- Earth case : Pt = 4.59 1011 Pa.

- Sun case : Ps = 1.57 1015 Pa.

3.2 Pressure values at atomic scale.

- Electron : Pe = 8.727 1029 Pa.
- Proton : Pp = 5.598 1034 Pa.

We can observe that pressures on space – time membrane are huge at atomic level. Considering results obtained through general relativity theory and pressures calculated for earth and sun which are largely under atomic particles values, deformations of space-time membrane at the atomic level are extremely important.

3.3 Classification through pressure scale.

Previous results allowed us to build a pressure scale where atomic and cosmologic worlds are mixed and give rise to more and more important space – time membrane deformations.






Earth atmosphere
Planets
Stars
Dwarf stars
Atomic particles, neutrons stars
Black holes
1030
1050
105
1010
1015
1020



On this scale, bodies of large size like planets and stars give relatively low pressures on space – time membrane and then relatively low deformations. Geometry of space – time membrane in that situation is made of low curvature lines but deformations produce effects on large distances. We are in the general relativity theory field where attraction forces have a low intensity due to low deformations of space – time membrane but their effects are observed on very large distances.

Atomic particles and stars at the end of their life are bodies with small sizes and huge densities. Pressures on space – time membrane are extremely high and produced deformations also. Membrane deformations are then much more abrupt and effects of curvature much more local. We can imagine that these bodies are deeply included inside space – time membrane. We are in the field of quantum mechanics where attraction forces have a high intensity. In that situation, "wells" produced by very high pressures give local deformations having a very short distance influence.

These two kinds of deformations explain how Einstein general relativity theory can be applied at both atomic and cosmologic scales. It opens the door of studies about space – time membrane physical characteristics in order to well characterize interactions between bodies.


4. Influence of pressure on space – time membrane deformations and attraction and repulsion phenomena.

Gravity only give attractive interactions between bodies. At the atomic scale interactions can be both attractive or repulsive depending on particles charge. The question is then extremely simple : how to obtain repulsive interactions with a pure Einstein model using only space – time membrane deformations ?

4.1 At the cosmologic scale.

Large size bodies gave low deformations but acting on large distances, in that situation, we only have attractive interactions.

4.2 At the atomic scale.

Small size bodies give rise to extremely local and deep deformations acting then on very short distances. As previously calculated, pressures of protons and electrons are different and then deformations of space – time membrane are also different. In that situation, there is an attractive interaction between protons and electrons (the same approach with neutrons which are just a little bit more heavy than protons). As shown in figure 1, proton is more deeply imbedded in the membrane than electron.
But two electrons or two protons give the same deformations of space – time membrane and then it is impossible to put them in close contact. Being able to put two electrons or two protons together means to make a loop in the space – time structure and this situation disagree with the causality principle.
In our model, intensity of attraction – repulsion forces at the atomic scale is closely linked to mechanical properties of space – time membrane. Trying to put electrons or protons together consist in trying to strongly bend the membrane and this need a lot of energy.

In our model, general relativity allows to explain attraction and repulsion phenomena at the atomic scale without electrical charges. Differences in gravity and electrostatic interactions intensities explained through completely different geometries of space – time membrane deformations coming from pressures applied by physical particles.


5. Consequences on the nature of light.

Photons can behave as both waves or particles; this is one of the most surprising property of quantum mechanics world. Moreover, photons are the only particle having no mass and general relativity explains why their trajectory can be influenced by space – time membrane deformations.
In our pressure model, black holes are the result of a break in space – time membrane due to extremely high pressures found around 1050 Pa. It means that just below this limit, we are in a situation where space – time membrane can break or recover depending on pressure variations.

5.1 Light as the result of a break in space – time membrane.

We think that at their level of pressure (between 1030 and 1040 Pa), atomic particles are always at the limit of break of space – time membrane. Pressure increase of electrons will cause a break of membrane and then emission of a fragment which is a photon. This small part of space – time membrane has no mass because space – time has no mass but it contains energy because it is the result of a strong membrane deformation. On the other way, when an electron will receive a photon, it will allow a small part of space – time membrane to return in the contiuum.
Absorption and emission of photons maintain space – time membrane energy balance. Without this fundamental equilibrum, space – time membrane will be destructed.
In our model, photons are not waves and not particles but a small part of space – time containing energy of an important deformation.