Applications

1 - Relativistic Particles


Why does the mass of a particle increase when its speed approaches the speed of light 300 000 km/s (relativistic particles)? The proposed theory solves this enigma with great simplicity.

  • At v = 0, a particle naturally curves spacetime.
  • If this particle moves at relativistic speed, an external observer sees a kind of spacetime compression. Geodesics seem condensed. This is a basic effect of length compression in special relativity.

If the spacetime density increases, the pressure force on the particle also increase, and its mass effect too.

relativistic particle

So, contrary to preconceived ideas,

 
At relativistic speed, the "mass" of a particle remains
unchanged. It is its "mass effect" due to the
apparent compression of spacetime that increases.
 

Note for physicists:
See the HTML page "Increase of the mass of relativistic particles" in the "Mathematical Demonstrations" section.


Close the window

2 - Light Deviation


During a total solar eclipse in 1919, Sir Arthur Eddington observed a light deviation made by the Sun. Here we simulate this phenomenon replacing elasticity of spacetime by elasticity of an expanded polypropylene foam. A set of lines is drawn on the foam and a half-cylinder, acting as a closed volume, is placed under these lines.

light deviation

As we see on this photo, lines are curved. We have exactly the same phenomenon in spacetime. The light follows geodesics of spacetime, as predicted by Einstein, but this curvature of spacetime is not a consequence of the mass - which is does not make sense -, but of closed volumes.


Note for physicists: No one knows exactly the structure of spacetime, and it is certainly more complex than it seems. Some arguments suggest that spacetime could be a part of continuum mechanics, more exactly rheology, despite the fact that this science is applied to non-Newtonian fluids. Obviously, spacetime isn't a "solid body", but could have however the behaviour of rheology. The magnitude of curvature of spacetime is very small, ΔR/R = 1.4166 E-39 for the proton. So, we are working in a linear part of elasticity curve in common situations. However, we have not the proof that this linearity also exists in particular situations as in black holes. This is why a rheology behaviour is such a possibility and must not be excluded.


Close the window

3 - Particle in a Crystal


Why does the mass of a particle moving inside a crystal increase? No one can explain this strange phenomenon. Here is the solution to this enigma.

The lattice of a crystal is an array of tunnels. The particle moves inside one of these tunnels.

Closed volumes of each atom of the crystal (nucleons, electrons) increase the curvature of the spacetime located inside the tunnel, on the path of the particle. Since "Curvature of spacetime ≡ Mass effect", the increase of spacetime density conducts to an increase of the mass effect of the particle.

This phenomenon is similar to that of a high-speed train entering a tunnel. Compression of air slows down the train and the latter needs more energy to keep its initial velocity.

Note : The following figure was drawn for educational needs. In reality, the volume remains unchanged.

particle in a crystal

Note for physicists:
We should not make confusion between this phenomenon and the increase of the mass of relativistic particles since the origin of the spacetime curvature is different. If a crystal moves at a relativistic speed relative to a "local observer", we will note two curvatures of spacetime, which conduct to two different mass effects: 1/ That made by atoms of the crystal and, 2/ that produced by SR.


Close the window

4 - Faster-than-light Neutrinos


This section has been removed


Close the window

5 - Mass Excess


The mass excess of a nuclide is the difference between its actual mass and its mass number.

Let's consider the simplified case of a nucleus having 19 nucleons (protons or neutrons). The "mass effect" is function of the closed volume of each nucleon, V, but also of its surface, S, because spacetime exerts pressure on the surface of each nucleon.

mass excess

  • Independent nucleons (a): The total volume is 19V and the total surface 19S.
  • Nucleus (b): The 19 nucleons are linked to make a nucleus. The orange surface represents a vacuum enclosed into the nucleus. Therefore, this open volume becomes closed volume and curves spacetime as any closed volume would do.
  • Nucleus (c): From an external view, figure (c) looks like (b). The global volume of (c) is greater to that of (a). This conducts to an increase of the spacetime curvature, and to the "mass excess" too. On the other hand, the surface of (c) is less than that of (b). Therefore, the pressure on the surface will increase too. This conducts to a global increase of the "mass excess".

Note for physicists: This simplified figure is not quite accurate for many reasons.
1 - This 2D scheme does not work in 3D but fully explains the basic principle.
2 - We do not know whether or not the nucleus contains open volumes in periphery. The "raindrop" or "Jensen and Goeppert-Mayer" models do not say anything about it.
3 - Some irregularities, such as the size of the triton compared to that of the deuteron, raise questions.
4 - Nuclei with halo, such as 11Li, may also have a mixing of closed and open volumes.
Finally, this problem seems to be much more complex than it looks, but these exceptions do not question the basic principle described here.


Close the window

6 - Nuclear fission


If an atom is broken into independent nucleons (precedent figure b to a), closed volumes in orange (fig. b) become open volumes. This depression produces "spacetime eddies", or a kind of "seism in spacetime", which are nothing but high energy waves, mostly gamma rays.

So, the principle of the A bomb is exactly the same as that of a tsunami. A closed volume is released and becomes open volume with gamma rays production.

Note for physicists: Discussion about chain reactions or nuclear power plants is out of the scope of this study.


Close the window

7 - Twin paradox (time dilatation)


The twin paradox is a "thought experiment" in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth.

We are faced with a problem of general relativity.

  • Fig. a shows a flat spacetime far from any object. Times t1 and t2 are identical.
  • Fig. b shows a spacetime curved by a closed volume. Time t2 is greater than time t1.

Without enter in the complex mathematics of general relativity, we see that the time is different near and far from a closed volume.

spacetime dilatation

Note for physicists: The accurate calculation for a static body with a spherical symmetry is given by the Schwarzschild Metric. Note that this topic concerns GR, not SR as many think. However, if a twin is moving at relativistic speed relative to a local observer, in this case, we will have a GR + SR combination.


Close the window

8 - E = mc˛


a/ An empty sphere is immerged in a container filled with water. The surface of water is quiet.

b/ If the sphere disappears suddenly by a thought experiment, the depression will make eddies.

Converting a mass, more exactly a closed volume, into energy follows the same principle. If a closed volume is transformed into an open volume, "eddies" in spacetime appear, mostly gamma rays.

E = mc˛

 
To fully understand E = mc˛ and how mass
can be transformed into energy, we must
think in "closed volumes" instead of "mass".
 


Note for physicists: In an unpublished (but registered) paper, the author explains, on the basis of closed and open volumes, the phenomenon of particle production from gamma, as the well-known γ → e+e-. The study of E = mc˛ developed in this section therefore needs to be extended to all particles, both fermions and bosons.


Close the window

9 - Nuclear Fusion (mass defect)


Nuclear fusion is the process by which some light atomic nuclei join together to form a single heavier nucleus.

A rearrangement of protons and neutrons takes place. The volume and surface of the nucleus are modified. Since the ratio volume/surface is modified, closed volumes may disappear in some nuclei. This release of closed volumes acts as E=mc˛ and produces a "seism in spacetime" with high energy waves, mostly gammas.

fusion

Note for physicists: In reality, it's not just the nucleons that have a rearrangement, but also quarks. Thus, in thermonuclear fusion, the rearrangement of the nuclei is a process far more complex than this figure shows.


Close the window

10 - Galactic Clusters


Why are galactic clusters moving away from each other despite gravitation laws?

Let's imagine two galactic clusters, A and B, containing 9 galaxies each.

  • Inside a galactic cluster, we have a traditional "gravitation", more exactly a pressure from the spacetime curvature as explained in this Web page.
  • Outside a galactic cluster, this curvature is very weak. The expansion of the universe exerts a force greater than the pressure of spacetime on galaxy clusters, and they move away from each others.

galaxy

Close the window

11 - Black Matter, Expansion of Universe


As this figure shows, the pressure of spacetime on galaxies could not be constant everywhere in the Universe. As a result, gravity could not be constant too. It depends on where one is.

These difference of pressure could explain the acceleration of expansion of the Universe (Perlmutter and Schmidt). In the figure, for example, galaxy A does not move but galaxy B does, because the pressure of spacetime which comes from the centre of the Universe is greater than that coming from its bounds. Result is that galaxy B will move toward the bounds of the Universe. This phenomenon could also explain other astrophysics enigmas, such as the speed of the edges of galaxies.

expansion

Close the window

12 - Galaxy Filaments


Spacetime pressure is "normal" perpendicular to the axis of a filament. In the axis, the pressure decreases because galaxies located on the filament absorb a small quantity of spacetime pressure. These galaxies produce a kind of "shadow" against each other.

All the galaxies normally would move closer to each other but this difference of spacetime pressure conducts to a difference of gravity. To summarize, the arrangement of galaxies in filaments is due to the fact that the axial spacetime pressure is different from the radial pressure.

expansion

Close the window

13 - Neutrons Stars


Neutron stars are supposed to be exclusively made of closed volumes (neutrons). Their spacetime curvature is maximum and their "mass effect" too.

Conventional sun-like stars are made of atoms plasmas: hydrogen, helium... as described by the Bethe Cycle and other theories. All these stars are combinations of closed and open volumes. Due to the presence of open volumes, their mass effect is much smaller than that of objects having exclusively closed volumes.


Close the window

14 - Black Holes


Please see our Webpage "Von Laue Diagrams" in the "Mathematical Demonstrations" section.

Close the window