Part 1

Spacetime Model



The theory proposed in this website, i.e. the "Spacetime Model", explains with great simplicity several enigmas of Modern Physics. These enigmas are described below.

Solving so many enigmas is not a simple matter of chance. This means that the Spacetime Model, despite its simplicity, is a reality.


This webpage explains the basic principle of phenomena, not their mathematical demonstration. For example, section 7 ("E = mc2) does not demonstrate this expression, which comes from special relativity, but gives the solution to a much more important question: "How a mass can be converted into energy?". Therefore, the reader must not confuse the basic principle of a phenomenon, explained with logic and good sense, and its mathematical description, given in the Mathematics webpage.

1/ This webpage has been written mainly for non-physicist people. Physicists are invited to read the PDF article in ArXiV format (see the Download PDFs command).
2/ This webpage is the 4th part of the website It is strongly suggested to also read the four previous parts.


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)? Modern Physics does not explain this strange phenomenon.

The Spacetime Model 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 seems to increase, the pressure force on the particle also increases, and its mass effect too, as explained in the Mass webpage.

Relativistic Particles

So, contrary to preconceived ideas,

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

Note for physicists:
A mathematical demonstration is given in the Mathematics webpage: "Explanation of the increase of mass of relativistic particles".


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. These geodesics are produced by closed volumes, not by mass.

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 do not have the proof that this linearity also exists in particular situations as in black holes. This is why a rheology behaviour must not be excluded.


3 - Particle in a Crystal

Why does the mass of a particle moving inside a crystal increase? The current scientific explanation to this phenomena (a gap potential) is not convincing. Here is a better 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 leads to an increase of the mass effect of the particle.

This phenomenon is similar to that of a high-speed train entering a tunnel. The compression of air inside the tunnel slows down the train and the latter needs more energy (i.e. mass since E = mc2) to keep its initial velocity. Here, the opposition to movement is due to the high density - or compression - of spacetime.

Please note that the following figure was drawn for educational needs. In reality, the volume of the particle 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 lead to two different mass effects: 1/ that made by atoms of the crystal and, 2/ that produced by special relativity.


4 - 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

a/ Independent nucleons
The total volume is 19V and the total surface 19S.

b/ Nucleus
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.

c/ Nucleus
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 also leads to a global increase of the "mass excess".

Note for physicists:
This simplified figure is not quite accurate for many reasons.
1 - In reality, only heavy nuclei have a mass excess. A nucleus with 19 nucleons does not have.
2 - This 2D scheme may not work in 3D but the basic principle is identical.
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 is much more complex than it looks, but these exceptions do not question the basic principle here described. Each problem has its own explanation.


5 - 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 part of the closed volumes of the nucleus is released and becomes open volumes, which produces gamma rays (see part 4 of the Spacetime Model). These gamma rays may be converted into particles such as electrons-positrons pairs, and so on...

Note for physicists:
Discussion about chain reactions or nuclear power plants is out of the scope of this study but these subjects share the same basic principle as that explained in this section.


6 - Mass Defect (nuclear fusion)

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 modification of closed volumes acts as E = mc2 and produces a "seism in spacetime" with high energy waves, mostly gammas.

Mass Defect

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 nuclei is a process far more complex than this figure shows.


7 - E = mc2 Enigma

This section explains one of the most
important enigmas of physics: E = mc2

E = mc2 is a part of Special Relativity. However, despite the fact that the calculus is quite simple, Modern Physics does not propose a rational explanation of this strange phenomenon.

The Spacetime Model demonstrates that the principle of converting mass to energy is very simple. This principle is shown by the following example.

  • Part a
    An empty sphere is immerged in a container filled with water. The surface of water is quiet.
  • Part b
    If the sphere disappears suddenly by a thought experiment, the depression will make eddies which have energy (E = hν).

Converting a mass to energy follows the same principle.

A closed volume disappears, and is transformed into an open volume. This produces "eddies" in spacetime, which are gamma rays. These gamma rays may be converted into particles such as electrons-positrons pairs, and so on...

E = mc<sup>2</sup>

So, to fully understand E = mc2 and how mass can be transformed into energy, we must simply think in "closed/open volumes" instead of "mass".

Note for physicists:
In the Part 2 of the "Spacetime Model", the author explains, on the basis of closed and open volumes, the particles production from gamma such as γ → e+e-.
In reality, the principle of E = mc2 developed in this section can be extended to all particles, fermions and bosons.


8 - 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.

In reality, we are faced with a problem of General Relativity. This phenomenon is explained in the following figure.

Twin Paradox

Figure a:
Shows a flat spacetime far from any object. Times t1 and t2 are identical.

Figure b:
Shows a spacetime curved by a closed volume. Time t2 is greater than time t1.

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

Note for physicists:
The calculus of the time dilatation is given in the Mathematics webpage. More exactly, the accurate calculation for a static body in a spherical symmetry is given by the Schwarzschild Metric. Note that this topic concerns General Relativity (GR), not Special Relativity (SR), as most people 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.


9 - Galactic Clusters

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

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

  • Inside a galactic cluster
    We have a traditional gravitation between the nine galaxies
  • 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. This repulsion also depends of the position of each galaxy in the whole universe (see the next section).
Galactic Clusters


10 - Dark Matter, Expansion of Universe

This figure shows two galaxies, A and B. The universe is drawn in light blue. The pressure of spacetime is constant on galaxy A (white arrows). On the contrary, on galaxy B, the pressure of spacetime is higher from the center than outside. Since gravitation is a function of the pressure of spacetime, gravity will be not constant in the whole universe. It depends of the location of galaxies in the universe, more exactly of the amount of spacetime around it.

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 (black arrow) is greater than that coming from its bounds (red arrow). Result is that this umbalance of pressure makes galaxy B moving toward the bounds of the Universe. The same phenomenon based on the pressure of spacetime could also explain other astrophysics enigmas, such as the speed of the edges of galaxies.

Black Matter, Expansion of Universe


11 - Galaxy Filaments

In the axis, the pressure is smaller that that perpendiculat to the filament 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 pressure of spacetime is different to that of the radial pressure.

Galaxy Filaments


12 - 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, which is the case of neutrons stars.


13 - Black Holes/Dark Matter

Please see the section "Von Laue Diagrams" in our "Mathematics" webpage.