Part 1

Spacetime Model



We consider that the curvature of spacetime is produced by mass. This assertion is speculative because the reverse is also possible. Indeed, mass could be the consequence of the curvature of spacetime. After all, why not?

Since we do not know the origin of mass, we must therefore consider the two possibilities.

Mass   >>   Curvature of spacetime ?


Curvature of spacetime   >>   Mass ?

This webpage demonstrates that, contrary to what we think, it is the second possibility which is right.

This webpage is the second page of the website
It is strongly suggested to also read the first page "Introduction".


Problem to solve

To understand the interaction between the curvature of spacetime and mass, let's consider a flat spacetime (a). The insertion of an object will curve this spacetime (b). Indeed, the internal spacetime of the object "pushes" the flat spacetime to make room.

Spacetime - Mass

As we see, it is the VOLUME of the object, not its MASS, that deforms spacetime. This is a logical observation ...but since 1919, experiments show the contrary.

Einstein demonstrated that spacetime is curved by masses, not by volumes. This assertion, which is verified by experimentation, is totally irrational since, to date, no one can explain how a mass can curve spacetime. So, the question is:

Is spacetime curved:
▪ by volume? (logical, but wrong...)
   ▪ or by mass? (irrational, but proven)


Solution to this problem

Spacetime is not curved by VOLUMES, neither by MASS, but by a special type of volumes: "Volumes with mass".

This kind of volumes satisfies both General Relativity (curvature by MASS) and common sense (curvature by VOLUMES). The explanation is quite simple but all our knowledge about the volumes must be questioned.


Volumes with/without mass

All objects in the universe can be classified in five classes of volumes. The three main types of volumes are:

  • (a) Closed volumes (volumes with mass), such as elementary particles. Their internal spacetime "pushes" the surrounding spacetime to make room. Thus, "closed volumes" produce a convex curvature of spacetime. The density of spacetime around the closed volume increases, and the latter has difficulty to move. As a result, a "mass effect" appears, i.e. an effect having all the characteristics of mass.
    Since spacetime has properties of elasticity (Einstein), it exerts a pressure on the surface of closed volumes. The mass component [M] can be extracted from the pressure [M/LT2] by simple mathematical operations. This leads to a 4D expression of the mass: m = f(x,y,z,t) (see the "Mathematics" webpage).
  • (b) Open Volumes (massless volumes). It is just a vacuum, but sometimes found in various forms such as the volume of orbitals or the space between atoms. These volumes exist but they are "porous" regarding spacetime. More exactly, they are subject to variations of spacetime but they do not curve spacetime themselves. Therefore, open volumes are massless since no curvature means no mass (Einstein).
  • Apparent volumes. Apparent volumes are explained later in this webpage.
Volumes - Mass
Example of closed volumes - Mass

Note 1 (for Physicists)


Closed volumes vs. open volumes

Closed open volumes - Mass



These two types of volumes can be found in atoms which are made of:

  • Closed volumes, with mass: Proton(s), neutron(s) and electron(s). These closed volumes deform spacetime. Since closed volumes → spacetime curvature → pressure → mass effect, the nucleus and electrons have a mass. This is confirmed by experimentation.
  • Massless Open volumes: Orbitals are geodesics in a vacuum. It is obvious that the volume of geodesics, i.e. an empty volume, can not curve spacetime. Therefore, the volumes of orbitals are massless. This is also confirmed by experimentation.
Atom - Mass

Note 2 (for Physicists)



Pen-eraser - Mass


Apparent Volumes

Objects we use daily are apparent volumes defined as:

Apparent volumes = Σ Closed volumes + Σ Open volumes

These volumes, mainly atoms, are a combination of:

  • Closed volumes (protons, neutrons, electrons). These volumes deform spacetime and, as explained, have a mass, more precisely a "mass effect".
  • Open Volumes (volumes of orbitals, space between atoms...). These volumes are transparent regarding spacetime since they do not curve it. They are massless.

We have the feeling that mass and volume are two different quantities. This view is correct in everyday life but wrong in some domains of physics such as astrophysics. In reality, it is the proportion of closed to open volumes which varies from one atom to another, from one molecule to another, and from one object to another, which gives us this feeling.

In reality, we have five different categories of volumes, not three (closed, open and apparent volumes). Please see note 3 (for physicists) for further information.



We must always take into account that the word "Volume" without any precision does not mean anything, at least in astrophysics, mass, gravitation, and general relativity. It is important to clarify our definition. Are we talking about:

  • Closed volumes?...
  • Open volumes?...
  • or Apparent volumes?

Since these three volumes have different behaviors regarding mass, we must differentiate them.