This page shows that gravitation is a phenomenon due to the pressure of spacetime on objects.
It also demonstrates that mass and gravity are two identical phenomena.
Both have their origin in the curvature of spacetime.
The mathematical demonstration of gravitation, including a complete rewrite of the Einstein Field Equations
(EFE), is given in the "Mathematics" webpage.
This webpage is the third page of the website
It is strongly suggested to also read the precedent pages.
What is Gravitation?
If we replace the closed volume (fig. a) by two or more closed volumes (fig. b), the pressure exerted
by spacetime on these volumes tends to bring them closer to each other.
The result is equivalent to an attraction.
For example, a pressure on one side of a sheet of paper is equivalent to an attraction on the other side.
In both cases, the sheet is curved.
Mass and gravitation are nothing but the consequence of the pressure of spacetime on closed
volumes. We are faced with the same phenomenon.
Gravitation is not an attractive force
between masses, but a pressure force
exerted by spacetime on closed volumes
that tends to bring them closer to each other.
Another way to understand gravitation is to use the "split principle" from the 1850's fluid mechanics.
Let's imagine a sphere that is subject to uniform pressure (fig. a).
Here, this pressure comes from elasticity of spacetime.
If we split this sphere down the middle by a thought experiment, we will have two forces (red arrows, fig. b)
exerting a movement of each half toward the other.
This movement of each half toward the other is simply that we call "Gravitation".
This phenomenon of pressure produces exactly the same result than an attraction.
An external observer could think that the two halves are "attracted" one toward the other.
Earth-Moon Curvature of Spacetime
Let's consider the following pedagogical presentation that shows the spacetime curvature
on the Earth on points L and R.
Point L (left side)
The curvature of spacetime of the Moon is simply added to that of the Earth.
Point R (right side)
The curvature of spacetime of the Moon is subtracted from that of the Earth because the two curvatures
are in opposition.
The curvature of spacetime on point R will be less than that produced in point L.
Since a curvature of spacetime automatically produces a pressure on the surface of the sphere, the pressure of spacetime on
the left side of the Earth (black arrows on the following figure) will be greater than that on its right side (red arrows).
In reality, these two figures, the curvature of spacetime (above) vs pressures (below), are
two different presentations of the same phenomenon: the pressure of spacetime on closed volumes.
This imbalance of pressures will generate forces that move the Earth toward the Moon and conversely.
It also explains tides.
Seas movements do not come from an attraction of the seas by the Moon, a phenomenon that no one can explain
(gravitation), but from the difference of pressures on both sides of the Earth (black arrows vs red arrows).
Please note that here we say "closed volumes", not "apparent volumes".
In reality, gravitation concerns exclusively the closed volumes included in the apparent volumes of the the Earth and Moon.
These closed volumes are protons, neutrons and electrons.
Open volumes such as orbitals are not concerned by gravitation since the do not have mass.
As shown in this website, mass and gravitation are two very simple phenomena.
Most scientists throughout the world agree with this point of view based on simplicity.
For example, to detect any trace of life on Mars, the biologists will not seek complex living organisms,
but on the contrary, elementary molecules like H2O.
Since Physics is a science, to explain phenomena, we must follow the same way which is logical, rational,
and full of common sense.
Einstein himself followed this view all his life.
He said: "If a child of 6 years old can not understand a theory, this theory is wrong".
This is why the Spacetime Model focuses on simplicity instead to imagine
complex and speculative theories using 5D or more, such as M-Theory or Quantum Gravity.