Forces in Spacetime

Part 2

Spacetime Model


Forces in Spacetime

This webpage affords the reader a more concrete vision of the role of spacetime in EM waves. We will deduce that EM waves = spacetime movements.

Spacetime is not motionless. It is continuously moving. Movements in spacetime means forces. This webpage covers one of the three fundamental forces (*) but for now, we do not know the properties of this force. This webpage and the next will attempt to identify this force.

(*) The three fundamental forces are gravity, electroweak force (unified in 1972 by Weinberg and Salam, Nobel Prize 1979) and the strong nuclear force.

This webpage is the 3rd part of the website
It is strongly suggested to also read the two previous parts.


Fields in Spacetime

Spacetime supports two differents fields:

  1. Electromagnetic (EM) field
    This field is responsible of the electromagnetic (or electroweak) force. The behaviour of this field is well known by physicists but no one can explain its origin.
  2. Gravitational field
    The gravitational field is created by a gravitational potential. It has been described by Einstein in 1910-1915 in his General Relativity. The force associated to this field is gravity. The nature of this field and its mechanism of propagation is described in Part 1, mass and gravitation. Gravity concerns all particles, charged or not, whereas EM acts only on charged particles.

This raises the following question:

How can a single spacetime support these two different types of fields:
    1/ an EM field concerning only charged particles,
    2/ a gravitational field for all particles, charged or not.

The only answer to this question is
that spacetime has a substructure

Note: Parts 3 and 4 give some suggestions to this sub-structure but in this webpage, for pedagogical purposes, we will ignore this sub-structure considering that EM waves are supported by spacetime without any other precision.


Movements in Spacetime

The universe is filled with EM and gravitational waves of all kinds. Thus, spacetime is not motionless but is vibrating continuously.

EM waves are movements in spacetime, like "whirlpools" or "eddies" in water. The propagation of EM waves in spacetime is similar to that obtained by a stone that makes rings when thrown into the water. The figure below shows these waves. Wave 1 is the main wave, and waves 2, 3, 4... are secondary waves. Here, the wave is propagated from left to right. In spacetime, these vibrations are variations of density of spacetime.

spacetime - 1


Mathematical Formalization

In quantum mechanics, we have a "wave packet".

spacetime - 2

For our further demonstrations, we will take the simple form of a damp sinusoid (figure below). Please note that this figure is not fully exact since the form of the wave depends of the phenomenon that created it. It has been simplified for pedagogical purposes. It represents the periods, from 1 to 4, of the waves of the previous section.

spacetime - 3


Polarity of spacetime

The following graphic is identical to the previous figure. Sign "+" was inserted in areas of high relative density of spacetime and sign "-" in areas of low relative density.

Spacetime has a "neutral density" before the arrival of the wave. The positive and negative variations of the wave are "relative" to this reference.

spacetime - 4

Note: Here we presume by convention that a high density of spacetime corresponds to a positive polarity, and a low density to a negative polarity.


Example of air cubes

To better understand vibrations in spacetime, let's imagine that ambient air is divided into small cubes. In this example, the EM wave is replaced by a soundwave.

spacetime - 5

Each cube has a density of air. When a soundwave arrives, the pressure of the air inside each cube changes to positive or negative pressures, i.e. high and low pressures. After the passage of the soundwave, the pressure of cubes falls back to its initial value.

This initial value of density of air is called "Neutral density" on the previous figure. The small cubes of air could be identified to the sub-structure of spacetime expected above.


EM vs. Gravity

Let's imagine that we have two MP3, one on a mountain and the other on a beach.

  • Mass and Gravity
    Atmospheric pressure on the two MP3 will be different. These pressures are assimilated to the pressure of spacetime on objects which leads to mass and gravity phenomena (see our website
  • Electromagnetism (EM)
    The sound produced by the speakers of MP3 are vibrations of the ambient air. These vibrations, 1000 Hz for example, are not dependant of the location of each MP3, on the mountain or on the beach.

As we see, air can support two kinds of forces: a pressure on objects, on the surface of the two MP3 and speakers, and local pressures (sound) in each cube or molecule of air.

In spacetime too, the mass-gravity forces can be combined with electromagnetism forces. The global spacetime makes pressures on objects (mass, gravity) whereas the local elements of spacetime, i.e. the expected sub-structure, can support EM waves.

Since we are front of two different kinds of forces, gravitational and EM, we have necessarily two structures in spacetime: a main structure, and a sub-structure. There is no other alternative. An unique spacetime can not carry two so different forces.

For the moment, it is pure speculation but we will see later, in the Parts 3 and 4 of the Spacetime Model, that this view is perfectly correct.


Principle of the Least Action

The principle of Maupertuis in 1744 indicates that nature always tends towards the least action. Koenig, De Fermat, Liebniz, Euler, Lagrange, Jacobi and Helmholtz have devised similar principles. Transposed to spacetime, this principle becomes:

spacetime - 6


Principle of the Least Density

The principle of least action can be stated in a different way, which will be useful for us later in this webpage. Since the density of spacetime of the global Universe is neutral, areas of polarized spacetime will tend to a neutral density. So:

spacetime - 7



For teaching purposes, the previous figures are grouped in the following figure which represents an EM wave on the left, and its simplified mathematical representation, on the right.

spacetime - 8


Annihilation process

Let's imagine that we take two "pieces" of EM wave noted A and B on the left part of the above figure. These two small parts are represented in the following figure. What happens if we put these two areas, A and B, in contact?

spacetime - 9

Intuitively, we might think that these two areas will cancel out each other. The area of high density of spacetime in A will annihilate the area of low density of spacetime in B.

We can also demonstrate that this phenomenon is in accordance with the Maupertuis Principle adapted to spacetime: The only way to get the least difference of density of spacetime is when areas A and B annihilate each other.


Example of Annihilation

Let's consider the example of an acoustic wave. As we know, it is a succession of pressures and depressions in air.

Let's isolate two small cubes of air, one in a pressure half period (A on the previous figure), and the other in a depression half period (B). Now, let's put them in contact. Intuitively, we might think that these two areas, A and B, will mutually cancel out each other. The result will be two neutral areas with zero relative density, like our "reference" the previous figures.

The same phenomenon occurs in spacetime when we put together two areas of opposite polarities.


Attractive Force

In spacetime, before annihilation, the positive area (A) of spacetime is attracted by the negative area (B). The principle of least relative density of spacetime (see before) can be applied to this attraction.

spacetime - 10


Repulsive Force

In the same manner, two areas with the same polarity of density of spacetime will tend to push each other away. The principle of least relative density of spacetime (see before) confirms this repulsive force.

spacetime - 11



Under certain conditions, two areas of identical polarity can merge.

For example, if the energy of one area is higher than the "barrier" of another, this barrier can be crossed over and fusion becomes possible. Thus, under some conditions of proximity, repulsion can become a fusion. This phenomenon of fusion is well known by physicists, but in spacetime, we have the same principle.

spacetime - 12



In this webpage, we have seen that:

  • Spacetime supports two forces, gravity and electromagnetism, which have different behaviours,
  • Therefore, spacetime has necessarily two different structures. The second structure is called here "sub-structure",
  • This sub-structure may have positive and negatives areas,
  • ...which produces attractions, repulsions, and fusions.