Quantification of space-time

The idea developed in this article is that energy, space and time are the direct result of interactions between particles. Each particle has quantity of matter invariant. This quantity of matter is contained in a finite volume, particle therefore has a volumetric matter density. Volumetric matter density fluctuations are at the origin of many physical phenomena such as time, energy, movement of particles, accelerating expansion of the universe, etc.

I Postulate

• Elementary particles are defined by a quantity of matter completely invariant. The space is a field entirely full of particles.
• Movement always occurs from high volumetric matter densities to low volumetric matter densities. Therefore, a particle will exert a pressure around it by moving towards balance. The quantity of matter is invariant but the volumetric matter density (mass of particle) varies. The particle can be diluted or contracted depending of the pressure exerted by other particles.
• The work of pressure forces is equivalent to an energy volumetric density. Energy is quantity of matter contained in a finite volume. Pressure depends on the volume with the following relation : pressure = We can express a particle energy with the following relation:

Energy of the particle =

Thus, when a particle's energy increases, the particle contracts itself because the quantity of matter is invariant and its volumetric matter density increases (so mass increases too). The energy of a particle at rest is not zero because the matter of a particle is compressed by other particles.

II Movement of a particle

Particles exert a pressure between them and move according the equilibrium of pressure forces.

The speed of a high-pressure wave (attracted toward low pressures) is unique: it’s the speed of light. Therefore, a particle’s speed is depending on the resultant of the pressure forces exerted on it. The particle is attracted into many directions at the same time, which explains why it doesn’t only move at the speed of light.

The work of pressure forces being equivalent to the energy, we can then rely on the energy conservation principle to describe the movement of a particle.

E = Pp + Pe

E: Total energy of a closed system. It corresponds to the sum of pressure forces.

Pp: Pressure of the particle. The volumetric energy density of a particle p.

Pe: External pressure to the particle. The volumetric energy density outside the particle p.

Analogy to the Venturi effect: When the velocity of a fluid increases, the pressure between the particles composing this fluid decreases, which causes a static pressure drop and an increase in dynamic pressure. In this theory, when the energy of the particles increases, their speed increases and they exert less pressure on other particles. Thus, the medium pressure decreases, which is the source of gravitation.

Circles symbolize particles and the black arrows symbolize pressure forces

The velocity of a particle depends on the resultant of its pressure forces compared to the resultant of external pressure forces acting on it.

0 is a zero velocity and 1 is the speed of light. Pressure of the particle tends towards infinity when the speed is close to 1.

In the case of a wave, the speed is constant and is equal to 1 because, therefore the  Indeed, no pressure can be applied to a zero volume.

The high-pressure waves move from high pressure to low pressure, the photon (although it must have a very small volume given that it carries energy) will be deflected by a low pressure.

Case of a particle at rest:

The velocity of a particle is zero when the resultant of the pressure forces is zero. In this case, the pressure forces of the particle are oriented outward the latter and are perfectly compensated by the pressure forces exerted by the other particles which converge towards the center of the particle. Thus  therefore the velocity is zero.

However, the energy of the particle is not zero. Indeed, the particle has a quantity of matter contained in a finite volume (mass). The volume of the particle being determined by the balance between the pressure of the particle Pp and Pe.

Therefore, the mass (energy) of a particle at rest is not strictly invariant but may change over time. For example, the expansion of the universe will impact the external pressure of the particles Pe therefore on the volumetric matter density of the particle. The quantity of matter of the particle is the one which is invariant.

Case of a particle in movement :

When Pp increases:

● The pulse increases and the particle accelerates.

● The particle contracts itself.

● Energy increases because the volumetric matter density increases. The inert mass increases (the pressure of the particle) tending to infinity with the particle never reaching the speed of light because that would imply a total lack of external pressure or a zero volume. Zero volume is impossible because of the conversation of the matter.

● The particle is somehow, more and more repelled by other particles. It seeks to balance.

● Speed of the particle is increasing.

Ambient energy is also important in the movement of the particles. When energy increases, the external pressure Pe decreases (by contracting themselves, particles move toward one direction and free up space). Thus, particles accelerate because they are less blocked. The movement depends on the resultant of pressure forces.

III Equivalence principle

The inertial mass and gravitational mass are completely equivalent. Both are directly related to the volumetric matter density of the particle. The difference lies in putting in motion the particle. The gravitational mass provides an attraction from a low pressure while the inertial mass provides a repulsion by high pressure.

IV Higgs field

The Higgs boson plays a key role in this theory. The Higgs field would consist of quantized particle also having a volumetric mass density. This particle would be the main responsible of the mass (the other particles also interact among themselves). By the pressure they exert, they block themselves and other particles. The action of the Higgs field decreases in the presence of energy. Indeed, when the energy increases, the particles are contracted and the external pressure Pe decreases. This contraction releases the movement. Particles less blocked, accelerate.

A gravitational wave (a wave of high pressure) contracts other particles by moving when it’s attracted by low pressures. Indeed, space is made of a particle field.

V General relativity

Gravitation: when the energy of a particle increases, its volumetric matter density (mass) increases and the particle contracts itself. Therefore, the external pressure decreases, which generates a pressure drop. This pressure drop is the source of the gravity. Particles, less blocked, are drawn into the depression.

Energy in relativity:

Relativistic energy = 𝛾.𝑚𝑐² and Lorentz factor

In this theory, the contraction of the distances is a decrease in the volume of the particle.

As soon as the velocity increases, the mass increases. In this theory, the contraction is the inverse of particle velocity.

The contraction is based on the volume of the particle at rest. Indeed, α = 1 when the particle is at rest. Thus, the contraction also depends on the pressure of the medium. The particle is stopped when the pressure of the particle and the pressure exerted on the particle balance :  therefore, 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 0 and 𝛼 = 1.

As the particle gains energy, it contracts. As it is contracted, α tends to 0 and the energy tends to infinity because the volumetric matter density (mass) tends to infinity.

The contraction of the particle takes place in the direction of movement. It’s repulsed by the other particles when its volumetric density is more important. The contraction results in a pressure drop. A low pressure is attractive, which explains why gravity can only be attractive. The particles are attracted in the depression because they are less retained.

All objects fall at the same speed in a gravitational field and this regardless of their mass because their fall speed depends on the resultant of pressure forces. The resultant of pressure forces does not vary according to the mass of the particle but it varies according to the ratio between the volumetric matter density of the particle and the pressure exerted on the particle.

Time deceleration:

There is less movement (e.g., the clock is ticking more slowly) when the velocity increases as the ratio of pressure forces is changed.

The velocity does not add up, they depend on the resultant of pressure forces whose velocity depends. When velocity increases, the particles move toward a single direction, which causes a decrease of velocity in the other directions.

Time is a consequence of an unbalanced system that tends towards equilibrium. This is a direct result to the difference of pressure between particles.

The effects caused by this theory would be similar to those of general relativity in its domain of validity but the effects on the movement strongly change at the quantum scale and very large cosmological scales.

VI Accelerating expansion of the universe

The world is experiencing an accelerating expansion. In this theory, the universe is attracted towards all directions by low pressures. The universe would be a high-pressure zone diffusing into a hyper universe that would have a lower pressure.

As the universe is expanding, the particles contract themselves and the pressure decreases (Pp increases and Pe decreases). Therefore, the particles are less and blocked and accelerate.

Thus, the energy of the mass of a particle at rest evolves during the expansion of the universe because its volumetric matter density decreases.

VII Black hole and dark matter

Black holes can be produced directly by the space. Space being quantified and shaped by the energy, black holes would be vortexes generated when a difference of pressure occurs.

Similarly, black matter is not necessarily an unknown exotic matter but possibly the manifestation of energy flow produced by a difference of pressure.

Therefore, black holes and dark matter are completely inseparable.

VIII Quantum mechanics

Quantum time:

Time is a consequence of the distribution of energy. A particle will go faster or slower depending on its energy compared to the energy of other particles. The direction of time is given by the entropy of the system who tends towards equilibrium, high pressures to low pressures.

Wave-corpuscle duality :

The corpuscular part of the particles relates to the particle field filling the space, the field that is the source of energy. Energy is the common basis for all interactions. Some of these particles react with other force fields. Thus, a particle can be subjected to two force fields simultaneously. Example of the electron in the Double-slit experiment:

➢ Single-slit:

The electron does not create an interference pattern. The "particle" is not deflected. The particle will create a one-time impact because it is a corpuscle in the 'energy' field. Wave portion occurs only if the wave created in another field (the two nuclear forces and the electromagnetic force) is changed.

➢ Double-slit:

The electron will create an interference pattern. The electron will generate a wave in an “electromagnetic” field to which it is sensitive. It is the interaction of this wave with itself which will move the particle of the “energy field”.

➢ Electron with an observer

Addition of a sensitive observer to the electromagnetic interaction (a photon) will crack the wave packet in the electromagnetic force field and thus will significantly alter the behavior of the particle. The electron is at the same time a "corpuscle" in the energy field and a wave in the electromagnetic field.

I wrote this article hoping interest of physicists having the capacity to develop it. For now, it’s more of a concept than a theory. Thanks for reading.

Thomas Perrier : tperrier@ymail.com