Particle Model

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Scientific Theory
Name Particle Model
Type Newtonian, Particle
Author(s) Bob de Hilster, David de Hilster
Keywords Newton, gravity, light, infinity
Year 2015

NOTE: This page will undergo a complete rewriting once the book Principia Mathematica 2 comes out.

The Particle Model is a model proposed by father-son team Bob de Hilster and David de Hilster that the entire universe and everything in it can be described as particles including light, gravity, electricity, magnetic fields, atomic structure, charge, polarity, refraction, reflection, and mass increase to name a few. The model was first proposed in 2015 and is currently being detailed in the book Principia Mathematica 2 which is to be released in 2020.


The first notions for the particle model were developed by Robert and David de Hilster starting in 2006 in Long Beach California and continues to this day in Boca Raton Florida where both authors currently reside.

Carezani Graviton Experiment

The particle model started with an experiment proposed by Argentinean physicist, Dr. Ricardo Carezani to detect if gravity, a particle known as the "graviton", could be the cause of gravity. The experiment is a variation of the wikipedia:Cavendish Experiment. The experiment was performed as part of the feature-length documentary Einstein Wrong - The Miracle Year directed by David de Hilster in which David asked his father to help with the experiment after Carezani pulled out of the documentary film.

The Gravity Equation

In order to make calculations for the experiment, Bob de Hilster developed a mathematical equation which summed up all the forces of gravitons entering, exiting, and hitting the objects. The model uses the actual geometry and mass of the objects in the experiment rather than use the points masses used in the Newtonian equation. These calculations need a precision of up to 50 decimal places and was written in C++ using a math package for ultra-high precision (up to 150)calculations.

The calculations lead to gravity "curves" that closely matched Newton's gravity curve. The curves match closely in shape, but not in value; but this was enough incentive for Bob to continue his studies even though the experiment did not prove that the graviton was the cause of gravity.

The mathematics used in the Particle Model is unique. It uses the concept that each time the G1 particle hits an atom, there is an instantaneous force applied that causes the object to move. The equation can be developed using algebra.

The Basic Equation

The equation below is a basic equation for calculating the force of gravity on the surface of the earth using the Figure above.

; is the net force on the earth caused by two opposing G1 particles and is the percent reduction of G1s as they pass through the earth.

The Complete Equation The complete equation requires a three dimensional summation of all possible paths through the earth.


where is the total net force pushing the earth; is the instantaneous force by the G1 particle acting on the earth; is the percent of force lost through the earth; P is the total number of planes; and A is the total number of angles in the plane.

Supporting Equations There are two supporting equations:

; The percent reduction of each path is equal to the interaction factor times the mass of the path through the earth.

; The potential force at any point is space is equal to the product of the instantaneous force of ach G1 particle times the number of paths in the calculation.

and are virtual constants. Virtual constant are not absolute constants since they are dependent on other factors. is dependent on temperature; while is dependent on where you are in the universe.

A more complete explanation of the Particle Model equation can be found in a paper titled "Mathematics for the Particle Model". This math has been applied to gravity and to circuits and should be possible in other applications.

Gravity is not Free

Following years of study and calculations, Bob de Hilster wrote down his findings in the book Gravity is not Free of which there are four parts. Part 1 explains how David got started in science. Part 2 is the personal story of Bob's work and how it developed over time. Part 3 is a technical explanation with out any personal history. Part 4 is a compilation of papers relating to the gravity work.

After 10 years of working on particle gravity, Bob defined a new model for light and suggested that there could be a second gravity. The development of these ideas are describe in the book Universe Hack 3.0.

The Speed of Gravity

One of the key aspects for the particle model is the claim that gravity and light both travel at the speed of light. Many scientists, including Newton, claim that gravity is "instantaneous action at a distance". Relativity states that an object cannot go faster than light. However recent experiments in China during an eclipse concluded that the speed of gravity is the same as the speed of light, or nearly so.

Bob was convinced in December of 2008 that the speed of gravity was at or about the speed of light by analyzing the experiments by Maurice Allais (1954 and 1959) and Qian-Shen Wang (1997).

A Solution to the Wave / Particle Duality

By far the biggest breakthrough and impetus for creating the particle model was a solution to the wikipedia::Wave Particle Duality by Bob de Hilster in April of 2015. While working in a gravity group from members of the CNPS, Bob was looking at possible wave solution to gravity concluding it must be a very low-frequency and low intensity wave.

Following that work, Bob asked the question: "How can I make a particle act like a wave?" It turned out that Bob could not make one particle act like a wave and cause white light. It takes at least three particles and then there are still other problems. It was then that Bob considered the possibility that a stream of particles with repetitive pattern could have a wave length. The peak of the wave would contain many particles and the valley almost none. The wave length is the distance between peaks. Hence: NO WAVE/PARTICLE DUALITY"

But Quantum Mechanics contends that light both particle and wave. Wave/particle duality is a consequence of the Double Slit Experiment. The Particle Models explanation is found in the paper titled "The Particle Model Explains the Double Slit Experiment"

Gravity 2

The particle model took shape up when Bob applied the stream of particles (light) to refraction. It was clear that there was a second gravity. See section "Refraction of light and a New Gravity" But what is it? Having worked on particle gravity for 10 years, Bob made the assumption that this second gravity was a particle. Could it be something else? Of course it could. But Bob's success during that 10 year period left him with one conclusion, there was a second gravity and hence there was a G2 particle whose speed is much faster than light and whose size is much smaller than the electron.

Electrons, Ionel Dinu, and Infinity

A few months after Bob de Hilster suggested solution to the wave / particle duality, his son David de Hilster added other aspects to the model that David collected over the years from other scientists working outside the mainstream.

Introduction to the Particle Model

Levels of the Universe

The Particle Model proposes that there are multiples levels of the universe which contain particles, atoms, and molecules.

We humans exist in Level 1 where there are two particles, the nucleon (N1) and the gravity 1 particle (G1). The atom is made up of nucleons, which replace the proton and the neutron, and the G1 replaces the electron. There is no electric charge in the particle model, it is a true mechanical model. Molecules and larger objects in Level 1 are made from these atoms. Of course there are many atoms which are listed in the Periodic Table of atoms. The atoms, molecules, and larger objects are held together by gravity 2 particles (G2) which come from Level 2.

In Level 2 there are two particles, the nucleon 2 (N2) and the gravity 2 particle (G2). These particles are much smaller than the N1 and G1 and are the components of subatomic atoms. Yes, the Particle Model suggests that there are atoms at a level 2, not just particles. There is no direct evidence to show that the N2 particle exists. But there is indirect evidence that the G2 particle could exist. This is based on the observation that light bends at it enters a prism. See the section on the "Refraction and Light".

Is there a Level 3 and more? The philosophical concept of infinity suggests that there could be many more levels. Given that there is no evidence, direct or indirect, for level 3, the authors will not press the issue.


Level 1 Atoms

The N1 particle replaces the proton and the neutron. The N1 is not electrically charged. The nucleons in atoms are held together by G2 gravity and form the nucleus. Hence G2 gravity is the nuclear binding force. The value of the mass of the N1 is not measured in kilograms (Kg). See definition of Mass. The speed of the N1 particle is limited by the drag caused by the G1 Particle Field and is generally much slower than the speed of light.

The G1 particle is the particle that orbits the nucleus of the atom. As such it has a very high speed, at or about the speed of light. The value of the mass of the G1 is not measured in kilograms (Kg). See definition Mass.

The G1 Particle Field is generated by all the stars in the universe. As the stars release visible light, they also releases individual G1 particles. These individual particles come from all directions and form the basis of G1 gravity that surrounds all objects.

Level 2 Atoms

There is no evidence that level 2 atoms exist. It is the Particle Model itself that suggests that there could be sub-atomic atoms. It is being suggested that the G2 particle comes from the orbital of these atoms. Since these atoms are much smaller than level 1 atoms, The speed of the G2 is much faster than the speed of light, maybe "c squared". This speed is required in order that the G2 can cause the G1 to change its speed or direction.

The N2 particle is used to form the nucleus of the Level 2 atoms. Could there be a periodic chart that lists all the types of Level 2 atoms? We may never know!

Level 3 Atoms

Let's not even go there!

Key Concepts


Probably the most important concept in the Particle Model is its definition of light. Light is "a stream of G1 particles moving at speed 'c' and it has a repetitive pattern".

Figure 1: The Particle Model for Light

Figure 1 shows idealized streams of particles where the peak of the stream has many G1s and the valley of the stream has very few or even none. This stream is based on a perfect sine wave, but can take any form. It can represent a square wave, a triangular wave, a radio wave, and all of the waves in the G1 spectrum.

Refraction of Light and a New Gravity

When this concept of light is applied to refraction, the concept of a second gravity was generated. The question asked was: "What force is required to cause the light to bend as it enters a prism?" This is type of question that Newton asked when he observed the motion of the apple and the moon. Figure 2a shows Newtonian gravity while Figure 2b shows the forces required to bend a beam of light.

Figure 2: G1 and G2 Gravity

G1 gravity (Newtonian gravity) acts on apple and the moon. The force lines for G1 gravity are all pointed toward the center of the object. The force lines for G2 gravity do not point that way. G1 gravity moves large objects while the G2 gravity moves light (streams of G1 particles). Clearly, if the direction is different and what moves is different, then maybe there is a second gravity (G2) that is the cause of refraction.

Bob de Hilster has stated several times that: "You have to give Einstein credit. He said gravity bends light. He just picked the wrong gravity".

N1 and G1 Mass

Mass is defined in the "Definitions" section. If you want to know the value of mass, we use a scale like the ones in the chemistry lab. These scales compare the gravitational force on the unknown object versus the gravitational force on a set of known standards. This is only possible when measuring atoms, molecules, and larger objects. Measuring the mass of the G1 particle using G1 gravity does not work. The mass of the G1 cannot have a value in terms of kilograms because it cannot be measured using a G1 gravity scale (Newtonian). The same is true of the N1 particle.

The G2 particle is the atomic binding force that holds the nucleus together and keeps the G1 particle in orbit. It is acting gravitationally on the G1 and N1. So we must use a G2 scale to measure the mass of the N1 and G1 particles. But there is no standard and there is no scale to do this. Much work has to be done!

N2 and G2 Mass

Subatomic atoms are made from N2 and G2 particles. Standard science does not mention subatomic atoms, only subatomic particles. The Particle Model proposes that there is a G2 particle that is moving faster than light, maybe at a speed of 'C squared'. If it exists, it must come from somewhere. One possibility is that there are Level 2 atoms that have particles that orbit the level 2 atom. There is no direct evidence that subatomic atoms exist. But there is indirect evidence of the G1 particle changing speed or direction, as in refraction, that must be caused by something moving faster than light.

To measure the mass of N2 and G2 particles requires G3 gravity. There is no evidence, direct or indirect, to support the idea of G3 gravity. So N2 and G2 mass cannot be measured and any guess is pure conjecture.

The Amazing G1 Particle

The G1 particle moving at speed 'c' applies to many if not all physics phenomenon.

Gravity: The G1 replaces the graviton.

Light: Light is a stream of G1 particles with a repetitive pattern.

Magnetic Field: The magnetic field is a high intensity stream of G1 particles flowing around and through a magnet.

Lightning: Lightning is a stream of high intensity G1 particles.

Electrical: The G1 replaces the electron.

Chemical: The G1 particle is released during most chemical reactions.

The Amazing G2 Particle

The G2 particle is the orbital of sub-atomic atoms and moves at speeds greater than 'c'.

Binding Force: G2 gravity is the nuclear, atomic, and molecular binding force for Level 1.

Refraction: G2 gravity is the cause of light bending around the sun and prism.

Magnetic Field: G2 gravity keeps the G1 in orbit around and through the magnet.

Lightning: G2 gravity surrounds the clouds and pushes the G1s to make lightning.

Battery: G2 gravity pushes the G1 out of the battery into the circuit.

Parallel Resistors; G2 gravity surrounds the two resistors and adjusts the flow of G1s to match Ampere's equation.

Detailed Descriptions

This section provides specific details for gravity, light, magnetics, electrostatics, circuits, and chemistry. They are explained using a mechanical model with no electric charge. Just particles in motion.

Particle Interactions

The basic interaction of particles with other particles and larger objects are the same when explaining gravity, light, magnetics, electrostatics, circuits, and chemistry. The G1s can pass through object, or they can hit an object and scatter, or they can be trapped as a G1 orbital. These options apply to all of physics.

Level 1 particles, G1 and N1, are elastic and bounce off of each other. Level 1 particles can pass through atoms and molecules. They can pass all the way through or they can hit other Level 1 particles and scatter. The G1 particle can be trapped by an atom or molecule and become a G1 orbital (like an electron orbiting a nucleus).

Level 2 particles, G2 and N2, are elastic and bounce off of each other. Level 2 particles can pass through Level 1 particles and larger objects. They can pass all the way through or they can hit other Level 2 particles and scatter. The G2 particle can be trapped by a subatomic atom become a G2 orbital.


G1 Gravity

G1 Gravity is based on the gravity concept developed by Georges L. Le Sage. Yes, Wikipedia clearly states that this model of gravity is convincingly discredited. [[1]]

Any object made of atoms, molecules, and larger objects of these, will develop a G1 gravitational field. This replaces Newtonian gravity but is considered more accurate. Newtonian gravity assumes that all of the atoms and molecules are located at the center of gravity of the object. G1 gravity takes the geometry of the object into consideration. The G1 particle interacts with each atom of the head of the hammer and along the body of the handle, not just at one point.

G1 particles come from all the stars in the universe. These are low intensity streams of G1 particles moving at or about the speed of 'c'. The particles come at the earth from all directions. They can pass all the way through, hit a G1 or N1 and scatter, or be trapped as a G1 orbital. When the G1 hits it not only scatters but it pushes the atom. This results in fewer G1s leaving the earth than are entering. An object on the surface of the earth is constantly being pushed up by fewer G1s and pushed down by more G1s giving a net pushing force downward toward the gravitational center of the earth.

G2 Gravity

There is no direct evidence of Newtonian gravity or G1 gravity. Newton observed the motion of the apple and the moon and suggested that there is a force called gravity. There is no direct evidence of G2 gravity. We observe the bending of light, the attraction of magnets, and the electron flow in circuits and suggest there is a force we call Gravity 2.

G2 particles come from all the stars in the universe. These are low intensity streams of G2 particles moving at or about the speed of 'c squared' (Estimated). The particles come at the earth from all directions. They can pass all the way through, hit a G2 or N2 and scatter, or be trapped as a G2 orbital. When the G2 hits, it not only scatters but it pushes the subatomic atom. This results in fewer G2s leaving the earth than are entering. An object on the surface of the earth is constantly being pushed up by fewer G2s and pushed down by more G2s giving a net pushing force downward toward the gravitational center of the earth. The G2 gravitational force around the earth is the cause of light refraction and our blue sky.

Caveat: The direction of G2 gravity does not always match the direction of G1 gravity. This means there is more to the generation of G2 gravity than is stated above. We need a more clear understanding of G2 gravity and so there is more work to be done.

Gravitational Attraction

The earth and the moon are being pushed towards each other by the G1 particles passing through both objects. When they hit, the G1 scatters and the object is pushed. Figure x shows the path of two opposing G1 particles. The loss of G1s through the earth causes a reduction of the G1s toward the moon. Hence there are more G1s pushing the moon towards the earth than there are G1s pushing the moon away from the earth. Although we talk about a net force on the moon towards the earth, the reality is the forces occur in both directions all the time.

For the same reason, the earth is being pushed towards the moon. According to the equations developed by the particle model the force on the earth and the moon are exactly the same. The acceleration of the earth is less than the acceleration of the moon due to the values of mass assigned to the earth and moon. A better way to say the same thing is to state: "The mass of the earth and moon are assigned sing the measured value of their mutual acceleration.


Newton had a particle theory of light, but it wasn't accepted. Quote from Wikipedia: This theory cannot explain refraction, diffraction, interference and polarization. Newton was a pioneer of this theory, in 1672. But Newton did not have the same model that the Particle Model proposes. The following is a brief description of how these issues are resolved.


The standard explanation shows that light slows down while in a prism, but regains the speed after it leaves. They say that the index of refraction explains this. The index of refraction is a measured value with no specific physical reason. The Particle Model suggests that the speed of the G1 stays about the same into, through and out of the prism. The speed of the wave appears to change because the particle takes a longer path. It is guided by the internal G2 forces.

The Particle Model suggests that the light bends as it enters the prism and when it leaves the prism because of G2 gravity. It also suggests that the speed of the G1 increases as it enters and slows down as it leaves. See Figure X.


Diffraction is when light bends as it passes by a corner or goes through a slit. It is the main reason that scientists claim that light is a wave. This effect seems to require a medium just like a water wave requires water. The Particle Model for light does not have a medium, the G1 particles move easily through open space.

The Particle Model suggests that the G2 gravity surrounding the corner or the slit is the force that causes the G1 particles to diffract, that is bend.


The Particle Model for light is shown in Figure x. There are two streams of light shown as a sine wave, but 180 degrees out of phase. Each wave is represented by a string of numbers indicating the number of G1 particles at each section of the wave. When these two streams of G1s hit a smooth surface together, the total number of G1s in each section is constant. The reflected stream has no peak or valley so will not be seen as light. This is why we can't see G1 gravity, it is a continuous stream of low intensity G1s with no peak or valley.


There is no polarized light in the Particle Model, not as normally defined. With the light defined as streams of G1 particles there can be no EM wave. Polarized lenses are built to block light in the horizontal or vertical direction. This can even be done mechanically. Light reflecting from a smooth surface can cause glare. This light is reflected as horizontal streams (horizontal layers of G1 particles). By putting horizontal barriers on your sun glasses, half of the streams are blocked.

Three D movies project two images on the screen. The right image is for your right eye and has a vertical pattern. Your left eye piece in the 3-D glasses has horizontal barriers that cancels most of the image. But not all. David, Pat, and I went to the Kennedy Space Center and watched a 3-D movie. Dave concentrated very carefully and claimed he could se the right image in his left eye.

Polarized light does not exist in the in the Particle Model, there is only layered light or un-layered light.


When a dc current flows through a copper wire, a magnetic field is generated. The Particle Model suggests that the G1 particles (electrons) escape from the copper wire and is trapped by G2 gravity. This suggest then, that the G1 particle not only replaces the electron but it also is the particle that forms the magnetic field.

The Magnetic field can be considered as high intensity gravity.

Gravity is developed when streams of low intensity G1 particles pass through and interact with an object. Gravity is weak because of how many G1 particles are available and because the probability of the G1 hitting the object is small. On the other hand, the G1 particles passing through and around the magnet can have a higher intensity, that is a higher linear particle density. Small magnets have weaker streams of G1s and larger magnets have stronger G1 streams.

In the Particle Model, one effect is never exclusive to the opposite effect. The net force of gravity on the earth is not just a pushing down, but at the same time there is a pushing up. With Magnets, there is not only G2 gravity pushing the magnets together, but there incidental collisions of G1 particles pushing the magnets apart. What happens depends on which of the effects provides the stronger force.


Figure x1 shows two magnets with the south end of one magnet facing the north end of the other magnet. The G1 flow though both magnets are in the same direction which minimizes the repulsion. The G2 force around the magnets are stronger and therefore the magnets move towards each other.


Figure x2 shows two magnets with the south end of one magnet facing the south end of the other magnet. The G1 particles flow out of the south end of each magnet causing the G1s to hit head on. The magnetic field around the magnet are being held in place by G2 gravity



The Particle Model does not accept the concept of charge. To accept this concept requires a physical description of what causes the electron to be negative; and what causes the proton to be positive; and what causes them to attract or repel. There is no explanation. But objects that are assigned a charge can attract and can repel. The Particle Model suggests that this attraction is caused by G2 gravity and repulsion is caused by G1 particle collisions.

There are materials that can accept extra G1 orbitals and there are other materials that can lose G1 orbitals and the materials do not change. These materials are identified in lists titled "Triboelectric Series". Extra G1 orbitals in a material are like extra electrons and the material can be considered negative even though the G1 particle has no charge. This is an assigned property of the material, not a physical property of the G1 particle.


When you walk across certain carpets your body can gain G1 particles. When your hand gets close to a door knob, G2 gravity will push the G1 particles out of your body and into the door knob. If there are enough of them, the G1s will cause a spark that you can hear, see, and feel.

The extra G1s in your body cause an imbalance of G1s relative to your surroundings. It is this G1 imbalance that causes the G2 particle field to set up a G2 force that moves the G1s. G2 gravity is the cause of sparks and lightning.

Lightning moves in strange directions because the G1 balance in a thunderstorm is random. Lightning will occur when the imbalance of the G1s in two clouds is sufficient to set up the G2 force and move the G1s. Lightning moves from the cloud with more G1s to the cloud with fewer G1s, wherever that is.


This is the most amazing application of the Particle Model. After years of electronic design work, I finally have a very good physical description of how the circuit works. The magnetic field around the battery is routed through the circuit at speed 'c'. It passes through copper, resistors, inductors, and capacitors and interact mechanically, not electrically.

Re-read the section on the "Particle Interactions", section 5.1. So, when the G1 passes through a resistor it can hit the resistor (push it) and the G1 will scatter (move away). There are fewer leaving the resistor than entered. The resistor lost G1s which is like losing voltage. This means that the G1 (electron) should be assigned a voltage, not a charge.

If the circuit elements lose G1s, then the battery must add G1s in order for the circuit to become stable. This process is the basis for Kirchhoff's equations. Losing G1s is a voltage drop and gaining G1s is a voltage increase.

Example Circuit

9 Volt Battery with 1 and 8 Ohm Resistors

Figure X shows a 9 Volt battery with two resistors in series. The standard equations for this circuit are as follows:




Remember that most of the G1s pass straight through an object. A very small number hit and scatter, so the percent of G1s lost through a circuit element is very low. It is the batteries job (using Chemistry) to generate enough G1s out of the battery such that there are 80 G1s lost in the 8 Ohm resistor and 10 G1s lost in the 1 Ohm resistor. N is the required number of G1s flowing through the circuit that provides enough G1s to generate the necessary loss though the resistors.

Starting the Circuit

When the On/Off switch is closed, the battery does not know how many G1s to release. If it releases too few, then not enough are lost, causing too many to pass through, causing more to enter the battery. If it releases too many, then too many are lost and then too few pass through, causing fewer to enter the battery. The circuit will stabilize when the number of G1s lost in the resistors matches the number added by the battery. Figure X shows the stabilized state after the G1s have cycled the circuit many times.

It may take many cycles, but they happen in a very short period of time. The speed of the G1 particle is near the speed of light. The measured speed will be less than the speed of light because the particles doe not follow a straight path. They are guided through the wire by the internal force of G2 gravity just like an asteroid is guided by G1 gravity as it passes through our solar system.


Figure X shows that there are N G1s that enter the battery. There are N+90 leaving the battery and entering the 8 Ohm resistor. After leaving the 8 Ohm resistor, there are only N+10 entering the 1 Ohm resistor. The number of G1s flowing through the circuit is not constant. So the current through the circuit is not constant. But the value of N is very high because the percent lost is very low. With N at a large value, the value of current is different at different points in the current. The values are close but not precisely equal. The equation for current, shown above, is useful for engineering, but it is the physicists job to the underlying mechanism.

Tests will be run using two and three resistors to verify that the current is not constant at all points in the circuit.


Atomic Structure


One assumption: The universe is made up of objects that move.

Space is a man made concept for locating objects. The dimensions of space are in meters.

Time is a man made concept for measuring motion. The units of time are in seconds.

Mass is not real. It is an assigned property that helps describe motion. The value of mass is assigned to each object relative a standard. The Level 1 standard is the gram and applies to the atom and molecules of Level 1. There is no standard for Level 2.