The Lattice Theory
Electrostatics without Coulomb’s Law
Mass is inherently electric. In this article, we unveil a new equation that calculates the precise electrostatic force between two elementary charges. What makes the equation exceptional is that it is based solely on the mass of the electron, the distance between two elementary charges and the speed of light. Coulomb’s Law is not used.
Introduction
We had originally planned to publish a two or three-part article to describe Lattice theory (LT), a theory of motion, gravity and particle properties. We eventually realized that it would be too long and tedious for most readers. We decided that it would be best to write a few articles about some of the more startling discoveries we made while formulating the theory.
Lattice Theory postulates that the universe is discrete and nonlocal; that space, distance and volume are abstract creations of the mind; that we exist in an immense 4-dimensional field (the Lattice) of energetic particles (photons); that the most important constant in physics is the absolute speed of light (c); and that the visible universe is moving in the fourth dimension of the Lattice at c. There is no physical time dimension because such a dimension would make motion impossible and result in a block universe in which nothing happens.
It took us a while but we eventually realized that the SI system of units was flawed because its base unit of mass, the kilogram, is arbitrary and incoherent with c. We were forced to create a new system of units for our purposes. We call it the ‘speed of light’ system or SOL. It is a simple system in that it retains the definition of the meter and the second but introduces a new base unit for mass which we dubbed the c-gram (cg). A familiarity with SOL is necessary in order to understand our electrostatic force equation.
The Speed-of-Light System (SOL)
SOL owes its name to the fact that, except for the meter and the second, it is based entirely on the speed of light. Even its base unit for mass, the c-gram, is based on c via the quantum mass. SOL also has derived units for force, quantum length, quantum duration and quantum mass. We use the term ‘quantum’ to denote discrete fundamental quantities. The prefix c in a SOL symbol denotes a unit that is coherent with the speed of light c. The prefix q means ‘quantum’ and symbolizes a fundamental discrete quantity.
Only the items shown in black in the table above are used in this article. The q-meter is the shortest possible length. The q-second is what we refer to as the quantum instant or the quantum moment. It is the shortest possible duration. The q-gram is the smallest possible mass. The c-Newton is similar to the SI unit for force, the Newton, except that it is defined in terms of the c-gram instead of the kilogram. Note that both the q-meter and the q-gram have equal numerical values even though they represent different units. The physics behind the definition of the SOL units will be explained in a future article on the Lattice theory.
An Astonishing Discovery
Early in our research, while investigating the cause of gravity, we calculated that the c-gram was equal to approximately 3.98 kilograms. We were not satisfied with that number because it depends on the value of the Newtonian gravitational constant G which is notoriously hard to measure on account of the force of gravity being so extremely weak. The accuracy of G measurements is also subject to the gravitational influences of the earth and other bodies in the solar system. But the 3.98 number was incorrect for an even more important reason that had escaped our understanding until fairly recently. We expand on this topic in our article (see link at the end) on the cause of gravity and the nature of dark matter.
Lattice Theory postulates that the quantum mass is the smallest possible mass. Since the universe is discrete, every mass must be an exact whole integer multiple of the quantum mass. While researching the nature of the electrostatic field, we made an astonishing discovery. We discovered that the mass of the electron was equal to exactly 1838 quantum masses or q-grams. Some readers will notice that this number is strikingly close to 1838.68, the published neutron-electron mass ratio. This is not a fluke. There is a direct physical connection between the mass of the electron and that of the more massive nuclear particles, that is, the proton and the neutron. We plan to write about this fascinating topic in an upcoming article.
How we arrived at that number is an interesting story in its own right that we may recount at a future date. Suffice it to say that this was exactly what we needed to accurately convert c-grams into kilograms. The conversion formula is straightforward. First we compute the mass of the electron (Me) in c-grams as follows:
Then we divide the published mass of the electron in kilograms by Me to obtain the conversion factor CF shown below:
CF represents the number of kilograms in 1 c-gram. We can now use it to calculate the quantum mass in kilograms:
Again, according to Lattice theory, the quantum mass (1 qg) is the smallest possible mass in the universe. This is one of the predictions of the theory.
A Liter of Water
A tangential but interesting question here is this: why is CF so close to 4? After all, the kilogram was originally defined as the mass of one liter (1 cubic decimeter) of water at about 4° Celsius. The density of water above freezing rises to a maximum value of 0.9998395 kg/l at about 4° Celsius before dropping. Had it been defined to be exactly 1 kg/l, CF would have been even closer to 4.
Whether or not this was the original intention of the scientists of the Bureau international des poids et mesures in 1799, the choice of 1 cubic decimeter entailed that a kind of physical coherence between mass and length units was automatically established. A random quantity of water, or one not based on the meter, would have broken the coherence. Although the current SI definition of the kilogram is no longer directly tied to water, it still agrees with the original definition to within 40 parts per million. We believe there is a connection here that should be investigated further.
One Equation to Rule them All
While researching electrostatics, we became convinced that mass and charge were directly related. We began to suspect that mass was inherently electric. To substantiate our hypothesis, we only needed to devise a formula with which to calculate the electrostatic force between two elementary charged particles directly from the mass of the electron. And we had to do it without Coulomb’s Law. Was that even possible? We thought so.
In Lattice Theory, the electrostatic field is caused by electric photons that radiate from a massive particle such as an electron or positron. Even neutral particles radiate photons all the time but the positive and negative photons cancel each other out, resulting in no electrostatic force. This neutral and invisible electric field that surrounds all massive bodies is an important component of our theory of gravity and dark matter.
Keep in mind that there is no actual physical field around a charged particle. There are only photons radiating at the speed of light. The field is abstract and nonlocal. This means that each photon acts as if its entire energy is spread evenly on the surface of a sphere expanding at the speed of light. This is a probabilistic distribution. That is to say, the photon has a certain probability of interacting with another particle anywhere on that sphere regardless of how far it is from its source particle. The farther away the photon is from the source, the bigger the sphere and the lower the probability of interaction. The force thus obeys an inverse square law. Also, according to Lattice theory, the electrostatic field is always perfectly centered around the source particle regardless of its motion or location. This nonlocal symmetry is necessary because nature must conserve a universal equilibrium.
Contrary to the claims of quantum physics, electric photons are not virtual but real particles. We have always been deeply suspicious of virtual particles. Where do electric photons come from? They come from the Lattice, of course. As the visible universe moves in the fourth dimension at c, matter particles collide with the electric photons in the Lattice, causing them to begin moving away from the points of collision.
Once we gained a firm understanding of the underlying physics, it did not take us long to derive the equation below directly from the postulates of Lattice Theory.
We thought that our first equation looked overly complicated. After simplification, we reduced it to the one shown below:
Equation 1 will work with any system of units that uses the meter and the second as base units. The constant k in equation 1 is equal to 1. It serves only as a unit conversion coefficient which is needed to match the units on both sides of the equation. It can be redefined for other systems of units:
Fe represents the force between two electrons measured in either c-Newtons or Newtons. Me is the mass (c-grams or kilograms) of an electron. The two particles are separated by distance r in meters. As explained previously, the number 1838 represents the number of elementary masses in an electron: Me/1qg = 1838. It is also the number of electric photons set in motion by an electron (or positron) at every quantum instant or 1 qs, the SOL quantum duration unit that is derived from c. In other words, even though c is not used explicitly in the equation, it is assumed implicitly by Lattice theory.
4πr² is the normal formula for the surface of a sphere. It is used in the denominator because the electrostatic force is inversely proportional to the surface of a sphere with a radius or distance r from the center of the sphere.
The square root of 3 looks rather mysterious and out of place but it serves a vital function in Lattice theory. It is the formula for the diagonal of a cube whose sides are equal to 1. It is used as a correction factor which is needed for two reasons: the universe is discrete (any distance is a discrete integer multiple of the quantum length or 1 qm) and the electrostatic force is mediated by electric photons that operate in 3 dimensions. If the force was 2-dimensional, we would have used the square root of 2 instead. The factor is not needed for the gravitational force because gravity is a fully nonlocal phenomenon and, as such, it is not mediated by any particle. This is explained in our article on the cause of gravity.
Since the electrostatic force on an elementary charged particle can be expressed as F = Ma, we can derive the electrostatic acceleration caused by an elementary charged particle thus:
Take a good look at equation 2. It is a precise formula for the acceleration of an elementary charged particle, such as an electron, caused by the electrostatic field of another elementary charge. What makes it special is that the only variable in it with a physical dimension is the distance r measured in meters for our purposes. We can simplify things further by creating a single constant that combines all the numerical values into one. We call it big K for the time being but we are open to suggestions.
We can now use big K to simplify equation 1 as seen below:
Even though only one Me is used, the equation still calculates the electrostatic force between two electrons or two elementary charges. Let us test equation 4 with a hypothetical example of two electrons separated by a distance of 1 meter. We can use the mass of the electron in kilograms directly to calculate the force in Newtons between two elementary charges thus:
For comparison, let us now use Coulomb’s Law to calculate the same force using the Coulomb’s constant and the published CODATA value of the charge of the electron:
The result from equation 9 is smaller than that of equation 6 by a factor of only 0.9997, which is remarkable given that two entirely different methods were used. While this slight discrepancy can be partially attributed to measurement error, we believe it might also be partly due to systemic errors related to the arbitrary definition of the kilogram in the SI system. Note that our equation eliminates the need to actually measure the electrostatic force between elementary charges, thereby reducing the chance for errors.
Discussion
In this article, we argued that the universe is discrete and that the speed of light is the most important constant in physics. We introduced SOL, a new system of measurement in which the speed of light serves as the basis for the unit of mass (the c-gram) and several fundamental units of physics. We believe that SOL should be adopted by the physics community because the c-gram, unlike the kilogram, is coherent with c. The mass of the electron could be defined as a fixed quantity equal to exactly 1838 quantum masses as seen below:
We presented a new formula to accurately calculate the electrostatic force between two elementary charged particles using only the distance between the two, the mass of the electron and, implicitly, the speed of light.
While equation 1 does not falsify Coulomb’s Law, we claim that it supersedes it. It assumes a discrete universe and strongly implies that mass is electric in nature since the electrostatic force is shown to be directly proportional to the mass of the electron. We conclude that the electric charge of the electron is not a separate property of matter but a direct consequence of its mass.
We believe that these revelations have sweeping consequences for the rest of physics, especially for particle physics. For example, the notion that the electrostatic charge of nuclear particles, such as the proton or the neutron, are caused by unseen quarks with 1/3 and 2/3 charges makes no sense in our model. It is much more likely that those particles are composed of a combination of electrons and positrons. In a future article, we will show how the mass and composition of protons and neutrons are a direct consequence of the mass and composition of the electron. Even the instability and decay time of the free neutron depend on the properties of the electron or positron. The number 1838 that we used in equation 1 is a vital piece of the puzzle.
Since equation 1 is based on Lattice Theory which is itself based on a discrete universe, we are forced conclude that any physics theory that relies explicitly on continuous structures cannot be correct. This includes the theory of General Relativity. It is interesting to note that, shortly before he died, Albert Einstein was beginning to suspect that nature is necessarily discrete and he expressed grave doubts about the validity of continuity and of his own theories. He wrote the following to his friend Besso in 1954:
“I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structures. In that case, nothing remains of my entire castle in the air, gravitation theory included, [and of] the rest of modern physics.” — From Subtle is the Lord by Abraham Pais.
It was too little and too late. The damage was already done and it was catastrophic in our opinion. It retarded progress in humanity’s understanding of the universe by more than a century. It continues to wreak havoc as we write. Hopefully, this article will lead to a renaissance in the field of physics.
Coming Soon
If you liked this article, you will enjoy the one (see link below) we wrote on the cause of gravity and the nature of dark matter. We propose that gravity is due to a violation of the principle of energy conservation caused by the motion of matter in the fourth dimension of the Lattice at c. Nature tries to correct the violation and this is manifested as gravity. We will introduce a new equation to calculate the gravitational force only in terms of mass, distance and the speed of light. It does not use the gravitational constant G. We will offer a plausible explanation for the high uncertainty seen in past measurements of G. Finally, we will propose a surprising candidate for the extra gravity that many in the physics community attribute to dark matter.
Read this article first because much of it is relevant to gravity. Thank you for reading.
