# Mass and Gravity

To recap what we have introduced in earlier articles, quantum-geometry dynamics proposes the existence of only two fundamental particles. The preon(+) is the fundamental particle of matter and the preon(-), the fundamental particle of space. Preons(+) interact with each other through the fundamental attractive force of p-gravity. Preons(-) interact with each other through the fundamental repulsive force of n-gravity. P-gravity has no effect on preons(-) and conversely, n-gravity has no effect on preons(+).

Preons(+) are singularly kinetic, which means they are always in motion. The fundamental unit of motion is the preonic leap, by which a preon(+) leaps from one preon(-) to the next along its trajectory.

P-gravity and n-gravity are intrinsic properties of preons(+) and preons(-) respectively and are conserved even in the transitory state when a preon(+) occupies a preon(-). In the transitory state, the preon(+)-preon(-) couple interacts with other preons(+) or matter and with preons(-) or quantum-geometrical space. Before showing how the combined effects of n-gravity and p-gravity produce what we know as gravity, we need to remember the following:

• The interaction between two preons(+) gives the fundamental unit of n-gravity or ${{g}^{+}}$.
• The interaction between two preons(-) gives the fundamental unit of p-gravity or ${{g}^{-}}$ .
• P-gravity and n-gravity have different relative strengths so that ${{g}^{+}}=k{{g}^{-}}$ and calculations indicate that $k\approx {{10}^{108}}$ .
• The mass of any object is the number of bound preons(+) that compose it.

Since preon(+) can only exist in transitory state, the gravitational interaction between two preon(-)/preon(+) pairs, which we’ll call preons for simplicity, must take into account both p-gravity and n-gravity interactions. Since we are dealing with discrete units, we simply must count the number of p-gravity interactions and n-gravity interactions and find the difference.

The number p-gravity interaction between two preons(+) is equal to 1. Since all preons(-) between the two preons interact with each other, then, if there are $d$ preons(-) between them, simple combinatorics will indicate that there are $\frac{{{d}^{2}}+d}{2}$ n-gravity interactions. Hence, the gravitation interaction between two preons is:

$G\left( a;b \right)={{g}^{+}}-\frac{{{d}^{2}}+d}{2}{{g}^{-}}$or, since ${{g}^{+}}=k{{g}^{-}}$, we can simply we can express the relationship in ${{g}^{-}}$ units and write $G\left( a;b \right)=k-\frac{{{d}^{2}}+d}{2}$ . Note that from here on, ${{g}^{-}}$ will served as the QGD gravity unit.

Gravitational interactions between two structures follow the same principle. For two structures containing ${{m}_{a}}$ and ${{m}_{b}}$ preons(+) respectively and since all the preons(+) of structure $a$ interact with all preons(+) of structure $b$ then there is ${{m}_{a}}{{m}_{b}}$ p-gravity interactions. And since there are $\frac{{{d}^{2}}+d}{2}$ n-gravity interactions between any two preons(+) and there are ${{m}_{a}}{{m}_{b}}$ such pairs, then there must be ${{m}_{a}}{{m}_{b}}\frac{{{d}^{2}}+d}{2}$n-gravity interactions. Thus, the gravitational interaction between two structures

$G\left( a;b \right)=k{{m}_{a}}{{m}_{b}}-\frac{{{m}_{a}}{{m}_{b}}\left( {{d}^{2}}+d \right)}{2}$ or more simply

$\displaystyle G\left( a;b \right)={{m}_{a}}{{m}_{b}}(k-\frac{{{d}^{2}}+d}{2})$.

This last equation describes how gravity emerges naturally from the interaction between matter at the fundamental scale (measured in preons(+)) and space (the distance measured in preons(-) or preonic leaps). The QGD equation for gravitational interactions provides a fundamental explanation of the Newtonian equation $F=\frac{G{{M}_{1}}{{M}_{2}}}{{{d}^{2}}}$ or, in QGD units $F=\frac{\alpha {{m}_{a}}{{m}_{b}}}{{{d}^{2}}}$ where ${{m}_{a}}$ and ${{m}_{b}}$ represent the masses of two bodies (in preons(+), $d$ the distance between them and$\alpha$ here represents the gravitational constant. Note that $\alpha$ is actually not a constant but varies more or less significantly depending on how narrow a scale we define. Both QGD and Newtonian equations describe the magnitude of gravity between two bodies as being proportional to the product of their masses. However, they differ in three important ways.

The first is that Newtonian gravity is a fundamental force whence the QGD equation implies that gravity is the resultant effect of the two fundamental forces.

The second is that while the Newtonian gravity implies that space is continuous and that it is a passive medium, according to QGD, space is discrete (quantum-geometrical) and is generated by the n-gravity field of preons(-). Therefore preons(-) dynamically participate in the gravitational interactions between bodies.

The third difference is that gravity in the Newtonian equation is strictly positive. The QGD equation also allows for gravity to have a null value when $~k=\frac{{{d}^{2}}+d}{2}$ or a negative value when $~k<\frac{{{d}^{2}}+d}{2}$.

But even considering the differences we outlined, Newton’ Law of Universal Gravitation can be derived from the QGD equation. The QGD equation implies that the magnitude of the gravitational interaction is proportional to the ratio between of the magnitude of the p-gravity interactions over the magnitude of the n-gravity interactions. Thus the Newtonian equation provides an approximation of the gravitational effect described by the QGD equation for distances such that $~k>\frac{{{d}^{2}}+d}{2}$ and $~k\approx \frac{{{d}^{2}}+d}{2}$ that is, at a scale where p-gravity is greater but in near equilibrium with n-gravity.

The QGD model also provides an explanation of the behaviour of gravity at the Newtonian scale. For instance, we can show that the change in momentum of an object $b$ due to gravitational interaction with an object $a$ between two positions in quantum-geometrical space is exactly equal to the difference in gravity between the two positions. That is: $\Delta {{P}_{b}}={G}'\left( a;b \right)-G\left( a;b \right)$ where ${G}'\left( a;b \right)$ and $G\left( a;b \right)$ are respectively the gravitational interactions at second and first position.

And since the speed of an object $b$ is equal to the ratio of its momentum over its mass or ${{v}_{b}}=\frac{{{P}_{b}}}{{{m}_{b}}}$
where ${{P}_{b}}=\left\| \sum\limits_{i=1}^{{{m}_{b}}}{{{{\vec{c}}}_{i}}} \right\|$ and ${{\vec{c}}_{i}}$ is the momentum vector of a preon(+) component of $b$, then its gravitational acceleration is:

$\Delta {{v}_{b}}=\frac{1}{{{m}_{b}}}\left( {G}'\left( a;b \right)-G\left( a;b \right) \right)$. In the same way we have $\Delta {{v}_{b}}=\frac{1}{{{m}_{a}}}\left( {G}'\left( a;b \right)-G\left( a;b \right) \right)$.

### An Example:

If, for example, we assume that $a$ is the Earth and $b$ is an object in freefall, we have

$\Delta {{v}_{b}}=\frac{1}{{{m}_{b}}}\left( {G}'\left( a;b \right)-G\left( a;b \right) \right)$. Since $G\left( a;b \right)={{m}_{a}}{{m}_{b}}\left( k-\frac{{{d}^{2}}+d}{2} \right)$ then

$\Delta {{v}_{b}}=\frac{1}{{{m}_{b}}}\left( {{m}_{a}}{{m}_{b}}\left( k-\frac{{{{{d}'}}^{2}}+{d}'}{2} \right)-{{m}_{a}}{{m}_{b}}\left( k-\frac{{{d}^{2}}+d}{2} \right) \right)$ and

$\Delta {{v}_{b}}={{m}_{a}}\left( \left( k-\frac{{{{{d}'}}^{2}}+{d}'}{2} \right)-\left( k-\frac{{{d}^{2}}+d}{2} \right) \right)={{m}_{a}}\left( \frac{{{d}^{2}}+d}{2}-\frac{{{{{d}'}}^{2}}+{d}'}{2} \right)$

This last equation shows that the gravitational acceleration of $b$ towards Earth is independent of its mass. This is consistent with the observation that free falling objects with different masses accelerate at the same rate towards the Earth. The acceleration remains constant as long as the mass of the Earth does not change but, as this last equation suggests, as its mass changes, so does the acceleration of objects toward it. Of course, the changes in the mass of the Earth are negligible at our scale and their effect on the acceleration of objects submitted to its gravity is so small that acceleration is nearly constant.

It is important to note that the equation for the gravitational acceleration of a body is a function of distance and mass, but not of time. This is in agreement with the idea that time is not a physical aspect of reality but only a relational concept.

### Gravity at other Scales

The QGD gravity equation can be applied to the fundamental scale where it would indicate gravitational interactions up to one hundred orders of magnitude greater than found at the Newtonian scale. At the nuclear scale, the equation would describe forces about sixty orders of magnitude greater than that of the Newtonian scale. Thus the QGD gravitational interaction equation describes forces at scales up to the Newtonian scale, but can it be applied to the cosmological scale?

If the QGD equation does apply to the cosmological scale, then it would make sense that what we understand as dark energy corresponds to distances for which $~k<\frac{{{d}^{2}}+d}{2}$. At such distances, gravitational interactions become negative; hence induce negative acceleration between the interacting bodies. The bodies would accelerate away from each other.

Also, if the QGD cosmological model is correct, that is, that the universe evolved from an isotropic state in which all preons(+) where free and only later bounded in more progressively more massive and complex structures. Then it would make sense that the preons(+) that are still unbound, though they interact too weakly to be detected, would collectively have a great mass. The free preons(+) in sufficiently large number would have the effect we attribute to dark matter. If, as QGD suggests, dark matter is made of preons(+), then most preons(+) in the universe are still unbound.

Note : The QGD model is consistent with what we call the cosmic microwave background radiation. If at the origin the universe in an isotropic state where preons(+) were unbound and evenly distributed in quantum-geometrical space, since the first structures they would form would be photons, then these photons formations would also be isotropic. This would explain not only the formation but the isotropy of the CMBR.

### Conclusion and prediction

As we can see, the QGD model is remarkably simple. Preons(+) being the fundamental units of matter, the mass of an particle or structure is simply the number of preons(+) it contains. Mass, that is, a collections of bounded preons(+), reveals itself through the two intrinsic properties of preons(+); p-gravity and its energy (the relation between mass and energy is discussed here). And because the properties of preons(+) are intrinsic, the QGD model does not required external or complicated mechanisms to attribute mass or to explain gravity or any other interactions for that matter.

For instance, using the QGD gravitational equation we find that, at the most fundamental scale, the forces binding preons(+)are up to ${{10}^{100}}$ times greater than gravity (the gravitational interaction at the Newtonian scale) and at the nuclear scale, the force binding nucleons can be up to ${{10}^{60}}$ times gravity. And, as we have suggested earlier in this article, the model is also consistent with observations of dark matter and dark energy effects.

But a new theory needs to do more than describe and explain, it needs to make predictions original to it. I would even say that a theory is only as good as the predictions it makes, so I will conclude this article with the following prediction.

Because p-gravity and n-gravity at the fundamental scale are intrinsic and because of the quantum-geometrical structure of space, QGD proposes that gravity does not propagate. All propagation require the motion of preons(+) or particles all of which have a maximum speed equal to c. Interactions on the other hand do not require the motion or displacement of preons(+) or particles and are thus not limited by the structure of quantum-geometrical space. Interactions are forces that connect preons. They simply exist intrinsically. Therefore, QGD predicts that variations in the mass of an object or region anywhere in the universe should instantaneously felt here. Hence, an instrument that could measure the gravitational interaction with an object affected by an event that changes its mass would perceive that change instantly.

This prediction may be tested by observing solar activity. Instruments with sufficient sensitivity to gravitational interactions should detect solar flares (events during which the Sun ejects large quantities of matter into space) approximately 8 minutes before we see them.

It is important here to note that in within the framework of quantum-geometry dynamics, it makes no sense to talk about speed of gravity. The notion of speed implies displacement or propagation; none of which taking place for interactions according to QGD.

Also, the reader would be correct in assuming that the QGD model implies that although the speed at which information can travel is limited by the speed of light, by modulating mass, hence gravitational interaction, information could be instantly communicated between any two points in the universe regardless of the distance that separates them.

For more detailed explanations, see Introduction to Quantum-Geometry Dynamics.