Note: The following article assumes that the reader has read part 1 and part 2 of this series on QGD optics.

The reason this section is given the title Space-Matter-Light Interactions and not the more common Matter-Light Interactions is that, according to QGD, quantum-geometrical space interacts dynamically with matter and light in all optical phenomena. In this third part of the series of articles on optics, we will use the principles we have introduced in part 1 and part 2 to describe and explain the phenomena of light absorption, light reflection and the photoelectric effect.

We will also examine the relation the fundamental forces that govern the motion of bodies which determine how they interact with light. We will therefore reinterpret Newtonian laws of motion and show how they are founded in fundamental reality. But first, we need to look at QGD’s definition of a concept central to all dynamics, that is, the notion of speed.

**QGD definition of Speed
**

The speed of an object is defined classically as a function of distance and time. Those who are familiar with the principles of quantum-geometry dynamics know that it considers time to be a purely relational concept (see article here); one which allows us to associate events to natural periodic systems (e.g. movement of celestial objects, emission of an atom) or artificial periodic systems which, when combined with a counting mechanism, constitute what we call clocks. Thus quantum-geometry dynamics proposes that time is not a physical aspect of reality and for this reason defines speed without this concept.

When we measure the speed of an object, we start counting the number of recurrences of a particular state of a periodic reference system when the object is at a chosen initial point along its trajectory and stop counting when it arrives at a second, distinct point. The length of the trajectory between the points divided by the number of recurrences counted (the ticks of a clock) gives what we understand as the speed of the object. This method of measuring speed which compares two quantities has so far defined speed for us, but what allows us to assume that the number of ticks of a clock is a quantity that corresponds to a physical aspect reality?

The fact is: clocks do not measure time. They never have. Clocks are counting devices. What they count is the recurrences of a particular physical state of its inner mechanism, which itself is causally related to all preceding and successive states. This means that there are identifiable physical mechanisms that causally link a clock’s different states. Unlike spatial measuring devices, which relate to the physical aspect of reality we call space, there is no relation whatsoever between clocks and a physical aspects of reality. Clock count the ticks of the clock, nothing else.

This assumption that time is physical is reinforced by the mathematical models we use which represent space and time as geometrical dimensions but without making distinctions between what exist only as a representation, that is, what is pure concept, from a representation of a truly physical aspect of reality. The assumption that time is physical can be singled out as the most misleading idea in the history physics; one that lead to paradoxes, singularities, infinities, all of which create severe inconsistencies in physical theories if not their complete collapse. These problems alone justify abandoning the time-as-physical assumption and even the concept of time itself. But how can we abandon the concept of time when so much of our physics theories are based on it? How, for instance, does one define the essential notion of speed without time?

Using the ideas introduced here we can define timeless speed as follow:

**The speed a body **** is the ratio of its momentum over its mass or **** where ****
**and is the kinetic energy vector of a component of whose magnitude is fundamental and equal to . Therefore, the speed of an object is defined using two physical quantities; the magnitude of the vector sum of the kinetic energy vectors of its component and its number of, its mass. We now have a working definition of speed that is timeless, observer independent and natural.

**Special cases:
**

As we have explained early in this book, the energy of any particle or structure is given by and the momentum by . In the special cases when the trajectories of the component are parallel, so that . In words, the momentum and energy of such particles or structures are equal quantities (but not equal qualities).

This is evident for a single

where, since , we have .

Similarly, if is a photon or a neutrino, we have . Also, according to the QGD definition of speed, , we have . This explains, amongst other things, the constancy of the speed of light without invoking time or the mechanism of time dilation.

The equality also holds for any structure whose component have trajectories are parallel regardless of its mass (see here). Such particles include the photon and the neutrino, but theoretically, any particle or structure can achieve a speed equal to if is subjected to strong enough interactions. And since the maximum momentum any object can have is equal to , its energy, the maximum speed is .

**Space-Matter Interactions
**

One of the fundamental assumptions of quantum-geometry dynamics is that space is not continuous, but discrete, made of fundamental particles we call and that spatial dimensions emerge from the repulsive interactions between them (n-gravity). This has already been discussed in detail in previous articles (see here. here and here).

In previous articles, we have seen that the gravitational interaction between two particles or material structures is described by the formula where and are respectively the masses of a bodies and measured in , is the proportionality constant relating between n-gravity and p-gravity and is the number of between and ; what we traditionally call distance. This formula accounts for the contribution of the two fundamental forces that make up gravity; that is, p-gravity and n-gravity. This is made more apparent when we know that the formula is the simplification of where the components and respectively represents the magnitudes of the p-gravity force and the n-gravity force between and .

But while we have so far been using the formula to calculate the gravitational interaction between two material particles or structure, it can be used to calculate the interaction between matter and space itself. We know that p-gravity only interacts between and that interaction is positive (attractive). But must exist in quantum-geometrical space, hence they exist as pairs. The part of the pair interacts with the which form quantum-geometrical space through n-gravity. In effect, because it has an effect opposite of p-gravity, we can think of the mass of as being negative mass so that, for the component , the negative sign can be interpreted as attributing a different meaning to the values and which now represent the number of and contain respectively. And since the is the mass of , we can by analogy interpret as being its negative masses. It follows that all particles and material structures have both positive and negative masses.

From the above, we understand that in the p-gravity component of the formula we must use the positive masses of, the number of they each contain. So, assuming that the region contains no , then and . For the second component of the formula, and represent the negative masses of and , that is, the number of pairing with or and the number of in the region or . It follows that the force acting between an object and an empty region of quantum-geometrical space is given by . This explains that, for an object to change direction, it must overcome the force exerted by space itself. Resolving the formula for a change equal to one unit of distance in one given direction, that is where and , the n-gravity that must be overcome by is .

*Note about the Distinction between Mathematical and Physical Meanings
*

*QGD shows that mathematical symbols also have specific physical meaning. The negative sign in the formula for gravitational formula implies that the masses following it are negative masses. The equal sign in the formula derived from the axiom set of QGD does not represent the equivalence between mass and energy, but proportionality relation between them.
*

*The same holds true for mathematical operations. QGD allows only for integer values of discrete quantities. That means that when we refer to division we mean the Euclidean division since, as we will be exemplified below, the quotient and remainder of the Euclidean division take different physical meaning.
*

*The distinction between the mathematical and physical meanings is essential, not only for quantum-geometry dynamics, but for any theory of physics. In fact, much if not all of the problems with the interpretations of mathematical models of physical phenomena come from having lacked to make the necessary distinction. *

**Laws of Motion and Optics
**

At this point some readers may wonder when this article will get on the subject of optics. I’d like to reassure them that we haven’t drifted from QGD optics and that this article is rigorously on course.

The introduction of a new timeless definition of speed and an understanding of the interaction between material objects and between matter and space are necessary prerequisites to a quantum-geometrical description of the phenomenon of absorption and reflection of light and the photoelectric effect. Also essential is the following discussion about the laws of motion (which are given quantum-geometrical explanations).

**First Law of Motion
**

*If an object experiences no net force, then its velocity is constant: the object is either at rest (if its velocity is zero), or it moves in a straight line with constant speed (if its velocity is nonzero). *

In quantum-geometrical terms the first law becomes:

*If the magnitude of the vector sum of all the interactions with object is null, then its momentum, hence its speed, will be constant. Expressed in mathematical terms the first law of motion express becomes:
*

This is a state in which that all external forces acting on cancel each other. These forces include the interactions with other particles and material structures, as described by the QGD gravity formula, as well as the effect of quantum-geometrical space on it. Thus an object moving at a constant velocity may be understood as one where the external forces acting on it are in equilibrium.

**Second Law of Motion
**

*The acceleration of a body is parallel and directly proportional to the net force acting on the body, is in the direction of the net force, and is inversely proportional to the mass m of the body. *

Expressed in QGD terms, Newton’s second law of motion simply says that if then .

For gravitational interactions, the second law of motion can expressed as .

To illustrate we’ll examine the simplest case. That is, when all interactions acting on two objects cancel each other except for the interaction between them . In this simple case. Since all QGD units are integers (and natural), we know that changes in momentum from interactions will also be integer; that is where .

This is consistent with QGD when you consider that for a body of mass to change momentum in a particular direction, each of its component must overcome an integer part of the n-gravity force exerted on it, as we have seen earlier.

Fundamentally, all motion imply that the component of an object leap from to so a fractional value would mean that could leap in between . That, as quantum-geometrical space implies, is not possible since nothing except the n-gravity field that keeps them apart and dimensionalize space and p-gravity though which matter interacts can exist between .

**Second Law and Optical Kinetics
**

Since the QGD gravitational interaction formula can only have integer value, what is the outcome of an event in which the momentum a particle colliding with a body would result in a non-integer change in momentum?

As we have seen in part 1 and part 2 of this series on QGD optics, if a photon is absorbed by an object then . What this law implies is that only that part of the photon which obeys the formula is absorbed. The question is then: What happens when ? We’ll look at two possible cases: the first is where and and the second where and .

**Reflection and the Photoelectric Effect
**

In the case where and , the momentum of the photon is less than the minimum possible change in the momentum of . In this case of the proverbial unstoppable force meeting an immovable object, the principle that comes into play is that of conservation of momentum of the system consisting of and . If the photon cannot be absorbed then it can do two things. Pass through if it is transparent (this is discussed here) or, if is not transparent, and the momentum of the system is to be conserved, then must be reflected.

As we have seen earlier, QGD predicts that the which form quantum-geometrical space act on through n-gravity interactions which force is in direct opposition to the direction of the momentum vector of the photon (see figure).

Here we see that we can break down the momentum vector of the incident photon into two components. The component in blue is in opposition to n-gravity interaction between quantum-geometrical space and the object. This component is reverted. The component in purple is not opposition and is thus conserved. The path of the reflected photon, labelled , is as shown. This explains why the angle of incidence is the same as the angle of reflection.

But this raises the question as to whether the incident and reflected photons are the same or distinct particles. Though it is possible that the incident and reflected photons are the same particle, a mechanism by which would absorb and emit a distinct particle to conserve momentum is more consistent with the principles quantum-geometry dynamics. It is also consistent with the well-known phenomenon we call the photoelectric effect.

Now, in the case where and , the momentum of is greater than the minimum allowable change in momentum of , but here the ratio being a non-integer, can only absorb by emitting a particle such that where is the remainder of the Euclidian division . It is here obvious here that , the momentum of , if this particle**
**is a photon, is also equal to its energy. The reflected photon will have a lower momentum and then the incident photon (which we perceive has having a different color). But can be a particle other than a photon as long as its momentum is equal to.

For instance, instead of a photon can emit an electron. Though the emitted electron from the photoelectric effect may have a much greater mass than that of the incident photon which caused its emission, it possesses the same momentum.

**A Note on Possible Applications to Optical Computing
**

Using the notions we have introduced, we see that the optical properties of a transparent structure can be changed predictably by bombarding it with photons having momentum that is equal to or greater than the structure’s mass. Such photons will be absorbed by the structure and will change its mass which in turn will change the allowed value for the momentums of incident photons, thus allowing photons that pass through it to do so and vice versa. QGD optics may be applied to create logical gates using only optical components making the theoretical optical transistor a possibility.

**To Conclude this Series on QGD Optics
**

We have seen in this series how the light-matter interactions can only be understood when taking into account the effect of quantum-geometrical space on matter and light. And once we accept that light, like all material structures, is made of , the fundamental particle of matter, light-matter interactions are really matter-space interactions. Thus optical phenomena are special cases of matter-space interactions and as such are governed by the same general laws that govern the motion of all matter.

Contrary to classical space, quantum-geometrical space is not a passive medium in which physical events and interactions occur, but an active component in all events and interactions. The effects of quantum-geometrical space are as tangible as the effects of matter.

Finally, it is important to remember that the examples given in the QGD Optics series of articles illustrate specific mechanisms which in nature do not act in isolation. The photons that compose the beam of light that hits an object can be partly absorbed and/or reflected and/or refracted and/or diffracted or all at once depending the properties of the matter they interact with.

The mechanisms we described also explain how the mass of photons change as they travel from a distant source. Photons emitted by a star, for example, will lose mass which equates into loss of momentum (or, since for photons momentum and energy are equal, less energy). This well-known and observed phenomenon is called the redshift effect (though QGD provides a different interpretation of its cause). The variation in the mass of photons provides some indication of the distance from the source (the larger distance it travels the more likely they are to interact with interstellar matter), but though there is a correlation between the distance and the amplitude of the redshift effect, the correspondence is not necessarily proportional. As we will see in a future article (and the upcoming 2^{nd} edition of Introduction to Quantum-Geometry Dynamics), the light from sources at equal distance from Earth can have greatly different redshifts.