# Archive for June, 2013

## On Measuring the Immeasurable

Key to our understanding of fundamental reality is our ability to measure the physical properties of objects such as mass, energy, speed, momentum, as well as quantify the forces acting between them. Measurement experiments are based on how we model certain fundamental aspects of reality, but how do we know if an such aspects truly is fundamental? And if not, what are we measuring when conducting a measurement experiment designed to quantify such an aspect? Can we even measure aspects of reality that are truly fundamental?

To answer these questions, we will look at one of the most important measurement in physics; that of the speed of light. The constant $c$ which represents the speed of light is critical to physics theories. It is therefore no surprise that experiments have been perfected so as to make as precise measurements of $c$ as technology allows. But do these experiments really measure the speed of light? And if not, what are they measuring?

Speed is classically defined as the ratio of the distance of displacement over time or $\frac{d}{t}$ where $d$ is the distance an object will travel during a time interval $t$ , both of which expressed in standardized but arbitrarily defined units. But QGD considers time to be non-physical and so offers a definition of speed that does not make use of the concept of time (see this article for a detailed discussion). QGD defines the speed of a body $a$ as the ratio of its momentum over its mass or $\displaystyle \frac{{{P}_{a}}}{{{m}_{a}}}$ with the understanding that ${{m}_{a}}$ is the number of preons(+) contained by $a$ and that its momentum is defined as the resultant of the momentum vectors of each of its component preons(+) or $\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|$ where $\left\| {{{\vec{c}}}_{i}} \right\|=c$ all of which are expressed in fundamental units which by definition are non-arbitrary and natural.

The speed of light corresponds to the speed of the photons that compose it. So using QGD’s definition we find that the speed ${{v}_{b}}$ of a photon $b$ is given by ${{v}_{b}}=\frac{\left\| \sum\limits_{i=1}^{{{m}_{b}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{b}}}$ and since all the momentum vectors of the component preons(+) of $b$ have the same trajectories, $\displaystyle \left\| \sum\limits_{i=1}^{{{m}_{b}}}{{{{\vec{c}}}_{i}}} \right\|=\sum\limits_{i=1}^{{{m}_{b}}}{\left\| {{{\vec{c}}}_{i}} \right\|}={{m}_{b}}c$ so that ${{v}_{b}}=\frac{{{m}_{b}}c}{{{m}_{b}}}=c$ . Note that $\displaystyle \sum\limits_{i=1}^{{{m}_{b}}}{\left\| {{{\vec{c}}}_{i}} \right\|}$ is the energy of $b$ so that for photons, energy and momentum have the same numerical value (see this article for detailed explanation).

It follows that light speed measurement experiments are designed to measure the “classical” speed of light (for example, see the Fizeau-Foucault apparatus) and so must result in measurements of $c$ that differ from the fundamental speed of light as expressed by the QGD equation.

What light speed measurement experiments do is compare the distance a reference object travelling at a known classical speed (time dependant speed) travels while light travels a known distance. Then using the classical definition speed, dividing the distance travelled by the reference object by its known speed gives the time that elapsed during which light travelled the known distance. Then, by dividing the reference distance travelled by light by the time elapsed, we get the classical speed of light. So ultimately, what such light measurements experiments provide are not measurements of the fundamental speed light, but the speed of light relative to the speed of a reference object.

Though these experiments cannot measure the fundamental speed of light (which from here on we’ll refer to as the absolute speed of light), dividing their measurement of speed of light by the speed of the reference object eliminates the time variable and gives us the proper ratio of the absolute speed light over the absolute speed of the reference object. That is, such experiments are useful in that we get a correct estimate of the ratio $\frac{c}{{{v}_{a}}}$ .

But although classical speed of light measurement experiments can provide a correct value of $\frac{{{v}_{a}}}{c}$ no experiment can ever the measure absolute speed of light or that of any other object for that matter. Since the speed of light is relative to the speed of the reference object, and vice versa, there is no way to isolate $c$ or ${{v}_{a}}$ from the ratio $\frac{{{v}_{a}}}{c}$ so that neither can be known. But what if we designed an experiment based, not on the classical definition of speed, but on QGD’s definition; that is, design an experiment which aims to measure to absolute speed of light?

Since the absolute speed of an object $a$ can be understood as its speed against quantum-geometrical space, it ${{v}_{a}}$ can be calculated by comparing the distance it travels with the distance traveled by reference free preon(+) or a photon $b$ using the relation $\frac{{{d}_{a}}}{{{d}_{b}}}=\frac{{{v}_{a}}}{c}$ so that $\frac{{{d}_{a}}}{{{d}_{b}}}c={{v}_{a}}$ . The problem here is that we can’t know ${{v}_{a}}$ without first knowing $c$ which requires that we measure the speed of a preon(+) or a photon. Now if $a$ is a preon(+) or photon then ${{d}_{a}}={{d}_{b}}$ so we get $\frac{{{d}_{b}}}{{{d}_{b}}}c=c$ or $c=c$ . Okay, we’re stating the obvious here, but what is not so obvious is what this means for experimental physics. That is, any experiment that attempt to measure the speed of an object against quantum-geometrical space will always come down to the tautology that the speed of light is equal to the speed of light. Hence, motion against quantum-geometrical space (or any fixed background) cannot be detected or measured (this explains why the Michelson-Morley experiment and similar experiments failed in their attempts to measure the motion of the Earth against the aether).

Now, you would be right to ask: if it is impossible to measure the absolute speed of an object, hence impossible to detect quantum-geometrical space, how can we prove it exists? How can we prove the existence of preons(-), which form quantum-geometrical space? How can we prove the existence of n-gravity which is carried by preons(-) and which with p-gravity produces the effect of gravity? Ultimately, how can we know quantum-geometry dynamics is a valid theory when we can’t test one of its defining axioms?

Though it is true that we will never be able to detect quantum-geometrical space, the assumption of its existence allows QGD to provide descriptions, explanations of observable phenomenon but, most importantly, to make unique predictions that can be tested at observable scales of reality, many of which have been described in earlier articles.

## Other Immeasurables and the Experimental Method

We have shown that all experiments that attempt to measure the absolute speed of light will be tautological and since knowing the absolute speed of light is essential to know the absolute speed of any object, we find that it is impossible to measure their absolute speed as well. But also tautological are experiments that will attempt to measure other fundamental aspects of reality. For instance, we know that the absolute mass of an object is the number of preons(+) it contains, but an experiment which will attempt to measure it will require that we know the mass of mass of a preon(+). And what is the mass of a preons(+)? The mass of a preon(+) is equal to the mass of a preon(+).

Similarly, it can be shown that experiments which aim to absolutely measure other aspects of reality such as the absolute distance between two preons(-), the absolute magnitude of gravitational interaction, etc., all are tautological. From the above discussion we can draw the following theorem.

Fundamental reality is the absolute limit of the experimental method.

What the theorem implies is that if something is truly fundamental it is not directly accessible experimentally. We have shown earlier that preons(-), hence quantum-geometrical space, cannot be detected. The same can be said about the fundamental unit of matter and second of only two fundamental particles assumed by QGD; the preon(+).

Preons(+) interact too weakly with matter to ever be detect directly, but the assumption of its existence explains perfectly the formation of the cosmic microwave background radiation, which photons its formed. The presence of preons(+) and how they interact with charged particles explain the electromagnetic effect. And though preon(+) gravitationally interact too weakly to be detected, the collective effect of free preons(+) contained in large regions of space can affect the motion of the largest objects in the Universe (see the Dark Matter Effect).

Not only are the effects of preons(+) observable at all scales of reality but by designing experiments that replicate at a small scale the formation of the CMBR we can indirectly prove their existence. Quantum-geometrical space contains a great number of free preons(+) and free preons(+), when they come in close enough proximity, will form photons. So all that would be needed is hollow sphere shielded exterior radiation which interior is a vacuum and which inner walls are lined with photo sensors. If QGD is correct, then free preons(+) within the apparent vacuum of the sphere will form photons that can be detected but which presence cannot be explained in any other way.

## Gravity and the Speed of Light

Another immeasurable is the “speed” of gravity. Since gravity is predicted to be instantaneous, we can’t really talk about speed. QGD proposes that all objects in the Universe are gravitationally interacting with only the magnitude in the interactions varying in accordance to the gravitational interaction equation. Changes in the mass of two objects or changes in distance will instantly affect the magnitude of the gravitational interaction between them. Instantaneity implies that there is no propagation and that gravity has no speed. In other words, gravitational interactions simply exist. Since gravity has no speed, QGD predicts that any experiment designed to measure the speed of propagation of gravity is bound to fail.

But though we can’t measure instantaneity, we can design an experiment which takes advantage of the fact that we can measure variations in the gravitational interaction to prove instantaneity.

The experiment would require two spheres, $a$ and $b$ , in space, having large enough mass for the gravitational interaction between them to be measurable.

Sphere $a$ would contain a powerful explosive, a detonator and an accelerometer. Sphere $b$ would carry an accelerometer calibrated to match that of the sphere $a$ and a data recording device. The experiment would measure the acceleration of the spheres towards each other in accordance to QGD’s law of gravity. The detonator, linked to the accelerometer of sphere $a$ would be set so that when it reaches a speed ${{v}_{a}}$ (which speed can be used to calculate the gravity and distance between the spheres), it would detonate the explosive. Note that the structure of sphere $a$ would need to allow for a non-symmetrical scattering of its fragments. There two possible outcomes to this experiment:

If the gravitational interaction is instantaneous, then the rate of acceleration of the second sphere would change instantaneously when it reaches the exact speed at which the detonation of first sphere $a$ occurs. So if ${{v}_{a}}$ is the speed at which the detonation of sphere $a$ is set to explode and ${{v}_{b}}$ is the speed it reached when the rate of acceleration of $b$ changes, then ${{v}_{b}}-{{v}_{a}}=0$ .

But if, contrary to QGD’s prediction, gravity did propagate, then would find that ${{v}_{b}}-{{v}_{a}}>0$ .

This is an example of a unique prediction that is a consequence of the existence of quantum-geometrical space.

One of the reasons the Michelson-Morley experiment was doomed to fail to detect the motion of the Earth relative to the aether is that all experiments designed to measure the absolute motion of an object are tautological. The other reason is that the possibility of detection of the motion of the Earth against the aether was based on predictions made using the wave-particle model of light.

Because of their resemblance with wave interference patterns observed at the surface of a body of water when waves produced by different sources intersect, it was assumed that fringe patterns produced during double-slit experiments implied that light possessed wave-like properties. The Michelson-Morley’s experiment was designed to observe of the specific interference patterns the wave model of light predicted the experiment, if successful, would produce. So though the Michelson-Morley experiment was designed to test of the aether theory, it may correctly be seen as a test of the wave-particle duality. So the failure to observe the predicted interference patterns may be taken as a refutation of the wave-particle duality.

The null result of the Michelson-Morley experiment is consistent with QGD’s explanation that the fringe patterns observed during double-slit experiments and other diffraction experiments are not caused by wave interference, but are scattering patterns resulting from the interaction between the corpuscular component of light, quantum-geometrical space, and the material structure of the apparatus, principally, the material in which the slit are cut (see this article for detailed discussion).

No experiments are irrelevant in that they all inform us about reality, but understanding what is measurable and what is not may help guide our efforts. Even tautological experiments are something to say about reality but to fully understand what they are saying we need to know when they are tautological.

## Determining Positions and Trajectories of Gravitationally Interacting Objects

The laws of motion we have explained in earlier articles can be used to calculate and predict the position, speed and trajectory of an object from any initial state.

Let’s consider the simple case of an object $b$ interacting gravitationally with an object $a$. We know from a previous article that for any object, changes in momentum must be multiple integers of its mass. That is, $\Delta {{P}_{b}}=x{{m}_{_{b}}}$ where $x\in {{N}^{+}}$. This implies that changes in momentum of an object $b$ due to gravitational interactions occur at positions that are at distances from the center of gravity of $a$ such that $\left\| {{{\vec{P}}}_{b}}+\vec{G}\left( a;b \right) \right\|={{P}_{b}}+x{{m}_{b}}$. We will call these positions transitional positions.

The spacing between the transitional positions along the trajectory of $b$ depends on its mass. The greater ${{m}_{b}}$, the closer the transitory positions will be. Based on the QGD gravitational interaction equation, $G\left( a;b \right)={{m}_{a}}{{m}_{b}}\left( k-\frac{{{d}^{2}}+d}{2} \right)$, we see that the spacing between the transitional positions is very nearly proportional to the square of the distance between $b$ and $a$ (see figure below).

Gravity induced changes in momentum occur at transitional positions are always equal to ${{m}_{b}}$ which corresponds to changes in speed that are equal to $\frac{{{P}_{b}}+{{m}_{b}}}{{{m}_{b}}}$ or $\frac{{{P}_{b}}}{{{m}_{b}}}+1$ . It follows that the speed of $b$ between two subsequent transitional positions ${{p}_{i}}$ and ${{p}_{i+1}}$ is constant and equal to $\frac{\left\| {{{\vec{P}}}_{\left( b/i \right)}} \right\|}{{{m}_{b}}}$.

The momentum vector providing both direction and the speed until it reaches the next transitional position, the previous or subsequent locations of $b$ can be calculated from an arbitrarily chosen initial position ${{p}_{i}}$. It is important to remember that classical time being a notion that has no physical meaning the distance $b$ travels is relative not to the mathematical dimension of time but relative to a chosen number of preon(+) leaps of any given preon(+) chosen as reference. The time reference is therefore replaced by a distance reference. For example, we do not talk about the distance an object $b$ travels over $n$ units of time, but rather the distance it travels will over $l$ preon(+) leaps. That is, $d=\frac{{{v}_{b}}}{c}l$ where $d$ is the distance travelled, ${{v}_{b}}$ the speed of$b$, $l$ the number of leaps and $c$the momentum of preon(+), which is also equal to its speed. Note that the although the reference we have used here plays a role similar to that of the classical notion of time has played in physics, it differs from it in that is based on a fundamental aspect of physical reality; the preon(+) leap which is the fundamental unit of distance. Thus, a fourth dimension, even a conceptual one, is unnecessary. Reality can be fully described without the concept of time or the purely mathematical dimension of time.

### Application at the Newtonian Scale

As we have seen above, the QGD laws of motion allows us to know the momentum, speed, direction at any position along the trajectory of a body. To better illustrate the law of motion, we will consider the classic example of a body for which $\displaystyle {{\vec{P}}_{\left( b/0 \right)}}=0$, that is, $b$ is a free falling body.

Since $\left\| {{{\vec{P}}}_{\left( b/i \right)}} \right\|=\left\| {{{\vec{P}}}_{b/0}} \right\|+i{{m}_{b}}$, the change in momentum between two transitional positions ${{p}_{q}}$ and ${{p}_{r}}$ is equal to $\left( r-q \right){{m}_{b}}$, and total acceleration is equal to $r-q$. But since the distance between two transitional positions is proportional to the difference between the squares of their distances from the center of gravity of $a$ , if we set ${{p}_{q}}$ at the center of gravity of $a$ then the change in momentum between ${{p}_{q}}$ and ${{p}_{r}}$ is given by

$\displaystyle r{{m}_{b}}={{m}_{a}}{{m}_{b}}\left( k-\frac{d_{q}^{2}+{{d}_{q}}}{2} \right)-{{m}_{a}}{{m}_{b}}\left( k-\frac{d_{r}^{2}+{{d}_{r}}}{2} \right)$ and since ${{d}_{q}}=0$

$r{{m}_{b}}={{m}_{a}}{{m}_{b}}k-{{m}_{a}}{{m}_{b}}\left( k-\frac{d_{r}^{2}+{{d}_{r}}}{2} \right)={{m}_{a}}{{m}_{b}}\left( \frac{d_{r}^{2}+{{d}_{r}}}{2} \right)$, the speed at ${{p}_{q}}$ is equal to ${{v}_{r}}=r={{m}_{a}}\left( \frac{d_{r}^{2}+{{d}_{r}}}{2} \right)$. Thus the rate acceleration of a body is proportional to the mass of $a$ and to the square of the distance of between its initial position and the center of gravity of $a$, but is independent of the mass of $b$, which explains why two bodies will have the same acceleration regardless of their mass. This is consistent with Newton’s law of gravity, which at the scale it is applied to, distances in leaps are large enough so that$\frac{d_{r}^{2}+{{d}_{r}}}{2}\approx \frac{d_{r}^{2}}{2}$. Newton’s law of gravity emerges from the principles of QGD and corresponds to an approximation of its gravitational interaction equation.

The distance between two successive transitional positions is proportional to the difference between the square of their distances from the center of gravity. This is also consistent with the inverse square of the Newtonian equation (see figure below).

### Conclusion and Experimental Prediction

As we have seen, according to QGD, an object interacting gravitationally doesn’t go through the infinite number of infinitesimal speed increments implied by Newton’s gravity equation. An object accelerates only at transitional positions. At non-fundamental scales, the relative distance between transitional positions is small and the acceleration of an object appears continuous. But the closer we get to the fundamental scale, the more evident it becomes that the acceleration is discrete rather than continuous. This is consistent with observation (see quantum leap).

Based on the notions we have introduced in this section, the discrete acceleration of objects at transitional positions should be observable. Data from a free fall experiment using an object coupled with a precise enough accelerometer should show that the speed of an object changes at transitional positions and that between them, its speed remains constant.