## The Measurement of Physical Properties and Frames of Reference

Note: the following is a section of Introduction to Quantum-Geometry Dynamics

According to QGD:

• ${{m}_{a}}$, the mass of an object $a$, is equal to the number of $preon{{s}^{\left( + \right)}}$ that compose it;
• ${{E}_{a}}$ , its energy, is equal to its mass multiplied by the fundamental momentum of the $preo{{n}^{\left( + \right)}}$; that is: where ${{\vec{c}}_{i}}$ is the momentum vector of a $preo{{n}^{\left( + \right)}}$ and $c=\left\| {{{\vec{c}}}_{i}} \right\|$is the fundamental momentum, then ${{E}_{a}}=\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}={{m}_{a}}c$.
• ${{\vec{P}}_{a}}$ , the momentum vector of an object, is equal to the vector sum of all the momentum vectors of its component $preon{{s}^{\left( + \right)}}$ or ${{\vec{P}}_{a}}=\sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}}$ and${{P}_{a}}$ , its momentum, is the magnitude of its momentum vector. That is: ${{P}_{a}}=\left\| {{{\vec{P}}}_{a}} \right\|=\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|$ and finally
• ${{v}_{a}}$ , its speed, is the ratio of its momentum over its mass or ${{v}_{a}}=\frac{{{P}_{a}}}{{{m}_{a}}}=\frac{\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{a}}}$.

All the properties above are intrinsic which implies that they are qualitatively and quantitatively independent of the frame of reference against which they are measured. We must however make the essential distinction between the measurement of a property of an object and its actual intrinsic property.

Take for instance the speed of light which we have derived from the fundamental description of the properties of mass and momentum and shown to be constant. That is: ${{v}_{\gamma }}=\frac{{{P}_{\gamma }}}{{{m}_{\gamma }}}$ and since, for momentum vectors of photons all point in the same direction we have ${{P}_{\gamma }}={{E}_{\gamma }}$ and $\displaystyle {{v}_{\gamma }}=\frac{{{P}_{\gamma }}}{{{m}_{\gamma }}}=\frac{{{E}_{\gamma }}}{{{m}_{\gamma }}}=\frac{{{m}_{\gamma }}c}{{{m}_{\gamma }}}=c$.

If we were to experimentally measure the speed of light, or more precisely, the speed of photons, we would set up instruments within an agreed upon frame of reference. We would map the space in which the measurement apparatus is set and though the property of speed is intrinsic, thus independent of the frame of reference, the measurement of the property is dependent on the frame of reference. But if, as we know, the speed of light has been observed to be independent of the frame of reference, then how can this be reconciled with QGD’s intrinsic speed?

Before moving forward with the experiment it is important to consider what it is that our apparatus actually measures. Speed is conventionally defined as the ratio of displacement over time, that is $v=\frac{d}{t}$ where $d$ the distance is and $t$ is time. Space and time here are considered physical dimensions and as a consequence the conventional definition of speed is never questioned.

Distance can be measured by something as primitive as a yard stick and its physicality is hard to argue with. Time and its physicality pose serious problems. Time is assumed to be measurable using a clock of some sort but, it is easily shown that clocks are simply cyclic and periodic systems linked to counting devices and they do not measured time but merely count the number of repetitions of arbitrarily chosen states of these systems.

So conventional speed in general, and that of light in particular, is simply the distance in conventional units something travels divided by the number of cycles a clock goes through during its travel. Therefore the conventional definition of speed, which is the ratio of the distance travelled by an object over the number of cycles, is not the objects speed, but of the distance travelled between two cycles. That goes for the speed of photons.

There is a relation between conventional speed and intrinsic speed and we find that the conventional speed of a photon is proportional to its intrinsic speed, that is $\frac{d}{t}\propto {{v}_{\gamma }}$, but while conventional speed is relational (and not physical since time itself is not physical) , the intrinsic speed is physical since it is derived from momentum and mass, both of which are measurable, hence physical.

Now going back to frames of reference, let us assume a room moving at an intrinsic speed ${{v}_{a}}$. A source of photons is placed at the very centre of the room which photons are detected by detectors placed on the walls, floor and ceiling. The source and detectors are linked are in turn linked to a clock by wires of the same length. The clock registers the emission and the reception of the photons in such a way that we can calculate the conventional speed of photons. For now, we will assume that the direction of motion of the room is along the $x$ axis.
QGD predicts that even though the intrinsic speed of photons is reference frame independent, their one way conventional speed to detector ${{D}_{{{x}_{1}}}}$ will be larger than their one way conventional speed at the detector ${{D}_{{{x}_{2}}}}$. The relativity theory predicts that the conventional speed of photons will be the same at both detectors independently of ${{v}_{a}}$. So all that is needed to test which theory gives the correct prediction is to make one way measurements of the conventional speed of photons. Problem is; all measurements of the speed of light are two way measurements and since any possible contribution of ${{v}_{a}}$ to the conventional speed of photons traveling in one direction is cancelled out when it is reflected in the other direction. In other words since both QGD and the relativity theory predicts the two way measurements will be equal at ${{D}_{{{x}_{1}}}}$ and ${{D}_{{{x}_{2}}}}$ such experiments cannot distinguish between QGD and the relativity theory.

However, a similar experiment which measures not speed but momentum can distinguish between the theories. The photons at detector ${{D}_{{{x}_{2}}}}$ will be redshifted while those at ${{D}_{{{x}_{1}}}}$ would be blueshifted. Both theories predict ${{P}_{{{D}_{{{x}_{1}}}}}}>{{P}_{{{D}_{{{x}_{2}}}}}}$but their predictions for the other detectors are different.

Assuming that the room’s motion is align with the $x$ axis*, the relativity theory predicts that ${{P}_{{{D}_{{{x}_{1}}}}}}>{{P}_{{{D}_{{{y}_{1}}}}}}={{P}_{{{D}_{{{y}_{2}}}}}}={{P}_{{{D}_{{{z}_{1}}}}}}={{P}_{{{D}_{{{z}_{2}}}}}}>{{P}_{{{D}_{{{x}_{2}}}}}}$. For the same experiment the QGD theory predicts ${{P}_{{{D}_{{{x}_{1}}}}}}={{P}_{{{D}_{{{y}_{1}}}}}}={{P}_{{{D}_{{{y}_{2}}}}}}={{P}_{{{D}_{{{z}_{1}}}}}}={{P}_{{{D}_{{{z}_{2}}}}}}>{{P}_{{{D}_{{{x}_{2}}}}}}$.

If QGD’s prediction is verified, then the intrinsic of the frame of reference can be calculated using the equations we introduced earlier to describe the redshift effect. That is; from our description of the redshift effect, we know that $\displaystyle {{P}_{\gamma }}=\Delta {{P}_{{{D}_{{{x}_{1}}}}}}$ then we have $\displaystyle \frac{c-{{v}_{a}}}{c}{{m}_{\gamma }}={{P}_{\gamma }}-\frac{{{v}_{a}}}{c}={{P}_{{{D}_{{{x}_{1}}}}}}-\frac{{{v}_{a}}}{c}={{P}_{{{D}_{{{x}_{2}}}}}}$and $\displaystyle {{v}_{a}}=\left( {{P}_{{{D}_{{{x}_{1}}}}}}-{{P}_{{{D}_{{{x}_{2}}}}}} \right)c$.

Once the intrinsic speed of a reference system is known, then it can be taken into account when estimating the physical properties of light emitting objects from within it.

QGD’s description of the redshift effect implies distinct predictions for all observations based on redshifts measurement but I would like to bring attention to one direct consequence which has been confirmed by observations; the observed flatness of the orbital speed of stars around their galactic centers .

* The alignment with the $x$ axis is found by rotating that detector assembly so that the ${{D}_{{{x}_{2}}}}$ detector measures the lowest momentum (largest redshift).

## Preonics (the foundation of optics)

Preonics (the foundation of optics) is a new section of Introductions to Quantum-Geometry Dynamics 3rd edition.

“Following the failure of classical physics theories to explain the interference patterns observed in double slit experiments and other light diffraction experiments and because of the similarities between these patterns and the interference patterns generated by waves at the surface of a liquid, physicists deduced that light was behaving as a wave which led to the so-called wave-particle duality of light. Since the particle model could explain phenomena such as the photoelectric effect and since the wave model of light described the interference patterns of light, it made sense to deduce that light had to corpuscular or wave-like depending on the experiment performed on it. But what experiments actually showed is that neither accepted models of light could explain both behaviours and emphasized the need for a new theory.”

Preonics-the-foundation-of-Optics

## Variation in Light Speed in Gamma-Ray Bursts (explained through QGD)

According to the authors of Light Speed Variation From Gamma-ray Bursts[1], photons from gamma ray bursts show a speed dependency on their energy. Though inconsistent with current theories, the observations described in the paper are consistent with predictions of quantum-geometry dynamics and easily explained by it without violation of the speed of light.

Observed-Light-Speed-Variations-and-QGD

## Calculating and Converting QGD Units and Constants

Note: Presented here section excerpt from the 3rd edition of Introduction to Quantum-Geometry Dynamics

We show how the two constants of QGD can be derived from experiments and how from these we can convert its natural units in measurable units.

Calculating-and-Converting-QGD-Units-and-Constants

## QGD Interpretation of the Redshift Effect

QGD proposes a model of light according to which it is singularly corpuscular, which model is a consequence of its discreteness of space axiom.

Note: There are other causes for the redshift effect with are dependent on the light source source (see article here).

The following summarizes an upcoming section of the 3rd edition of Introduction to Quantum-Geometry Dynamics (in progress).

new-interpretation-of-the-redshift-effect

## Gravitational Waves or the Elephant in Room

QGD precludes the existence of gravitational waves so how can this be reconciled with the advanced LIGO observatory detections of signals that are consistent with gravitational waves predicted from general relativity? How does QGD explain these signals if, as it predicts, there is no gravitational waves?

Note: the following are pages from Introduction to Quantum-Geometry Dynamics 3rd edition.

## Re-thinking Through some of Einstein’s Thought Experiments (part 1a)

In this section of the upcoming 3rd  edition of Introduction to Quantum-Geometry Dynamics, we analyze some of Einstein’s thought experiments which inspired his equivalence principle and paved the way to general relativity.

What we have shown that though there is only one kind of mass, the effects of gravity and non-gravitational force can never be equivalent. And even when cut off from the outside world, as is imagined in Einstein’s thought experiments, observers can correctly describe and distinguish between the forces acting on their environment through experiments as long as measurements are made of the initial, transitory and final states of the experiments and a minimum of two distinct experiments are conducted for each measured property.

Introduction-to-QGD-3rd-edition-part-1a

## Introduction to Quantum-Geometry Dynamics 3rd edition (part 1)

All efforts are made to present the concepts of quantum-geometry dynamics in logical order; providing the reader with all the concepts necessary to move from one section to the next (view below or download the PDF here.)

Further parts of the book will be added as they are completed.

introduction-to-quantum-geometry-dynamics-3rd-edition-new

## Derivation of the Equivalence Principle from QGD

The article can be viewed or downloaded in PDF format at bottom of the page.

## Weak Equivalence Principle

The weak equivalence principle is easily derived from QGD’s equation for gravity $\displaystyle G\left( a;b \right)={{m}_{a}}{{m}_{b}}\left( k-\frac{{{d}^{2}}+d}{2} \right)$ where ${{m}_{a}}$ and ${{m}_{b}}$ are respectively the masses of $a$ and $b$ and $d$ the distance, all in natural fundamental units.

According to QGD, the change in momentum of due to gravity between two points in space is exactly equal to the gravity differential between two points $\Delta G\left( a;b \right)$ . That is $\Delta \left\| {{{\vec{P}}}_{b}} \right\|=\Delta G\left( a;b \right)$ .

QGD defines speed of a body as ${{v}_{a}}=\frac{\left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}}$ , so the acceleration of a body is $\Delta {{v}_{a}}=\frac{\Delta \left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}}$ . Since $\Delta \left\| {{{\vec{P}}}_{b}} \right\|=\Delta G\left( a;b \right)$ , the acceleration of an object $a$ due to the gravitational interacting between $a$ and $b$ is $\Delta {{v}_{a}}=\frac{\Delta \left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}}=\frac{\Delta G\left( a;b \right)}{{{m}_{a}}}$ .

Since $\Delta G\left( a;b \right)={{m}_{a}}{{m}_{b}}\left( k-\frac{d_{1}^{2}+{{d}_{1}}}{2} \right)-{{m}_{a}}{{m}_{b}}\left( k-\frac{d_{2}^{2}+{{d}_{2}}}{2} \right)={{m}_{a}}{{m}_{b}}\left( \left( \frac{d_{1}^{2}+{{d}_{1}}}{2} \right)-\left( \frac{d_{2}^{2}+{{d}_{2}}}{2} \right) \right)$ then $\Delta {{v}_{b}}=\frac{1}{{{m}_{a}}}{{m}_{a}}{{m}_{b}}\left( \left( \frac{d_{1}^{2}+{{d}_{1}}}{2} \right)-\left( \frac{d_{2}^{2}+{{d}_{2}}}{2} \right) \right)={{m}_{b}}\left( \left( \frac{d_{1}^{2}+{{d}_{1}}}{2} \right)-\left( \frac{d_{2}^{2}+{{d}_{2}}}{2} \right) \right)$ . Therefore, gravitational acceleration of an object $a$ towards $b$ is independent of its mass ${{m}_{a}}$ and only depends on ${{m}_{b}}$ , the mass of the objects it falls toward, and the distance it travels. Conversely, the gravitational acceleration of an object $b$ towards $a$ is given by $\Delta {{v}_{b}}={{m}_{a}}\left( \left( \frac{d_{1}^{2}+{{d}_{1}}}{2} \right)-\left( \frac{d_{2}^{2}+{{d}_{2}}}{2} \right) \right)$ is independent of ${{m}_{b}}$ .

We have shown that the weak equivalence principle is a direct consequence of QGD’s equation for gravity which itself is derived from QGD’s axiom set and by doing so, have promoted the principle to a law.

However, there is an inherent problem arising from the equivalence principle when describing a system from the acceleration imparted by gravity. The problem is it hides intrinsic physical properties which allow us to distinguish between objects. Since gravitational acceleration of an object is independent of its mass or composition, then the effect gravitational does not inform of those two intrinsic properties.

According to QGD, the momentum of object is an intrinsic property given by $\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|$ where ${{m}_{a}}$ is the number of bounded $preon{{s}^{\left( + \right)}}$ of $a$ and each ${{\vec{c}}_{i}}$ correspond to the momentum vector of a bounded $preo{{n}^{\left( + \right)}}$ . The speed of object is is given by $\frac{\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{a}}}$ .

Given two object $a$ and $b$ both at the same distance from a massive structure, the equivalence principle makes it impossible to distinguish between them based on their respective acceleration, which makes acceleration the wrong property to measure if one wants to compare the effect of a force on particles, structures or frames of reference. To distinguish, for example, between gravitationally and non-gravitationally accelerated objects or systems of objects, we should measure, for example, the imparted changes in momentums which as we will see are not only mass but also force dependent.

Changes in momentum of an object due to gravitational interaction is independent of its mass while changes in momentum due to non-gravitational interactions is mass dependent.

## Inertial Mass and Gravitational Mass Equivalence

According to QGD, the inertial mass and the gravitational mass of an object are fundamentally one in the same thing. This equivalence is a fundamental assumption of quantum-geometry dynamics which naturally emerges from its axiom set. In fact there is only one definition of mass: the mass of an object is simply the number of $preon{{s}^{\left( + \right)}}$ it contains. That number determines not only the effect of gravity but all behaviour of dynamic system. But while gravitational mass and inertial mass are the same thing, describing a dynamic system requires that we understand an important distinction between gravitational and non-gravitational forces. The acceleration of an object is given by $\Delta {{v}_{a}}=\frac{\Delta \left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}}$ where $\Delta \left\| {{{\vec{P}}}_{a}} \right\|=F$ and $F$ is the force imparting the momentum. For non-gravitational force, the denominator ${{m}_{a}}$ is not cancelled out. It follows that

• gravitational acceleration is independent of the mass of the accelerated object

while

• non-gravitational acceleration of an object is dependent on the mass of the object being accelerated

Based on the above, we see that the equivalence between the gravitational mass and the inertial mass does require the equivalence implied by Einstein who stated that that “There is no experiment that can be done, in a small confined space, which can detect the difference between a uniform gravitational field and an equivalent uniform acceleration. ”

The equivalence Einstein suggests is not equivalence between the gravitational and inertial masses, but an equivalence between gravitational and non-gravitational forces.

Let us consider the experiment in figure 1 based on Einstein famous thought experiment. Here we have two rooms; a green room and a red room. Each room is a rectangular rigid structure possessing the same mass and structure. In each room a rigid rod fixed on one end to the ceiling and its other end is rigidly attached to a sphere of equal composition and mass.

The green room is at rest in gravitation field. The red room is imparted and acceleration by the force $F$ such that that $\Delta G\left( green;b \right)=\Delta \left\| {{{\vec{P}}}_{red}} \right\|$ .

The force $F$ being non-gravitational (the thrust of a rocket engine to take common example), its imparted momentum propagates from the point of application through the rest of the structure. Here, the momentum is imparted first to the floor, which then imparts it to the sides of the room, which then imparts it to the ceiling, which then pulls the rod and lastly imparts momentum to the sphere.

The experiment consists of randomly releasing the spheres and determine whether or not instruments within each room will measure the same dynamic changes.

The sphere in the green will accelerate uniformly at the rate describe by QGD equation for gravity (of which Newton’s law is an approximation). As we have shown, the acceleration here is independent of the mass of the sphere.

However, at the moment the sphere in the red room is released, the momentum imparted to the room by $F$ no longer reaches the sphere. The sphere stops accelerating and will move at the speed it had when it had when released until the floor accelerating towards the sphere impacts it. Also, since the acceleration of the red room with the sphere attached is $\Delta {{v}_{redr}}=\frac{\Delta \left\| {{{\vec{P}}}_{F}} \right\|}{{{m}_{redr}}}$ , at the moment the sphere is released, the mass which is subject to $F$ decreases by the mass of the sphere so that $\Delta {{v}_{redr}}=\frac{\Delta \left\| {{{\vec{P}}}_{F}} \right\|}{{{m}_{redroom}}-{{m}_{sphere}}}$ . If the mass of the sphere is a significant portion of the total mass of the system, then from within the red room, instruments will measure a sudden change in the rate of acceleration the instant the sphere is released and an equivalent sudden deceleration when the floor finally impacts the sphere. The change in the rate of acceleration when the sphere is release is $\Delta \Delta {{v}_{B}}=\frac{\Delta \left\| {{{\vec{P}}}_{F}} \right\|}{{{m}_{redroom}}+{{m}_{sphere}}}-\frac{\Delta \left\| {{{\vec{P}}}_{F}} \right\|}{{{m}_{redroom}}}$ . The instruments in the green room will show no such change in the rate of acceleration. It follows that we can distinguish between a uniform gravitational field and an equivalent uniform acceleration simply because there can’t be a uniform non-gravitational acceleration.

Of course, one may object that we can assume a mechanism which by will the force acting on the red room will be adjusted to compensate for the drop of the sphere. But that would imply communication of the exact moment at which the sphere is released in the green room, which would imply that measuring equipment and communication devices different from those found in the green room and prior knowledge of the distinction between the different accelerations. But then, we may assume that the exact same equipment is installed in both the green and red rooms, but that wouldn’t solve the issue since monitoring the communication equipment would show distinguishing behaviour. The signalling of the impact of the sphere on the red room floor would be sent sooner after release than the signaling of the impact of the sphere in the green room. Contrary to Einstein’s statement we can show that it is always possible to distinguish between a gravitationally accelerated frame of reference and a non-gravitationally accelerated frame of reference.

At this point, if he hasn’t earlier, the reader should ask how to explain the bending of light in proximity of massive structures or the slowing down of clocks due gravity; two important predictions of general relativity which require Einstein’s equivalence principle? For answers to these questions as well as the derivations of the gravity and the laws of motion from a simplest axiom set that can describe dynamic systems, we refer the curious reader to An Axiomatic Approach to Physics.

Now consider figure 2 showing an experiment also inspired by Einstein’s thought experiment. Here, each room has a laser rigidly attached to the left wall firing photons towards the opposite wall. The first and second diagrams from the left respectively show what an observer in the green room and an observer in the red room will see.

Without the assumption of equivalence, an observer in the red room must conclude that the curvature of the path of light describes the motion of the red room relative the trajectory of the photons (which without Einstein’s equivalence principle the observer must assume is along a straight line). If QGD’s description of space is correct, the distance travelled relative to the photons trajectory axis can be used to calculate the speed of the room along the axis of motion which would then be given by $\frac{d}{l}c$ .

This implies that given if we positioned three lasers in the red room so that the trajectories of their beams are perpendicular to each other, then the absolute speed of the room, which is the speed relative to quantum-geometrical space, would be given by $\displaystyle {{v}_{redroom}}=\frac{c}{l}\sqrt{d_{1}^{2}+d_{2}^{2}+d_{3}^{2}}$ . Since we’re essentially describing classical motion, from the curve or the trajectory (figure 3) the observer can determine if the room is accelerating, decelerating or moving at constant speed.

This illustrates an essential distinction between quantum-geometry dynamics. Physical properties such as position, momentum, speed, mass of any particle or structure is independent of the frame of reference. Position is absolute in quantum-geometrical space and momentum, energy and mass are intrinsic to the particles and structures. This is discussed in some detail in An Axiomatic Approach to Physics.