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

PDF file can be downloaded here

 

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

The PDF can be downloaded here.

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.

Gravitational-Waves-or-the-Elephant-in-the-Room

The pdf can be downloaded here.

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

You can also download the PDF here.

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.

Note: see below for PDF version.

Derivation-of-the-Equivalence-Principle-from-QGD

Could the LIGO have picked up some seismic activity?

Did some preliminary calculations today using QGD’s equation for gravitational interactions and it appears that the differential in magnitude of the interaction with a binary system along the length of the arms would be too small to give the signal that was detected by LIGO.

I’m starting to think that LIGO detected some seismic activity. The pattern of the signal, frequency and amplitude would fit seismic activity very well and that would explain why the two LIGO detectors saw the signal and explain the differences between the shapes of the individual detections. Should this be the case, taking into account the delay between the detections by the two observatories, the propagation speed of the seismic activity, it may be possible to pinpoint the source.

Hope some geophysicist friend will have time to look into it.

The LIGO Announcement Event or How Fast Can a Wave of Embarrassment Move through the Media?

First, I would like to acknowledge the amazing engineering feat that is the LIGO. Its completion is an achievement of historical proportion. I have nothing but admiration for the work that has been done. But without taking away any of the well deserved credit, I think we need to look closely at the observation of what is assumed to be a gravitational wave made in September 2015 and which motivated the claim that gravitational waves have been discover at long last and, by some incredible serendipity, a century after their existence has been predicted.

I’m not going to go into the detail as to why I believe gravitational waves do not exist since that I have explained this at length. And I will reserve for later a discussion of the fact that there is no matter energy mechanism that allows for conversion of matter into gravitational energy as is required for the general relativity prediction to hold. In fact, I will not in any way criticize general relativity and its predictions, many of which coincide with QGD’s prediction (see An Axiomatic Approach to Physics). My criticism here is not due to a theoretical bias, but about how scientists, as they have recently done with the BICEP 2 result, have again jumped the gun and make what can only be qualified as the most extraordinary claim in the history of science.

When we ignore all the biases due to the assumed certainty of the existence of gravitational waves, all the theoretical biases regarding the properties of the source of the signal (distances, masses, etc,. all of which have been calculated using the very equations that made the prediction we’re trying to prove and not based on actual measurements) and take an objective look at what was observed, what are we left with?

We are left with is a single low resolution, noisy, signal of origin, source and location unknown, that has yet to be independently corroborated, and of a type that has never been observed before, thus without any reference signals to compare it to. However one looks at the data, a singular event such as the observed signal is far from sufficient to claim discovery.

That said, I can understand that after hundred years, scientists were eager to settle the question, but it makes all the more paradoxical to claim discovery prematurely.

I fear and predict that further observations will show that the signal is not what physicists hoped for and that they’ll have to live down a larger embarrassment than even the BICEP 2 claim caused.

First Impressions about the LIGO Observation of a Gravitational Signal

I had hoped that the shape of the signal would be clear enough to falsify either GR or QGD, but we will have to wait for more data and for a third gravitational observatory to pin point the location of the source of the next event and compare it to electromagnetic signals from the same source.

First impressions (detailed analysis to follow).

1. The signal is much larger than GR simulations predict for an event located at 1.6 billion light years from us. It should be something like 50 times smaller in amplitude, but this larger amplitude is consistent with QGD equation for gravity. The first part of the signal shows how much larger than predicted by GR

and

2. when we look closely at the part that is closer to predictions, we see reduction in amplitude as frequency increases. This again is in agreement with QGD’s prediction for instantaneous tidal effect.

That said, the observed signal is the first and only one we have and the amplitude of a signal may be affected by factors such as the rotation of the plane on which lies the orbits of the black holes (or whatever system caused it).

Don’t get me wrong. This is an amazing achievement, but still, in itself, the signal doesn’t prove that gravitational waves exist. We’ll have to wait a little longer for that.

About the Advanced LIGO Rumours and Gravitational Waves (part 3)

In part 1 and part 2 of this series of article, I have made some predictions that set quantum-geometry dynamics apart from predictions made using general relativity. I have explained that gravitational signals would be similar. I will clarify what I meant here. Below is a graph figure taken from this paper which describes the shape of a gravitational wave signal produced by merging of two black holes as predicted by general relativity (black curve). I have drawn (somewhat crudely) over the graph, in red, the shape of a gravitational signal predicted by quantum-geometry dynamics. If GR prediction is correct, there would be an increase in amplitude and frequency as the black holes spiral towards collision. But if QGD is correct, there would be an increase in frequency similar to that predicted by GR but we would see decrease in the amplitude of the signal as the black holes spiral towards collision.

 

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