General relativity correctly predicted the precession of the perihelion of Mercury and the correct angle of deflection of starlight by the sun both of which Newton’s theory of universal gravitation apparently had failed to correctly predict.

Newton’s theory of universal gravity also fails to describe the orbital decay of binary systems such as the Hulse-Taylor binary system which observation was consistent with general relativity. Favoring general relativity as the theory that correctly describes gravity is a clear cut decision considering its successes. General relativity succeeded where Newton’s theory of gravity had failed. But is the matter really settled? Let’s take a closer look at how Newton’s theory of gravity has been applied to the observations cited above.

In order to describe the evolution of two gravitationally interacting bodies    and    , the magnitude of the gravitational force is calculated using Newton’s equation for gravity    where    and    are the masses of the bodies, then substituted in the equation for Newton’s second law of motion; the familiar    where   is the acceleration of . This is as straightforward a calculation as can be but there lays the problem.

Gravity, according to Newton’s law, is instantaneous. It follows that if gravity is instantaneous, so must the action of gravity be instantaneous. So applying the second law of motion (which is time dependent) to describe the effect of Newtonian gravity introduces a lag in the action that is incompatible with instantaneous gravity. This lag of the action of gravity introduced by using the second law of motion is precisely what caused predictive errors in Newtonian mechanical description of the precession of the perihelion of Mercury, of the bending of star light and of the orbital decay of binary systems. In fact, once the time dependency and consequently the time lag are eliminated from the gravitational action, we find that Newtonian gravity is in perfect agreement with observations (see Special and General Relativity Axiomatic Derivations).

The fact is that Newtonian gravity (when correctly applied) and general relativity can and with equal precision predict the behaviour of gravitationally interacting bodies for the above phenomena is problematic. This forces us to find other ways to answer the question as to whether gravity is a force that acts instantaneously between bodies or if is the effect of curvature of space due to the presence of matter. Clearly, the two explanations of the nature of gravity are foundationally incompatible.

It follows from QGD’s equation for gravity    that gravity becomes repulsive when bodies separated by distances such that   . That is, there is a threshold distance     (from observations) beyond which gravity becomes repulsive and increases proportionally to the square of the distance.  The effect of repulsive gravity as described by QGD is consistent with the observed expansion of the universe which is currently attributed to dark energy. This allows for new predictions that are distinct from those of general relativity.

If QGD is correct, the magnitude of the gravitational repulsion between the Earth and the black holes that caused the GW150914 event must be    greater than the magnitude of the attractive gravitational force in close proximity to the binary system that caused the event. Such gravitational effect is astronomically greater than the signal detected by LIGO in 2015. In fact, the repulsive force would be enough to tear our galaxy apart from the gravitational tidal force and accelerate it to speed approaching the speed of light. And the repulsive force between the Earth and the recently observed GW170104 event, presumed to be a twice the distance, would be four times as great. The reason our galaxy (and others) is not torn apart is that the distribution of matter in the universe is nearly homogenous so that the repulsive gravitational forces from distant massive systems acting on each individual particle that compose our galaxy are nearly cancelled out by the repulsions from systems in the opposite directions; resulting in a weak net gravitational effect. So, if the GW150914 and GW170104 events are gravitational, the detected signals would be tidal effects of the net gravitational forces acting on the detectors . That is, the signals are not gravitational waves but the measurement of the instantaneous gravitational tidal effect    where     is the detector and    is one of a total of    massive structures forming the universe. So, LIGO may be thought as measuring the fluctuations of the gravitational tidal effect of the universe on its instruments.

Some Distinctive Predictions of QGD that Are Now Being Tested (or will be in the near Future)

If gravity is instantaneous as predicted by QGD and Newton’s law of universal gravity, then

• we will never detect multi-messengers signals from events predicted to simultaneously generate gravitational and electromagnetic signals.  Electromagnetic signal from the merging, for example, of neutron stars, would arrive up to billions of years after the gravitational signal.
• Gravitational signal from the merging of massive objects at distance close the threshold distance would be undetectable.
• No loss in mass of the merging massive objects in the form of gravitational waves (in fact, there is no mechanism that may account for the conversion of mass into gravitational waves). The mass of the object resulting from the merging will be equal to the sum of the masses of the merged objects.
• Angular radius of the shadow of Sagittarius A* should be 10 times larger than predicted by general relativity

(more can be found in different section of this blog and in Introduction to Quantum-Geometry Dynamics)

Last year was all about Advanced LIGO’s announcement that they had for the first time detected gravitational waves predicted to exist a hundred years earlier. Understandingly, the press coverage was proportional to the importance of the discovery. The conference which was released in the entire world was, to my knowledge, amongst the events that received the widest press coverage ever for a scientific discovery.

In the field of astrophysics, the only comparable event was probably the detection of primordial gravitational waves by the BICEP2 experiment announced with great fanfare in 2014.

Immediately after the BICEP2 announcement, I predicted that the results would be refuted by further observations. It was not that I was skeptic. It was not just a random opinion, but a direct consequence of quantum-geometry dynamics. The level of confidence in the BICEP2 discovery was so high than very few doubted the validity of the results. I was one of few people who immediately predicted that the results would not hold and as we all know the BICEP2 discovery was refuted later that year.

I made a similar prediction for the LIGO detections the days prior and following the announcement in February 2016. Since the announcement, the sensitivity of LIGO was increased and the second run of observation started in November 2016. Tomorrow, the results of the second run of observations will be released, but this time, there is no press coverage except from two minor local news sources. The release is not even mentioned on the Facebook page of the LIGO collaboration. Why is the release so hush hush? One would think that after the last year’s announcement of the detection of gravitational waves (and the unrelenting news coverage since then) that any news from LIGO would be treated as a highest priority by the media if that is what the LIGO collaboration made the slightest effort to publicize it. But the lack of any attempt to draw attention to the results is probably, as I predicted, because the earlier detection have not be corroborated by new detections.

Good science requires that before being considered a discovery the results of any observation or experiment must be reproducible. Considering its higher sensitivity, the duration of the second run and the theoretical probability of more detection, Advanced LIGO should have made more detections in its second run and it had in its first. Because of that, null results are even more significant than the detection announced last year as they cast doubts on the validity of the discovery.

My prediction is no new detections of black hole mergers announced tomorrow but not to worry, that only provides new constraints on the frequency of events capable of producing detectable gravitational waves, right?

[UPDATE] It seems that they are announcing the detection of one black holes merger (see article here).

From the article:

“Normally, an event like this would trigger an alert to the astronomy community, which could then attempt observations in the area of the sky where the event took place. But, in this case, a recent period of maintenance had left one of the two detectors set in a calibration mode.”

That is disappointing since the simultaneous independent detections of the non-gravitational signals would test the predicted speed of propagation of gravitational waves and would put to rest the prediction of QGD that gravity is instantaneous and that the signals detected by LIGO are due to the tidal effect of gravity.

If QGD’s equation for gravity is correct, gravity becomes repulsive at distances greater than 10Mpc and the magnitude of the repulsion increases as a function of distance (this would account of the expansion of the universe we attribute to dark energy). That means that the greater the distance, the greater the tidal effect of gravity.

Non-locality is based on the assumption that an event which affects a system cannot affect another system which is independent of it. Independent systems being defined as systems which are separated by a distance sufficiently large to prohibit one from influencing the other without violating the speed limit imposed by special relativity. But if gravity is instantaneous, then no systems is truly independent which means that all systems are local and can affect each other instantaneously regardless of distance.

Under instantaneous interactions, the entire universe is local.

The pdf file can be downloaded here.

[UPDATED FEB 2nd 2015]

By simply assuming that a detector does not detect electrons having spins relative to an axis, but rather only discriminates between ranges of spin angles, we derive an inequality which predictions are in agreement with Bell experiments and are thus indistinguishable from the predictions of quantum mechanics for the same experiments.

See paper below:

Download Does the Violation of Bell’s Inequality Refute All Local Realisms

In part 1 of this series we have shown that the results from quantum entanglement experiments using Mach-Zehnder Interferometer setups can be explained in a locally realistic way. In fact, we can see that quantum entanglement is not required to explain the observations and that result from such experiments, in themselves, do not in actuality support the existence of quantum entanglement. In the present article, we will show quantum-geometry dynamics provides an explanation of the results of experiments based on the Stern-Gerlach experiment , which according to Wikipedia “has become a paradigm of quantum measurement,” that does not violate the principle of locality.

Prerequisites for the Present Article

Readers who are not familiar with the Stern-Gerlach experiments should read the excellent introduction provided here before reading on. Also, readers are not familiar with the quantum-geometry dynamics should minimally have read the article titled Quantum-Geometry Dynamics in a Nutshell or, for an in depth understanding read Introduction to Quantum-Geometry Dynamics (from here on referred to as ITQGD).

The Experiment

Figure 1

In the above setup (figure 1), the red beam represents an electron beam and the green arrows represent magnetic preons; which according to QGD, are polarized which compose all magnetic fields (see relevant section of ITQGD for a detailed explanation). The first filter allows only up-spin electrons to go through (50% of the electrons). The second filter (filter 3) is rotated 180° relative to filter 1 so that only down-spin electrons are allowed through. Since only up-spin electrons exit from filter 1 to reach filter 3, the above setup filters out both up-spin and down-spin (relative to filter 1) electrons so that 0% of electrons from the source exit the setup.

In the setup shown in figure 2, a second filter has been added between filter 1 and filter 3 which is at 90° relative to the direction of filter 1.

Figure 2

As we have seen above, only up-spin electrons exit filter 1 (50% of the electrons). These up-spin electrons go through filter 2, which filters out electrons down-spin electron relative to filter 2. The electrons not filtered out by filter (25% of electrons) enter filter 3. Since only up-spin electrons relative to filter 1 will exit filter 2, classical physics predicts that since the electrons exiting filter 2 are up-spin relative to filter 1 the, as in the setup in figure 1, they should be filtered out by filter 3 so that no electrons should exit the setup. However, observations show that 12.5% of the electrons from the source exit the setup.

Quantum mechanics attributes the results of this experiment to the phenomenon of quantum entanglement. According to quantum mechanics, detecting the orientation of the spin of one electron of a pair of entangled electrons will change the orientation of the spin of the other instantly regardless of the distance that separates them. In other words, even if two entangled electrons were separated by a distance of the order of magnitude of the universe, measuring this property for one electron of an entangled pair must instant affect this property in the other. This phenomenon which Einstein called spooky action at a distance is thought to refute the principle of locality.

Going back to the results from the setup shown in figure 2, the quantum mechanical explanation requires that all electrons are entangled at the source so that only pairs of entangled electrons enter the apparatus. Then detecting the spin of one electron of an entangled pair instantly changes the spin of the other. So according to quantum mechanics, the electrons passing through the setup do not behave classically because the act of detecting their spins in filter 2 (filter and detector are synonymous) changes the orientation of their spin so that up-spin electrons relative to filter 1 become down-spin electrons, hence are allowed through filter 3.

There are a number of inconsistencies in the above explanation. First, we know that only one of each pair of entangled electrons is allowed through filter 1. It follows that if the electrons existing filter 1 and entering filter 2 are not entangled pairs so that detecting down-spin electrons in filter 2 should not change the orientation of the spin of the up-spin electrons passing through filter 2 so that the electrons exiting filter 2 should be filtered out by filter 3. Observation shows this to be incorrect which leads to the assumption that the electrons exiting filter 1 are also entangled pairs. We may chose to ignore or explain away the inconsistencies of the quantum mechanical explanation but doing so creates an even graver inconsistency.

Going back to the setup shown in figure 1, if the electrons that enter filter 1 are entangled pairs then detecting a down-spin electron should change the other electron of a pair in such a way that, to be consistent with the explanation of the figure 2 setup, 50% of electrons should through the setup 1 and not the 0% observed. Therefore, electrons appear to behave classically when going through the apparatus of setup 1 but quantum mechanically when passing through the apparatus of setup 2.

QGD’s Interpretation of the Stern-Gerlach Experiment

In order to interpret the above results using quantum-geometry dynamics, we have to remember that QGD proposes that are the only fundamental particles of matter. As a direct consequence, all other particles are composites particles, hence must have structure.

We must also keep in mind QGD’s description of the electromagnetic effect and magnetic fields; the latter being composed of unbound which are polarized as result of their interactions with the bound component of electrons (or any other so-called charged particle).

Note: The reader may be interested in a recent experiment conducted by a group of physicists at the National Institute of Physics in Italy which results are in strong agreement with QGD’s description of the electromagnetic effect and the magnetic field. Their results also imply that electrons have structure and that gravity and the electromagnetic effect are related as described by QGD (see relevant sections of ITQGD). Also, see this article for distinct experiment which results support QGD’s prediction that electrons have structure.

According to QGD, electrons and positrons belong to the same class of particles with the only distinction between them being their dynamic structure. Electrons are made of a series of pairs of bounded whose trajectories are within either open or closed regions of quantum-geometrical space. As we will see, the experimental results from the Stern-Gerlach experiments are consistent with electrons having closed structure.

Figure 3 shows representations of an electron and a positron, the trajectories of the component of one may be thought as the mirror image of the trajectories of the component of the other. This allows QGD to predict that an electron moving through a magnetic field must deflected towards the same direction as a positron moving in opposite direction. Note that this implies that positrons, the anti-particle of the electron, are made of the same matter as electrons and that electron-positron annihilation is due a dynamical mechanism (see ITQGD for a detailed discussion).

Figure 4 illustrates the interaction between an electron and the electromagnetic field generated by the plates of a spin filter. As per the laws of motion described in here, the momentum of an electron can only change by integer multiple of its mass (the number of it contains). We also know from the mechanics of particle formation that for to become bound, they must move in the same direction, that is, if they must interact over a long enough quantum-geometrical distance. Therefore the magnetic from can bound with the component represented by the blue arrows and the magnetic from can bound with the component vectors moving along the periphery represented by the red arrows. Since the “red” interact with a larger volume of quantum-geometrical space than the “blue” , for a given density of the magnetic field they will interact with a greater number of magnetic . If the difference between the sum of the momentums of the interacting magnetic from and the sum of the momentums of interacting magnetic from is equal or greater to , the mass of the electron, a number magnetic from and such that where , and are the sum momentum of the interaction preons(+) from and respectively. It follows that where and are respectively the momentum vectors before and after the absorption of polarized . The change in speed of the electron, here away from , is given by .

Note that Figure 4 shows the special case when the electron is oriented so that is perpendicular to the magnetic field. More generally, and will be proportional to the projection of orbital region on the planes perpendicular to the magnetic field. But for the purpose of this article, we only need to consider the orientation of the electrons relative to planes coincident with the filters magnetic plates.

Following our description we find that an electron moving through a magnetic field will absorb polarized which will impart it their momentum and will change the direction and magnitude of its momentum vector.

We will see how the very property of an electron which the experiments attempts to measure (here the spin) is changed, not via spooky action at a distance, but by the filter itself following the absorption of magnetic that form the magnetic fields. Therefore, the property of the electron is changed before it enters the next filter. So though a filter answers the question as to whether the spin of an electron is up or down relative to the orientation of the filter, if the electron has structure, the question is incomplete since it ignores that the other directional components of the spin which are essential to fully describe it. The binary up or down question also ignores that the changes an electron will undergo as it moves through a magnetic field. So the answer to the binary question provides an incomplete description of the spin property of the electron. We will see that when describing completely the electron and how it changes we can explain the results of any Stern-Gerlach without having to resort to the phenomenon of quantum entanglement.

But before we continue, we will use the simplified representations of electrons shown in figure 5 (the symbols on the right sides of the equality signs).

As you see, the figures take into account both the spatial orientations of electrons and the general orientation of the moving on the periphery, represented by the red arrow and which corresponds to orientations of the bound that interact most with either the top or bottom electromagnetic fields. The orientation of those determines to the spin of the electron represented by the red vector in the in simplified representations.

We can now precisely describe what happens to electrons going through each of the three filters of the setup illustrated in figure 2.

Figure 6 shows electrons entering filter 1 from the left as indicated by the cameo on the bottom right section. The top right coordinate axes provide the relative orientation of the filter.

Given a number of electrons with all possible orientations relative to the magnetic fields, it is easy to see that 50% of them are oriented in such a way they will absorb magnetic coming primarily from the bottom magnetic field resulting in a change of momentum towards the up direction. The other 50% will interact mainly magnetic coming from the top which will result in changes of their momentum towards the bottom. But as they do so, their momentum vectors, hence their spin changes so that the component will come tend to align with the trajectories of the magnetic (this corresponds to the magnetic lines of force).

In figure 7, we changed to perspective to show how the electrons are split into up-spin and down-spin relative to the filter 2. As they move through the magnetic fields, the electrons align with the line of force.

Figure 8 shows the observed results of experiments that use the setup shown in figure 2.

The orientations of electrons which, passing through filter 2, hence the orientation of the motion of its component which determines the orientation of the magnetic spin, change as the result of their interaction with the magnetic field as described earlier. Though all electrons exiting filter 2 will be up-spin relative to filter 2, they will have one of two possible orientations relative to filter 3 (see figures 9 and 10). Electrons oriented as shown in figure 9 will be up-spin relative to filter 3 (12.5% of the electron from the source) and those oriented as shown in figure 9 will be up-spin relative to filter 3 (12.5% of the electrons from the source). The down-spin electrons relative to filter 3 will be filtered out so that 12.5% of the electrons from the source will exit the apparatus.

The observed results from quantum entanglement experiments using Stern-Gerlach are in agreement with predictions that follow naturally from QGD’s axioms set. The reason electrons from the source exit the setup shown in figure 2 while none exit the figure 1 setup can be attributed to the changes in the orientation of the electrons itself undergo when passing through filter 2.

Conclusions

We have explained in a locally realistic way the results of the Stern-Gerlash experiments. According to QGD, the spins of electrons do not change because of quantum entanglement, but as a result of their interactions with the magnetic fields. Therefore, quantum entanglement experiments such as the one we have described here do not reveal some weird counterintuitive behaviour of nature, but rather support the prediction that electrons have structure and that magnetic fields are made of polarized unbound .

Implications

In an earlier article, we have shown here that the principle of quantum state superposition is unnecessary to explain the observed results from double-slit experiments. And in the present series of articles, we have shown that from the axiom set of QGD we can provide locally realistic explanations of the experiments which most strongly support quantum entanglement. It follows that the universe, even at its most fundamental scale, is strictly causal and deterministic.

If QGD is correct in that quantum entanglement and quantum state superposition are non-physical mathematical consequences of quantum mechanics, then no technology that exploits these phenomena can be realized.

Note: The present article summarizes a more detailed discussions which will be found in the next edition of Introduction to Quantum-Geometry Dynamics.

This article assumes basic knowledge of quantum-geometry dynamics; minimally the concepts presented in the short article Quantum-Geometry Dynamics in a Nutshell.

Extraordinary experimental results sometimes go unnoticed, unrecognized, ignored or, when they disagree with predictions of well-established theories, are met with a healthy dose of skepticism. This appears to be the case for a recent experiment conducted by A. Calcaterra, R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo and G. Pizzella of the Istituto Nazionale di Fisica Nucleare,Laboratori Nazionali di Frascati (National Institute for Nuclear Physics) and which is the subject of an article they posted to Arxiv in November 2012 under the title Measuring Propagation Speed of Coulomb Fields.

As the title suggests, their experiment was designed to measure the speed of propagation of Coulomb fields generated by a beam of electrons. Theories predict a finite propagation speed that can be no faster than the speed of light (the universal speed limit according to special relativity) but instead the researchers “[…] have found that, in this case, the measurements are compatible with an instantaneous propagation of the field.”

These results, though in disagreement with predictions based on dominant theories, confirm predictions made using QGD that date as far back as April 2010. If the results of this experiment are confirmed by future experiments, these results may be the first to provide strong experimental evidence in support QGD’s description of the relationship between the gravitational and the electromagnetic interactions.

According to quantum-geometry dynamics, electrons are composite particles made from bound ; one of only two fundamental particles predicted to exist by QGD. are strictly kinetic particles that move at the speed of light (actually, for those who are familiar with QGD, it is light that moves at the speed of not the reverse). The speed and momentum of are intrinsic fundamental properties that never change but their directions can change under the influence of gravitational interactions. P-gravity, the attractive force acting between the of an electron, binds them into helical trajectories (see this article).

Also according to QGD, the majority of in the universe are free and distributed isotropically in space. They form what we will call the preonic field. Magnetic fields would then result from the interactions between the bound of electrons and their neighboring regions of the preonic field. The electrons (or other charged particles) affect the direction of free , which otherwise would move in random directions, thus polarizing regions of the preonic field (a detailed explanation can be found in relevant chapters of Introduction to Quantum-Geometry Dynamics). Using QGD, the observed repulsive and attractive effects of magnetic fields on/between objects could can be simply explained as being caused by the absorption of the free polarized which impart them their momentum.

Now, though QGD predicts that no particles or structures can move (propagate) faster than , it imposes no such limit on interactions. In fact, QGD predicts that gravitational interactions (of which gravity is a manifestation at the Newtonian scale) must be instantaneous. It follows that, as an electron moves through space its neighboring region of the preonic field instantly becomes polarized. This instantaneous polarization is exactly what was observed during the experiment.

If confirmed, the experiment conducted by Calcaterra, de Sangro, Finocchiaro, Patteri, Piccolo and Pizzella not only will be a strong indication that gravity and electromagnetism are connected in the way that QGD predicts, but it would also support a number of other predictions and implications of quantum-geometry dynamics. It would, to give a few examples, support the ideas that space may be discrete rather than continuous, that particles we assume to be elementary have structure and are composed of , that there are only two fundamental forces, n-gravity and p-gravity (all other forces being resulting effects), that gravity is instantaneous (which would prohibit gravitational waves and would explain why they have never been directly observed or ever will be) and that the universe evolved, not from a singularity, but from an initial state in which were all free and distributed isotropically through quantum-geometrical space (which is consistent with the isotropy of the CMB).

They conclude their paper with the invitation: “We would welcome any interpretation, different from the Feynman conjecture or the instantaneous propagation that will help understanding the time/space evolution of the electric field we measure.” Quantum-geometry dynamics not only provides an explanation of their results, it predicted them.

***UPDATE (nov/10/2014)*** I received confirmation that the group who had performed the experiment repeated the experiment in 2014. The new measurements confirm the results publish in 2012 on Arxiv.

Or How Physics at Our Scale Emerges from Subatomic Physics

Note: This article assumes some familiarity with the ideas and concepts of quantum-geometry dynamics. If you are not familiar with QGD, you may want to read the short article titled Quantum-Geometry Dynamics in a Nutshell.

A postulate of quantum-geometry dynamics is that space is fundamentally discrete (quantum-geometrical, to be precise). Of course, proving this using our present technology may appear to be beyond difficult especially if, as QGD suggests, the discreteness of space exists at a scale that is orders of magnitude smaller than the Planck scale. The task of proving that space is made of may even be impossible because, if as discussed in On Measuring the Immeasurable, fundamental reality lies beyond the limit of the observable. That said, in the same article I explain that though , which according to QGD are the discrete and fundamental units of space, and , its predicted fundamental unit of matter, must be unobservable, their existence implies consequences and effects that must be observable at larger scales.

This implies that we already observed consequences of space and matter being quantum-geometrical but only lacked the theory capable of recognize them. It then makes sense to re-examine observations which, when interpreted by QGD, may provide proof of that space is quantum-geometrical. And this is exactly what we will do in the present article. But before doing so, we need to explain how QGD’s explanation of the law of conservation of momentum at the fundamental scale can be used to explain the conservation of momentum at our scale.

According to QGD, the momentum of a particle or structure is given by where is the magnitude of the momentum vector of a particle or a structure , the momentum vectors of the component of and its mass measured in . The speed of particle is defined as . We saw that when a structure absorbs a photon of mass , then its new momentum is given by . We also saw that when is subjected to gravitational interaction, , the change in momentum is equal to so that . This is explained in more details in earlier articles. Now, let us see how QGD’s equations can be applied to explain and predict reality at our scale. To illustrate this, we will apply the QGD’s equations to baseball.

Let be a baseball and a baseball bat and let’s look at what happens when the ball, traveling towards the bat at speed is hit by a baseball bat, itself going at speed . Using the definitions above, we know that the momentums of and are respectively given by and and their speed by and . We also know that saw that, if space is quantum-geometrical, any change in momentum of an object must an exact multiple of it mass. That is : . As a consequence, unless the mass of the bat is an exact multiple of the mass of the ball, it cannot transfer all of its momentum to it. Then and , where the brackets represent the floor function.

Both bat and ball cannot occupy the same region of quantum-geometrical space, nor can they move through each other; which is prevented by the preonic exclusion (a can be occupied by only one ) and the electromagnetic repulsion between the atomic electrons of the ball and the bat. In short, the ball’s momentum along the axis of impact is not allowed. Similarly, the momentum of the bat along the perpendicular axis that passes through the point of impact is also not allowed. We will show that the momentums of the ball and the bat at impact must momentarily become is zero.

To resolve the impact event and at the same time conserve momentum, the ball and the bat must emit particles that carry with them the forbidden momentums and which bring their momentum along the axis of impact down to zero. If is one of particles emitted by the ball and is one of particles emitted by the bat at impact then and where and are respectively the forbidden momentums of ball and the bat along the axis of impact (in gray in see figure below).

Now we know from observation of such mechanical systems that the ball and the bat will transfer part their forbidden momentums to each other. What happens is that the bat will absorb the particles emitted by the ball and the ball will absorb the particles which have been emitted by the bat at impact. For a perfectly elastic collision, the momentums of the ball and the bat after impact, respectively and are given by the equations and . These equations provide a sufficiently precise description of the dynamics of momentum transfer at our scale, but they differs significantly from reality when we examine the impact at the microscopic scale at which, as we have seen in earlier posts, space is not continuous but quantum-geometrical.

If are to remain consistent with the axioms of QGD, then the momentum particles or structures (here the ball and the bat) can only change by discrete values which must be integer multiples of their mass; which QGD defines simply as the number of they contain. For the ball, this means that , where and ; the quotient of the Euclidean division of the sum of the momentums of the emitted particles over the mass of the ball after absorption of the particles so that . This implies that given the remainder of the above Euclidian division must correspond to sum of the momentums of the particles emitted by the bat but which the ball is forbidden to absorb. That is; where is the unique cardinal number attributed to one of particles that are absorbed or one of the particles which absorption by the ball is forbidden and .

If the impact preserves the physical integrity of the ball, the momentum that is not transferred to it will be radiated away carried by photons (mostly as infrared). If the impact is such that physical integrity of the ball is not preserved, then the particles could also be electrons, atoms or molecules.

Similarly, the bat will absorb photons from the ball and its momentum after impact will be and .

Using QGD’s definition of speed we find that the speed of the ball after impact is with . So if the momentum of the ball along the impact axis is less than that of the bat, then the ball after impact will have greater momentum, hence speed. If the momentum of the ball along the impact axis is greater than that of the bat, then the ball will have less momentum and speed after impact.

The physics of baseball bat hitting a baseball illustrates the fundamental mechanisms responsible for transfer of momentum. It is an example of how the physics at quantum-geometrical scale determines the behaviour at larger scales. For instance, it can be shown that much of the same equations we used to describe the physics of baseball can be used to describe nuclear fission. This is not surprising since, according to QGD, the same forces and laws apply at all scales.

Note that the following article assumes that the reader is familiar with the basic notions about quantum-geometry dynamics.

Those who are familiar with quantum-geometry dynamics know that it excludes quantum entanglement. Yet, as we will show in this article, QGD remains consistent with the results from all experiments which are thought to support quantum entanglement. Not only is QGD consistent with the experimental data of so-called quantum entanglement experiments but, unlike quantum mechanics, precisely explains the mechanisms responsible for the apparent quantum entanglement effect without violating the principle of locality.

In the setup shown in figure 1, which is called a Mach-Zehnder Interferometer, we have a source of light which beam is split in two by a half-silvered mirror. The classical prediction is that 50% of the light will be reflected to the mirror on the top left (path 1) and 50% will be refracted to the mirror at the bottom right (path 2). The light which arrives at the top left mirror will be reflected towards the back side of the half-silver mirror on the top right where it will be split into two beams towards detector 1 and detector 2, each of which should be receiving 50% of the photons coming through path 1 or with 25% of photons emitted by the source.

The photons that follows path 2 (50% of the photons from the source) are reflected by the mirror at the bottom right towards the half-silvered mirror at the top right where it will be split into two beams each having 50% of the photons following path 2 (or 25% of the photons from the source beam). So classical optics predicts that 50% of the photons from the source will reach D1 and the other 50% will each D2. But, see figure 2, experiments show that 100% of the photons from the source reach D2 and none reach D1.

The explanation provided by quantum mechanics, which is similar to that given for the results of double-slit experiments, proposes that the wave function of each individual photon travels both paths and engages in interference at the half-silvered mirror on the top right and that they interfere destructively at D1 and constructively at D2 (a detailed explanation can be found here).

Applying the QGD optics to the setup, we arrive a different and much simpler explanation.

We know from QGD’s description of optics and motion that an electron can absorb a photon only if . After absorption of a photon the mass of the electron will be increased by the mass of the photon, that is . And since electrons can only absorb a photon if then electrons will reflect photons .

So what happens according to QGD is that photons following path 1 are absorbed by the atomic electrons of the transparent part of the half-silvered mirror at the top right (since the distance from the source is shorter, they reach that part earlier). Since and , all photons which momentum is smaller than will be reflected back by these electrons. So, if the transparent part of the mirror exceeds a minimum thickness, the photons coming in from path 2 going through it will meet electrons along their path and, since which mass , will be reflected by them. (see figure 3, electrons at phase are in yellow area).

As for the photons from path 1 that reach the silvered surface of the top right mirror (figure 4), half will pass through towards D2, half will be reflected back towards their surface of entry. Those last photons will encounter electrons along their path back, but since their momentum of is less the momentum required for absorption by the electrons , , they will be reflected back towards the half-silvered surface of the mirror where half of these photons will be refracted towards D2 and the other half reflected back towards their surface of entry. This will continue until all photons are directed towards D2.

Now consider the setup shown in figure 5. Here we have 50% of the photons that will reach D3, 25% of the photons that will reach each of D1 and D2.

According to quantum mechanics, the photons moving along path 2 that reach D1 can only do so if the photons moving along path 1 are deflected towards D3. This raises the question: How the photons that reach D1 know that the photons of path 1 were deflected towards D3?

Quantum mechanics’ answer to that question is that the photons from path 1 and path 2 are entangled, a phenomenon known as quantum entanglement, by which a change done to photons on path 1, by a measurement for example, and which instantly affects the photons moving on path 2 even though the photons of path 1 are not in contact with the photons of path 2. And, according to quantum mechanics, it does so instantly and independently of the distance that separate the two groups of photons. If quantum mechanics is correct, that entangled photons be separated by a meter or billions of light-years does make any difference. This explanation of course violates locality, but this violation is essential to quantum mechanics if it is to correctly describe the result of experiments such as the ones we described above and which in turn, as interpreted by quantum mechanics, support the existence of quantum entanglement and non-locality.

That said, QGD optics provides a simpler interpretation of the results. Based on QGD’s explanation of the results from the setup shown figure 1 and figure 2, we understand that if photons in the second setup that move along path 2 will reach D2 simply because, without incoming photons from path 1, the atomic electrons of the transparent material remain in the state. Hence the photons from path 2 that are not reflected within the transparent part of the top right half-silvered mirror.

Thus quantum-geometry dynamics describes and explains the results without quantum-entanglement and without violating locality. That in itself does not mean that QGD better describes reality. It does however offer a much simpler and local realistic explanation. As such, it contradicts Bell’s theorem which implies that no local hidden theory can explain the correlations of such experiments as those described in this article. That said, any number of theories can be made to be consistent with data and thus explain physical phenomena a posteriori. The only valid tests of a theory are the predictions that it makes that are original to it and that can be verified experimentally.

QGD Experimental Predictions of “Non-Locality” Experiments

If QGD’s explanation of the result of the first setup is correct, and since as we explained, the refractive material needs to be of a certain minimum thickness so that any photons from path 2 will be intercepted by an atomic electron with mass , then reducing the thickness below a certain value (figure 6) will allow photons from path 2 to reach D1.

The minimum thickness being a number of electrons that exceeds the number of photons arriving from path 2 plus the photons from path 1 that are reflected back towards D1 by the reflecting surface of the top right mirror.

Also implied by QGD’s explanation is that, if the number of photons from path 2 moving through the top left mirror exceeds the number of electrons, then photons from path 2 will reach D1. This means that if the photon density of the source is increased passed a certain value, past the number of electrons which have absorbed photons from the path 1, then photons from path 2 will reach D1. Similarly, photons from path 1 reflected by the silvered side of the mirror will also reach D1. The actual number of photons that will reach is the difference between the number of photons from path 1 and path 2 moving towards D1 and the number of electrons in the state along their paths.

Each articles of this series will examine other experiments understood to support quantum entanglement and non-locality.

If you are interested in knowing more about QGD, I suggested reading earlier articles or the pdf book Introduction to Quantum-Geometry Dynamics.

Quantum mechanics essentially describes the Casimir effect as being caused by virtual photons which spring into existence out of the nothingness of the vacuum to impart the plates of the apparatus and pushing them towards each other. The introduction of virtual particles, which is required if quantum mechanics is to explain the phenomenon, also creates a number of problems (though not seen as problems within the framework of quantum mechanics) among which is the violation of the principle of conservation of energy and the consequential infinite vacuum energy.

QGD also attributes the Casimir effect to free preons(+); the single elementary particle of matter the theory requires. Thus QGD’s explanation of the effect does not violate the law of conservation or introduce any of the problems that arise from the assumption of virtual particles.

As we know, preons(+) are isotropically distributed throughout quantum-geometrical space. They constantly bombard all material objects. Consider the figure on the left where we have a plate . The plate divides quantum-geometrical space into two symmetrical regions and . Since the regions are symmetrical, and since the preonic density is the same in both, the resulting momentum of the preons(+) simultaneously hitting the plate from is equal that that from . That is: . The momentum of the free preons(+) hitting the plate cancel each other out.

But when we put two plates in close proximity as is the Casimir effect apparatus, we divide quantum-geometrical space into three regions; , and .

In this arrangement, the same number of preons(+) hit from as does the number of preons(+) that hit from , but the number of preons(+) that hit from is equal the number of preons(+) from minus the preons(+) that are absorbed or reflected by . Hence, if and are respectively the resultant momentum of the preons(+) hitting from and , then we must have . And, if , then net momentum imparted to will be . In other words, if was free, it would be pushed towards and its speed will increase by. Similarly, would move towards at .

Cosmological Implication

If QGD is correct then the Casimir effect must affect all objects which divide quantum-geometrical space asymmetrically. It follows that the Casimir effect must affect objects at the cosmic scale as well; pushing cosmic structures towards each other and thus contributing to the dark matter effect.

(The above is an excerpt from Introduction to Quantum-Geometry Dynamics)

Or How Our Two Cents May Be Worth 10,000 Times More

Suggested prior reading: Why Can’t Anything Move Faster Than Light?

I’ve been following the well written and often thought provoking blog of Johannes Koelman. One of his articles titled Einstein On Steroids: Dirac, The Higgs, And Speeding Neutrinos in which he discusses some of possible implications of the OPERA results (which appear to show that neutrinos can violate the speed of light limit imposed by special relativity) caught my attention.

In his interesting and entertaining article (which you should definitely read if only as an example of the sociology of science), Johannes suggests that no theoretical physicists would bet in favor of the confirmation of the OPERA results while there would be plenty of them that would bet against it (the results are overwhelmingly dismissed as being an experimental error).

Now, having predicted the possibility of relative superluminal particles (absolute speed cannot exceed the speed of light), specifically that relative superluminal photons and neutrinos. Both particles share some characteristics which allows them to move at relative speed in excess of c but with actual intrinsic speed equal to c. I confidently responded that I would take the bet.

As readers of this blog (see here and here) and Introduction to Quantum-Geometry Dynamics know, I believe that the speed in excess of the speed of light corresponds to speed of the Earth relative to the quantum-geometrical background along the axis connecting CERN to Gran Sasso.

I was pleasantly surprised that, like me, Johannes was willing to put his money where his “blogging mouth” is. So after exchanging a few email we agreed to the terms of a bet. You can read them on his blog appropriately titled Putting My Money Were My Mouth Is.

Of course, neither of us are doing this for the money (though $200 can buy an outing in a pretty decent restaurant and I love restaurants), but mainly as a way to stimulate discussions and awareness of the very fundamental question the OPERA group poses to physics.

I think this could be a lot of fun.