The Quantum-Geometer

Monday, April 28, 2014

On the Singularity of Light (QGD optics part 1)

The theoretical interpretations of observations of the behaviour of light indicate that it possess the mutually exclusive properties of the wave and the particle; a paradox that is known as the particle/wave duality. That light may have wave properties was hypothesized following observations of how light behaves in diffraction experiments, particularly in interference experiments such as the double-slit experiment where light produces diffraction and interference patterns that appear similar with diffraction patterns produced from observable waves in nature (such as waves on the surface of liquid). The similarities between the diffraction patterns are thought to imply that light may fundamentally be a wave.

Yet, some experiments, particularly those using a Talbot-Lau interferometer, have shown that material structures such as protons, neutrons, atoms, and even very large molecules display wavelike behaviour, that is, they display optical properties in the form of diffraction patterns. That calls the question: Does the wavelike behavior of light imply that it is fundamentally a wave? In order to answer that question, we need to understand what a wave is.

First, it is important to note that waves which we have observed and which inspired the wave model of light actually emerges from the motion of discrete structures; the motion of molecules of air or the molecules of water, for example. Thus the mathematical representation we call wave function models the motion and distribution of discrete particles that constitute a medium and describes the absorption and transfer of perturbation energy to other molecules of the medium, which create the waves which will eventually restore the state of equilibrium that existed prior to the perturbation (as when a stone is thrown in a pond, causing the displacement of water molecules).

Thus waves emerge from the interactions between discrete particles. That brings the questions: Is there really a wave-particle duality? Considering the above the answer is obviously “no.” Waves can be understood as the change in distribution in space of particles under the influence of a perturbation (kinetic energy) (and gravity for liquids submitted to Earth’s attraction). The wave properties are emergent, thus they cannot be fundamental.

Consider this: When studied under a powerful microscope, waves disappear leaving nothing but the motion of molecules. So would it make sense that we attribute to water molecules the fundamental property of the wave? Of course not! So why do we attribute the fundamental wave property to light? A property cannot at the same time be fundamental and emergent. And if we’re going to use the wave model for light, then isn’t not possible that its wavelike behavior is also emergent? Couldn’t waves emerge from the discrete interactions between photons and, for instance, the material slits are cut into to create the familiar diffraction or interference patterns? QGD’s answer to the question is unequivocally “yes.”

We will show that the diffraction and refractions patterns of particles, including that of photons, are actually scattering patterns that can be fully explained in terms of gravitational interactions between photons and the experimental apparatus. Therefore, diffraction experiments with larger particles dot not show that they possess wave properties similar to that of light, but the opposite. That is, light shares the discrete structures of larger particles so that diffraction patterns of light, too, emerge from the discrete gravitational interactions between photons and the blocking material in which slits are cut. In other words, the diffraction and refraction patterns can be fully explained without invoking any intrinsic or fundamental wave properties. As a consequence, it can be argued that light is singularly corpuscular and the diffraction patterns and interference patterns are simply scattering patterns of discrete particles caused by gravitational interactions and the structure of quantum-geometrical space.

For those who haven’t read the book or earlier blogs, QGD proposes that all that is not space must be made of preons(+). That includes all particles we currently believe to be elementary, even photons. QGD also proposes that energy is an intrinsic property of preons(+) which is their kinetic energy. The energy of a particle or material structure is then equal to the number of preons(+) it contains (which also corresponds to its mass $m$ ) multiplied by $c$ , the intrinsic energy of the preon(+), which gives the familiar $E=mc$ .

Note that unlike Einstein’s interpretation, E=mc is not an equivalence equation, but a proportionality equation. In QGD, energy is an intrinsic property of matter and so cannot exist without it. So energy can never be converted into matter nor matter be converted into energy. Thus nuclear reactions are not events in which matter is converted into energy, but ones in which bound particles are separated and carry with them their intrinsic momentums. The mechanisms of nuclear reactions is explained in greater detail in Introduction to Quantum-Geometry Dynamics, but for those who have no time to read it, consider the following image.

Imagine two massive spheres in space, in absence of gravity, each equal in mass and moving at high speed but attached by a string forcing them to orbit each other. Imagine that the system consisting of orbiting spheres, taken as a whole, is at rest. Then, the momentum of the system is equal to zero. Now, imagine that we suddenly cut the string. Taken as a whole, the energy of the system does not change, but the spheres now move freely. The energy of each sphere hasn’t changed, but the sphere being free, they carry with them their momentum. Now, can we conclude that part of the mass of the spheres changed into energy? No, since they number of preons(+) that compose them is unchanged. And since we know that energy is an intrinsic property of preons(+), the energy of the sphere hasn’t changed either. This in essence is what happens in a nuclear reaction. Photons and other particles composing the nuclear material which are bounded into a structure become free as a result of a nuclear reaction and carry with them their momentum (in the special cases of photons and neutrinos, the momentum is equal to the energy). The number of preons(+) of a system is unchanged by nuclear reactions, so mass and energy do not change either. The only difference is that previously bounded particles are now free to interact with other systems, imparting them with their momentums.

Now back to our subject; the singularity of light.

When distance is very short, as when light passes through a physical medium or comes very close to it, applying the QGD motion equation shows that the interaction between photons and the matter of the apparatus produces diffraction patterns identical to those observed in diffraction experiments. Consider the simple apparatus below in which light from a single source passes near a massive structure (the blue circle) and hits the screen represented here by the black solid line.

Using the equations for gravitational interaction and motion through quantum-geometrical space (discrete space) found in Introduction to Quantum-Geometry Dynamics, we find that the deflection angle $\theta$ is given by $\theta =\frac{G\left( a;\lambda \right)}{c}$ . where $G\left( a;b \right)$ is the form of the QGD equation for gravity that applies at the fundamental scale (see Introduction to Quantum-Geometry Dynamics) .

From this, we see that the angle of deflection will depend upon the mass of the photon, that is, the number of $preon{{s}^{\left( + \right)}}$ it contains.

We also know from the laws of motion described in Introduction to Quantum-Geometry Dynamics that though the magnitude of the momentum vector of a photon does not change, its direction does as per the equation above. But we have seen that any change of direction implies a change the momentum along that direction and that only change that are integer multiples of the mass of the object is allowed. That is, if $\Delta \left\| {{{\vec{P}}}_{\lambda }} \right\|=G\left( a;\lambda \right)=x{{m}_{\lambda }}$ where $x\in {{N}^{+}}$ .

It follows that if photons are emitted from a single source, as in our apparatus, angles of deflection such at $\frac{\left( x-1 \right){{m}_{\lambda }}}{c}<\theta <\frac{x{{m}_{\lambda }}}{c}$ will be forbidden .

The allowed deflection and forbidden region will contribute to produce diffraction patterns as shown in the following image and the fringe patterns we normally associate with wave interference.

As you can see, the diffraction patterns are produced using only the particle model of light, producing he patterns we attribute to a wave-like property. The width and spacing between the fringes will be a function of the mass of the photons and their distance from the massive structure. More massive photons will, according to the equation above, have larger the range of forbidden deflection angles and narrower fringes. Note that this result is only possible if space is quantum-geometrical as defined by QGD. Note that if $a$ were the corner of a structure, then light would be bent around it in a manner consistent with our model and which behavior of light has been observed.

It is interesting to note that when we apply the same equation to photons passing through slits or double slits, they will invariably produce the diffractions patterns that have been observed and which we have come to associate with waves. The main difference with our above example is that in slit experiments, light passes through the massive structure and the photon course deflection is the net resultant of the gravitational interaction between the photon and the massive structure, which will depend on both shake and density of the material the slit(s) is(are) cut into. Applied to different shapes, the interaction equation predicts patterns consistent with observations. Below are some examples of observation consistent with the singularly corpuscular model of light.

diffraction pattern for single slit square aperture

diffraction pattern for single slit round aperture

single and double slit patterns

Refraction

When applied to photons moving through material, such as the glass of a prism, the QGD equations describe exactly the deviation of photons from their course. The magnitude of the deviation is, according to QGD, directly proportional to photon’s mass. So more massive photons, which are correctly associated with higher energy (bluer photons) will be deviated more than their lighter counterparts. The interaction with the material, in a prism or any other form, is the resultant of the gravitational interactions between the photon and material it passes through. The deviation will thus be towards the more massive part of the structure. For a prism, that will be the base (see image below).

Refraction is discussed in more detail in part 2 of this series.

The Notions of Frequency and Wavelength in the Light of Quantum-Geometry Dynamics

As we have seen, the patterns of diffraction and refraction of light are completely described by a model of light in which it is singularly corpuscular. If light, as QGD proposes, light is singularly corpuscular, that is, all wave-like behaviour are emergent, then we must reinterpret our observations of optical phenomena and revise, if not abandon altogether, the application of the concepts of frequency and wavelength to light.

In part 2 of this series of articles on QGD optics, we will discuss refraction of light. Part 3 will be on reflection of light and the photoelectric effect.

Sunday, April 6, 2014

Experiment Supports Key Predictions of 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 $preon{{s}^{\left( + \right)}}$ ; one of only two fundamental particles predicted to exist by QGD. $Preon{{s}^{\left( + \right)}}$ 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 $preon{{s}^{\left( + \right)}}$ not the reverse). The speed and momentum of $preon{{s}^{\left( + \right)}}$ 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 $preon{{s}^{\left( + \right)}}$ of an electron, binds them into helical trajectories (see this article).

Also according to QGD, the majority of $preon{{s}^{\left( + \right)}}$ 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 $preon{{s}^{\left( + \right)}}$ of electrons and their neighboring regions of the preonic field. The electrons (or other charged particles) affect the direction of free $preon{{s}^{\left( + \right)}}$ , 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 $preon{{s}^{\left( + \right)}}$ which impart them their momentum.

Now, though QGD predicts that no particles or structures can move (propagate) faster than $preon{{s}^{\left( + \right)}}$ , 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 $preon{{s}^{\left( + \right)}}$ , 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 $preon{{s}^{\left( + \right)}}$ 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.

Wednesday, March 5, 2014

Baseball Physics as Explained by Quantum-Geometry Dynamics

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 $preon{{s}^{\left( - \right)}}$ 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 $preon{{s}^{\left( - \right)}}$ , which according to QGD are the discrete and fundamental units of space, and $preon{{s}^{\left( + \right)}}$ , 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 $\left\| {{{\vec{P}}}_{a}} \right\|=\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|$ where $\left\| {{{\vec{P}}}_{a}} \right\|$ is the magnitude of the momentum vector of a particle or a structure $a$ , ${{\vec{c}}_{i}}$ the momentum vectors of the component $preon{{s}^{\left( + \right)}}$ of $a$ and ${{m}_{a}}$ its mass measured in $preon{{s}^{\left( + \right)}}$ . The speed of particle is defined as ${{v}_{a}}=\frac{\left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}}$ . We saw that when a structure $a$ absorbs a photon $b$ of mass ${{m}_{b}}$ , then its new momentum $\displaystyle \left\| {{{{\vec{P}}'}}_{a}} \right\|$ is given by $\displaystyle \left\| {{{{\vec{P}}'}}_{a}} \right\|=\left\| {{{\vec{P}}}_{a}}+{{{\vec{P}}}_{b}} \right\|$ . We also saw that when $a$ is subjected to gravitational interaction, $\displaystyle \vec{G}\left( a;b \right)$ , the change in momentum $\Delta \left\| {{{\vec{P}}}_{a}} \right\|$ is equal to $\displaystyle \left\| \vec{G}\left( a;b \right) \right\|$ so that $\displaystyle \left\| {{{{\vec{P}}'}}_{a}} \right\|=\left\| {{{\vec{P}}}_{a}}+\vec{G}\left( a;b \right) \right\|$ . 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 $a$ be a baseball and $b$ a baseball bat and let’s look at what happens when the ball, traveling towards the bat at speed ${{v}_{a}}$ is hit by a baseball bat, itself going at speed ${{v}_{b}}$ . Using the definitions above, we know that the momentums of $a$ and $b$ are respectively given by $\left\| {{{\vec{P}}}_{a}} \right\|=\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|$ and $\left\| {{{\vec{P}}}_{b}} \right\|=\left\| \sum\limits_{i=1}^{{{m}_{b}}}{{{{\vec{c}}}_{i}}} \right\|$ and their speed by ${{v}_{a}}=\frac{\left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}}$ and ${{v}_{b}}=\frac{\left\| {{{\vec{P}}}_{b}} \right\|}{{{m}_{b}}}$ . 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 : $\Delta \left\| {{{{P}'}}_{a}} \right\|=x{{m}_{a}}$ . 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 $x=\left\lfloor \frac{\left\| {{{\vec{P}}}_{b}} \right\|}{{{m}_{a}}} \right\rfloor$ and $\Delta \left\| {{{\vec{P}}}_{a}} \right\|=\left\lfloor \frac{\left\| {{{\vec{P}}}_{b}} \right\|}{{{m}_{a}}} \right\rfloor {{m}_{a}}$ , 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 $preo{{n}^{\left( - \right)}}$ can be occupied by only one $preo{{n}^{\left( + \right)}}$ ) 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 ${{a}_{i}}$ is one of ${{n}_{a}}$ particles emitted by the ball and ${{b}_{i}}$ is one of ${{n}_{b}}$ particles emitted by the bat at impact then $\displaystyle \sum\limits_{i=1}^{{{n}_{a}}}{{{{\vec{P}}}_{{{a}_{i}}}}}={{\vec{P}}_{a}}\left( a;b \right)$ and $\displaystyle \sum\limits_{i=1}^{{{n}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}={{\vec{P}}_{b}}\left( a;b \right)$ where $\displaystyle {{\vec{P}}_{a}}\left( a;b \right)$ and $\displaystyle {{\vec{P}}_{b}}\left( a;b \right)$ 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 ${{a}_{i}}$ emitted by the ball and the ball will absorb the particles ${{b}_{i}}$ 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 ${{{\vec{P}}'}_{a}}$ and ${{{\vec{P}}'}_{b}}$ are given by the equations ${{{\vec{P}}'}_{a}}={{\vec{P}}_{a}}-{{\vec{P}}_{a}}\left( a;b \right)+{{\vec{P}}_{b}}\left( a;b \right)$ and ${{{\vec{P}}'}_{b}}={{\vec{P}}_{b}}-{{\vec{P}}_{b}}\left( a;b \right)+{{\vec{P}}_{a}}\left( a;b \right)$ . 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 $preon{{s}^{\left( + \right)}}$ they contain. For the ball, this means that $\displaystyle \Delta {{\vec{P}}_{a}}=x{{m}_{{{a}'}}}$ , where ${{m}_{{{a}'}}}={{m}_{a}}-\sum\limits_{i}^{{{n}_{a}}}{{{m}_{{{a}_{i}}}}}+\sum\limits_{i}^{{{n}_{b}}}{{{m}_{{{b}_{i}}}}}$ and $x=\left\lfloor \frac{\sum\limits_{i=1}^{{{{{n}'}}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}}{{{m}_{{{a}'}}}} \right\rfloor$ ; 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 ${{{\vec{P}}'}_{a}}={{\vec{P}}_{a}}-{{\vec{P}}_{a}}\left( a;b \right)+\left\lfloor \frac{\sum\limits_{i=1}^{{{{{n}'}}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}}{{{m}_{{{a}'}}}} \right\rfloor {{m}_{{{a}'}}}$ . 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; $\displaystyle \sum\limits_{i=1}^{{{{{n}''}}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}=\sum\limits_{i=1}^{{{{{n}'}}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}-\left\lfloor \frac{\sum\limits_{i=1}^{{{{{n}'}}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}}{{{m}_{{{a}'}}}} \right\rfloor {{m}_{{{a}'}}}$ where $i$ is the unique cardinal number attributed to one of ${{{n}'}_{b}}$ particles that are absorbed or one of the ${{{n}''}_{b}}$ particles which absorption by the ball is forbidden and ${{{n}''}_{b}}={{n}_{b}}-{{{n}'}_{b}}$ .

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 $\displaystyle {{{\vec{P}}'}_{b}}={{\vec{P}}_{b}}-\sum\limits_{i=1}^{{{n}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}-\left\lfloor \frac{\sum\limits_{i=1}^{{{n}_{a}}}{{{{\vec{P}}}_{{{a}_{i}}}}}}{{{m}_{{{b}'}}}} \right\rfloor {{m}_{{{b}'}}}$ and $\displaystyle \Delta {{\vec{P}}_{b}}={{{\vec{P}}'}_{b}}=-\sum\limits_{i=1}^{{{n}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}+\left\lfloor \frac{\sum\limits_{i=1}^{{{n}_{a}}}{{{{\vec{P}}}_{{{a}_{i}}}}}}{{{m}_{{{b}'}}}} \right\rfloor {{m}_{{{b}'}}}$ .

Using QGD’s definition of speed we find that the speed of the ball after impact is ${{v}_{{{a}'}}}=\frac{{{{\vec{P}}}_{{{a}'}}}}{{{m}_{{{a}'}}}}$ with $\Delta {{v}_{a}}=\frac{-{{{\vec{P}}}_{a}}\left( a;b \right)}{{{m}_{{{a}'}}}}+\left\lfloor \frac{\sum\limits_{i=1}^{{{{{n}'}}_{b}}}{{{{\vec{P}}}_{{{b}_{i}}}}}}{{{m}_{{{a}'}}}} \right\rfloor$ . 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.