If so one should be able to derive the strong force in those terms.

The strong force, also known as the strong interaction, is the strongest force in the universe, 10³⁸ times stronger than gravity and 100 times stronger than the electromagnetic force.  However, it is only effective on length-scales of the atomic nucleus and drops rapidly off as the distance from the nucleus increases.

Earlier in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
(Louis de Broglie was the first to predict the existence of a matter wave when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.)

Briefly it was shown the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in an environment consisting of four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four *spatial* dimensions.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

Later in the article “The geometry of quarks” Mar. 15, 2009 it was shown that one can understand why a particle is made up of three quarks of different “colors” again by extrapolating the geometric of three-dimensional space to a fourth while the article “Embedded dimensions” Oct. 22. 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Using the concepts developed in those articles one derive the mechanism responsible for why observe of particles are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom.  The Up, Charm and Top have a fractional charge of 2/3.  The Down, Strange and Bottom have a fractional charge of -1/3.  Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green.

The explanation is based in part on the fact that we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its “surface” with respect to a fourth *spatial* dimension will be observed by us as being directed along that “surface”.  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a “surface” of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that “surface”.

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article “Embedded dimensions” there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the configuration or “colors” of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it also explains why it takes three quarks of different “colors” to form a particle because, as mentioned earlier one can define a particle in terms of a resonant system on a “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not be stable.

A proton contains two up Quarks with a +2/3 charge and one down quark with a -1/3 charge.  This tells us because they are stable that the resonant interaction of their geometries contains more energy that the electrical repulsive energy associated with their positive charge.

It is this excess resonant binding energy associated with their dimensional properties defines the causality of the strong force and the stability of a nucleus.

However, its components or protons and neutrons must be physically close enough for them to share this excess energy to create a stable one.

The sharing of this excess binding energy is also responsible for the creation of neutrons because geometrically it takes less energy for a volume to contain the two up quarks and two down quarks of a proton and neutron instead of four up quarks and two down quarks of two protons. In other words their electrical repulsive energy associated with the quarks is cut in half when the volume contains a proton and neutron instead of two protons and therefore energy/mass component of that volume will be in the lowest energy state possible.

However, the addition of a neutron to a nucleus adds the excess binding energy associated with its resonant system without the repulsive effects associated with of the positive charge of a proton.

Therefore, the existence of neutrons in a nucleus allows for creation of larger ones consisting of multiple positively charged protons because they add the binding energy associated with their resonant system without adding any repulsive electrical charge.

Yet this indicates that the binding energy of the strong force would be related to the size of the nucleus after a certain atomic weight is reached a nucleus will become physically too large for the individual resonant “structures” associated with the protons and neutron to uniformly share the energy require to maintain its structure.  This will result in that nucleus expelling the energy/mass required to reduce its physical size to a point where a stable nucleonic structure can be maintained.  Therefore, any nucleus that is physically larger than this critical value will be radioactive.

Additionally, the nucleus of atoms that have an atomic weight less than the critical value would increase its weight and size by “absorbing” energy/mass from an external source.  This will result in increasing the size and atomic number of that nucleus.

This indicates that the effectiveness of the strong nuclear force in absorbing or emitting energy/mass would only be effective on length-scales of the atomic nucleus and would drop rapidly off as the distance from the nucleus increases.

This shows how one can derive mechanism responsible for the strong nuclear force by extrapolating the classical laws governing resonance in a three-dimensional environment to one made up of four.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The Strong force in four *spatial* dimensions appeared first on Unifying Quantum and Relativistic Theories.

If so one should be able to define the weak force in those terms.

The weak force is responsible for changing to one quark to another or a lepton to another lepton – the so-called “flavor changes” when particles undergo radioactive decay.  In Physics speak the weak interaction involves the exchange of the intermediate vector bosons, the W and the Z.

Earlier in the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown that one can derive the quantum mechanical properties of energy/mass by extrapolating the laws of classical resonance in three-dimensional space to a matter wave on a surface of a three dimensional space manifold with respect to four *spatial* dimension.
(Louis de Broglie was the first to predict the existence of a matter wave when he theorized that all particles have a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer. )

Briefly it was shown the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in an environment consisting of four *spatial* dimensions.

The existence of four *spatial* dimensions would give a matter wave the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.

These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital.  This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate at the frequency associated with the energy of that event.

However, the oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four *spatial* dimensions.

These resonant systems are responsible for the quantum mechanical properties energy/mass.

Later in the article “The geometry of quarks” Mar. 15, 2009 it was shown that one can understand why a particle is made up of three quarks of different “colors” again by extrapolating the geometric of three-dimensional space to a fourth while the article “Embedded dimensions” Oct. 22. 2007 showed it is possible to define all forms of energy including electrical in terms of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

Using the concepts developed in those articles one derive the mechanism responsible for why observe of particles are made up of distinct components called quarks of which there are six types, the UP/Down, Charm/Strange and Top/Bottom.  The Up, Charm and Top have a fractional charge of 2/3.  The Down, Strange and Bottom have a fractional charge of -1/3.  Scientists have also determined that quarks can take on one of three different configurations they have designated by the colors red, blue, and green.

The explanation is based in part on the fact that we as three-dimensional beings can only observe three of the four *spatial* dimensions.  Therefore, the energy associated with a displacement in its “surface” with respect to a fourth *spatial* dimension will be observed by us as being directed along that “surface”.  However, because two of the three-dimensions we can observe are parallel to that surface we will observe it to have 2/3 of the total energy associated with that displacement and we will observe the other 1/3 as being directed along the signal dimension that is perpendicular to that surface.

This means the 2/3 fractional charge of the Up, Charm and Top may be related to the energy directed along a “surface” of a displaced three-dimensional space manifold with respect to a four *spatial* dimension while the -1/3 charge of The Down, Strange and Bottom may be associated with the energy that is directed perpendicular to that “surface”.

The reason why quarks come in three configurations or colors with a fractional charge of 1/3 or 2/3 may be because, as was shown in the article “Embedded dimensions” there are three ways the individual axis of three-dimensional space can be oriented with respect to a fourth *spatial* dimension.  Therefore, the configuration or “colors” of each quark may be related to how its energy is distributed in three-dimensional space with respect to a fourth *spatial* dimension.

However, it also explains why it takes three quarks of different “colors” to form a particle because, as mentioned earlier one can define a particle in terms of a resonant system on a “surface” a three-dimensional space manifold with respect to a fourth *spatial* dimension.  If the colors of each quark represent the central axis associated with its charge then to form a stable resonate system would require three quarks that have different central axis to balance its energy with respect to the axes of three-dimensional space.  A particle could not exist if two quarks have the same central axis or color because it would cause an energy imbalance along that axis.  Therefore, a particle consisting of anything but quarks of three different colors would not stable.

This suggests that the stability of the energy/mass components of particles are related to a resonant interaction between the components of three and fourth *spatial* dimensions.

As mentioned earlier the weak force manifests itself in the transmutation of a quark from one flavor or color to another when nuclear particles decays and manifest itself by changing one quark to another, or a lepton to another lepton, the so-called “flavor or color changes”.

However this is what one would expect if their stability was related to, as mentioned above the geometric configuration of their central axis because the only thing that distinguishes their color or flavor is how their central axes in the fourth *spatial* dimension orientated with respect to three-dimensional space.   If the individual quark components of a particle were not in the lowest energy configuration they would rotate around that axis until they were. 

However, as mentioned earlier a particleâ€s stability is related to how the central axis of its component quarks are oriented with respect to a fourth *spatial* dimension.  Therefore the weak force could be defined in terms of the energy associated with their most stable geometric configuration.  In other words to form a stable particle the central axis of its quarks would have to rotate around their fourth dimensional axis until the particle they were a part of had obtained the lowest geometric energy configuration possible with respect to a fourth *spatial* dimension. 

Hence one could derive the casualty of the transmutation or the flavor or color change of quarks from to another in terms of the reconfiguration of its central axis with respect to a fourth *spatial* dimension required to form a stable particle.

This is analogous to the central axis of a wind vane rotates in three-dimensional towards the direction of the wind to reduce the amount of force or energy on its two-dimensional surface by the wind.

Similarly the three-dimension axis of quarks will rotate in four *spatial* dimensions to reduce the energy content of a particle to its lowest level.

As mentioned earlier the binding energy holding quarks together is dependent on the resonant interaction their central axis.  Therefore, magnitude of weak nuclear force binding them together would be associated with the flavor or color change that occurs when an atomic decay takes place.

The reasons the weak force manifests itself in the exchange the vector particles called the W and  Z bosons is because as was shown in the article “Why is energy/mass quantized?” all energy is propagated in discrete resonant structures.  Therefore, it will have particle properties that article associates with them.

This shows how one can derive mechanism responsible for the weak force by extrapolating the classical laws governing resonance in a three-dimensional environment to one made up of four *spatial* dimensions.

Later Jeff

Copyright Jeffrey O’Callaghan 2011

The post The weak force in four *spatial* dimensions appeared first on Unifying Quantum and Relativistic Theories.

We have shown throughout this blog and its companion book “The Reality of the Fourth *Spatial* Dimension” it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einsteinâ€s Special and General Theories of Relativity while at the same time defining several theoretical advantages to adopting this perspective over that of his theories.

One is that it would allow theoreticians to conceptually define the origin of antimatter by extrapolating the classical laws of three-dimensional space to the geometry of four *spatial* dimensions.
In Einstein’s Theory of Relativity the total energy of body consist of two parts, its rest energy defined by the equation E= mc^2 and its kinetic energy defined by KE=1/2mv^2.  However, Einstein tells us that because of the interaction of time and space the total energy of a body is defined by Pythagoras rule for right triangles or that the square of the hypotenuse equals the sum of the square of the other two sides.  In other words according to Einstein the total energy of a body “E” is equal to the square root of the sum or the squares of it rest energy or mc^2 and its kinetic energy or 1/2mv^2.

However, when Oscar Klein tried to derive the quantum mechanical properties of an electron defined by Schrödinger’s equation he discovered that there were positive and negative solutions to the equations that defined its energy because the square root of a number can be either positive or negative.  Paul Dirac had a similar problem when he attempted to solve the total energy problem in terms of matrices.  He also discovered that it predicted the existence of electron with both positive and negative energy.

The symmetry imposed upon matter by these two solutions indicated to many scientists in1928 that there might be an “antiparticle” to the electron.  In other words it showed that there should be a particle with the same energy/mass as an electron but with an oppositely directed or positive charge that would annihilate each other if they came in contact. 

In 1932, Carl D. Anderson confirmed their suspensions when he discovered its antiparticle the positron

But how can one define the negative energy of an electron or a positron in terms a vacuum.

Dirac explanation was that a vacuum was not actually empty but instead is a bottomless pit into which is a ladder whose rungs correspond to the positive and negative energy stated in his equations.  The top run of the ladder corresponds to zero energy and all the rings below it correspond to negative energy states for electrons.  His insight was that if the top of the ladder correspond to zero energy all the runs below it would correspond to negative energy.  If one was to remove a negative energy electron from a vacuum it would essentially leave a hole in it.  Therefore in electron positron annihilation would fill in the hole raising the level of the vacuum to zero.

However, there is a conceptual flaw within his arguments which is that the energy of a vacuum does not return to zero because when electrons and positrons combine they release the energy associated with their combine masses.

Yet  the existence of four *spatial* dimensions provides a classical interpretation of what happens in a vacuum when electrons and positrons meet and annihilate each other.

As mentioned earlier, we have shown throughout this blog it is possible to define a universe in terms of four *spatial* dimensions in a manner that makes predictions identical with those of Einsteinâ€s General and Special Theories of Relativity.

In the article “Gravity in four spatial dimensions” Dec. 15, 2007 it was shown that one can define mass in terms of a “depression” or downward directed displacement in a “surface* of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, this means one could define the symmetry between the energy/mass of matter and antimatter as being the result of oppositely directed displacements in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension because a spatial dimension can move in two directions up and down with respect to each other.  In other words one could define the negative energy/mass associated with a electron in terms of a “depression” in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension while define positive energy/mass of a positron in terms of a “elevation” in that “surface”.

Unfortunately time is only observed to move in one direction forward and therefore a vacuum composed of four-dimensional space-time would not allow the “surface” of three-dimensional space to “move” up and “down” with respect to it.  Therefore, it does not permit the existence of the negative energy.

Earlier the article “Embedded dimensions” Oct. 22, 2007 showed that one can define the total energy of a volume in terms of the magnitude of a displacement in a “surface” of three-dimensional space.

Therefore, the total energy/mass of a particle / anti-particle system would be equal to the sum of their relative displacements associated with their energy/mass.

Hence the reason particles and anti-particles annihilate each other when they meet while releasing the sum of the energy associated with their combined masses is because the “depression” in a “surface” of a three-dimensional space manifold associated with the mass of an electron will “filled in” or be cancelled by the “elevation” associated a positron’s thereby leaving no displacement in that “surface” and therefore no mass in the volume associated with it.  However as was shown in the article “Embedded dimensions“ because their displacements are oppositely directed with respect to a fourth *spatial* dimension their energy components will be additive and therefore, when the combine they will release the energy associated with their combined masses.

Therefore, it does not have the conceptual flaw inherent in Dirac solution because the energy of a vacuum would not return to zero when electrons and positrons combine instead they will release the energy associated with their combine masses.

However, it also allows one to define a conceptual mechanism in terms of the classical hydrodynamics for the creation of particle / antiparticle pairs that is independent of abstract mathematical logic. 

Classical hydrodynamics tells us if we push down on a small area on the surface of water it will become displaced.  However, it also tells us that the volume of water displaced by that downward pressure will be offset by an equal but opposite volume displaced in the upward direction.

Similarly if mass is a result of a displacement in a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension any “downward” displacement in its “surface” will be offset by an equal but oppositely “upward” directed displacement.

Therefore, according to classical hydrodynamics a particle could not be created without the creation of its antiparticle because as mentioned earlier it tells us that when a surface undergoes a displacement an equal but opposite one must be creates on that surface.

yet on can using the concept understand why there is more matter than antimatter in there universe.

As was mentioned earlier, one can derive the energy/mass of a particle in terms of a “downward” directed displacement in a “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension while the energy/mass of an antiparticle in terms of an “upward” directed one in that same surface.

But this indicates on average it would require less energy to form a particle than an antiparticle for the same reason that it takes less energy to fill a bucket with water by pushing it down below its surface than it does by lifting the water into a bucket that is above its surface because that bucket is a higher gravitational potential . 

Therefore, there would be some energy left over if an equal number of particles and antiparticles were annihilated.  This left over energy is responsible of energy/mass of particles presently in the universe.

However, the reason this left over energy/mass takes the form of a particle and not anti particles is because the relative properties of energy means it can be defined in terms of a reference frame that would make it a particle instead of an antiparticle.

This defines the reason in terms of the geometry of four *spatial* dimensions for the asymmetry between particles and antiparticles and the observations regarding there interactions.

Later Jeff

Copyright Jeffrey Oâ€Callaghan 2011

The post The Geometry of antimatter. appeared first on Unifying Quantum and Relativistic Theories.