The Imagineer's Chronicles: A theoretical blog

Chapter Twenty-Four

Maxwell's equations can be derived from the existence of four *spatial* dimensions, a continuous non-quantized form of mass and the laws of classical physics.

Chapter two derived the quantum characteristics of mass, energy and a photon in terms of the integral energies associated with a resonant "system" formed in space by "oscillations" in a continuous non-quantized form of mass.

Chapter three defined the propagation of a photon and electrical energy in terms of "oscillations" in a continuous non-quantized form of mass caused by a matter wave moving at the velocity of light in a continuous non-quantized form of mass.

(Chapter fifteen will shown the velocity of light is universally constant, despite the fact that it is transmitted on a physical medium consisting of a continuous non-quantized form of mass, because of a relativistic property of time and four *spatial* dimensions.)

Therefore, Chapters two and three define a common mechanism responsible for both the quantum and wave characteristics of an electrical energy because they define both in terms of "oscillations" caused by a matter wave in continuous non-quantized form of mass.

(Louis de Broglie was the first to theorize that all particles had a wave component.  His theories were confirmed by the discovery of electron diffraction by crystals in 1927 by Davisson and Germer.  However, this means there must be a continuous non-quantized medium for it to be propagated on because even the smallest possible particle must have a wave component. Therefore, there must exist a continuous non-quantized medium to propagate the wave of the smallest possible particle. However, macroscopic observations of wave energy indicate that it can only be propagated on a medium made up of mass. Therefore, the success of Louis de Broglie theory indicates that a continuous non-quantized form of mass exists.)

However, the existence of a continuous non-quantized form of mass and four spatial dimensions also provides the ability to define a mechanism responsible for Maxwell's equations in terms of the laws of classical physics

The "oscillations" in a continuous non-quantized form of mass responsible for generating a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension is analogous to oscillations associated with a wave on the surface of water.

In a classical world, the trough of a wave on water displaces the vertical volume of water below the surface of the water with air while its peak displaces the air above the surface of the water with water.

Similarly, a "trough" of a matter wave on a "surface" of a three-dimensional space manifold would displace a volume of three-dimensional space below a "surface" of a three-dimensional space manifold with a component of four-dimensional space.  While a "peak" of a matter wave would displace a "volume" of four-dimensional space above a "surface" of a three-dimensional space manifold with a continuous non-quantized mass component of three-dimensional space.

Chapter ten derived all forms of energy in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This means the sinusoidal displacements in a "surface" of a three-dimensional space manifold caused by the "peaks" and "troughs" of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be responsible for the propagation of electromagnetic flux.

Electric flux is a result of the energy associated with a matter wave that is directed parallel to the velocity vector of the matter wave "along" a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

However, because of the geometry of four *spatial* dimensions the "peaks" and "troughs" of a matter wave will cause a force to be developed that will be tangential to the velocity vector of a matter wave on a "surface" of a three-dimensional space manifold.  This force is responsible for magnetic flux and will always be 90 degrees out of phase with the electrical flux component of the matter wave.

First the mechanism responsible for Gauss's law of Electricity, the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity will be derived in terms of the geometric properties of four *spatial* dimensions.

Next Gauss's law of Magnetism, the net magnetic flux out of any closed surface is zero and that there are no magnetic monopoles will be defined in terms of the alignment of a "W" axis of a fourth *spatial* dimension with respect to the axes of three-dimensional space.

(The W axis of the fourth *spatial* dimension was defined in Chapter ten.)

Following that the physical mechanism responsible for Ampere's Law, the magnetic field in space around an electric current is proportional to the electric current that serves as its source will be derived in terms of an energy gradient in a three-dimensional space manifold that Chapter thirteen derived as being responsible for an electric charge. 

Then the fourth of Maxwell's equations or Faraday's law of induction that any change in a magnetic environment of a coil will cause a voltage to be "induced" in the coil that is equal to the negative rate of change of the magnetic flux times the number of turns of the coil will be derived in terms an energy gradient associated with a unit electric charge and inertial properties of a continuous non-quantized form of mass defined in Chapter one.

Gauss's law of electricity states the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity or "integral of E*dA =Q / permittivity".

The mechanism responsible for the total electric flux out of a closed surface being equal to the charge enclosed is related to the "peaks" and "troughs" of a matter wave on a "surface" of a three-dimensional space manifold.

Chapter nine derived the magnitude of an electric charge in terms of separation between two surfaces" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  A positive electric charge was defined in terms of a "depression" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while a negative electric charge was defined in terms of an "elevation" in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

As mentioned earlier the displacements in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension caused by the "peaks" or "elevations" and "troughs" or "depressions" of a matter wave are responsible for the propagation of electrical flux through space.

Therefore, as was shown in Chapter nine the displacements caused by the alternating "elevations" and "depressions" in a "surface" of a three-dimensional space manifold generated by a matter wave would be responsible for the transmission of positive and negative electrical energy through space.

However, as was shown in Chapter two and three the energy of a matter wave associated with charged particles form resonant "systems" or photons of electromagnetic energy in a continuous non-quantized form of mass.

Therefore the number photons of electric flux radiated through space will be dependent on the number of charged particles that generate those photons.

This indicates the total electric flux or energy out of a closed "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension surrounding an electrical charge will be equal, as Gauss's Law of Electricity states, to number of charge particles enclosed by that surface.

The fact that the total electric flux out of a closed surface must be divided by the permittivity of the volume of space an electric flux is transversing is related to the mechanism responsible for the propagating electric flux in space.

As mentioned earlier a electrical flux is propagated thought space by a matter wave in a continuous non-quantized form of mass moving at the velocity of light.

However, Chapter twelve showed there would be direct relationship between the density or permittivity of space and the density of a continuous non-quantized form of mass in that space. 

Therefore, the electric flux out of a closed surface must be divided by the permittivity of the volume of space because the attenuation of a matter wave moving though a continuous non-quantized form of mass would be directly related to the density of the continuous non-quantized form of mass that it was moving through.

This completes the derivation of the physical mechanism responsible for Gauss's law of electricity in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass.

We will now derive the mechanism responsible for Gauss's law for magnetism, that the net magnetic flux out of any closed surface is zero and that magnetic monopoles do not exist or the integral of B*dA=0 in terms of the existence of four *spatial* dimensions.

The mechanism responsible for net magnetic flux out of a closed surface being equal to zero is related to the "alignment" or angle the "W" axis of a fourth *spatial* dimension has with respect to coordinate planes of a three-dimensional space.

(As mentioned earlier the "W" axis of the fourth *spatial* dimension was defined in Chapter ten.)

Chapter eleven indicated that magnetic flux was due a "tangential" force generated on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension by a "misalignment" of a "W" axis of a fourth *spatial* dimension with respect to the coordinate plains of three-dimensional space.

Therefore, the misalignment of a "surface" of a three-dimensional space manifold with respect to the "W" axis of a fourth *spatial* dimension caused by the "peaks" and "troughs" of a matter wave on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension would be responsible for the alternating polarity of the magnetic flux associated with propagation of electromagnetic energy.

However the "angle" or "alignment" a "W" axis of the fourth *spatial* dimension makes with a coordinate plain in a three-dimensional space manifold would be analogous to the angle a line makes when drawn through a plain on a coordinate graph.

A line will always make symmetrically equal and opposite angles above and below the coordinate plain it transverses.

Similarly, a “W” axis of a fourth *spatial* dimension will always make symmetrically equal and opposite angles "above" and "below" the coordinate plain in a three-dimensional space manifold it transverses.

Therefore, as was indicated in Chapter eleven the magnetic force or flux associated with a magnetic flux must always be equal and opposite "above" and "below" the three-dimensional coordinate plain it traverses.

This results in the net magnetic flux or force out of any closed surface always being equal to zero because the magnitude and "direction" of a force responsible for magnetic flux will be equal and opposite "above" and "below" a three-dimensional coordinate plain it is transversing.

This also defines the physical reason why magnetic monopoles cannot exist.

Magnetic monopoles cannot exist because the "W" axis of the fourth spatial dimension is infinite in length

This is analogous to how the each axis in three-dimensional space is infinite in length.

Therefore, magnetic monopoles do not exist because of the fact that the "W" axis of a fourth *spatial* dimension is infinite in length it must generate two magnetic fields of equal and opposite polarity "above" and "below" any coordinate plain in three-dimensional space it transverses.

This completes the derivation of the physical mechanism responsible for Gauss's law of Magnetism in terms of the orientation of "W" axis of the fourth *spatial* dimension with respect to the axes of three-dimensional space.

We will now move on and derive a physical mechanism responsible for Ampere's law that the magnetic field in space around an electric current is proportional to the electric current which serves as its source or the integral of B*ds=the permittivity of space times the current or “I”.

The mechanism responsible for Ampere's law can be derived from the "alignment" of a "W" axis of a fourth *spatial* dimension with respect to the tangential forces associated with an electron defined in Chapter thirteen.

Chapter thirteen derived electrical charges in terms of a displacement in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension while Chapter eleven defined the magnetic flux associated with a moving charge in terms of a tangential force on a "surface" of a three-dimension space manifold caused by this displacement.

In an electric current, the tangential forces associates with the magnetic flux of a charge will have a common "alignment" along the velocity vector associated with the electrically charged particles.

Therefore, the "tangential" force, which defines magnetic field in Chapter eleven, generated on a "surface" of a three-dimensional space manifold by an electric current will be aligned and additive because each will contribute  to the "tangential" force on a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This results in the magnetic field in space around an electric current to be directly proportional to the electric current because, as was shown in Chapter eleven, the magnitude of a magnetic field is directly proportional to the magnitude of a "tangential" force along a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension.

This completes the derivation of the mechanism responsible for Ampere's law in terms of the "alignment" of the "W" of the fourth *spatial* dimension and the existence of the existence of four *spatial* dimensions

Lastly we shall derive the mechanism responsible for Faraday's Law of Induction, that any change in a magnetic environment of a coil will cause a voltage to be "induced" in that coil that is equal to the negative rate of change of the magnetic flux times the number of turns of the coil or the integral of E*ds= -dB/dt.

The mechanism responsible for Faraday's Law of Induction is related to the inertial properties of a continuous non-quantized form of mass responsible for a unit electric charge defined in Chapter thirteen.

In the derivation of Gauss's law of Electricity it was shown why the total electric flux out of a closed surface is equal to the charge enclosed in terms of the existence of a continuous non-quantized form of mass and four *spatial* dimensions.

Therefore, each additional turn of a coil will add additional charges to the space effected the movement of those charges through that coil.  This will increase the total "tangential" or force generated on a continuous non-quantized form of mass in the space effected by those charges.

Later in the derivation of Ampere's law, it was shown the "tangential" force generated on a continuous non-quantized form of mass by the photon or electron in an electric current is directly related to the number of changed particle

This means each additional turn of a coil will make a proportional increase the magnitude of the magnetic flux or force associated with the current in that coil.

This defines the mechanism responsible for why the magnitude of the magnetic flux around that coil that is carrying an electric current is directly proportional to the number of turns in that coil. 

One aspect of electrical energy that has not yet been mentioned in this chapter is the mechanism responsible for the force or voltage associated with the unit electric charge.

Chapter nine derived the energy associated with the voltage and magnetic flux of an electric charge in terms of energy gradients, which as mentioned earlier, are caused by the "peaks" and "troughs" of a matter wave in a continuous non-quantized form of mass.

This suggests the change in the magnetic environment of a coil, which causes a voltage to be "induced" in that coil, may be related to the inertial properties of a continuous non-quantized form of mass associated with a charged particle.

This means that Newton’s third law of motion involving an interaction between masses which states "For every action there is an equal and opposite reaction" may be applied to the magnetic environment of a coil.

In other words, the voltage is induced in a coil is equal to the negative rate of change of the magnetic flux because a change in a continuous non-quantized component of space associated with a voltage could be considered to be an equal and opposite reaction to the change in a continuous non-quantized mass component space associated with a magnetic flux based on Newton's third law of motion.

This completes the derivation of the physical mechanism responsible for Faraday's law in terms of the energy gradient associated with the unit electric charge and inertial properties of the mass component of a "quantum mass unit of space".

This also completes the derivation of Maxwell's equations in terms of the existence of four *spatial* dimensions and a continuous non-quantized form of mass and the laws of classical physics.

“The universe's most powerful enabling tool is
not knowledge or understanding
but imagination"
Jeffrey O'Callaghan

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