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 Academic Journal of Science, Engineering and Technology 

Vol.6, Issue 1; January - Febuary 2021; 

1252 Columbia Rd NW, Washington DC, United States 

https://topjournals.org/index.php/AJSET/index; mail: topacademicjournals@gmail.com 

  

 

 

48 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

THE ROTATING WAVE THEORY: A UNIFYING THEORY OF PHYSICS  

  

Bill Christie and Benny Wong 

Architect AIBC OAA Port Coquitlam, British Columbia 

 

Abstract: The Michelson-Morley experiment was a famous experiment that attempted to detect the motion of the 

Earth through the luminiferous aether. The experiment was unsuccessful, and this led to the development of the 

special theory of relativity by Albert Einstein. 

Keywords: Michelson-Morley experiment, luminiferous aether, special theory of relativity, length contraction, 

time dilation, Lorentz transformations  

  

1. Introduction  

It is well known that in 1887 A.A. Michelson and E.W. Morley could not detect any luminiferous ether by 

detecting a path length difference between light transmitted in the direction of the earth’s travel through the 

stationary ether and perpendicular to that direction by a fringe shift. In 1889, H.A. Lorentz suggested that the null 

result of this famous experiment might be due to an actual physical length contraction of the interferometer as 

measured in the direction of its motion of the earth’s orbit. According to Lorentz, the length contraction was 

merely due to an electrodynamic effect on physical processes within the electron particle make-up. Lorentz also 

suggested that such physical processes had a cyclical function, or local time, which must slow down or dilate in 

conjunction with their length contraction. However, the reasons for local time dilation and length contraction as 

suggested by Lorentz required a complicated and unconvincing model of an electron to be composed of many 

like charges bound by a nonelectric force infinitely strong at the centre. Ironically, the Lorentz transformation 

equations of time dilation and length contraction survived to form the basic math of a much more acceptable, 

although revolutionary, theory put forth by Albert E. Einstein in 1904. Albert E. Einstein’s Special Theory of 

Relativity was much more acceptable because it was simple and universally consistent. His Special Theory stated 

that all laws of nature, including mechanical as well as electromagnetic field laws, must be invariant with respect 

to the Lorentz transformations.  

 He proved the consistency of his theory by applying the principle of equivalence to the Special Theory and 

created his General Theory of Relativity, which in turn correctly predicted the influence of a gravitational field 

on light. Also in 1904, Albert Einstein demonstrated that light behaved as individual particle – like packages of 

energy called photons in order to explain the photo-electric effect. Thus, in a quasi-corpuscular theory akin to that 

of Sir Isaac Newton, Einstein stated that the nature of light must have a wave-particle duality. However, matter 

was still considered to be only particle-like until twenty years later when Louis de Broglie suggested that matter 

as well as light might have a dual, wave-particle nature. Both the Lorentz and Einstein interpretations of the 

Michelson– Morley experiment required that the interferometer be “particle-like" only.    

I began to wonder how the Michelson Morley experiment might have been interpreted had the dual, wave-particle 

nature of matter been established prior to this famous experiment. Furthermore, I considered that matter might 

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49 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

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simply be a localized wave and that its particle-like nature is simply a phenomenon derived of its 

localization.According to Einstein’s definition of simultaneity there is no need for a physical length contraction 

of the Michelson–Morley interferometer. However, if as Lorentz contended, the length of the interferometer did 

indeed contract in the direction of its motion, then there could not be any fringe shift detected on the interferometer 

and real time could remain constant. One could disagree with Einstein’s assumption that his operational definition 

of simultaneity is valid in any inertial reference frame and revert back to the nineteenth century classical view of 

light which accepts such a definition as “valid only in the rest frame of ether” (EM vacuum field). My alternative 

conclusion about the experiment, coupled with the fact that matter is localized energy and that energy in the form 

of electromagnetic waves is indeed transmitted as light, compelled me to find a basic form of matter: a particle 

equivalent to a localized electromagnetic wave with an innate time cycle that would explain the fact of time 

dilation and a configuration that would require its own physical length contraction. Most other forms of matter 

that arise out of the EM vacuum field would only be variations or further developments in the evolution of this 

principle form of matter which is from hereon referred to as the Rotating Wave (or RW for short). The EM vacuum 

field is here stated as a universal reference frame only to a degree of which our perception is capable. The intent 

of this work is, therefore, to explain by the EM vacuum field, the creation of the principle form of matter and the 

phenomena of relativity, gravity, and quantum mechanics beginning with two postulates which compare with 

those of Einstein’s theory as rephrased by Casper and Noer in  The Evolution of Physics on p. 330:   

I. The Principle of Relativity According to the Rotating Wave: No physical measurement can distinguish 

one inertial reference frame from any other inertial reference frame - because - such distinction is obviated by 

changes in the actual physical time cycle, length, and mass of a particle with respect to that particle’s motion 

relative to the stationary, EM Vacuum field. Such changes are illustrated by the Rotating Wave.  

II. Independent of the motion of the light source, only wave fronts of light which proceed in a straight line 

with respect to a Euclidean universal reference frame (defined by the stationary EM vacuum field) always 

propagate in empty space (the vacuum state of the EM field) with a definite velocity C relative to that universal 

reference frame.  

Other wave fronts which do not proceed in a straight line, propagate with an angular velocity such that all wave 

fronts remain planar.  From the two postulates above, I can simply state that the null result of the Michelson-

Morley experiment is due to an actual physical length contraction of the interferometer in the direction of its 

motion. The actual physical time cycle of the whole interferometer apparatus slows down in unison and therefore 

time is not the culprit. The two postulates above also provide an explanation to the outcome of another experiment: 

the low rate of decay of mesons entering the earth’s atmosphere is due to a combination of some degree of actual 

physical length contraction of the earth’s atmosphere and some degree of actual physical slowing of the time 

cycle decay of mesons.  

2. The Electron as a Basic Form of Matter  

The electron and its antiparticle, the positron, elegantly fit the requirements of this basic form of matter. The 

electron RW complies with the universal laws of electromagnetism and the previous two postulates. By doing so, 

it inherently explains relativity, mass, and quantum mechanics. According to the electromagnetic theory of light, 

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the change in the electric field of the photon induces a magnetic field and, conversely, the change in the magnetic 

field induces an electric field. These changes are made with particular direction at the speed of light through the 

electromagnetic field, which was once labelled as “ether”. In order to exist, the photon must move forward through 

this electromagnetic field such that the changes in both the electric and magnetic fields induce each other. The 

photon cannot be at rest with respect to the electromagnetic field and therefore does not have any rest energy or 

rest mass. However, there are two types of motion: translational (linear) and rotational (angular). We perceive the 

photon to move forward through space in translational motion. If the two vectors of the electromagnetic wave of 

a photon could be brought to spin, not as in the case of a circular polarized wave, but as in the case of the electron 

model shown in Figures 1 and 2, then it might create a magnetic dipole and an electric monopole.   

 
Figure  1: Sectional Plan View of counter clockwise rotating (spinning) electron wave inducing magnetic lines of 

force B (as arrows coming up from the page) and electric field E. 

 
Figure 2: Sectional Side View of spinning electron wave inducing magnetic dipole and electric monopole. At 

some small radius (very close to the axis of spin) where the velocity of the rotating wave is less than C, the 

direction of the magnetic and electric fields might reverse with respect to their cross product to allow for the 

singular connection between the north and south poles. Just as the magnetic field of a photon changes in 

translational motion, thus inducing an electric field, so does the magnetic field of the electron change in rotational 

motion thus inducing the electric field of the electron. Likewise, as in the photon, the change in the electric field 

of the electron induces the magnetic field of the electron. In compliance with the electromagnetic theory of light, 

the electron RW (and likewise the positron) is nothing but one half of a gamma photon brought into rotation by a 

binding energy equivalent to another half of a gamma photon. This is confirmed by experiment. If a gamma ray 

  

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is brought under enough localized energy, an electron-positron pair will be created. All of the energy will be 

conserved as rest mass and kinetic energy of the particles. When the electron and positron are then brought 

together in annihilation in free space, they produce two photons whose total energy is equal to that of the original 

photon and the localized energy from which the particles were created. When positive and negative charged 

particles are oscillated towards each other they will induce an electromagnetic wave which spreads out in every 

direction except the path of their oscillation. Similarly, two photons are emitted in opposite directions during the 

annihilation of an electron-positron pair in free space. Note that the counter-clockwise spinning electromagnetic 

wave which is shown as a dark straight line in Figure 1 is actually a sectional view of a planar wave front with 

the maximum (or nodal) electromagnetic magnitude. Other lines representing lesser magnitudes are not drawn 

for the sake of simplicity. Also note that the speed of the wave must be greater at distances further from the centre 

of spin. 

As noted in Figure 2, the singular connection between the poles of the electron and thus the curved magnetic lines 

might be due to a reversal of the electric and magnetic directions with respect to the direction of rotation at very 

low speeds and thus in close proximity to the axis of spin. At a greater radius the rotating nodal wave front might 

be interpreted as a virtual particle blinking into existence with negative charge while at a lesser radius the rotating 

nodal wave front might be interpreted as a virtual particle of positive charge. The boundary between the reversal 

might not be so definite. Furthermore, the reversed fields might provide a binding energy which sustains the 

speculated rotating wave of the RW. 

Figure 3: Photon wave existing in translational motion.  

  
It is not fully apparent how the originating electromagnetic wave of the photon, as illustrated in Figure 3, is 

brought into rotation by a local binding energy. However, given a nodal planar wave front which extends to 

infinity in accordance with the wavicle, one can deduce that any curvature in the photon’s translational path will 

require a definite point of rotation for that wave front and thus an associated magnetic dipole along with a 

symmetrical electric field. Therefore, any curvature in the photon’s path will immediately result in fermion type 

particles, albeit with negligible and short-lived mass. Given sufficient and local binding energy, the curvature will 

result in the sustained electron and positron as illustrated in Figure 4.  

Figure 4: In this case the formation of the electron (left) and the positron (right), each with their own self-

sustaining and rotating electromagnetic wave, conserves electric field (charge), magnetic moment, and spin 

angular momentum.   

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52 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

  

 
One immediate variation of the foregoing concept of a rotating electromagnetic wave could be that which creates 

a magnetic monopole and an electric dipole. Or perhaps the rotating wave might show that the electric and 

magnetic fields of light are merely two different directions of stress, distinguished from each other only upon the 

creation of the dipole of the electron.   

Other immediate variations, such as the muon and tau fermions, could simply be created by the rotation of waves 

which have different frequencies than that of the gamma photon. Virtual photons, gluons, and gravitons causing 

electrodynamic, chromodynamic, and gravitational interactions amongst particles might simply be the rotating 

waves of the particles themselves. However, any speculation of immediate or evolved variations of the rotating 

electromagnetic wave form will not be further discussed in this paper.  

3. Relative Time (Dilation) Redefined  

According to the Special Theory of Relativity, the spin of a moving electron, as measured by an outside observer, 

must be slower than the spin of a stationary electron. 

 However, without regard to relativity, the angular velocity of an electron wavicle’s spinning electromagnetic 

wave must slow down as it gains translational motion simply because the speed of light remains constant at the 

same distance from its axis of spin. This is illustrated in Figure 5.   

Figure 5: Cylindrical model of the vectors of the RW (spinning) electromagnetic wave of an electron with 

translational velocity V and spin 1/2. 

  

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53 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

 At a certain distance R0 from the centre of the electron and midway between its magnetic poles, let us say that the 

electron wavicle’s electromagnetic wave is moving at a tangential velocity vR (here defined as the rotational 

velocity) about the center. If the electron is stationary (without translational motion), then the time it takes the 

electron wave to complete one cycle about the centre will be T
0 If the electron is given a translational motion of 

velocity v , then the new time it takes the electron wave to complete one cycle about the centre can be called T . 

The permeability 0 and the permittivity 0 of free space will remain constant about the same radius R0 from the 

axis of the electron’s rotation regardless of whether or not the electron is in translational motion. Therefore the 

resultant rotational velocity vR of the electron wave must decrease as the translational velocity v of the electron 

increases in the direction of the axis of the electron’s spin.    

From Figure 5.    vR = (c2 v2)1/2  

Without translational motion (v = 0) and we have,    

 2 R 2 R 

   T0 = =   

 vR c 

 With translational motion v 0 we get,    

 2 R 2 R 

  T = = 2 2 1/2 vR (c v ) 

1/2 

2 

  v  

and therefore T = T0 1 c2  which agrees with the time dilation formula of the  

Special Theory of Relativity.   

Since this concept of the electron contains only a spinning electromagnetic wave, then it is only the 

electromagnetic wave that exhibits time dilation. Furthermore, according to Quantum Mechanics, ionic and thus 

mechanical functions must slow down merely in response to the time dilation of the electron’s electromagnetic 

wave. Therefore, Real Time does not slow down according to the Special Theory of Relativity; rather, the fact of 

time dilation is due to the electron’s (and positron’s) spin of its electromagnetic wave coupled with the constant 

speed of light at a given radial distance from the axis of the electron’s rotation.  

4. Required Length Contraction  

The direction of propagation of an electromagnetic wave must always be at right angles to the direction of both 

its electric and magnetic fields. Therefore, an RW with translational motion will have each rotating planar wave 

front reoriented such that each respective resultant velocity c , as previously shown in Figure 5, will be normal to 

the wave front. Figure 6 shows a side elevation of an electron moving with a translational velocity v and viewed 

at an observed radius R = 0/2 . Since the electric field of an electron must always point to the centre, then the 

rotating wave of a moving electron wavicle will be inclined from the normal axis of rotation of a stationary 

electron such that the rotating wave of a moving electron will trace a helical path through the electromagnetic 

vacuum field. 

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54 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

Figure 6: Side Elevation of moving electron wavicle with translational velocity V at an observed radius R 

= 0/2  

From Figure 6 we can see that for a given electric field at an observed radius  

R = 0/2 , is the length of the wavicle contracts in the direction of its motion by a factor of vR/c such that:    

  v
R 2 2 1/2 

    = and vR = (c v )   

 0 c 

1/2 

  v2  

   = 0 1 c2    

which is the length contraction formula for the transformation laws of the Special Theory of Relativity. Since the 

equilibrium distance between wavicles is assumed to be ultimately determined by their electromagnetic fields, 

then the distance between RW’s should contract correspondingly in the direction of their motion. Therefore, the 

required length contraction is due to the RW’s spin of its electromagnetic wave, coupled with the fact that the 

direction of propagation of an electromagnetic wave must always be at right angles to the direction of both its 

electric and magnetic fields. Note that as indicated in Figure 6, the magnetic poles of the electron are displaced 

from the line of the electron’s translational motion, thus inducing the required magnetic field of a moving field 

of a moving charge. At any one instance this displacement would be characterized by two polar cones: one 

extending out forward and one extending out backward from the direction of the electron’s motion. A stroboscopic 

detection of this polar cone by an apparatus similar to a cathode ray oscilloscope would prove the physical length 

contraction of the electron as required by the concept of the RW.Figures 7, 8, and 9 further clarify how the 

configuration of the RW transforms when put in motion. Figure 9 more clearly illustrates the forward polar cone 

(rear polar cone is hidden) and illustrates the induced, right-handed magnetic field.  

Figure  7:  Stationary Wavicle vR = c Oblique Elevation of stationary electron RW with magnetic lines of 

force B (electric field not shown here for simplicity) and nodal wave front spinning with tangential velocity 

c .  

  

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55 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

Figure  8:  Moving Wavicle v
R = (c2 v2)1/2 Oblique Elevation of moving electron RW with magnetic lines of 

force B and nodal wave fronts reoriented at an angle as previously illustrated in Figure 6.   

  
Figure  9:  Moving RW Creating a Right-handed Magnetic Field - Oblique Elevation of moving electron RW 

with wave fronts of lessor field strengths shown as well as the nodal wave front (highlighted lines with arrows). 

This figure clearly indicates a right-handed induced magnetic field.  

 
5. A Definition of Rest (Energy) Mass  

Rest Mass is localized energy without translational motion; therefore, according to the concept of the electron 

RW, the energy of Rest Mass called Rest Energy E
0 is simply the Rotational Energy ER of the half-photon which 

is rotating in one spot, plus the Binding Energy EB which keeps the half-photon in that rotation. The half-photon 

has a kinematic rotational energy ER = h /2 which is equal to the binding energy such that the electron’s total 

Rest Mass Energy E0 = ER EB = 2ERE0 is thus equal to a whole photon’s energy h  as given by Planck’s constant 

h and the frequency of the photon . According to Rotational Kinematics, where ER is the rotational energy, k is 

an assigned constant for the derivation of rotational inertia I , m0 is a non-relative mass of a symmetrical spinning 

object, and vR is the velocity of spin at the radius R
0 of the object, then E

R = (1/2)km
0
v
R

2 can be derived. Since, 

according to the RW concept, all mass is assumed to be derived from electromagnetic waves, then the rotational 

energy and non-relative mass of the stationary RW can be equated in the same manner.   

  

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56 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

|  https://topjournals.org/index.php/AJSET 

By convention, k is assigned the value of unity for the wavicle, such that all objects are thus correctly allowed to 

have their rotational inertia computed as the summation of point wavicle masses at their respective radii. 

Therefore, E
R = (1/2)m

0c
2 for a stationary electron and a stationary electron will thus have a total rest energy E

0 = 
m

0c
2 . The rotational energy of a stationary electron can also be defined in kinematic terms by its angular frequency 

0 and its angular momentum L0 such that ER = 0L0 = 2 0L0 = h /2 , where 0 is the frequency of electron 

spin. Since we know the values: h = 6.63 10 34 Joule-sec.   

and L0 = 0.52723 10 34 Joule-sec., then 0 = 2  which is as it should be because according to Quantum 

Mechanics the spin of the electron must be quantized with respect to the originating gamma photon. Finally, since 

c = 2 R0 0 , then h = 4 R0m0c.  

6. Relative Mass with Respect to Motion  

According to the foregoing Figures 5 and 6, an electron with translational motion will have an angular momentum    

 pR = mvR = m(c2 v2)1/2 which according to the conservation of momentum is equal to the angular 

momentum p0 = m0c of a stationary electron. A relative mass m is defined with respect to its translational velocity 

v because the configuration of the mass as indicated in Figure 6 and 9 changes with respect to v . Note the increased 

flux or density of electromagnetic lines as illustrated in Figure 9. Therefore:    

1/2 

2 

v m = m0 1 c2   (06)  

which agrees with the Special Theory of Relativity where m is the relative mass with respect to translational 

motion. The total energy E of an electron must be the sum of its rest energy E) plus its kinetic energy K due to its 

translational motion such that:    

  E = E0 K and since  

X 

 K =Fdx=mc2 m0c
2  

0 

while F is constant force over a distance X to give the electron translational motion, then E = mc2 . Furthermore, 

the translational momentum p
v and resultant momentum p of a moving electron RW can be vectorially related 

such that:    

 p2 = pv
2 p0

2 and then multiplying by c2  m2c4 = pv2c2 m02c4 hence  

  E2 = pv2c2 E02                                             (08)  

 According to the RW concept, the correct relative mass and its associated momentum and energy have been 

derived with respect to translational motion regardless of the Special Theory of Relativity because real time has 

been kept constant.  

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7. An Electromagnetic Wave Theory of Gravity  

According to the Wavicle, free space or vacuum is defined as the electromagnetic ether field in which light and 

matter waves are able to propagate. The basic premise of this theory of gravity is that the binding energy EB holds 

the classical wave of the RW in rotation by affecting the permittivity and permeability of free space.   

Thus any other incidental wave will similarly be affected by the binding energy of the RW, although indirectly 

and to a lesser degree. Figure 10, illustrates a passing test photon with a given Huygen’s wavelet at distance R 

from the center and midway between the magnetic poles of a single stationary electron RW. Regardless of the 

RW charge, the wavelet will be permitted to go at the velocity u1 = pu = 2 pR 0 either in the same or opposite 

direction of the rotating wave. 

Figure 10: Vectorial description of Rotating Wave showing resultant gravitational acceleration of wavelet.  

  
While u is the tangential velocity of the rotating wave at distance R , and 0 is the frequency of the RW’s rotation, 

p is a variable dependent upon the strength of the vector field generated by the RW at radius . However, as 

illustrated in Figure 10, changes with respect to time and direction and therefore the photon wavelet would also 

be accelerated by the amount:    

du u2   a0 = p = p  

 dt R 

In other words the plane of the passing test photon or electromagnetic wave would be bent to some degree by the 

rotating wave and would account for the phenomenon of gravity. Obviously, according to the RW concept, a 

Huygen’s wavelet closer to either of the magnetic poles, but at the same distance from the centre of the electron 

RW, will experience less gravitational acceleration.   

However, the second premise of the theory of gravity is that uniformity of gravitational acceleration at a constant 

distance about a spherical mass is simply due to the fact that such mass is composed of many RW’s at various 

angles of spin and random motion. Therefore, while the electron has a gravitational field severely distorted by its 

magnetic poles, larger non-elementary particles of matter have more uniform gravitational fields at a given radius. 

While p is the real constant assigned to the gravitational acceleration of the basic particle, a modified p1 = k1p can 

be assigned in a limiting case to the more uniform gravitational fields of larger particles at a given radius. 

However, as p1 is only an average value of p , then it can be renormalized to p for simpler calculations that follow.  

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Since the wavicle must comply with Gaussian law at distances beyond which charge is screened, then the 

macroscopic laws of gravity must be able to be deduced in the same way. Gauss’s Law gives a connection between 

the flux E for the Gaussian Surfaces dS and the net charge q enclosed by the surface: 0 E dS = q where E 

= E dS and E is the  

electric field strength; 0 is the universal permittivity constant. Similarly, a universal constant c3/(Gh) , which 

can be proved by deduction, operates on the gravitational field strength a0 and its surface integral such that:   c3

 u2 

  a0 dz =  or  

 Gh R 

 1 c3 

 = dS  

 p Gh 

Since h = 4 R0m0c and the surface integral is a sphere, then:    

1 c3 2 c2R2 

= 4 R =   (11) p Gh GR0m0 

 and from above    

2 2 2 2 u Gm0 R0 u Gm0 R0 c R 

 a0 = p = 2 2 = 2 2 2 and thus R R c R R c R0 R 

Gm0 R   a0 = 2   

 R R0 

However, according to the General Theory of Relativity, our clocks run faster at higher heights and 

therefore, our acceleration at higher heights is actually greater than it appears to be such that:    

 a R0 R Rateof Real time 

  = where =   

 a0 R R0 Rateof Perceived time 

and therefore a = Gm
0/R

2 , where a is the apparent acceleration and m0 is the apparent constant mass.  

8. The Principle of Equivalence and the Gravitation of Matter  

Albert Einstein predicted correctly by the "principle of equivalence" in his General Theory of 

Relativity that matter would gravitate or bend light and slow down time. He found a deeper significance than 

mere coincidence that a gravitational reference system could be made equivalent to a uniformly accelerated 

reference system because it enabled him to extend his Special Theory of Relativity to his all-encompassing 

General Theory. However, according to the foregoing Electromagnetic Wave Theory of Gravity, light is simply 

bent by the rotating wave (or matter wave) of the RW.   

  

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Since the rotating wave is itself light, then the path of that rotating wave will be bent in the same manner by 

another RW; thus two RWs each other by such gravitation. The gravitation of anRW by a larger mass M centered 

at point Q is illustrated by Figures 11 and  

12.  

Figure 11: Sectional plan view of rotating wave front centered at distance R from mass M centered at Q .  

  
Figure12: Sectional Side View of rotating wave front of RW centered at distance R from massM centered 

at Q. 

  
Since the motion of the electron RW is limited to the direction of the axis of its spin, thenthe acceleration of the 

RW as illustrated in Figures 11 and 12 need only be considered in the direction of the axis of its spin. In figure 11 

the rotational velocities of the RW’s wave front are indicated as arrows ( S1 and S2 ) coming up from the page and 

the wave front lies in the plane of the page. Note that at different distances along the same radial direction from 

Q , the ratio of velocities QS1/(QS2) = r1/r2 = R1/R2 and, therefore, the instantaneous effects of both the RW and 

larger mass M on the permittivity and permeability of free space are consistent. However, the lines drawn radially 

from point Q reveal different rotational velocities at a constant radius R1 where the permittivity and permeability 

of free space is affected to some degree by the larger mass M.   

Since the permittivity and permeability of free space is also instantaneously affected by the RW, such that the 

observed rotational velocity of the RW increases in direct proportion to its observed radius of spin, then the wave 

front of the RW must remain planar. However, as illustrated in Figure 12, the RW’s planar wave front will be bent 

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instantaneously as it rotates about its axis of spin which is directed towards Q . Although the wave front of the 

rotating wave remains planar, its inclination with respect to its axis of spin increases as the wave rotates and the 

RW is thus accelerated to point Q . The RW equally shows by Huygen wavelets how light is gravitated or bent 

and thus how matter is gravitated. Also, the Electromagnetic Wave Theory of Gravity shows by Huygen wavelets 

how light is permitted to go at greater speeds at distances further from the centre of the RW. Again, since the 

rotating wave of the RW is light, then the velocity of that rotating wave will be affected in the same manner by 

the proximity of another RW. Hence the spin frequency of the two RWs in close proximity will be less than that 

of two RWs separated by a greater distance. Therefore, the Electromagnetic Wave Theory of Gravity enables a 

reinterpretation of the General Theory of Relativity by predicting, first, the gravitation and slowing down of light 

and, second, the gravitation and slowing down of the time cycle of matter. The “principle of equivalence” can be 

explained by the equivalence of light and matter according to the concept of the RW. 

9. Graphical Derivation of the Rk  and Gk  in the General Theory of Relativity  

Tensor math forms the mathematical foundation upon which the laws of Einstein’s General Theory of Relativity 

are defined. The Rotating Wave also shows how tensor math allows for the calculation of intrinsic curvature of 

space-time. According to relativity, it must be just as valid in one reference frame to analyze the path of free 

falling light influenced by the gravitational field of a stationary mass in order to describe the curvature of space-

time as it is to postulate in another reference frame the curvature of space-time by the mass energy density tensor 

of an attracting mass which is in motion. Furthermore, according to the above 8. The Principle of Equivalence 

and Gravitation of Matter, the analysis of the path of free falling light in the the Rotating Wave must be equivalent 

to describing the gravitational field about a stationary attracting mass.  

When there is an attracting mass, gravity will accelerate a free falling Rotating Wave. The axis of rotation of the 

Rotating Wave will of course be in the direction of motion towards the attracting mass. As the forward motion 

increases, the planar wave fronts of the Rotating Wave will incline as illustrated in Figure 6. While potential 

energy is converted into kinetic energy (as per E2 = pvc
2 E

0
2 above), extra work will also be done and thus energy 

expended on the Rotating Wave to incline or bend the rotating planar wave fronts. This is just like the bending of 

light by mass in the above 7. An Electromagnetic Theory of Gravity. This extra change in energy is thus associated 

with the slowing down of the time cycle of the Rotating Wave regardless of whether it is in free fall motion or 

not. The fact is that mass does slow down time (“clocks run faster at higher heights”) and a stationary Rotating 

Wave thus must slow down in the presence of an attracting mass. When there is no attracting mass present, the 

radius R0 at which the Rotating Wave rotates at velocity vr = c v stays constant as per Figure 5.   

When there is an attracting mass present, the radius at which the Rotating Wave rotates must increase as its time 

cycle of rotation slows down. This increase in the radius of the Rotating Wave will be referred to as the Spiral 

Condition. Note the velocities of the Rotating Wave in one reference frame must correspond to those velocities 

of the mass energy density tensor of an attracting mass in another reference frame. Whereas in the General Theory 

of Relativity the attracting mass is defined by the mass energy density tensor and related to the Reimannian 

curvature of space-time, the following derivation of the R
kl  is directly deduced by first defining the path of the 

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Rotating Wave as a geodesic on a generated surface and then second deriving the intrinsic curvature 

of that surface. Consider the dashed helical path of the Rotating Wave as illustrated in the previous Figure 

13. The helical path can be defined by a time derivative of the position vector POSc = POSv POST POSv is the 

vector in the forward moving translational motion of the Rotating Wave and same direction of rotational axis. 

POST is a rotor and is the vector in the purely rotational motion. If the velocity vector vT is greater than zero (or 

less than zero), then the velocity vector c of the Rotating Wave with constant speed of light will spiral outwards 

(or inwards):  

Figure 13: Rotating wave of the Electron (fermion). Position vectors   

  
POSc = POSv POST , where POST rotates. Velocity vectors, c = vv vR vT .  dPOSC dPOSv dPOST dET

 dPOST 

 c = = = vv POST ET  dt dt dt dt dt 

    

Vectorially:     c = vv vR vT  

Note vectors are not embolded, but implied with base vectors.  

  

Note: c2 = vv2 vR2 vT2 and thus dc/dt = 0 = vv Av vR AR vT AT .  

Also the base vectors for the Riemannian space time located along the light line are defined by the partial 

derivative of the position vector:    

e = POS c/ x = POS v/ x POST / x = POS c,  = POS v, POST ,   

 Thus ecc = e u = (POSv, )u (POST , )u = dPOSv/dt dPOST /dt . Thus the path of the Rotating Wave with 

constant speed of light is defined by five vectors in our familiar three dimensions of space by:   c = vv vR vT  

of which vv = vX vY vZ .  

The spiral helical path also lies within a generated surface that can be described in Riemannian five dimensional 

space-time with  

c = e u = evu
v eru

r etu
t  (17)  

 of which again evu
v = exu

x eyu y ezu
z (with implied Einstein summation on  ).  

(1 

(1 

(1 

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The “light–line” of the Rotating Wave is defined as the geodesic where c = vv vR vT and the magnitude c (of 

c = ecc ) is kept constant at the speed of light. So, vv, vR , and vT vary while c (of c = ecc ) is kept constant. vv is the 

forward (translational) motion of the  

Rotating Wave along the direction of the axis of rotation. vR is the purely rotational motion of the Rotating Wave. 

vT is the velocity of outward radial expansion of the light–line such that the light–line traces a spiral helical path. 

To be clear, at any point on the light–line: c = e
cc = e u = v

v 
v
R 

v
T and the base vector e

c varies while the 

magnitude c is kept constant. Also, note the spiral helical surface extends radially from the centre of axis of spin 

and is normal to the wave front.  

Note that in the spiral condition: c = vv vR vT whereas before the simple helical  

(cylindrical) form of the Rotating Wave in accordance with the Special Theory of Relativity, vT = 0 and thus c = 

vv vR as illustrated in figures 5 and 6. Note v = vv and the subscript is added to clarify the forward velocity. 

Clearly, vT has been added to the Rotating Wave model to allow for the added Spiral Form (or Condition) in 

accordance with the General Theory of Relativity.  

We now have the Spiral plus Helical conditions in which all possible directions of motion are allowed for the 

Rotating Wave. It is allowed to rotate, move forward, and now also move outward (or expand). It will be seen and 

further expounded in the R
k  derivations that the rotational velocity vR is of course greater at greater radii. 

Likewise, the u  components will be greater at greater radii. Note also that the generated spiral helical surface 

can equally be defined at any angle about the Rotating Wave’s axis of spin, just as the planar wave fronts are 

rotated and arrayed around the axis of rotation in Figure 9. Likewise, the  

“light–line” as defined above can be rotated and arrayed infinitely around the axis of rotation. With no expansion 

and magnitude vT = 0 (of vT = ETvT ), this array would take the shape of a cylinder which has no intrinsic curvature.   

Even with a constant expansion speed vT and constant forward motion vv this array would form the shape of a cone 

that also has no intrinsic curvature. (A cone can be cut down its length to its point and laid out flat just as a cylinder 

can.) If the expansion speed vT increases or the forward motion v
v decelerates, then the cone shape would curve 

and take the shape of a “flute” (or horn or bell) which would then of course have intrinsic curvature. So, in order 

to have intrinsic curvature on this array, the Rotating Wave must have forward motion and radial expansion plus 

acceleration (or deceleration) in either the forward motion or radial expansion or both. Note also that the e
ru

r 

certainly corresponds to the rotational velocity vR of the Rotating Wave while c = ecc corresponds exactly to c = 

vv vR vT , so the e
vu

v = e
1u

1 e
2u

2 e
3u

3 must as a result correspond to the forward (translational) velocity of 

the Rotating Wave. While any helical surface is extrinsically curved, it can be shown that the helical surface of 

the Rotating Wave does not necessarily have intrinsic curvature. If there is no attracting mass, then the axis of 

spin will not change and the above generated helical surface will be intrinsically flat. Such a helical surface when 

unwrapped from its helical path will become extrinsically flat. When there is an attracting mass, gravity will 

accelerate a free falling Rotating Wave and also cause it to spiral outwards. The combination of spiral and helical 

path will create intrinsic curvature. The helical path illustrated in Figure 13, can also be described by:    

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   erur = e1u1 e2u2 e3u3 e4u4 = esus c  

 such that the curvature invariant – (uR )
2 = giju

iu j with the use of the metric tensor and Einstein’s summation 

convention of summing on repeated indices. According to Minkewski space-time coordinates, u4 = ic and (u4)2 = 

c .  

Note that the tensor relationship, which is graphically illustrated by the RW, can be more fundamentally described 

by the equation: c2 = biju
iu j in which b

ij is an equally valid metric tensor and now u4 =uR . This enables us to 

eliminate the imaginary component i and construct the bij from conventional base vectors.   

From here on the summation convention will be used implicitly and the bkl = gkl = ek e  such that c2 = gklu
ku  to 

keep things simple. At the conclusion of the following derivation of Rk  and thus Gk , one can then compare 

the Rotating Wave with that of the Minkewski space-time coordinate system and the mass energy density tensor 
T

k .  

 General Surfaces – Curvature Calculation – Rk    

The intrinsic curvature of the spiral helical surface can be calculated by the  

Reimannian curvature tensor R
ik

n  and sufficiently by the Ricci tensor R
k = R

k n which is the contraction of the 

curvature tensor. Note vectors are not embolded, but implied with base vectors.  

Rikn = T ni,k T nk,i TsinT sk TsknT si = [T ni,k TsknT si ] [T nk,i TsinT sk ]  

 Note: Rc = curvature due to the rotational motion of the wave. Further derivation:    

e ,nk = Rc,ku unc 2 Rcu ,kunc 2 Rc,ku un,kc 2  (24)  

 and by applying the Chain Rule again:    

  e ,nk = Rc,c( xc/ xk )u unc 2 Rcu ,c( xc/ xk )unc 2  

 Rc,ku un,c( xc/ xk )c 2  and thus:    

  e ,nk = Rc,cuku unc 3 Rcu ,cukunc 3 Rcu un,cukc 3 and   e ,kn = Rc,cunu ukc 3 

Rcu ,cunukc 3 Rcu uk,cunc 3  

   Note wherever you have ukun , then for Rk  the terms will obviously commute and thus the first two terms are 

discarded:    

Rk = (e ,nk e ,kn )en = Rcu c 3(un,cuk uk,cun )en (27)  Again using the Chain Rule as above:    

 Rk = Rcu c 4(anuk akun )en  (28)  

 Note: c = e
cc = e

nu
n is always perpendicular to cR

c = de
c/dt and thus the scalar dot product between R

c and c = 0. 

Thus for the Rotating Wave:    

Rk = Rcauku c 4  (29)  

 while a = acceleration of the u  velocities and the Ricci scalar    

 R = gk Rk = Rcac 2  (30)  

 and    

1 Rca  2 1  

 Gk = Rk  gk R =2 uku c  gk (31)  

2 c  2  

(1 

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 which compares somewhat with the Einstein Tensor Gk = 8 kTk  where the  

mass energy density tensor     

Tk = ( p)UkU gk p   has been 

written. Also, the scalar    

(32)  

   G = gk Gk =Rcac 2 

   (33)  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Note again, we are deriving the surface curvature where the light line follows the path of the wave which is going 

at velocity c at certain radii from the axis of spin. That light– line spirals out and the angular velocity thus 

decreases, slowing down the time cycle of the rotating wave. This is relevant to the apparent expansion of the 

universe and the apparent slowing down of time. Without this expansion and slowing of time, there can be no 

intrinsic surface curvature of the path of the rotating wave and thus no gravity. An Electromagnetic Wave Theory 

and thus summing on n and  plus reorganizing:    

Rk = [T nn,k TsknT sn ] [T nk,n TsnnT sk ]  (20)  

   Now let a vector: A= es A
s = e ,k = e / xk and another vector B= es A

s = el, j = e / 

x j thus:    

  Rikn = [A,nk (es,ken )As ] [B,ni (es,ien )Bs ] and :  

  Rikn = [esen A,sk (es,ken )As ] [esenB,si (es,ien )Bs ]  

 

  Rikn = [A,k B,i ]en = (e ,ik e ,ki )en  

   Summing on i and n , we thus have another mathematical formula for the Ricci 

Curvature  

(2 

Tensor Rk :    Rk = (e ,nk e ,kn )en  

 for any form of curved continuous surface. It is interesting that it looks a bit similar to 

the Faraday Tensor Fk = A,
n

k A,
k
n .  

 Rotating Wave Position Vectors and Curvature Calculation – Rk   

  Since ec and e  lie within the surface c = ecc = e u  then by the Chain Rule:    

  e ,n = e / xn = e / xc( xc/ xn ) = ec/ x ( xc/ xn )  

  = ec/ xc( xc/ xl )( xc/ xn )  

  = ec/ xt ( xt/ xc)( xc/ x )( xc/ xn)  

  = (dec/dt) c 1(ece )c 1(ecen)c 1  

(2 

  = (dec/dt) u unc 3 = Rcu unc 2  (02 

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of Gravity, the Binding Energy ( EB ) of the Rotating Wave affects the permittivity and permeability of space 

which in turn causes incidental waves to slow down and accelerate towards the attracting mass.   

Thus the slowing of time, spiral expansion of the light–line, and the gravitational force all go hand in hand to 

explain the expansion of the universe from the quantum mechanical level. The Binding Energy given up through 

the interaction of Rotating Waves thus appears to go into the background radiation.   

Line Eq. (29) is very telling. If a = 0 or a is perpendicular to Rc , then there will be no intrinsic curvature. In order 

to get intrinsic curvature, we need spiral expansion of the helical light line plus the forward motion and use of 

Riemannian geometry. A spiral light line of a stationary rotating wave would indeed spiral, but remain on a flat 

plane. A helical light line without spiral expansion would remain on a cylindrical surface that has no intrinsic 

curvature. A helical light line with spiral expansion could trace a path on a cone which again has no intrinsic 

curvature. If the radial expansion is increasingly faster than the forward motion, then the resultant helical spiral 

light line can be infinitely arrayed around the axis of wave rotation (albeit with with varying amplitude accounting 

for quantum mechanics) and the array will form the shape of a “flute”.   

A flat space “cone” tangent to the “flute” would represent a local inertial reference frame. Thus according to the 

Rotating Wave, the requirement for intrinsic curvature and hence gravity is a range between two extremes: the 

Accelerating Spiral and Constant Forward Motion or Constant Spiral and Accelerating Forward Motion. Note the 

Spiral Condition (or form) of the spiral helical Rotating Wave immediately suggests the slowing down of time 

and expansion of matter. Where the Rotating Wave had a rotational velocity vR before at lessor radius of rotation, 

the time cycle of the Rotating Wave slows down in a gravitational field and vr is now at a greater radius. Thus the 

Rotating Wave of the RW has a built-in function that manifests itself in the apparent slowing down of time and 

expansion of the universe. The Spiral Condition immediately obviates the need for the Cosmological Constant. 

According to the Rotating Wave, the Cosmological Constant is not required because the spiral helical Rotating 

Wave is already slowing down and expanding. In order to maintain the law of energy conservation, the    

1 8 G 

 Gk = Rk  gk R = 4 Tk   (34)  

2 C is sufficient.  

10. An Explanation of Quantum Mechanics  

 The concept of the RW simply explains why Plank’s constant h is intimately included and quantized in the 

characteristics of the electron and all cyclical functions. According to the Definition of Rest (Energy) Mass, h 

automatically enters any equation of matter. Also, since the two nodes of the RW rotate, the effect of their 

electromagnetic and gravitational field strengths on an adjacent particle must vary in a cyclical fashion. Therefore, 

an orbiting electron RW must have a distance from the nucleus which undulates in direct correspondence to the 

electron’s spin. Relativistic effects of the orbiting electron and nuclear particles would of course further define 

the path of orbit.  

Furthermore, since the nuclear particles themselves spin and therefore must have cyclical variations in their 

effective field strengths, then the electron RW must make an integral number of spins for each orbit in order to 

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stabilize in that orbit. Thus orbital energies must be quantized with respect to spin or rotational energies ER . 

Matrix quantum mechanics requires that the energy level of an electron orbiting in an atom be h (n 1/2) where 

 is the frequency and n is the number of typical photons which are absorbed or emitted. According to Rotational 

Kinematics, the energy level should be equivalent to the total angular energy of the electron RW, which is equal 

to its orbital energy plus its innate rotational energy ER . The rotational energy ER = h /2 explains why the ground 

state or “zero point” energy of the electron in an atom must be h (n 1/2) where n = 0 for an electron with no 

orbit.   

Also, the concept of the RW simply explains why matter has a wave probability distribution. Since the wavicle is 

purely a rotating electromagnetic wave, then the probability of detecting the wavicle near some point in space 

should be described by a wave function. 

The derivative operators, postulated by Erwin Schródinger, are simply deduced from the basic wave equation of 

the RW and the effects of relativistic quantum mechanics are graphically illustrated with the addition of potentials. 

The only real wave function of the RW is that which describes the amplitude  at a certain time t and length S as 

measured along the wave’s helical path shown in Figure 14.   

Figure 14: Cylindrical model of the helical path of real wave of amplitude   and measurements of  &  in the 

direction of the particle motion and   in the direction of the wave’s rotation. Vector ally.  

  
 Given an arbitrary maximum amplitude N , wavelength , and spin angular velocity , the sinusoidal real wave 

function of the traveling RW must be defined as:    

 2   

   = N sin S t   

   

11. Comparison of Dirac Matrix Equation with Rotating Wave vectors  

 It was a busy time for new physics in the first three decades of the twentieth century. After the photoelectric 

effect, relativity, and Bohr’s atom, came Louis de Broglie’s insight in 1924 to suggest that if light photons can be 

considered as particles as well as waves, then matter might also have a wave nature and its wave function must 

comply with relativity.  Later in 1924 Wolfgang Pauli suggested an inner degree of freedom of the electron, 

followed by Ralph Kroenig and then in 1925 George S. Uhlenbeck and Samuel E. Goudsmit had theorized that 

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the electron must have an inner rotational motion (later termed “spin” by Pauli) in order to have an associated 

magnetic moment and thus explain spectroscopic evidence. Hans C. Ohanian in his review ( What Is Spin?) [1] 

states it apparently was immediately recognized by Goudsmit and Uhlenbeck that  spin would very likely lead to 

serious problems with Special Relativity”. However, much concentration at the time was on the developing 

Quantum Mechanics and classical concepts were deemed insufficient to describe the macroscopic world. Then in 

1926 Schrödinger really started Quantum Mechanics with his wave equation and had then tried to further it with 

relativity, but did not derive electron spin. 

 Also, Pauli knew that the spin of a rotating body could be described by matrices and hence introduced matrices 

into the wave equation, which in turn suggested pairs of opposite spins of the electron. Knowing that the light 

wave can have two possible directions of polarization, C.G. Darwin suggested that the electron might also have 

two opposite polarizations which then yielded the correct fine structure of the hydrogen spectrum. It was Paul 

A.M. Dirac who in 1928 then used the matrices to combine the Special Theory of Relativity with wave mechanics 

and naturally derived electron spin. However in his “Quantum Theory of the Electron” [2], Dirac further clearly 

credits Gordon (and thus Klein) for suggesting that the time derivative operator for the relativistic Hamiltonian 

W = ih /  t should be linear in the first order (and likewise the momentum operator pr = ih / xr ), just as in 

the case of the non-relativistic wave equation. Quoted from P.A.M. Dirac: 

 What is the probability of any dynamical variable at any specified time having a value lying between any 

specified limits, when the system is represented by a given wave function n . The Gordon-Klein interpretation 

can answer such questions if they refer to the position of the electron (by use of nm ), but not if they refer to its 

momentum, or angular momentum or any other dynamical variable. We should expect the interpretation of the 

relativity theory to be just as general as that of the non-relativity theory.  Thus Dirac got the idea to factorize the 

relativistic wave equation in order to get the first order derivative operators which then suggested a positive charge 

(positron later discovered) as well as the electron. Again quoted from P.A.M. Dirac:  The true relativity equation 

should thus be such that its solutions split up into two non-combining sets, referring respectively to the charge 

e and the charge e. 

11.1 Derivation of Dirac’s Matrix/Wave Equations  

 Dirac first considers the case of no field present and and posits the form of the four dimensional wave equation    

  (p0 1p1 2 p2 3 p3 ) = 0.  

  this is the same as Dirac [2] Eqn 4. which we shall refer to as D4. Then he multiplies the conjugate (with minus 
p

0 ) and the non-conjugate in his equation [2] D5,    

  0 = ( p0 1p1 2 p2 3 p3 )(p0 1p1 2 p2 3 p3 )  

  (37)  

 To get the required equation (D3) with no field present: (vectors in bold):    

  0 = ( p0
2 p2 m2c2)   

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  With derivative operator: p0 =W/c = (ih/c) / t = Relativistic Hamiltonian. Readers can refer to the Quantum 

Theory of the Electron/PAM Dirac online. Dirac derives the various matrices required to get his wave equation 

(D9):    

  [p0 1( , p) 3mc] = 0  

  where  denotes the vector ( 1, 2, 3). Finally Dirac considers the electron in an electromagnetic field and 

adds in the vector potential and scalar in his equation (D14):   e e 

 [p0 A0 1( , p A) 3mc] = 0 c c 

 And then analogous to his equations (D3) and (D5) he multiplies the conjugate [with e 

(p
0 

A
0) ] and the non-conjugate in his equation (D15):    

c 

   e   e   

 0 = p0 c A0 1 , p c A 3mc   

   e   e   

 p0 A0 1 , p  A 3mc   

  c   c   

   e 2  

 = p0 A0 , 

   c   

  e  

2 

e 2 2 p A m c c

 e  

 1 , p c A p0 c A0   

 

 p0 c A0 , p c A   

 

 The last equation above is D15. Note rewritten, equations (D5) and D15) can take the form:    

  p0
2 = [ 1( , p) 3mc]2   

  e  e  

 2 2 

  e   e  

  p0 c A0 = 1( , p c A) 3mc   

 The first Eq. is D3 last Eq. is D15a. Upon squaring the terms in equation (D15a), Dirac finds extra terms:    

  e 2  e 2 e  e  2 2  

  p0  A0 = p  A  ( , H) i 1( , E) m c  

  c   c  c c  

  (43)  where this is D15a, again, here: = h/2 . From that, Dirac divides by 2m and finds:   e ( , H) 

e  

 = = magneticmomentof 1Bohr Magnetonand  

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c 2m mc 

e ( , E) e  

i 1 = i 1 = electricmoment with imaginarynumber c 2m mc   

  (44)  

Quoted from P.A.M. Dirac: This magnetic moment is just that assumed in the spinning electron model. The 

electron moment, being a pure imaginary, we should not expect to appear in the model.  

It is doubtful whether the electrical moment has any physical meaning, since the Hamiltonian in (14) that we 

started from is real, and the imaginary part only appeared when we multiplied it up in an artificial way in order 

to make it resemble the Hamiltonian of previous theories.  

 11.2 Rotating Wave - Vectors and Derivative Operators   

Again refer to figure 14., where the sinusoidal wave function was defined as;  

 2 S  

  = N sin t   

 

 Since for a light wave P = h/  then for a Rotating Wave Pc = h/  and thus:    

 PcS  

  = N sin  t .  

   

   It is also apparent from Figure 10. that: Pc = Pvc/vv = PRc/vR and S = Svc/vv = SRc/vR such that:  

 PS P S c2 

  = N sin c t = N sin vvv2v t   

    

 P S c2  

  = N sin RvR2R t   

 

and thus,    

  = NPc cos PcS t   

 S    

  Sv = NPv v c2 cos PvvSv2v c2 t   

2 

 v  

 SRNPvRR c2 PRvSR2R c2 t   

  = 2 cos 

 deriving further we get,  

  

 2 NPc2 PcS Pc2c4 

  2 =  2 sin  t =  4 2  

(4 

(4 

(4 

(4 

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 S    c  

2 v2 = NP4v2c4 sin PvvSv2v c2 t = vPv4v 2c24   2 

 S vv   

S2 R = NPvRR 2c4 sin PRvSR2R c2 t = vPR4R 2c24  

  2 4 2 

 

  

 c4 

2 

 Thus:  Pc
= 

4 2  c  

v4 

 2 v 

  Pv = 4 2   

c v4 

 2 R 

  PR = 4 2   

c  

 and thus: Pc
2 = (P

v
2 P

R
2) . with Pc, 

P
v, and PR as either simple variables or derivative operators. Note, one can 

extend the Rotating Wave equation into the General Theory of  

Relativity:    Pc2 = (Pv2 PR2 PT2)   

 11.3 Comparison of Derivative Operators between Dirac & Rotating Wave.   

 In order to compare with Dirac’s equations we of course need to limit our discussion here to the Special Theory 

of Relativity. When the electron is in  constant motion, the momentum operators of the Rotating Wave can also 

be related in the vector sum: Pc = Pv PR which upon multiplication by the amplitude of the wave function and 

then squaring yields the equations:    

  Pc = (Pv PR )   

  Pc
2 = (Pv

2 PR
2) .  

   Note in above equations (D3) and D15a) the Dirac terms which relate to the vectors of the Rotating Wave are: 

p0 = Pc, p = Pv and mc = m0c = PR for constant motion (where m0 is the Rest Mass of the Rotating Wave). Thus 

when an electromagnetic field is introduced to the electron, the associated vector potentials can be added 

respectively (see Figure 15):    

  e   e   e  

  Pc  Ac = Pv  Av PR  AR   

  c   c   c  

which represents another (boosted) state of constant motion. See Figure 15. The newly introduced potential e/c 

AR has a magnitude and direction such that the spin momentum is always conserved in magnitude and changed 

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only in direction in order to maintain itself at right angles to the direction of motion of the particle. Vectors noted 

are embolded. 

Figure 15: The vector potential is added to the 3–space vector momentum while the spin 

momentum is maintained at right angles to the direction of motion. The dashed lines indicate the resultant 

momenta with added potentials.. 

  
If we are going to conserve the rest mass energy and momentum in the rotational direction (as in the Special 

Theory of Relativity), while applying potentials from an electromagnetic field that change the direction of the 

electron’s angular and magnetic moment, then the magnitude of mvR will remain = m0c = PR, but note PR must 

change in direction in order to remain at right angles to the translational motion and momentum of Pv = mvv .    

  p02 = 1( , p) 3mc 2   

 2 2 

  e   e  

  p0 c A0 = 1( , p c A) 3mc   

 In comparison, as noted in previous sections, the Rotating Wave momenta can be added vectorially: Pc = Pv PR 

for Special Theory of Relativity (constant motion),    

  Pc = Pv PR PT  for General Relativity and likewise when squared:    

  Pc2 = Pv2 PR2 = mc2 = (mvv )2 (mvR)2   Pc2 = Pv2 PR2 PT2 = mc2 = (mvv)2 (mvR)2 

(mvT )2  

 Also note in the above it is implicit that: Pv = p1 p2 p3 = PX PY PZ . These are mutually 

orthogonal 3 dimensional momentum vectors and when squared’    

Pv2 = p12 p22 p32  (57)  

 Also note    

  0 = Pc2 Pv2 PR2   iPR = ( iPc Pv )(iPc Pv )  

 If the vector potential and scalar are added in the same way as Dirac:    

  e  e  e  

  Pc  A0 = Pv  Av PR  AR   

  c  c  c  

 where here Av = the real 3 dimensional vector potential = AX AY AZ , and then after squaring we get:    

 2 2 2 

 e   e   e  

Pc  Ac = Pv  Av PR  AR  (60)  

 c   c   c  

(5 

(5 

(5 

(5 

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 However, Dirac gets:    

 2 2 

  e   e  2 

  Pc  Ac = Pv  Av PR extra terms noted in (D15) above. 

  c   c  

  (61)  

 Since we are conserving magnitude of momentum and energy in the rotation, then    

2 

 e  2   PR  AR = PR and thus:  

  c  

 e  

   AR = 2PR = 2m0c = 2  c R0 

Recall from the previous section 5. A Definition of Rest (Energy) Mass that h = 2 R0m0c and thus = R0m0c . 

Thus the Rotating Wave has an angular moment  

L =  which agrees with an orbital state of N =1 where N = [ ( 1)]1/2 and = 0 . The magnetic dipole moment 

is thus:    

 e e e 1 

  =  L =  =  R0m0C = eR0c  

 2m0 2m0 2m0 2 

 Note, a light wave has an energy defined by the Poynting Vector: S= E B/ 0. S is in the direction of motion of 

the light wave, thus the Poynting Vector for the Rotating Wave will be in the spiral or helical direction: S= ecS .  

Since in the light wave E =cB , then for the Rotating Wave:    

 EB E2 

  S = = and  

 0 c 0 

 dS E dE E kQvT 

  = 2 = 4 3   

 dt 0c dt 0c d 

  

12. An Explanation of the Kaluza 5th Dimension by the Rotating Wave.  

 My initial references on Kaluza’s idea are from the internet article of William Straub PhD: Kaluza-

Klein for Kids June 27 2014 [3] and I appreciate his sharing of knowledge as I do by many others. I also 

reviewed the Kaluza Klein site by Victor Toth as he always tries to make physics as simple as possible 

and intuitive, yet comprehensive. [4] I looked at many other sites but got the Kaluza idea clear from those two.  

In 1919 the German mathematician Theodor Kaluza developed a theory in 5 dimensional Reimannian geometry 

from which electromagnetism appeared to be a natural consequence of the 5th dimension. Finnish physicist 

Gunnar Nordstrom had proposed a similar idea earlier in 1914 but it was ignored. Kaluza immediately approached 

(6 

(6 

(6 

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Einstein who became very interested and it was finally published in 1921 under Einstein’s recommendation.  For 

almost a hundred years physicists and mathematicians have studied and tried to make clear sense of the Kaluza 

“miracle”. The basic idea is that the extra components of the 5 dimensional metric seem to materialize in 4 

dimensions as components of the electromagnetic vector potential.  After rechecking the derivation of the G
k  in 

previous section 12 and becoming sure of the intuitive model of the Rotating Wave, I began to realize that its 5th 

vector vT was most likely the same 5th dimension as suggested by Kaluza. Without the radial (outward or inward) 

vT vector part of the Rotating Wave, one cannot derive intrinsic curvature of the surface on which the Light Line 

travels. In other words, the General Theory of Relativity GTR could not be explained by the Rotating 

Wave function, unless it is allowed to spiral outwards (slowing down) or inwards (speeding up). The vector vT 

essentially turns the Light Line inwards or outwards and thus deforms the metric.  Also, the fact that 

electromagnetic energy adds curvature in addition to mass energy very clearly suggested to me that the Kaluza 

5th dimension must be the same as vT , the 5th vector of the Rotating Wave. Most recently, I came across the 

article Geometrical Interpretation of Electromagnetism in 5-Dimensional Manifold by TaeHun Kim & Hyunbyuk 

Kim [5]. In the article, they suggest the 5th dimensional manifold is constructed by dragging the 4D space-time, 

resulting in deformation. Clearly, as shown in Figure 13, one can see that the Rotating Wave vT vector likewise 

redirects the 4D space-time manifold inwards (or outwards).  In analyzing the Kaluza Klein theory, physicists 

usually start with the equation of motion. As Straub states, the Lorentz Force in the usual 4 dimensional space 

can be derived from an arbitrary coordinate variation x  of the invariant quantity:    

 I = mc ds q A dx     and carrying the variation and setting it to zero yields the expression for the Lorentz 

Force:    

 d2x  dx dx  q dx  

  2  = F    

 ds ds ds mc ds 

 Now let ds/dt = c (speed of light) as defined in the Rotating Wave Figure 13 where     c2 = g u u thus:  

1 d2x  dx dx  q dx  

2  2  = 2 F    

 c dt dt dt mc dt 

 and thus:    

q   a , u u = F u  

m 

 Now a vector can be constructed by pairing the contravariant components with covariant base vector components 

so:  

    e  

  (a u u )e = ( F u )e   

m q 

    e a u u =  F u   

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M where F  is now embolded because it acts like a base vector. Note that as indicated previously Eq. (16) for the 

Rotating Wave model:    

  c = ecc = vv vR vT = e u vT  

 Also, as is common practice when analyzing Kaluza Klein theory, Greek indices are again here used to denote 4 

dimension quantities (c4 = e u ) while Latin indices are used to denote overall 5 dimensional quantities (c5 = 

e u = e u vT ). To be clear: c5 = c4 
v
T  

Thus for 4 dimensions when vT = 0 (Rotating Wave cylinder condition of constant translational motion):    

 dc4 dec 2 de  

  = c = c R4 = e du  u  dt dt dt 

   q  

  = e a u u =  F u   

m 

 And for the Rotating Wave 5 dimensions (or 5 vectors):    

 dc5 2 de dvT 

  = c R5 = e du  u   dt dt dt 

  dvT 

  = e a u u    

dt 

   Now, as per the standard model of General Relativity the Equation of Motion (EOM) is set to zero for the 

straightest geodesic and thus the rotation curvature R5 is not considered nor observed. So for the moment let:    

 2  dvT 

  c R5 = 0 = e a u u   dt 

   dvT 

  e a u u =    

dt 

 but from the variational principle Eq.(67) leads to Eq.(72)    

 2   q  dvT 

  c R4 = e a u u =  F u =    

 m dt 

 Thus according to the Rotating Wave model, the extra term (ET ) generated by the Kaluza Klein 5 dimensional 

model is clearly:    

 dvT q  

  ET =  = F u   

 dt m 

 Also note as per the Rotating Wave model,    

2 2 dvT   c R5 = c R4   

dt 

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 So according to the Rotating Wave, the F u  would appear to rotate like the R5 and  

R4 .    

  

 Expanding further,    

 e  

 ET =  F u 

m 

 e v 

2 2 e c R5 c R4 =

  F u  m 

 dvT d bET T dvT 

= = v ET  dt dt dt 

  =  F u = R vT ET AT m PT 

 So when a homogeneous electric field is present, there appears to be a boost in potential that is both rotational 

(v
R

P
T

1v
T ) and radial ( E T AT ).  One can imagine this intuitively when using the right hand rule of thumb: it 

is like tightening the fist while pushing the thumb forward. When the homogeneous electric field is attracting the 

negative field of the electron?s Rotating Wave, then the potential is positive and the rotation and forward 

translational motion is immediately amplified. In that case, the Light Line (radius at which Rotating Wave speed 

is c) spirals inwards (tightens) creating the bullet form of intrinsic curvature and the mass energy is increased. 

When the potential is negative, the rotation and translational motion are immediately decreased. In that 

negative case, the Light Line spirals outwards and mass energy is dissipated. In comparison to the gravitational 

theory and its slowing down of time and energy, this suggests some additional impact on the expansion of the 

universe by electromagnetic interactions.  

 Consider a Rotating Wave held stationary (on the wall) while in a homogeneous attracting electric field. At a 

certain radius RR , the tangential velocity of the rotating wave is traveling at the speed of light cR = vR and thus;    

 dcR 2 q R 

 = c RR = F Ru  

 dt m 

and the RR is simply the inverse of the radial vector.  

Now consider a Rotating Wave (off the wall) and free falling straight in a homogeneous attracting electric field:    

 c4 = vv vR = vvcR  c5 = vv vR vT  

 dc4 2 q  

   = c R4 =  F u  dt m 

 dv q R 

  = Ev  F R u  

 dt m 

  

  c2R4 = Av (q/m)FR u
R  

 dc5/dt = c2R5 = (q/m) F u dvT /dt = Av (q/m) F R u
R dvT /dt  c2R5 = Av (q/m) F R u

R d E T/dtvT E TdvT 

/dt  

  = Av (q/m) F R uR vRPT 1vT AT  

   Letting c2R
5 = 0, then the extra term,  

(7 

(7 

(7 

(7 

(7 

(8 

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 ET = vRPT 1vT AT = AV (q/m) F R uR    and thus:    

 dvv/dt = (q/m) F vu
v  dvR/dt = (q/m) F RuR  dvT /dt = (q/m) F TuT .  

 TaeHun Kim and Hyunbyuk Kim also suggest “is possible to imagine a mechanical wave propogating along a 

particle-thread”. That thread according to the Rotating Wave model would appear to be the Light Line at a radius 

where the wave front has the constant speed of light (c ). Again that Light Line would be dragged or deformed by 

an electric field outwards or inwards depending on charge. Essentially the enormous difference between the 

strength of electromagnetism and gravity can probably be accounted for by comparison of the direct and 

immediate deformation of electric field verses the slight and indirect affect of a Rotating Wave on another wave 

via the bending interaction through the permeability and permittivity of EM Vacuum field. The Rotating Wave 

theory is grounded in the 3 dimensional space we are very familiar with and observe everywhere. The Rotating 

Wave theory suggests that the  

5th dimension as suggested by Kaluza is likely the 5th radial vector vT of the Rotating Wave. The Rotating Wave 

obviously requires faster than light velocities at greater radii plus nonlocal interaction. What one observer sees 

might be just another perspective compared to others. In an article prepared by Lance L. Williams [6] he states 

that:“It has been little – appreciated but motion in the 5th dimension is identified with electric charge. He also 

notes:  The 5 D Theory would seem to offer an avenue toward breakthrough physics (breakthrough propulsion) 

because it satisfies the expectations for such a theory as well as hinting at a possible approach to hyper–luminal 

travel: the 5th dimension.”    

Note that as per the Rotating Wave, the speed of light increases at greater radii. Perhaps it is possible to detect 

Rotating Waves like beacons of light at great distances, albeit with associated weak fields. With futuristic applied 

technological advances, that might permit communication across stellar distances and significantly further the 

potential of quantum entanglement. In the more near term, perhaps we could just try to model the Rotating Wave 

and see what technological applications it might have. The Rotating Wave suggested to me long ago that we might 

be able to create an electromagnetic propeller that can “push or pull” against the EM Vacuum field of space. The 

“push or pull” traction is due to transmission and rotational energy could be redirected into forward motion. 

Certainly, if we are going into space for the long haul, we can’t afford to pollute it with micro particles from 

propellant along the same trajectory. Also, a massless rocket (like an electromagnetic propeller) would certainly 

be much more efficient overall with much less fuel payload. Furthermore, the acceleration and deceleration along 

trajectories would save time and have fewer moving parts, making space travel more comfortable and safe. 

Newton wondered why gravity worked. Einstein explained that mass bent space. But again, then why does mass 

bend space? I think it is the Rotating Wave affecting the permeability and permittivity of the EM Vacuum field. 

What binds the photon into rotation in the first place is imparted to other interacting waves.    

13. Zitterbewegung (zbw) as Evidence of the Rotating Wave    

Many people are familiar with David Hestene’s work on Zitterbewegung as well as geometrical algebra and his 

space time algebra (STA). I came across his article of 1990 [7] and immediately noticed a similarity between 

Zitter and the Rotating Wave. Right at the outset of the abstract, Hestenes states:  The Zitterbewegung is a local 

circulatory motion of the electron presumed to be the basis of the electron spin and magnetic moment.  

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Hestenes notes that the rest frame S (= m0c
2 where here m0 = rest mass) energy has a familiar form of rotational 

kinetic energy for a body with angular momentum S and rotational velocity . The S= mc2 suggested to 

Hestenes  that the “rest mass” of the electron has a kinetic origin. Refer to previous section 5. A Definition of Rest 

(Energy) Mass. According to the Rotating Wave, the Rest (Energy) Mass E0 = Rotational Kinematic  

Energy (E
R =1/2m

0c
2) E

B (Binding Energy) = m0c
2 and thus ER = EB . The mass is due to kinematics of a Rotating 

Wave brought into classical rotation by a binding energy.Hestenes states that “In analyzing free-particle wave 

packet solutions of the Dirac wave equation, Schrödinger noted the existence of “interference” between positive 

and negative energy states oscillating with circular frequency 0= 2m0c
2/ =1.6x1021s 1 . That would be like a 

wave rotating at a billion billion times a second. No wonder it interacts like a hard particle as well as a wave.   

Hestenes further states:“But the greatest challenge will be to prove that the zbw is a real physical phenomena and 

not just a metaphorical trick.”He had already thought that “barrier penetration can be interpreted as manifestations 

of the zbw”. Apparently, Louis de Broglie in his 1924 doctoral thesis had already proposed that the electron has 

an internal clock, with frequency at about a billion billion times a second.   

While Schrödinger adopted de Broglie’s wave hypothesis in his famous equation, de Broglie’s clock hypothesis 

was ironically forgotten.  In a later article Hestenes reveals that he met with French experimental physicist Michel 

Gouanere “who argued that if the electron clock is physically real, channeled electrons should interact resonantly 

with the crystal periodicity at some energy to produce a dip in transmission rate.” Gouanere and colleague M. 

Spighel had already conducted an electron channelling experiment which supported the electron clock and was 

published in Annales de la Fondation Louis de Broglie in 2005, but was rejected by Physical Review Letters and 

many said it was implausible. I suspect that implausibility was the billion billion times a second. One reviewer 

said perhaps it could be explained by Zitterbewegung, so Gouanere got in touch with David Hestenes.As noted 

in previous section 11. Hans C. Ohanian [1] noted that Goudsmit and Uhlenbeck in 1925 immediately realized 

that their proposed electron “spin” would very likely lead to serious problems with Special Relativity, but 

Quantum Mechanics was just starting to develop and was drawing more attention at the time. The Dirac matrices 

appeared to refer to some characteristics of the electron itself and thus Dirac commented on their presence in the 

energy equation of an electron:“They must therefore denote some quite new dynamical variables, which may be 

pictured as describing some internal motion in the electron. We shall see later that they just describe the spin of 

the electron.” – Paul A.M. Dirac The key to the Rotating Wave and Relativity is that: when a light wave travels 

in a straight direction it moves at the speed of light, but when it rotates, it travels at greater velocity at further radii 

from it center of spin. In 2008 Michel Gouanere along with Denis Dauvergne, Robert Kirsch, JeanClaude Poizat, 

Joseph Remillieux, Michel Chevallier, Cedric Ray, Etienne Testa, Robert Chehab, Marcel Bajard, and Philippe 

Lautesse proposed RICCE (Research for an Internal Clock by Channelling of Electrons), [8] . I don’t know the 

details nor the outcome of RICCE, but I suspect that if one posits relativistic properties purely as a function if the 

Rotating Wave and not a connection between space and time itself, alternate findings might be considered and 

observed. 

14. Stern Gerlach and 720 Degrees 

 Stern Gerlach: 

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 In 1922 Otto Stern and Walter Gerlach performed an experiment which involved sending a beam of silver atoms 

through an inhomogeneous (non-uniform) magnetic field and onto a detection screen. The silver atoms were each 

considered neutral in charge, but had an extra electron. Classical spinning particles would be expected to just 

show up on the detection screen in a random pattern, but the beam split into exactly two which indicated that half 

of the electrons had an intrinsic quantized angular moment of /2 (spin up) and the other half had /2 (spin 

down).The Stern Gerlach quantum mystery still is: Why does one particle appear to have a possible spin of either 

up or down and not just in one way? Electrons have a spin opposite to that of positrons, but they are two types of 

particles which cancel each other out in annihilation. Electrons do not cancel each other out, but appear to have 

two types of spin. Note that the Rotating Wave model of the electron has a forward (translational) motion in line 

with its axis of spin.   

Thus if an electron orbits clockwise around a silver atom nucleus, it will have a specific direction and angular 

moment of spin. Furthermore, the most stable motion of a whole silver atom would require that the orbital plane 

of the extra electron be in line with the trajectory of the atom towards the detection screen. However, for each 

silver atom with a clockwise (or upside up) orbit there is an equally statistical chance of having a counterclockwise 

(or upside down) orbit. One is just the mirror of the other. Hence, the orbit-up motion of the silver atom could be 

observed and interpreted as spin-up while the orbit-down motion could be observed and interpreted as spin-down. 

That might invite discussion and argument, but it is one possible way that I can think of in explaining quantized 

spatial orientation of spin with the classically Rotating Wave.  

 720 degrees and Spin ½ 

Apparently a rotation of 360 degrees does not return the electron to its original state. It requires a 720 degree 

rotation to do that. Also note that this is true not just for electrons but any spin-1/2 particle. Now note that as per 

Figure 4, there are two symmetrical nodes so when the Rotating Wave is spun 1/2, it looks the same as the original. 

The intrinsic spin angular moment is one half of the orbital moment, so for each orbit the electron spins only half 

the way around. It would take two orbits or 720 degrees of rotation to get the electron a full spin and back to the 

original state. I also note that there are two nodes on the ½ spin Electron RW. Perhaps there are three nodes on 

others particles, such as Quarks with -1/3 and 2/3 charge.  

15. Possible Solutions to Paradoxes of Modern Physics  

The foregoing concept of the electron wavicle might resolve well known paradoxes of physics such as the wave-

particle duality of both light and matter, the EPR (Einstein, Podolsky and Rosen) paradox, and the age-old Zeno’s 

paradox of motion. By this concept one would expect the electron to be affected by a double diffraction slit in 

just the same way that a photon would, simply because the electron is composed of half a spinning photon plus 

binding energy. Similarly, the photo-electric effect might be explained by the consequent oneon-one relationship 

of the photon and the electron RW. In 1935 Einstein, Podolsky and Rosen published a paper on a thought 

experiment which stated that if the position and momentum of only one of two particles is measured after an 

initial measure of their combined position and momentum, then the final momentum of the two particles cannot 

be the same unless there is some kind of instantaneous “action at a distance” or “non-local reality” between the 

two particles. However, modern experiments, which have measured the polarization of twin photons instead of 

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position and momentum of particles, have confirmed the violation of Bell’s inequality and thus support the “non-

local reality” of Neils Bohr’s Quantum Theory and the EPR paradox. The apparent action at a distance might be 

simply due to the action of the infinitely extended rotating wave of the RW. The apparatus which interferes with 

one photon while measuring its polarization would, according to the RW, also interfere with its twin photon of 

equal and opposite momentum. The twin photon, although at a greater distance from the centre of the interfering 

apparatus, would still be affected by the same electromagnetic wave function of that measuring apparatus. The 

locality of a particle might be thus better interpreted as the centrality of spin of the RW’s electromagnetic wave.  

Zeno’s paradox prescribes discrete motion of particles.   

However, the electron RW is transmitted through the EM Vacuum field as a wave. The EM Vacuum field might 

also be predicated upon a substrata energy fieldof wave functions and perhaps enable the creation and 

transmission of electromagnetic waves and move themselves very likely with speeds much greater than that of 

light. Given an infinite amount of real time and space, an infinite number of energy strata could have evolved into 

something as substantial as light and thus the existence and motion of matter.  

16. Conclusion  

The Rotating Wave (RW) model of the Electron provides an elegant and simple solution for wave function of 

matter and in doing so, it explains the apparent relativistic connection between space and time. A number of 

physicists have considered the “circular motion” within the electron, but tried to maintain the direct connection 

between space and time. An in depth study of Louis de Broglie’s thesis would be interesting because he studied 

relativity, was the first to consider matter as a wave form, and apparently also considered there might be circular 

form of motion in the electron. Basically, the RW agrees with the assumption that the speed of light is independent 

of it’s source and is constant at speed = c in a straight direction. However, the RW also requires that the bending 

of light allows for speeds greater than c at greater radii. Given that, everything seems to naturally derive from a 

classical rotation of “spin”: mass, charge, magnetic dipole, relativity, quantum mechanics, and a number of 

paradoxes. Relativity and quantum mechanics are thus inseparably innate to the real wave equation of the RW. 

Furthermore, rotation of the wave clearly explains how a magnetic dipole field is self-induced and thus how a 

magnetic field is induced by the motion of a charged particle.The RW form also allows one to derive the G
k  

intrinsic curvature in detail and is congruent with the mass energy density tensor. That is perhaps not surprising 

because after all, the mass energy density tensor is itself indirectly derived from rotating wave forms of mass.  

One thing the detailed G
k  of the RW does in addition is to inherently explain the expansion of the universe. 

Without expansion there is no curvature. Any energy expended by the RW in its coupling with other particles or 

waves would, by its definition of mass, require its gravitational field to decrease as the RW’s time cycle of spin 

slows down. The RW’s inherent connection between gravity, spin and time thus provides an elegant explanation 

to the expansion of the universe.The RW model does yield additional insights which might stimulate unification 

theory as well as provide alternate models for teaching current theory. For example, by applying the Definition 

of Rest (Energy) Mass according to the RW, a radius Rq, at which a hypothetical wave of the quark is rotating at 

the speed of light, can be defined as: Rq = (m
e
R

e)/
m

q where m
e and m

q are the stationary masses of the electron and 

quark respectively. Re is, of course, the radius of the electron wavicle at which its rotating wave is traveling at the 

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speed of light. The radial distance Rq could be compared with the distance to which the strong force extends. Such 

speculations might provide some enlightenment upon current QCD theory.   

S.A. Emelyanov in his 2012 [9] : “Toward a real synthesis of quantum and relativity theories: experimental 

evidence for absolute simultaneity”, states that their observations leads them to believe that the de Broglie-Bohm 

and aether related Lorentz-Poincare theories are capable of providing a real synthesis of quantum and relativity 

theories. Again, the RW model has two nodes of maximum amplitude (see Figure 4) which create quantum 

mechanics and the planar wave fronts of these nodes incline and with a longer helical wavelength, thus creating 

relativistic effects (see Figures 5, 6, and 8).  

Dr. Louis M. Houston at the University of Louisiana at Lafayette posted his 2013 article in IJESIT: “The Physics 

of a Rotating de Broglie Wave Packet” [10]. As per his abstract, Dr. Houston finds that the field generated by a 

rotating de Broglie wave packet results in a “quantized electromagnetic-centripetal field for a small angular 

range”.Dr. Robert Close in Portland has developed a Classical Wave Description of Electrons [11] that is likely 

similar to the RW model and which he uses for comparative modeling in teaching Physics. [00] One thing I agree 

with on the Classical Wave Description is that the wave function actually causes relativistic effects rather than 

just complying with relativity. In the Emelyanov, Houston, and Close concepts, it could be very revealing in 

comparing the Rotating Wave vectors with the Dirac matrix equations and Rotating de Broglie wave packet. After 

some analysis, that would be greatly facilitated by in person discussion groups, also including Hestenes and Kim. 

A revisit of the Gouanere et el channeling and RICCE type experiments [8] might be done in order to find out if 

the classical Rotating Wave model is correct.Refer to Figure 16 below. While comparing the spin and charge of 

an electron with its anti-particle the positron, I noticed that the quarks were of a different size as well as charge. 

The electron positron pair annilihate each other while the proton is formed of two up quarks plus one down quark. 

It is speculation only, but perhaps the next higher complex form of spin is the figure eight. The electromagnetic 

wave would be able to wind in a figure eight fashion because there are two maximum nodes with half spin for 

both the quarks and the electron (as shown in Figure 4).   

Figure 16: The Rotating EM Waves are shown winding through the proton and the neutron in figure eight 

fashion, possibly manifesting the strong force.  

  

   

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Regardless of whether the Rotating Wave model is absolutely correct or not, more study might be done in that 

direction to advance theory and also see what technological applications might be developed. Finally, the Rotating 

Wave theory might not have be so radical if the de Broglie wave nature of matter had been established prior to 

the famous Michelson-Morley experiment. The RW model requires that all matter is being transmitted through 

space, after all it is energy. That would have avoided any discussion about aether drag. Aether really is just the 

homogeneous electromagnetic field of empty space. It allows the transmission of light, matter, and other forms 

of radiation. It appears to extend through the universe as we know it, but perhaps there are more substrata fields 

which are so far undetected and extend much further.   

 Acknowledgements 

I wish to thank Ernest Von Rosen M.Sc. Physics for his support and earlier attempt at publication. Also, thanks 

goes to Steve Belleguelle for his program AmiWeb. I first heard the term "Wavicle" mentioned by Dr. Carl Sagan. 

I admire H.A. Lorentz for all of his work as I do others, particularly Albert E. Einstein, all of whom I could not 

envisage the Rotating Wave without their diligent math and logic. To all of my teachers who inspired me to 

"always learn to be aware of what we are dealing with" - thank you. W.H.F.Christie.  Word document transcribed 

to Latex by H. Fearn and later transcribed to Word for final publication. 

General References  

Belinfante, F., On the current and the density of the electric charge, the energy, the linear momentum, and the 

angular momentum of arbi- tray fields, Physica 6, 887 and 7, 449-474, 1939.  

Crossley, Dennis, Conceptual Barriers to a unified theory of physics, Dept of Physics, University of Wisconsin-

Sheboygan, Sheboygan, WI 53081 August 31, 2012  

Overduin, J.M.,Wesson, P.S., Kaluza-Klein Gravity, arXiv:gr-qc/9805018v1, 1998 http://arxiv.org/abs/gr-

qc/9805018 de Broglie, L.V., Recherches sur la Theorie des Quanta, Ph.D. thesis, University of Sorbonne, Paris 

(1924)  

Schrödinger, E, (1930), Uber die Kraftfreie Bewegung in der Relativistischen Quantenmechanik, Sitzungb. 

Preuss. Akad. Wiss. Phys.-Math. Kl. 24: 418.  

Stenson, Jared R., Representations for Understanding the Stern-Gerlach Effect, Thesis, Brigham Young 

University, August 2005  

Van Huele, Jean-Francois, Stern, Barut, and Gerlach Today, Department of Physics and Astronomy, Brigham 

Young University, N151 ESC BYU Provo, Utah 84602-4681 E-mail: vanhuele@byu.edu (Received 28 Feb 2005)   

References  

Ohanian, Hans C., What Is Spin?, Rensselaer Polytechnic Institute, Troy NY, published May 1,1986 American 

Journal of Physics (54) 6  

Dirac, Paul.A.M. Dirac, The Quantum Theory of the Electron, Published 1 February 1928.DOI: 

10.1098/rspa.1928.0023 http://rspa.royalsocietypublishing.org/content/117/778/610  

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82 | A c a d e m i c  J o u r n a l  o f  S c i e n c e ,  E n g i n e e r i n g  a n d  T e c h n o l o g y  

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Straub, William O., Kaluza-Klein for Kids, Pasadena, California, 91104, June 27, 2014 

http://www.weylmann.com/kaluza.pdf  

Toth, Viktor T., Kaluza-Klein Theory, http://www.vttoth.com/CMS/physics- notes/118-kaluza, December 01, 

2004 http://www.vttoth.com/CMS/physics-notes/118-kaluza-klein-theory  

Kim, TaeHun and Hyunbyuk Kim, Electromagnetism in 5-Dimensional Manifold, July 12 2015 

arXiv:1507.03184v1 (gr-qc). http://arxiv.org/abs/1507.03184  

Williams, Lance L., The Nature of the 5th Dimension in Classical Relativity, Konfluence Research,Man itou 

Springs, Colorado 719-685-1163;http://www.konfluence.org/ final_AIPv 1103p 243_1.pdf  

Hestenes, D. The Zitterbewegung Interpretation of Quantum Mechanics, Found. Phys.  20 (10), 12131232 (1990) 

http://modelingnts.la.asu.edu/html/Impl_QM.html  

Gouaniere, Michel et al, (2008), A Search for the de Broglie Particle Internal Clock by Means of Electron 

Channeling, Foundations of Physics 38: 659-664.   

  https://www.lnf.infn.it/acceleratori/public/BTF_user/RICCE/RICCE.pdf  

Emelyanov, S. A., Toward a real synthesis of quantum and relativity theories: experimental evidence for absolute 

simultaneity, Division of Solid State Electronics, Ioffe Institute, 194021 St. Petersburg, Russia DICE2012 

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Houston, Louis M., The Physics of a Rotating de Broglie Wave Packet, The Louisiana Accelerator Center, The 

University of Louisiana at Lafayette, IJESIT Vol 2, Issue 6, November 2013 

http://www.ijesit.com/Volume%202/Issue%206/IJESIT201306_78.pdf  

Close, R. A., Classical wave description of Electrons, 2015 07 29   

  http://www.classicalmatter.org/Classical Electron.html 2015-07-29 

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