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PowerPedia:Zitterbewegung Hydrogen Atom of Quantum Ring Theory

Lasted edited by Andrew Munsey, updated on June 15, 2016 at 1:38 am.

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In the model of the hydrogen atom proposed by Niels Bohr the electron is assumed to be corpuscular. So, his model is incompatible with the model of quantum mechanics, where the electron is considered to be a wave described by the famous equation developed by Schrödinger.

Bohr model is unable to explain some phenomena that require a wave model of the electron, and therefore his model is not correct.

Paradoxically, Bohr model has supllied the Theoretical Physics with many spectacular successes, pointing out that his model cannot be entirelly wrong. But after the development of Quantum Mechanics, the quantum theorists concluded that Bohr successes are accidental.

Here we analyse the paradoxes of the hydrogen atom, and show how they are solved in Quantum Ring Theory.

QUESTION: what is zitterbewegung ?

The electron does not move with a Newtonian rectilinear motion. It moves with a trembling motion, a helical trajectory named zitterbewegung in the Dirac theory of the electron. Schrödinger was the first to point out such strange trembing motion in the Dirac equation.

QUESTION: what is the principle of complementarity ?

Sometimes, when quantum theorists are required to explain a phenomenon that requires a corpuscular model, they use some tools used by Bohr when he developed his corpuscular model for instance, the concept of reduced mass.

QUESTION: is acceptable the solution of Quantum Mechanics, from the philosophical viewpoint ?

Such a procedure is very strange, since the theorists are mixing concepts appropriate for a corpuscular theory with those applicable to a wave theory.

And so, they believe that Nature can work by using two incompatible model: sometimes she uses the wave, sometimes she uses the corpuscular model.

Bohr supposedly solved this paradox by proposing his principle of complementarity, according to which two incompatible models are necessary for the explanation of the phenomenon.

QUESTION: then the paradoxes of the hydrogen atom have been solved by the principle of complementarity ?

The quantum theorists believe that yes.

However, as it will be shown ahead, they are wrong. There is a terrible paradox that Quantum Mechanics cannot solve: the successes of Bohr imply that QM is not entirelly correct.

QUESTION: is the Bohr’s model of hydrogen atom wrong ?

Paradoxically, the answer is YES and NO.

Bohr’s theory obtained some of the most spectacular successes of Theoretical Physics, although the physicists nowadays claim that they are accidental.

Ahead we will understand why Bohr model can be, at the same time, correct and wrong.

QUESTION: what are the successes of Bohr ?

Bohr discovered his model because he decided to find an explanation for the Balmer’s series.

He used his theory for the calculation of several properties of the hydrogen atom. The theoretical calculations supply results confirmed by the experiments.

Thanks to his model of hydrogen atom, several predictions were made, as for instance the existence of other series similar to Balmer’s scale, later discovered.

QUESTION: can Bohr’s successes be accidental ?


Look for instance the Rydberg’s cosntant calculated by the Bohr’s theory, compared with the value obtained by experiments:

Experimental: Rh= 10.967.757

Theoretical: Rh= 10.968.100

Such “coincidence” cannot be accidental, as the quantum theorists claim.

There are many other fantastic impossible “coincidences” obtained from the Bohr theory.

QUESTION: why do the quantum theorists claim that Bohr’s successes are accidental ?

So that to undestand why they claim it, we need to understand what happens in the Bohr model when the atom emits photons.

In the Bohr theory, the point of departure for the calculations is two equations. They are:

- The electric force Fe of repulsion between the proton and the electron.

- The centripetal acceleration Fc on the electron, due to its motion with velocity “v” in circular motion about the proton.

QUESTION: can exist a centripetal acceleration on the electron in the hydrogen atom of Quantum Mechanics ?
QUESTION: why from Quantum Mechanics the electron cannot have trajectory ?

Consider the electron into the proton’s electrosphere, they forming the hydrogen atom.

According to QM, the atom emits a photon when the electron passes from a level of energy to another level, for instance from the level n=1 to n=3.

Suppose that the electron travels the space between the levels n=1 and n=3. Then we have the following conditions:

1- The electron is submitted to an attraction force with the proton.

2- So, going from n=1 to n=3, the electron must suffer disacceleration, since it is submitted to a force against the direction of its motion.

3- Then the atom must emit a continuous spectrum of photons during the time when the electron goes from n=1 to n=3.

4- But it’s known that the atom does not emit a continuous spectrum of light. It emits discrete photons.

5- Therefore, the electron cannot travel the space between two levels of energy. That is, the electron cannot have a trajectory, according to Quantum Mechanics.

QUESTION: is Bohr theory correct ?

No. His theory is not able to explain many phenomena, and therefore his model of hydrogen atom cannot be correct.

QUESTION: is Bohr theory 100% incorrect ?

No. From the mathematical viewpoint of probablility, it’s impossible that Bohr theory is 100% incorrect.

QUESTION: “Bohr theory cannot be 100% incorrect. What is the meaning of such conclusion ?
QUESTION: can Quantum Mechanics be 100%¨correct ?
QUESTION: Consider a theory on the hydrogen atom, unable to explain the successes of Bohr theory. Can such theory be successful ?

Of course not, because:

1- Bohr theory shows that a centripetal acceleration exist on the electron, in the instant of the photons emission

2- Therefore, in the real atom that exists in the Nature, there is a centripetal force on the electron

3- Therefore a satisfactory theory must be able to explain the existence of the centripetal acceleration on the electron, otherwise the theory is not the correct image of the model existing in the Nature.

QUESTION: What are the fundamental premises to be filled by that a correct theory on the hydrogen atom ?
QUESTION: Bohr theory considers that centripetal acceleration on the electron plays a fundamental role in the photon’s emission in the hydrogen atom. Is it correct ?
QUESTION: is then Quantum Mechanics correct, concerning the mechanism of emission?

Yes, the mechanism of photons emission proposed in Quantum Mechanics is correct, because the centripetal acceleration does not play any role in the photons emission (as wrongly supposed by Bohr).

QUESTION: as the centripetal acceleration does not play any role in the photon’s emission, why is not Quantum Mechanics 100% correct ?

From Bohr theory we realize that, when the hydrogen atom emits a photon, the electron is submitted to a centripetal force.

In spite the centripetal force does not play any role in the photons emission, nevertheless into the real hydrogen atom existing in Nature the electron is submitted to a centripetal force in the instant of photons emissions, as predicted in Bohr theory (although the emission of photons does not depend on the centripetal force, as inferred from Bohr theory).



It’s easy to understand why. Look:

QUESTION: why is not Quantum Mechanics 100% correct ?

Consider the facts ahead:

QUESTION: The centripetal acceleration does not play a role in the photons emission. Nevertheless, the centripetal acceleration do exists in the instant of the photons emission. How to explain such paradox ?

We will see that Quantum Ring Theory explains such paradox.

QUESTION: What are the implications of the successes of Bohr for the Theoretical Physics ?



As shown earlier , the successes of Bohr’s theory imply that the mechanism of photon emission according to quantum mechanics cannot be hundred percent correct. Something is missing in the model of quantum mechanics.

Here it will be shown that the success of quantum mechanics concerning the hydrogen atom and also the successes of Bohr’s model are due to some coincidences existing in the hydrogen atom.

QUESTION: Did Schrödinger believe that Bohr successes should be accidental ?

Definetivelly no, he didn’t. He never accepted that Bohr successes could be accidental.

In his article intitled On a Remarkable Property of the Quantum-Orbits of a Single Electron , published in 1922, Schrödinger wrote about a result obtained from Bohr theory:

QUESTION: Is there a chance to find a theory capable to conciliate the Bohr’s corpuscular model with the Schrödinger's wave model of Quantum Mechanics ?

Quantum theorists claims “NO”.

Quantum Ring Theory responds “YES”.

Although Bohr’s model appears flawed, some fundamental concepts of his theory are retained in the hydrogen model of quantum mechanics. They are:


QUESTION: Is the space within the atom Euclidian, as supposed by Bohr ?

No, because actually there is a dilation of the space within the electrosphere of atoms.


In the hydrogen atom of Quantum Ring Theory an electron moves with a helical trajectory (zitterbewegung) within the electrosphere of a proton.

The aether that constitutes the electrospheres of the proton and the electron has dilation. Such dilation of the space is caused by two repulsive gravitons G(+) and G(-), which belong to the structure of the aether, as we will see later in the script entitled AETHER.

The proton and the electron in physics belong to a class of particles known as fermions, which have charge and spin ½ . In Quantum Ring Theory it is proposed that the fermions, like the proton and the electron, produce a flux of gravitions “g”, that fulfils the aether around them, like several strings of gravitons. Two gravitons g attract one another, while two gravitons G repel one each other.

QUESTION: What is the cause of the dilation of the space within the electrosphere of atoms ?

The space within the proton’s electrosphere is non-Euclidian. Due to the repulsive gravitons G, the distance between the strings constituted by a flux of gravitons g depends on the distance of a considered point with respect to the proton. Fig. 1 shows an electron that moves in a radial direction, crossing the strings of gravitons g, in the Euclidian space considered in Bohr’s model (the distance “d” between the strings is constant).

Fig. 2 shows the electron moving within a non-Euclidian space, where the distance “dR” decreases when the electron goes in the direction of the proton.

QUESTION: Is the electron’s inertia constant with regard to the proton ?


Consider that ao is the acceleration applied to the electron due to its attraction with the proton, into the Euclidian space, as considered in the Bohr’s model (figure 1).


Figure 2 shows that within the non-Euclidian space the acceleration applied on the electron is a, and is greater than ao , because in the Figure 2 the quantity of strings crossed by the electron increases when the electron moves toward the direction of the proton (in radial direction). The mass of the electron does not change, but the phenomenon (with regard to the proton) happens as if the electron’s mass would be changing.

QUESTION: Is there a connection between this “apparent” changing of electron’s mass in the zitterbewegung model and the constant mass of the electron in the Bohr’s model ?

Yes, there is. In the Bohr’s model the electron changes its velocity when it jumps between two orbits, while the mass is constant. So, the kinetic energy E= ½m.V2 changes because the velocity changes. In the zitterbewegung model the electron’s velocity is constant when the electron jumps between two orbits, and the kinetic energy changes because the mass (with regard to the proton) changes according to the relation: m = mo/n2 , where n=1, 2, 3…


QUESTIONS: 1- How does the non-Euclidian space intervenes in the features of the helical trajectory? 2- Does the repulsive gravity produce any force on the electron?

The helical trajectory has basically two properties: the pitch and the radius.

Within the non-Euclidian space of the proton’s electrosphere, the helical trajectory has several properties, for instance:

1. If the electron moves in a radial direction (with respect to the proton), if its speed is constant, then the radius of the helical trajectory increases when the electron moves away from the proton but the radius decreases when the electron approaches to the proton.

2. Due to the dilation of the aether, an electron that moves in a radial direction experiences a force F(R) of repulsion, trying to expel it from the electrosphere of the proton. Such a force F(R) has the same value of the force F(a) of the Coulomb attraction between the proton and electron. Therefore, when the electron moves in a radial direction, the total force on it is null. Therefore, when moving in a radial direction, the electron always moves with constant speed within the proton’s electrosphere.

Such a property of the helical trajectory of changing its radius is called zoom-effect in Quantum Ring Theory. So, it happens as follows:

1. In the Euclidian space (considering a free electron), the radius of the helical trajectory decreases with the growth of the electron’s speed. When the electron aproaches the speed of light, the radius tends to zero (the electron becomes a boson when the helical trajectory becomes a Newtonian linear trajectory).

2. In the non-Euclidian space (electrosphere of proton) the radius of the electron’s helical trajectory decreases when it approaches the proton 'with constant speed'.

QUESTION: Is the Quantum Ring Theory the unique one to propose a solution through the zitterbewegung ?


The physicist, Dr. David Hestenes, developed a research program on Zitterbewegung at Arizona State University , by using the Spacetime Algebra (STA).

He does not propose a hydrogen atom. He researches the electron’s zitterbewegung.

QUESTION: Is the zoom-effect predicted in the Hestenes research ?


For a free electron moving in a Euclidian space, Hestenes shows that the variable radius of the electron’s zitterbewegung due to the zoom-effect is:


which is equation 124 in his paper “Zitterbewegung in Quantum Mechanics – a research program”.

QUESTION: How is the pitch of the helical trajectory influenced by the dilation of the space ?

Fig. 3 illustrates how changes in the pitch “h” of the helical trajectory when an electron leaves a region AB with constant density of the aether, and enters a region BC with decreasing gradient, and ahead enters again a region CD with constant gradient (but lower density than in the region AB)

QUESTION: How are the photons emitted in the zitterbewegung model of hydrogen atom ?

QUESTION: How to interpret the results of Bohr’s calculations when we introduce the concept of electron’s zitterbewegung ?

Fig. 4 shows what happens in the calculus due to Bohr, when the concept of the electron’s helical trajectory is introduced.


Fig. 5 shows what really happens within the hydrogen atom, and the cause of the success of the Bohr model. There is a coincidence: the Coulomb force Fc used by Bohr has the same value as the force Fe of the aether on the electron (the force Fe of the aether that keeps the electron moving with a helical trajectory).

QUESTION: Is the Bohr success on hydrogen atom accidental ?

Paradoxically, the answer is YES and NO.


1- The proton-electron distance (considered by Bohr) is equal to the distance between the electron and the center of its helical trajectory:


2- The centripetal force considered by Bohr (which in his calculation is considered equal to the Coulomb force of the proton-electron attraction) is equal to the force with which the aether keeps the electron moving about the center of its helical trajectory:

QUESTION: Is the proton the centre of the potential, as considered in both the Bohr’s model and in the Schrodinger’s model ?

No, the centre of the potential in the instant when the atom emits a photon is not the proton, as Schrödinger wrongly considered when he developed his famous equation. The centre of the potential is actually the centre of the helical trajectory, and such coincidence also explains the success of the Schrödinger theory.

So, the new hydrogen atom proposed in Quantum Ring Theory brings compatibility between the Bohr theory and the Schrödinger Equation. In this way, the new hydrogen atom proposed in QRT is able to explain all the phenomena associated with the hydrogen atom (the phenomena that require a corpuscular model, as proposed by Bohr, and also those phenomena that require an undulatory model, as proposed by Schrödinger).

Bohr’s absurd principle of complementarity may be discarded finally.

QUESTION: Are the Bohr’s successes a theoretical support for the zitterbewegung model ?

Yes, as any serious physicist may realize, the success of Bohr is stronger support for the hypothesis of the helical trajectory, because the helical trajectory is the only theoretical way capable to explain his successes. As a theory cannot be acceptable if it is unable to explain Bohr’s successes, then it may be concluded that, for any theory to be acceptable, it must be developed by considering the helical trajectory.

QUESTION: Are there another features of the zitterbewegung model ?

Yes, there are many other ones, and we will speak about them.


Imagine an atom tied to a molecular network of a solid body. Obviously, all the electrons of such a body have no freedom their fields are tied by the linking of the molecular frame.

Now imagine a free atom that is, one in a gaseous state. Let us take the same atom considered by Bohr, the hydrogen atom consisting of one electron orbiting a proton. In this case, the field of the electron has a degree of freedom: it is not tied to a molecular frame, and therefore it can get an additional increase in the angular velocity of its spin.

Consider a gas of hydrogen with temperature T, and suppose that, in each hydrogen atom, the electron and the proton experience Coulomb attraction. Then suppose that we supply energy to the hydrogen gas. Each hydrogen atom absorbs photons and there is an increase in the electron’s speed v in its orbit about the proton in order that its final speed is V>v. Let us see what happens.

In figure 1, (A) and (B) show the fields of a free electron and free proton. The actuation of repulsive gravity around the proton and electron causes an expansion of the aether around the body of each of them.


The density of the two fields is greater in the neighborhood of the electron’s body and the proton’s body, and decreases with the growth of radius “R”, as shown in the figures.

Obviously, a region with high density of the aether will have its inertia greater than another region with slighter density. Therefore, in region “1” of Figure 1-(C), (where the field of the electron overlaps the field of proton), the inertia of the fields is greater than in region “2”, where there is no overlap. So, the fields are submitted to two forces. The result is obvious: when the electron increases its translation speed around the proton, the speed of the electron’s spin becomes faster. In addition, because the proton and the electron are together, the motion of the electron also drags the field of the proton, and the two fields increase the speed of their spins. Consequently, an additional large magnetic field ?M appears. As we will see, the additional magnetic field ?M is

responsible for drastic changes in the properties of the electrosphere.

QUESTION: How the expansion of the aether influences the electron’s behavior ?

The dilation of the space within the electrosphere influences the electron’s behavior in many ways.


A new model of the hydrogen atom must be developed through the proposal of three fundamental postulates of the aether:

QUESTION: Are the three postulates capable to conciliate the Bohr’s model with the Schrodinger equation ?

Yes, the three postulates can effect conciliation between Bohr’s model and Schrödinger’s equation. Schrödinger’s success is accidental, because, although there is a central potential in the hydrogen atom (as considered in his theoretical development), the centre of the potential is not the proton (as he has considered) . The centre of the central potential is actually the line centre about which the electron turns when it is following its helical trajectory.

The answer is given by the three fundamental postulates of the aether, which are a requirement for the proposal of a new model of the hydrogen atom. Indeed, in such a new model, the electron is submitted to a null resultant force (because the attraction with the proton is cancelled by the repulsion due to the repulsive gravity responsible for a gradient of the aether’s density within the electrosphere).

The force of attraction of the proton on the electron is FA. Then from postulate number 3 of the aether we see that the electron is submitted to a repulsive force FR = -FA , due to the gradient of the aether’s density, which tries to expel it from the interior of the electrosphere in a radial direction in order that FA+ FR=0.

We realize that, within the atom’s electrosphere, the electron is submitted to the same condition as a free particle, since the resultant of the forces on the electron in the electrosphere is null. Therefore, it has a constant potential V(x,t)=VO.

Well, Schrödinger has just used as a point of departure the potential V(x,t)=VO.

In their book Quantum Physics, Eisberg and Resnick say:

"This is exactly the case of the free particle, since the force that actuates on the particle is given by F= -dV(x,t)/dt, which gives F = 0 if V(x,t)=VO is a constant".

So, Schrödinger has simply considered a constant potential for the development of his equation.

QUESTION: How does occur the rectilinear electron’s motion into the electrosphere ?

This is explained ahead


Let us analyze the laws and mechanisms of the rectilinear motion in the electrosphere of atoms, when we consider the helical trajectory (HT) and a gradient G(?). Firstly, let us analyze what happens to the pitch when the aether is non-homogeneous.

Consider Figure 3, where the line centre of the HT of a particle describes rectilinear motion between the points A and B, with constant speed V, in a region with density ?=k. There is not any external force applied on the particle.


Therefore, the HT has a constant pitch h in that region between A and B.

The particle arrives at point B, where it enters a region with decreasing gradient. Then the particle acquires a constant acceleration dV/dt during all the time as it crosses the region between B and C, although any external force is not applied to the particle. The aether applies an internal force F

to the particle. This is the consequence of the fact that the helical trajectory is constrained to keep the flux of aether crossing into it constant. However, the radius RHT of the HT does not change. In addition, obviously, there is a conservation of momentum in the region BC. In the region, CD the particle loses its acceleration, moving again with constant speed.


1. In Physics the acceleration a is described mathematically by a= dv/dt, where dv is the change in velocity, and dt is the period of time.

2. If we want the particle to have constant speed V in the region BC, with dV/dt=0, we have to apply an external force against the direction of the motion.

3. Now consider that a force is applied against the direction of the particle’s motion, in order to keep its speed v constant along the x-axis in a region with decreasing density gradient.

Figures 4A and 4B compare the trajectory of the particle when ?=1 with the trajectory when it crosses a region with decreasing gradient (in Figure 4B an external force is applied to the particle, in order to get dv/dt=0).

QUESTION: Is null the total force on the electron, when it moves in radial direction into the hydrogen atom ?

Now we are able to understand what happens. In the electrosphere the gradient of the aether’s density is G(?). This gradient represents a potential energy which tries to expel the electron from the influence of the proton’s attraction, along a radial direction.

This means that, due to the repulsive gravity within the hydrogen electrosphere, the resultant force on the electron is null when the electron’s displacement is along a radial direction.

According to the present proposal, when the electron leaves the level n=1 with speed V, it keeps the speed V along its displacement in the electrosphere but, as the density of the aether decreases, there is an increase of the radius RHT (of the helical trajectory) from rHT to RHT, (Figure 4B).

QUESTION: By what mechanisms are the photons emitted ?

Photons are emitted under some special conditions, as we will see.


The emission of photons by the atom happens according to two postulates of emission:


The circular motion of the electron is unable to induce emission of photons through the resonance of the helical trajectory. The electron can move in a circular trajectory within the atom without emitting energy. Indeed, considering the electron with circular motion, the helical trajectory does not have a defined pitch: on the interior side of the HT’s trajectory, the inside pitch ?IN is short, and the outside ?OUT is long that is why it is impossible to obtain resonance with REM through a circular trajectory of the electron about the proton. So, we realize that the atom emits photons due to its helical trajectory only when the trajectory of the electron is rectilinear with constant speed V, because it is the unique trajectory with ?IN = ?OUT (an indispensable condition for the resonance between ?HT and REM ) required for the photon’s emission.

QUESTION: What is the origin of the Bohr’s successes ?

Probably the spectator already has realized by himself the reasons of the Bohr’s successes. But we will emphasize it again.


As shown in the begginning of this chapter, the success of the Bohr model is due to a serie of coincidences, in the instant when a photon is emitted by the atom:

1. The proton-electron distance (considered by Bohr) is equal to the distance between the electron and the centre of its helical trajectory:


2. The centripetal force considered by Bohr (which in his calculation he considered equal to the Coulomb force of attraction between the proton and the electron) is equal to the force with which the aether keeps the electron moving about the centre of its helical trajectory:


Due to this series of coincidences, Bohr’s calculations

became a most spectacular success in Physics.

Finally, we are able to respond to the following question: “is Bohr’s spectacular success accidental?”

Admirably, the answer is NO, but at the same time it is YES. Part of his success is not accidental because the origin of such a success is due to the existence of the centripetal force on the electron (due to the helical trajectory). The other part is accidental because the emission of the photon has no connection with the existence of the centripetal force, as he imagined it is only a coincidence.

QUESTION: How to explain the Bohr’s quantization of the angular momentum in the zitterbewegung model ?

It’s explained ahead


The angular momentum of a body is defined by L=mVR, where m is its mass, V its velocity, and R the radius of its orbit.

Suppose that you gyrate a stone tied to the end of a string. You can gyrate it with any velocity, and the radius of orbit R can be anything. So, you can apply any angular momentum to the stone. This is according to classical theories.

In quantum physics, the angular momentum of the electron within the atom cannot have any value. The angular momentum is always a multiple of Planck’s constant h.

In his model, Bohr considered the quantization


In Quantum Ring theory the quantization is not of L. Actually, there is a quantization of the mass:


where m is the electron’s mass in level n=1, and mn are the masses of the electron in the other levels where heavy photons are emitted that is, all the resonance points.

The kinetic energy of the electron in the model of Bohr is Ec=½.m.V2 .

In order to understand the variation of the kinetic energy in Quantum Ring Theory, consider the levels n=1 and n=2.

Due to the decrease of the aether’s density from ?1 = 1/r to ?2, the electron actually changes its inertia from m in level n=1 to m2 = m/n2 in level n=2.

Therefore, the variation of the kinetic energy E is due to the change in the electron’s inertia, and not due to the change in the velocity as Bohr concluded. Look at the difference in the variation ?En of the kinetic energy E=½Mv2 for the electron going along the radial direction:

QUESTION: Are the reasons of the Bohr’s successes capable to explain the success of the Schrodinger equation too ?

Yes. Let’s see why.


Schrödinger’s equation is accidental. He considered a potential V(x,t) with regard to the proton in the atom that is, such a potential is responsible by the force FP of the proton on the electron.

Nevertheless, the potential V(x,t) concerns the force FE of the aether on the electron, which keeps it turning about the centre line LCHT of the helical trajectory, as shown in Figure 7.



1. Schrödinger considered the electron within the variable potential VP(x,t) with regard to the proton. So, the proton applies a force FP to the electron.

2. In the present new model of the hydrogen atom, the potential with regard to the proton is VP(x , t) = 0, because the resultant forces on the electron in the radial direction are null.

3. There is a variable potential VHT(x,t) associated with the centre line LCHT of the helical trajectory. Due to this potential, the aether applies a force FE to the electron in a direction orthogonal to the centre line LCHT of the helical trajectory.

4. Since Schrödinger’s potential VP(x , t) is equal to the helical potential VHT(x,t) , then this coincidence is responsible for the success of his equation. He considered the proton to be the centre of the potential VHT(x,t) , but actually the centre of such a potential is the centre line LCHT of the helical trajectory.

5. Therefore, the mechanism responsible for the success of Bohr’s model is also responsible for the success of Schrödinger’s equation.

QUESTION: What the repulsive gravity is ?

Such question is explained ahead.


The galaxies are formed by stars, planets, comets, asteroids, that atract one another by the force of gravity. These galaxies attract one another also. By considering a static Universe, one would have to expect, therefore, that after billion of years of existence it should be shrinking, compressed under the action of gravity, and finally it would collapse.

In order to avoid the idea of a static Universe, Einstein introduced a cosmological constant into his calculations. This had the effect of introducing an expansion of the Universe into the theory. This was some sort of force of anti-gravity that has resulted nowadays in a situation where, according to the accepted theory the Universe could be either in a state of expansion or of contraction.

Later, Einstein considered this introduction of a cosmological constant the greatest error of his life. Ironically, however, the Universe’s expansion was observed by astronomers years after Einstein had pronounced his cosmological constant an error. The greatest error of his life was converted to wisdom.

From analysis of a phenomenon called red shift, the astronomers concluded that the Universe is expanding in accelerated form. The red shift is a Doppler effect of light. The Doppler effect of sound you will have noted already, by perceiving how the sound of an ambulance’s siren changes from sharp to grave when it passes by you. When it approaches to you, the sound is sharp. When it goes away, the sound becomes grave, because the direction of the ambulance’s motion (with respect to you) changes the sound’s wavelength. The astronomers measured this Doppler effect for the light that comes from the stars and concluded that the Universe is expanding and that expansion is accelerating.

Under the action of gravity, the Universe would have to contract but, as it is expanding, as observed by the astronomers, this implies that there is a force opposing gravity to cause this expansion. How might this be explained through the aether’s structure as proposed in the former chapter ?

On the night of 25 May 2007 I received a call from Claudio Nassif, telling me that he was in Juiz de Fora city, and he invited me to go next morning to eat a “cigarrete” (a Brazillian fast-food made with ham and cheese in a shape of a cigar). That already became a custom. Always when he came to JF city, we went each morning to eat such a cigarrete that he so much appreciated, while we talked on fundamental questions in Physics.

Nassif was making his post graduation in the CBPF, Brazilian Center of Physical Researches, in Rio de Janeiro, and sometimes he went to Juiz de Fora, where his parents live. He had started to develop an alternative theory for relativity by the end of the 80’s, when he was a student of Physics, and in 1993, when we met for the first time, I had convinced him that what was missing in Einstein’s relativity was the ether concept. He undertook to incorporate it into his theory. Nassif’s theory is named Symmetrical Special Relativity (SSR).


The QRT has been developed since 1990 with emphasis on the microscopic world, while Nassif’s relativity was applied to the cosmology. But until that day of our meeting on 26 May we did not succeed in establishing a conection between the two theories. It was at that 26 meeting that we finally forged a conection.

Throughout our deliberations, I recognised that it was necessary to incorporate one more gravitational particle in QRT. I named it particle G.

The irony is that Nassif had told me already of repulsive gravity some years ago, when I told him that in my model of hydrogen atom there is a contraction of the ether. Nassif guessed that such contraction could have a relation with the expansion of the Universe. But at that time I did not pay him too much attention, because I felt the idea of a negative gravity absurd. During the years that passed, Nassif sometimes returned to talk of the repulsive gravity. But there were occasions, when he insisted on talking about the mystery of the Universe’s expansion and, irritated, I replied: “You stay worrying about the infinitely big, but have not discovered yet the laws of the infinitely small. First we have to discover the laws of the atomic world, and later apply it to the cosmos. Cosmology is not science. All you are touching is in the dark. There will never be an experiment for confirming the Big-Bang theory, and no experiment can be made for confirming negative gravity. First we have to discover the fundamental laws. One cannot develop a Big-Bang theory by keeping some wrong principles of Quantum Mechanics” .

But just that cosmology came to suggest to me the answer for the mechanism of the contraction of the space within the electrosphere of my hydrogen atom model. Rather to say the expansion of space in the electrosphere, an expansion similar to that that occurred in the accelerated expansion of the Universe both being phenomena tied to the idea of repulsive gravity.

QUESTION: How many sort of repulsive gravitons do exist ?

The idea of repulsive gravity enables us to propose an explanation for the expansion of the space within the electrosphere of atoms, and the properties of the gravitons G were deduced by starting from the behavior of the hydrogen atom, by considering the models of proton and electron proposed in QRT.

Let us see the properties of the particles G as follows:

Properties of the partícles G(+) and G(-):

1. The particles G(+) e G(-) repel each other

2. Two particles G(+) repel each other

3. Two particles G(-) repel each other

4. The particles G(+) attract the particles g(+), and that explains their gravitational nature

5. The particles G(-) attract the particles g(-), and that explains their gravitational nature

6. The particles G(+) do not interact with the particles g(-)

7. The particles G(-) do not interact with the particles g(+)

QUESTION: What are the consequences of the repulsive gravity ?

Let us see the consequences.


Close to a high concentration of matter, such as the galaxies, there is a large concentration of gravitions g(+) and g(-) because they are attracted by the fluxes of gravitions g(+) and g(-) within the atomic nuclei. In the case of regions of concentration of galaxies, the repulsion between gravitions G is counterbalanced by the attraction with the gravitons g. But, in the intergalactic regions which are without matter, not having fields of particles g (fields formed by the atomic nuclei) the gravitions G fill the intergalactic space and, as these gravitons G repel one another, this implies the ether’s expansion in those regions and the Universe’s space expands.

This negative gravity due to the repulsion between the gravitons G must cause the lifter to levitate.


The hypothesis of a new Planck constant, of gravitational nature, disturbed me for a long time, but there was something else that also disturbed me in Quantum Ring Theory it was the contraction of the space within the electrosphere. I had not found the mechanism that could provoke it and did not know whether it would be of electromagnetic or gravitational nature or a mixture of both.

Let us see whether, from the properties proposed for the gravitons G, we can explain the behavior of the hydrogen atom and how they act in the expansion of the ether in the electrosphere.

QUESTION: How repulsive gravity fulfils the proton’s field ?

Fig. 53 shows the body-ring of a proton, surrounded by its principal Sp(p) field but does not show the secondary Sn(p) field.


In such a principal field Sp(p), particles G(+) gather about the fluxes n(o), attracted by gravitions g(+) that comprise the flux n(o). But, as the gravitons G(+) repeal one another and are gathered around the lines of fluxes n(o), then the lines of fluxes n(o) start to move away from one another and the distance between them increases with the growth of the distance to the proton (see figs. 53 and 57).


As these lines are responsibles for the clustering of magnetic particles of the ether then, as the distance of a point A from the proton becomes larger so the concentration of magnetic particles of the proton’s field Sn(p) at this point A becomes smaller.

The same decreasing of ether density occurs in the secondary field Sn(p). That is why the hydrogen has a Coulomb potential 1/R.

QUESTION: are the models of QRT compatible with the “wave structure of matter” theory ?


Instead of belonging to the proton, it actually belongs to the ether that comprises the whole Universe involving the proton. In another words, the secondary Sn(p) field is a disturbance of the Universe that surrounds the proton’s principal Sp(p) field.

Obviously the same may be said of the electron’s Sn(e) secondary field. Therefore, the Sn(p) secondary field is not something that belongs to the proton and is dragged by the proton’s motion in its displacement in the Universe. The Sn(p) field is a disturbance of the ether that is transmitted along the proton’s motion, like waves of water when a ship crosses the surface of a sea. The Sn(p) field belongs to the ether that fills the Universe and it is the intermediary in the interaction between the proton’s Sp(p) principal field and the rest of the Universe.


“Noble Laureate Erwin Schrödinger a co-discoverer of quantum mechanics adopted the view of Clifford and wrote in 1937: What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just schaumkommen (appearances)”. He believed that quantum waves were real, not probability distributions with a particle hidden inside. He saw that abolishing the discrete point particle would remove the paradoxes of ‘wave-particle duality’ and the collapse of the wave function. He studied with Einstein, opposing the Bohr school that believed in probability functions for ‘discrete particles’. Like Einstein and Clifford he recognized that discrete ‘point particles’ were impossible. He wrote that the puzzle of matter will be found in the structure of space, not in point-like bits of matter, and that the physical world is based upon the geometry of space”.

So, again, we realize that Nature takes an intermediary solution between that defended by Bohr and its rival solution defended by Schrödinger-Einstein because she does not use particles only, as supposed Bohr, and she does not use waves only, as supposed Einstein and Schrödinger. Actually she uses both: a central particle (which has the form of a body-ring) surrounded by two fields, one of which propagates as waves of the ether: the secondary field Sn(x).

Among the reasons why Milo Wolff’s theory is not accepted by most theoreticians, we can mention the fact that quarks were detected by experiments but, in his paper, he states that quarks do not exist.

QUESTION: how does occur the Coulombic interactions in Quantum Ring Theory ?


As the secondary fields Sn(e) and Sn(p) belong to the ether of the Universe, they do not rotate, unlike the principal fields Sp(e) and Sp(p) which do rotate. It is this rotation that induces that disturbance of the ether which takes the form of the secondary field Sn(e) that is, the secondary fields Sn(e) and Sn(p) are induced by their principal fields Sp(e) and Sp(p).

The eleectron’s principal field Sp(e) is composed of a flux of gravitons g and, therefore, its rotation does not produce any additional magnetic field that could contribute to increase the magnetic field of the electron. But the fluxes of gravitons agglutinate the massless electric particles of the ether around them and so the field Sp(e) has electric properties too.

QUESTION: The principal fields Sp(e) and Sp(p) girates Such spin would have produce a strong magnetic field. Is it produced ?


At first glance, it seems that the rotation of electric particles due to the spin of Sp(e) would have to produce an additinal magnetic field with magnitude larger than that of an electron. Such a conclusion would be correct if the space within the field Sp(e) was Euclidian. However, the space within the field Sp(e) is non-Euclidian.

Let’s analyse what happens by considering at the fig. 54, showing two magnetic fields produced by two electric particles that belong to the electron’s field Sp(e).


1. There is a flux of gravitons g of the ether, shown as the black string.

2. Consider a massless electric particle “e”, shown as a green ring, captured around the black string.

3. Another electric particle “e” is captured by the black string within the body-ring of the electron, shown as a yellow ring.

4. Due to the spin of the field Sp(e), the “green” particle produces a magnetic field indicated by the upside down white arrow, while the “yellow” particle produces a magnetic field indicated by the up white arrow.

5. So, the two magnetic fields have opposite directions.

6. The green particle has an orbit with radius R, while the yellow particle has an orbit with radius r.

7. If the ether within the electrosphere was Euclidian, the magnetic field indicated by the upside down white arrow would be stronger because its orbital radius about the center of electron’s body is R >> r.

8. As the space is non-Euclidian within the electron’s electrosphere and the density of the ether varies as 1/R then the total magnetic field produced by the two electric particles - green and yellow - is null and, therefore, the field Sp(e) does not produce any additional magnetic field although it has a spin.

Such a property of the electron’s Sp(e) field is valid during the time Sp(e) retains its symmetry when the electron moves in a radial direction with respect to the proton.

QUESTION: How is a free electron captured by a proton ?


Now to see what happens when an electron is captured by a proton.

Fig. 55-A shows the proton and the electron. The principal Sp(p) field of proton has negative electric charge, and its rotation induces a secondary Sn(p) field which charge is positive. And the principal Sp(e) field of electron has positive charge, and its rotation induces a secondary Sn(e) field which charge is negative.


Fig. 55-B shows what happens when the electron is captured by the proton, when there is overlap between their secondary fields only. Let us name it first overlap. It’s easy to realize that in such first overlap there is a Coulomb attraction between the proton and the electron, since their secondary fields have contrary electric charges.


Fig. 55-C shows what happens when the secondary fields start to overlap with the principal fields. Let us name it second overlap. There is Coulomb repulsion in the overlaps between Sp(e) & Sn(p) and between Sp(p) and Sn(e), while continues to have Coulomb attraction between the Sn(e) & Sn(p) fields.


So, when the second overlap occurs, the electron is submitted to repulsion and attraction, in order that it’s null the resultant of force on it. And so it means that along the second overlap the resultant force on the electron is null, and then it moves with constant speed in the proton’s electrosphere.

Suppose a free electron is attracted by a proton. When the second overlap did not occur yet (and therefore theres is only proton-electron attraction), the electron is accelerated toward the proton.


So, it means that when the second overlap begins the electron continues to move with constant velocity in the radial direction due to the kinetic energy stored during the first overlap (when the electron moved with acceleration toward the proton). When the body of the electron approaches the body of the proton, the electron cannot continue to move in the radial direction and it is forced to rotate about the proton in the fundamental orbit n=1.

So, the symmetry of the fields Sp(e) & Sp(p) is broken in the orbit n=1 because the interactions of the second overlap distorts the Sp(e) & Sp(p) fields. It occurs a distortion of the principal fields.

QUESTION: What is the BIG JUMPING of the electron ?

The distortions of the two principal fields is responsible for the appearance of a very strong additional magnetic field, because the magnetic field of the gray particle in fig. 54 is not cancelled by the field of the black particle anymore:


Then, in the fundamental state, the electron is attracted by a very strong force. As consequence of such an additional magnetic field of Sp(e) and Sp(p), a large kinetic energy is stored in the orbit n=1 by the electron before it jumps. Such a large amount of energy is sufficient to enable the electron to perform several jumps and, when its energy is used up, it returns to the level n=1 in order to store kinetic energy again before jumping again, and so on. Such consecutive jumps are termed BIG JUMPING in Quantum Ring Theory.

The laws governing the emission of photons by atoms are shown in detail in the paper Mechanism of Selection Rule, which begins on the page 62 of the book QRT, and where the laws that control the mechanism of BIG JUMPING are shown also.

QUESTION: are the flux n(o) responsible for the changing in the electron inertia into the proton’s electrosphere ?

Yes, let’s understand it in detail now.


From the properties of the particles of the ether, the repulsive gravitons G are captured by the strings of gravitons “g” of the two principal fields Sp(e) and Sp(p). As each graviton, G, repulses each other graviton, G, the big concentration of gravitons, G, about a string of gravitons “g” is responsible for the growth of the distance “d” between the strings, the distance “d” shown in fig. 56.


This causes the dilation of the ether within the proton’s and electron’s electrospheres. So, when the electron penetrates the electrosphere of the proton and the fields Sn(e) and Sp(p) overlap, a force F(R) of repulsion between proton and electron appears. Such a force is equal to the Coulomb force F(a) of attraction between proton and electron. Therefore, when the electron moves in a radial direction within the proton’s electrosphere, the resultant force on the electron is null and it moves with constant speed within the electrosphere in a radial direction.

It is interesting to note that, through the lines of gravitational fluxes n(o) of fig. 53 we are able to undertand clearly why the electron’s inertia, with respect to the proton, varies within the electrosphere.


Indeed, how would there be lines of flux in the Bohr model, where the space is homogeneous? Answer: the distance “d” between the lines of flux n(o) is constant, which is characteristic of a Euclidian space.

Suppose there was NO repulsive gravity in the atom. In this case, suppose that a proton acts with an electromagnetic force F on the electron, producing an acceleration ao in Bohr’s Euclidian space. The change of the electron’s kinetic energy in the Bohr model with Euclidian space is ?E = mv2/2.

Now let us consider the space with expansion, in fig. 57, where repulsive gravity is acting. As the proton-electron distance "D" is the same in figs. 56 and 57 then, in fig. 57, the electromagnetic force on the electron is also F.

Compare the figures 56 and 57:


But the electron will have to cross more flux lines n(o) in its motion toward the proton. These gravitational flux line are responsible for the electron’s inertia with respect to the proton. Therefore, in the expanded space, the same force F of proton-electron attraction serves to produce an acceleration “a” on the electron smaller than in the Bohr space that is, a < ao.

However, the kinetic energy in the two figures will be the same because, in the Bohr space, the electron’s speed increases but it has constant inertia (mass) with respect to the proton.

Also, in the expanded space, the speed remains constant, while the inertia increases so that the kinetic energy stays the same for the two spaces.

The changing of electron’s inertia follows the relation mo/m= n2 , where n=1, 2 , 3... , and mo is the inertia in the fundamental state n=1).

As the velocity V is constant and the inertia changes, the change of the electron’s kinetic energy in the non-Euclidian space is ?E=m(nV)2/2, which is equal to the change in the Bohr model with Euclidian space.

QUESTION: how is the circular motion of the electron about the proton ?


In the book QRT, the electron’s motion along the helical trajectory is denoted as follows


When the electron moves in an orbit about the proton with a circular motion HT-UCM, the proton’s principal Sp(p) field is distorted, in order that the situation shown in fig. 54 does not occur.


Then the Sp(p) field produces a very strong magnetic field, and the electron is submitted to the following forces:

1- A Coulomb attraction force F

2- A Coulomb repulstion force -F

3- A magnetic attraction force Fm

4- A centripetal force Fc

The electron continues moving with HT-UCM motion thanks to the equilibrium between the magnetic force Fm and the centripetal force Fc .

QUESTION: can Planck’s constant be changed by repusive gravity ?

Probably yes, and as the quantum theorists do not take in consideration that Planck’s constant perhaps may be changed by repulsive gravity into the structure of elementary particles, it can be the reason why they are unable to eliminate some troubles in Physics.




The present discovery that repulsive gravity provokes an expansion of the ether within the hydrogen atom shows clearly that the theoreticians do not know of some of the fundamental mechanisms of Nature. Hence, it is reasonable to suppose that they don’t know of the mechanism by which repulsive gravity reduces the value of Planck’s constant within the nuclei. Such a conclusion allows the theoretical model n=p+e of a neutron formed from a proton and an electron to become viable.

QUESTION: as there is not attraction proton-electron into the hydrogen atom, how can the electron be captured by the proton in the Borghi experiment ?


In normal conditions, when the electron is captured by a proton, they form a hydrogen atom. For the formation of the neutron, the body ring of the electron must penetrate within the principal field Sp(p) of the proton.

Fig. 58 indicates that, in the hydrogen atom, the electron’s body-ring is always present in the space along the black arrow (with two heads) in the horizontal direction which represents the radial direction with respect to the body-ring of the proton.


In order to form the neutron, the electron must penetrate the proton’s field Sp(p) in the way indicated by the single headed yellow vertical arrow. Therefore, Don Borghi’s experiment must be able to supply to the free electron conditions enabling it to approach the proton by taking the vertical path indicated in fig. 58. Just as in the plasma there are collisions between protons and electrons, so there is a small percentage of electrons that suffer collisions with protons in the direction of the vertical arrow shown in fig. 58. They form neutrons.

Note that hydrogen atoms are also formed in Don Borghi’s experiment. However, as these hydrogen atoms absorb a large amount of energy from the oscillatory electromagnetic field used in the experiment - the absorption occurring by resonance between the proton’s field Sp(p) and the external electromagnetic field - such energy is captured by the electron, and it jumps with high energy and gains freedom again. As far as the neutron’s formation is concerned, after been captured by the proton, the electron loses its helical trajectory becoming a boson, liberating its zitterbewegung energy and emitting a neutrino. As the energy captured by the proton from the external electromagnetic field applied in Don Borghi’s experiment is due to the resonance of the proton’s field Sp(p) then, when the electron penetrates via the vertical path shown in Fig. 58, it is not able to capture energy from the proton’s field Sp(p) because the electron’s field Sp(e) is not positioned radially with respect to the proton’s field Sp(e). That is why the electron is not expelled immediatelly from the proton’s body-ring, and the two form the neutron.

Fig. 59 shows the neutron with its principal field. As the neutron’s secondary field is a perfect overlap of the electron’s field Sn(e) and the proton’s field Sn(p) and those two fields have opposite charge, the neutron has a neutral field.


QUESTION: is it possible to achieve the Schrödinger Equation from this zitterbewegung hydrogen model of atom ?

After the discovery of the “coincidences” that explain the successes of the Bohr hydrogem model, and the mechanims shown herein from which works the new zitterbewegung hydrogen atom of Quantum Ring Theory, I tried to develop a mathematical formalism so that to arrive to Schrödinger Equation, by starting from the working of the model of QRT.

Such enterprise is very complex, and I did not succeed to get his equation.

But after so many unsuccessfull attempts, finally in 2008 I understood that such development was already made by the own Schrödinger.

Indeed, in the begginning of the 20th Century, Schrödinger has developed the equation for the zitterbewegung hydrogen model of Quantum Ring Theory, in spite of he did not know that.

Schrödinger Equation is in fact the equation of the new zitterbewegung hydrogen model proposed in QRT.

The development of the Theoretical Physics is very intriguing. In the begginning of the 20th Century, Schrödinger has discovered an equation, but at that time he was unable not understand the true meaning of this famous equation.

Only in 2008 the Schrödinger Equation has finally been entirelly understood.

In another words:



PowerPedia:New model of neutron: explanation for cold fusion