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PowerPedia:Guglinski on the De Broglie Paradox

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

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Elementary particles, such as the electron, proton, neutron, etc., suffer diffraction, as proved experimentally by Davison and Germer. They performed the experiment because a theory proposed by Louis de Broglie predicted that matter possesses wave-particle duality and the wavelength of the wave is given by

? = h/mv

where h is the Planck’s constant, m is the mass of the particle, and v its velocity.

So, according to de Broglie, matter has a fundamental feature:

wave-particle duality is a property of the matter

Here it's shown that de Broglie's interpretation on the duality is wrong.


Diffraction is shown in the figure 1: electrons fall upon a crystal, and are deflected through an angle ? by the planes of the crystal.


Only waves have the property of suffering diffraction particles cannot undergo diffraction. That is why, after the Davison-Germer experiment, physicists started to think that elementary particles, such as the electron, cannot be corpuscular in nature..

But, as elementary particles like the electron also exhibit properties that only corpuscules can have, then they are considered to possess this property of wave-particle duality.

So, in Quantum Mechanics wave-particle duality

is considered through the interpretation proposed by de Broglie, according to which the duality is a property of the matter.


At the end of the 19th Century the engineer Albert Michelson performed an experiment that would change theoretical physics in the begginning of the 20th Century. Michelson’s experiment tried to detect the interference of the Earth’s motion with the speed of light since, according to the current theory in the 19th Century, physicists considered that light would be a propagation of the disturbance of waves in a luminiferous aether and, therefore, the velocity of the disturbance would have to be influenced by the velocity of the planet.


Michelson’s idea was simple.

Suppose a man is at rest in the ground, with a gun in the hand. He fires a gunshot that leaves the gun with speed 2000km/h with respect to the ground.

Then he takes a car at speed 100km/h, and he fires again, with the gun pointing out in the direction opposite to the car’s displacement. With respect to the ground, the gunshot has a speed 2000-100=1900km/h.

Then the man points the gun in the same direction as the car’s displacement and fires again. Now, with respect to the ground, the gunshot has a speed 2000+100=2100km/h.

Such a phenomenon is known as the principle of addition of speeds. Both waves and particles are subject to this principle

Michelson’s idea was to use such a principle. The Earth has a speed of 32km/s about the Sun. By measuring the speed of light in both directions (one in the direction of the Earth’s translational motion, and the other in the opposite direction), the experiment should detect two different speeds of light, with a difference of 64km/s, since light was considered by physicists to be a propagation of waves in the aether and waves are subject to the principle of addition of speeds.


No he didn’t. His experiment did not find any difference in the speed of light. The Earth’s motion does not influence the speed of light.

From Michelson’s experiment, we infer that light is not subject to the principle of addition of speeds.

The light, therefore, is not wave-like or particle-like, since both waves and particles are subject to the principle of addition of speeds.


When the physicists started to perform experiments with the atom at the beginning of the 20th Century, they noted that the matter at the micro-level exhibited strange behavior. But what is matter?

In the 1920’s, the physicist Louis de Broglie proposed a postulate, according to which matter possesses a property: wave-particle duality.

According to de Broglie’s postulate, matter behaves like a wave with wavelength of value is calculated by the equation ?= h/mv, where h is Planck’s constant, and m and v are the mass and the speed of the particle.

The physicists Davison and Germer performed an experiment designed to test de Broglie’s theory. They fired a beam of electrons with speed 4000km/s at a crystal and the electrons suffered diffraction within the crystal.


By using the distance “d” between the atomic planes in the crystal, the two scientists calculated what the wavelength of a wave would have to be for it to be diffracted. They used Bragg’s relation:


where “d” is the distance between two consecutive planes of the crystal, ? is the angle shown in the figure, and n is an integer.


The calculus has confirmed de Broglie’s equation

? = h/mv

As particles cannot suffer diffraction (only waves can), the conclusion of the physicsts was the following:

CONCLUSION OF THE THEORISTS: the de Broglie postulate is correct

In other words, they concluded that matter really has the property of wave-particle duality.

The experiment was performed with protons and neutrons, and de Broglie’s equation was confirmed again.

The theoreticians concluded that elementary corpuscles, such as the electron, the proton, the neutron, and others, are actually wave-particles.


Yes, we can.

We can associate the Davison-Germer experiment with the Michelson experiment in the following way:

1. Michelson used an interferometer for measuring the influence of the Earth’s velocity on the speed of light.

2. Davison and Germer used a crystal for measuring the wavelength of the electron when diffraction occurs.

3. We can perform an experiment like Michelson’s by replacing the light by a flux of electrons and, instead of an interferometer, we can use a crystal.

So, if a flux of electrons is emitted in the same direction as the Earth’s translational motion, and another flux is emitted in the opposite direction, the speed of the Earth must influence the wavelength of the electrons, since they are subject to wave-particle duality, and both waves and particles obey the principle of addition of speeds.

Such a new version of Michelson’s experiment, agglutinated to Davison-Germer experiement, is called the '''Michelson-Morley experiment for protons in the Quantum Ring Theory.

We also can refer to it as Michelson-Davison-Germer experiment.


Actually, the Michelson-Davison-Germer experiment has already been performed in several laboratories throughout the world, but the physicists did not realize this.

Indeed, as the gun that fires the beam of electrons, protons, etc., used in the experiments, is pointing in different directions in each laboratory of the world, then each laboratory should detect a different wavelength of the proton for the same conditions of a certain experiment repeated in several laboratories.

In the case of the electron, it would be difficult to detect the difference, because the speed 4000km/s used in the experiments is so much faster than the speed, 32km/s, of the Earth.

But the experiment with protons can be performed in a range of speeds between 2km/s and 30km/s and, therefore, the speed of the Earth should change the wavelength of the protons quite dramatically.

Such a difference in the wavelength has never been detected, and as such the result represents a paradox.


No the physicists interpreted the Davison-Germer experiment incorrectly.

The experiment did not confirm de Broglie’s postulate.


The experiment has confirmed the de Broglie equation, and it has also confirmed that particles, such as protons and electrons, do suffer diffraction. But such fact does not mean that matter has a dual property.

The Michelson-Davison-Germer experiment shows that de Broglie’s interpretation of the duality is incorrect because:


as de Broglie wrongly supposed because, if his supposition was correct, the Michelson-Davison-Germer experiment would have detected the influence of the Earth’s speed on the measurements.

A new explanation for the diffraction of elementary particles can be found in the helical trajectory (zitterbewegung). For having diffraction, it is necessary only that the pitch of the helical trajectory be an exact multiple of the distance “d” between the atomic planes in the crystal.


Light is neither a wave nor a corpuscle. That is why light is not subject to the principle of addition of speeds and this fact was used by Einstein when he formulated the principles of the Theory of Relativity.

But, as protons and electrons are considered wave-particle in Modern Physics, they would have to be subject to the principle of addition of speeds and so, if de Broglie was correct, the speed of the Earth would have to influence the results of the Michelson-Davison-Germer experiment.

As the speed of the Earth does not influence in the results of the Michelson-Davison-Germer experiment we conclude:



When we use the principle of the addition of speeds for interpreting the Michelson-Davison-Germer experiment, we are using Galileo’s principle of relativity. It states that uniform rectilinear motion has a meaning only when compared with a fixed point of reference. According to the principle, there is not an absolute reference frame with respect to which all the other motions can be measured.

Let us see how to eliminate the need for an absolute reference frame in the Michelson-Davison-Germer experiment, by introducing the energy “E” of the particle in the de Broglie equation.

de Broglie’s equation becomes:


So, we have to verify if the energy of the particle changes due to the influence of the motion of the Earth.

Consider again the man with a gun at rest on the ground. He fires a gunshot which moves with speed 2000km/h and hits a target on the ground with energy E.

The gunshot has speed 2000km/h with respect to the ground, and its mass “m” collides with the target with speed 2000km/h, and the energy of collision is Es.

Now consider that the man is inside a car with speed v, and fires a gunshot against a target that moves with speed v too.

The gunshot collides with the target with speed 2000km/h. But the speed of the gunshot is v+2000 with respect to the ground and, according to Einstein’s theory of relativity, the mass of the gunshot will have suffered an increase of mass, compared with the mass “m” when the gunshot was fired when the mass was at rest on the ground.

Therefore, the energy of collsion is Em > Es, and de Broglie’s equation ? = h.v/E is changed by the increasing of the energy of collision.

So, the speed of the Earth influences the energy of the protons and electrons in the Michelson-Davison-Germer experiment and, therefore, it would have to change their wavelength.

Another way to interpret the experiment is by considering two planets rotating with different speeds about the same star.

Consider a planet A rotating about a star with speed 32km/s. and consider a planet B rotating about the star with speed 64km/s.

On planet A, a proton fired by the gun with speed v in the Michelson-Davison-Germer experiment has an energy due to a velocity v+32km/s and, on planet B, the energy is due to a velocity v+64km/s. Obviously, if de Broglie's postulate is correct, the wavelength of the proton could NOT be the same on the two planets.


Let us see how the helical trajectory is able to eliminate the Michelson-deBroglie paradox.

The unique solution, able to eliminate the paradoxes of the Theory of Relativity, is to consider the space fulfilled by an aether constituted by two aethers:

1. A stationary gravitational aether. Therefore the Earth has a speed of 30km/s relative to this ether, due to the translation motion of our planet about the Sun.

2. A magnetic aether dragged by the translational motion of the Earth in space (therefore an aether at rest with regard to the Earth)

Then we have to consider two interactions of the elementary particles:

1.An interaction responsible by the inertia.

2.An interaction through the helical trajectory, responsible by the duality wave-particle.

Analyze these two interactions:

1.Inertio-gravitational interaction: the particle interacts with the gravito-aether at rest, and such an interaction is responsible for the increase of its mass with the speed's growth. The Lorentz transformations are due to the interaction of the particle with this aether at rest but there is no connection with wave-particle duality.

2.Magnetic-helical interaction: the particle’s motion, through the interaction with the magnetic-ether, yields the helical trajectory. So, because the particle’s magnetic-helical trajectory is induced by the interaction with the magnetic aether and because the magnetic aether is at rest with respect to the Earth, such a helical trajectory of the particle has no connection with the gravitational aether at rest in space.

In the same way, in the case of the proton, its helical trajectory (responsible for the wave-particle duality) is always connected to the magnetic aether and, therefore, the speed 30km/s of the Earth does not have any influence in the Michelson-Morley experiment for protons as proposed here.


It is of interest to note that, although the photon has a constant speed c with respect to the magnetic aether, as a consequence of the constant flux of the aether into the helical trajectories of the particles that constitute the photon, nevertheless the photon is not dragged transversely by the motion of such an aether.

This fact explains the aberration of the stars. The physicists of the 19th Century believed that the hypothesis of an aether dragged by the Earth is incompatible with the star’s aberration phenomenon because they were thinking of a luminiferous-ether, i.e., a medium transporting a light-wave (disturbance of the medium). Because the photon is not a disturbance of the medium, as we have seen in the script A Model of Photon, it does not need the aether in the sense of a luminiferous medium, a fact that the physicists of the 19th Century were unable to understand at that time.

We can realise also that it is not necessary to adopt, as a solution for the problem of the constant speed c of light propagation, Einstein’s proposal through a new non-classical kinematics where light is not subject to the principle of addition of velocities. Obviously a postulate which infringes a principle of Physics like the addition of velocities is a very strange postulate. Besides, through a non-classical model of light propagation, we can solve the problem through a classical concept, keeping the classical kinematics, because light does not infringe the principle of the addition of speeds.


Actually light is not subject to the principle of addition of velocities, but this does not represent the breakdown of such principle. Indeed, the principle of addition of velocities is applied to waves or particles.


This explains why light is not subject to the principle of addition of velocities, because a thing which is neither wave nor particle cannot be subject to such a principle. Note that light does not infringe the principle since light is not a particle, and it is not wave. Light is not subject to the principle, but this does not mean that light infringes it.

Remembering what happened in the History of Physics, Einstein had proposed empty space because a classical luminiferous aether in the sense of the 19th Century was not able to eliminate the paradoxes of light propagation. Nevertheless, the introduction of the empty space hypothesis brought two undesirable problems:

1.Empty space is not an hypothesis able to solve the problems concerning relativity and light propagation satisfactorily.

2.In spite of the fact that Einstein had tried to eliminate the paradoxes through the idea of empty space, such an idea introduced many other undesirable paradoxes. We can mention, for example, that the idea of empty space is not compatible with the idea of a field in the sense of Faraday. Then we realize that Einstein actually had introduced a serious problem into Physics with his idea of empty space, because it is impossible to solve the problem of gravity without a concept of field in the sense of Faraday. Although Einstein attempted to solve the problem with his idea of gravity working through a deformation of the geometry of the space.

Recent discoveries (Wagner, O. E. Gravity as a Wave Phenomenon, Frontier Perspectives, 8(2), 40-43) are suggesting that general relativity does not explain gravity.


Lorentz convinced Einstein to take up again the idea of the aether, according to the Kostro’s (Kostro L. , 1988, Einstein’s New Conception of the Ether, Proc. Conference “Physical Foundations of Relativity Theory”, Imperial College, London , M.C. Duffy, British Soc. for the Philosophy of Science):

“The history of the new aether begins in June 1916 i.e. after the definitive formulation of the General Relativity Theory. The introduction of the new aether was provoked by H. A. Lorentz and P. Lenard . Lorentz who rejected his own theory of gravity and accepted Einstein’s theory, arrived at the conviction that the General Theory of Relativity admits a stationary aether hypothesis. On June 6th 1916, Lorentz wrote a long letter to Einstein in which he tried to convince Einstein of that. In reply, Einstein proposed his new definition of a nonstationary relativistic aether”.

When we have a problem, and we try to solve it starting from an incorrect idea, sooner or later many other problems will appear as consequence of the new discoveries in science. Today the Theory of Relativity is facing the consequences of the adoption of this incorrect idea of empty space. When Einstein faced the paradox of light propagation, he decided to eliminate the luminiferous aether, which is a classical model of the aether.

Nevertheless, the solution is not to reject the idea of the aether just because a classical luminiferous aether is not compatible with the phenomena and the experiments. The solution is to replace the classical aether by a non-classical aether. The more interesting fact to be noted is the following: the solution was before Einstein’s eyes. We realize this fact when we ponder Ludwik Kostro’s article, when he says that Einstein obtained two different aethers, one for special relativity, and the other for general relativity. Let us consider the two different aethers, proposed by Einstein in the period 1918-1955, according to Kostro:

• The aether for the special relativity: “The related aether is rigid, flat and infinite. Its metric is pseudo-Euclidean”

• The aether for the general relativity: “This aether is no longer rigid and flat. Its metric is pseudo-Riemannian”

If Einstein had pondered these two different solutions deeply, one trying to solve the problems concerning to special relativity, and the other trying to solve the problems of general relativity, he would have arrived at the following unavoidable conclusion: the aether used by Nature is not unique, actually Nature uses two different aethers.

This is the unique solution able to eliminate the paradoxes of the relativity, without introducing other new paradoxes.


It is of interest to emphasize here again that, in the whole History of Science, physicists tried to obtain solutions for the paradoxes of the Nature starting from classical models. For example, the luminiferous aether of the 19th Century is a classical model of an aether. But Nature does not solve problems making use of classical models. Actually, Nature adopts non-classical models. As a consequence, because the scientist tries to find a solution starting from classical models, he is obligated to introduce non-classical concepts, as Einstein had introduced a new non-classical kinematics as a solution for the problem of the constant light speed detected by the Michelson-Morley experiment.

Conclusion: we can try to discover the working of Nature by two Solution-Systems:

1) SYSTEM 1: We can try to solve the problems starting from classical models. But then we are constrained to adopt non-classical concepts, such as happened with the Theory of Relativity, which works through a non-classical kinematics for the light.

2) SYSTEM 2: We can adopt non-classical-models, trying to discover the models used by Nature. If we discover them, our models can work using classical concepts.

There is a principle of equivalence between SYSTEM 1 and SYSTEM 2:


Such an equivalence means that the two systems are able to yield the same result: to describe a phenomenon. But only SYSTEM 2 can eliminate the paradoxes, if its solutions are the same used by Nature.

For example: Einstein developed his special relativity starting from a classical treatment for the problem of light propagation, replacing the classical idea of the aether by the hypothesis of empty space to enable him to explain the Michelson-Morley experiment. If we start from a non-classical model of the photon, working through a non-classical model of aether, we can explain the Michelson-Morley experiment, but with a fundamental difference: free of paradoxes.


Lorentz had developed his transformations from the following two premises:

1. First Premise: The inertia principle must be satisfied for two Galileo systems

2. Second Premise: The velocity of light must be the same in two Galileo systems

So, in Lorentz’s treatment, inertia is a property connected to the velocity of light and, since Einstein has developed relativity by having the Lorentz transformations as a point of departure, from Einstein’s viewpoint there is a connection between the increase in inertia and the behavior of light.

However, we can develop the Lorentz transformations by replacing his old second premise by a new version, as follows:


From this second new premise one can obtain all the equations of relativity and, in this way, the success of Einstein’s Theory of Relativity is well understood: its success '''is accidental.


From a incorrect point of departure, Einstein had arrived at a correct result: the increase of inertia. On the other hand, the time dilation is a phenomenon that is merely a consequence of the increase of inertia.