The effect of electrons with negative mass in novel semiconductor nanostructures

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A large international research collaboration led by Dr. Kai-Qiang Lin and Professor John Lupton from the Institute of Experimental and Applied Physics at the University of Regensburg has been able to measure the effect of electrons with negative mass in novel semiconductor nanostructures.

The international team includes scientists from Berkeley and Yale (U.S.), Cambridge (England) and Tsukuba (Japan).

Many things in everyday life ring familiar only as positive quantities, the weight of an object, for example. Why matter always seems to have positive mass is one of the unsolved mysteries of physics.

We may nowadays have almost become accustomed to the concept of negative interest rates, but what would happen if mass could turn negative?

Newtonian mechanics describes the consequences with the well-known equation Force=MassAcceleration, oder F=ma. If a force acts on an object, it is accelerated. But watch out—if you try jump starting a car of negative mass, it will move towards you! Likewise, a golf ball of negative mass falling into water would not be slowed down by friction but would instead sink faster and faster!

Matter as we know it is basically composed of three elementary particles, the atomic nuclei with heavy protons and neutrons, and the light electrons.

In general, the weight of a body is determined by the atomic nuclei. While the mass of the nuclei is a fixed quantity, the effective mass of the electrons is determined by the composition of the material in which they move. The mass directly affects the electronic properties of a material.

Illustration of negative mass using a golf ball in a glass of water. The fall of a conventional golf ball is slowed down by the water. A golf ball of negative mass, on the other hand, would be accelerated by the frictional resistance. Credit: Felix Hofmann

We all learnt in driving school that the braking distance increases quadratically with speed, another consequence of Newton’s formula: the motional energy of a car rises with the square of the speed v, E=1/2mv^2. If the mass m were negative, however, the energy of a particle such as an electron would decrease with increasing speed—the “braking distance” decreases!

When an electron moves through a material it collides frequently with other electrons and nuclei. As with driving a car, such collisions lead to a slowing down of the movement in the case of positive mass. An electron with negative mass, on the other hand, also loses energy, but is accelerated thereby.

The researchers have now been able to observe precisely this effect for the first time.

The Regensburg scientists used a new type of semiconductor material, a single atomically thick sheet of the crystal tungsten diselenide. When the material is irradiated with a laser, it begins to glow: an electron absorbs the energy of the laser and emits it again in the characteristic color of the material, red.

This color corresponds to the fundamental energy of an electron in the semiconductor. Just as water always flows downhill, one would expect electrons with higher energy to always tend to this lowest fundamental energy. The semiconductor should always glow red.

However, the team observed an astonishing effect. When irradiated with a red laser, the electrons emit not only red light, as expected, but also show a faint blue glimmer. Low-energy red light is therefore converted into blue light of higher energy, an extraordinary effect. By looking closely at the color distribution and brightness of this blue light, i.e. the optical spectrum, it can be concluded that the blue glow arises from electrons with negative mass.

This unexpected experimental finding could be substantiated with detailed quantum mechanical calculations of the electronic structure, which were carried out in this form for the first time.

At present, the discovery may still seem like more of a scientific oddity, but the scientists already have a number of possible applications in mind. For example, the concept may aid the development of superfast computers, where electrons move almost without resistance.

The transition from positive to negative mass also creates so-called singularities. Such singularities—familiar from trying to divide something by zero on a calculator—are not entirely dissimilar to the black holes of cosmology.

Finally, due to the fact that the electrons in the semiconductor can apparently assume discrete energy states, as in an atom, it should be possible to transfer concepts of atomic quantum optics directly to the semiconductor. This could be used, for example, to develop new electronic components that convert the wavelength of light, store or even amplify light, or function as optical switches.


A few hundred years have passed since the discovery of electricity and electromagnetic fields, a tremendous progress has been achieved in details and applications of the electron theories [1].

However, the nature of the electron has been a mystery confronting physicists of past generations as well as contemporaries [2] [3].

While electrons are useful in the understanding of diverse phenomena, the nature of the electron have never been really understood and the nature of the electron has been an enigma confronting physicists of past generations as well as contemporaries [2] [3].

In fact, many questions related to the nature of the electron still without answers such as: what is the structure of the electron, what is the origin of the mass of the electron, what is the spin, why must be a positron, why and how does the electron manifest wave properties and how does the electron manifest wave properties?

What guides the interaction between two electrons to cause attraction or repel, why do particles with the same charge repel and opposing charges attract, how electron interact with positron at short distances? And finally what is electric charge?

In 1746, the American physicist named Franklin first propounded the idea of positive charges and negative charges.

After finding the quantized character of charge, in 1891 George Stoney proposed the unit “electron” for this fundamental unit of electrical charge. The discovery of the electron in the 1890’s, based on several independent experiments a negative charge e, and mass m were assigned to the electron.

A few hundred years have passed since the discovery of electricity and electromagnetic fields, and Maxwell’s equations have been subjected to countless experimentation based on the current definition of electric charge and are definitely correct; however, the nature of an electric charge remains unknown.

Attempts have been made to clarify the nature of the electric charge [4] – [8].

None of these works provides an explicit formula for the exact value and the nature of electric charge based on proven facts.

The main obstacle remains related to the failure to attribute structure to the electron.

Therefore, the unit is today treated as nameless, referred to as elementary charge, fundamental unit of charge, or simply as e. However, almost all physical parameters (constants and variables) have a combination of the dimensions of mass, length, and time.

The dimension of electric charge is 4πε0 ML3/T2. One can easily decompose ML/T into, e.g., mass (M) and velocity of a particle (L/T), and find a formula for the linear momentum of a particle. This has not been accomplished for electric charge.

Prediction of the anti-electron (positron) by P. Dirac in 1931, which was discovered by C. Anderson in 1932. However, there is no scientific explanation for the origin of difference between properties of electron and positron or really explained the internal mechanism of positive and negative charges.

Although the electric charge seems to be a primary abstract intrinsic property of a particle, nonetheless, the electric charge and electromagnetic field are the physical property of matter, can be directly measured and formulated. Therefore, the relation between electric charge and known physical parameters should be addressed and clarified.

This cannot be done until the very nature of the electron mainly its structure is identified, to provide explicit general formulas for the relation between electron attributes and known physical parameters into which all attributes of the electron could be incorporated in a self-consistent way.

The aim of this study is to present a new physical concept to fill this gap and to constitute a physical explanation of the nature and the origin of charge.

This paper provides a new approach to this problem, considering the vacuum as superfluid and the electron as an irrotational vortex of the vacuum.

Comprehensible interpretation of electric charge is developed, based on the hydrodynamics a meaningful and explicit description of the nature of the obscure physical parameter of electric charge is found, and an explicit formula that addresses the relation between electric charge and known physical parameters is presented.

This approach allows to express the complicated dimension of the electric charge in M, L and T units (ε0 ML3/T2) and converts it in an observable, measurable, and explicable physical parameter.

2. The Vortex Structure of the Electron

Vacuum density is generally viewed as a fundamental property of the cosmos.

Therefore, the physical vacuum is assumed to be a non-trivial medium filled with quantum mechanical zero-point energy to which one can associate certain energy and density.

In superfluid vacuum theory, the physical vacuum is described as a quantum superfluid and is characterized to behave like a frictionless fluid with density and proposes a mass generation mechanism that may replace or supplement the electroweak Higgs theory. It has been shown that the masses of elementary particles could be a result of interactions with a superfluid vacuum, similar to the gap generation mechanism in superconductors [9] [10].

Although according to quantum mechanics the electron is cloud of probabilities, therefore has no physical structure, many efforts are made to study the shape of the electron. The current model predicts that electrons are slightly aspheric, with a distortion characterized by the electric dipole moment. However, no experiment so far has detected this deviation [11].

Jehle spent a large part of his life developing a theory of the electron and elementary particles based on quantized magnetic flux loops, spinning at the Zitterbewegung frequency [12] [13] [14] [15] [16].

Also, Dirac suggested the existence of the magnetic monopole to describe the charge of the electron [17].

Both these theories rely on a physical relationship between flux and charge. The question of the relation between the electric and magnetic properties is fundamental to electrodynamics. One expects a relationship as moving charge produces magnetic flux.

In previuos articles [18], the electron is proposed to be a frictionless vortex with conserved momentum made out of virtual photons that acquire mass when moving in the vortex at the speed of light. The vortex shape electron allowed to resolve the enigmatic wave-particle duality [19].

The vortex shape of the electron and the Hydrogen atom give a full explanation for the origin of fine structure constant [20]. The same model was presented to explain the origin of gravitation force [21] and gravitation constant G [22] indicating the universality of the phenomena.

Thus the proposed idea in this paper is that the electron is an irrotational vortex of frictionless superfluid space with concentric streamlines that was created from the primordial vacuum that converted to Higgs particles during the Big Bang.

The vortex of the electron is made up by massless Higgs particles which acquire mass when they travel around the vortex center. The rate of rotation of the fluid in the irrotational vortex is greatest at the center and decreases progressively with distance from the center until there is no gradient pressure on the boundaries of the vortex where the flow is laminar and the friction is null.

In such a case, the absence of friction would make it impossible to create or destroy the vortex motion.

There are two types of vortices, the first one like the whirlpool, in which the flow goes from the periphery to the center, in such vortex the centripetal forces prevail. This kind of vortex related to the electron. The second kind of vortex is like the tornado where the flow goes from the apex to the periphery, related to the positron in which the centrifugal forces prevails Figure 1.

The electric charge density in the core of the electron is less than the vaccum density, while the core density of the positron is major than the vacuum density. Furthermore, the charge density is inversely related to the radius of the vortex.

Therefore, if the vacuum density is ρ and the vortex core density is ρ0 then the electric charge density would be:

q=ρ0−ρ/2πrρ0q=ρ0−ρ/2πrρ0(1)

The charge density is positive if ρ0 > ρ. The charge density is negative if ρ0 < ρ.

Necessarily, only two types of electric charge exist, positive and negative. Let n be the number of boson Higgs particle in a given volume V. Since n = ρ0V‘ and also n = ρV we get: V = n/ρV‘ = n/ρ0, Hence: (V−V′)/V′=−(ρ0−ρ)/ρ0(V−V′)/V′=−(ρ0−ρ)/ρ0

If V‘ > V is dilation, V‘ < V is contraction

The centripetal force of the electron pulls the surrounding Higgs field into the centre of the electron vortex, hence causing a tension in the surrounding field causing pull force to act on other particles.

Figure 1. The vortex is curling in the plane, expansive (red) or contractive (blue) except in the core center where it is pointing out-of-plane, either up (polarity p = +) red or down (p = −) blue.

The centripetal forces of the electron and the lines of force made of Higgs particles are shown entering, allows due to attractive force to interact with protons to form different chemical elements and the attraction between two electrons with opposite spins. The positron instead in which the centrifugal forces and the lines of force exerted are always shown leaving the center push the other particles thus cannot interact with matter in a stable manner.

3. The Nature of Electric Charge

One of the fundamental laws of electricity is expressed by coulomb’s law which states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.

In equation form, Coulomb’s law can be stated as

F=kQ1Q2/r2F=kQ1Q2/r2,(2)

where Q1 represents the quantity of charge on object 1 (in Coulombs), Q2 represents the quantity of charge on object 2 (in Coulombs), and r represents the distance of separation between the two objects (in meters). The symbol k is a proportionality constant known as the Coulomb’s law constant = 1/4πε0. The value of this constant is dependent upon the medium that the charged objects are immersed in.

However, the electric charge nature still mysterious and the reason of such behavior still enigmatic. Furthermore, it is not clear why electrons with different spin they attract despite they have the same charge. The vortex structure model of the electron resolves completely all aspects related to the attributes and the behaviour of the electron including the electric charge.

The field about a charged body is generally represented by lines which are referred to as electrostatic lines of force. The electron as a vortex made up of spiral arms from which stems the fields of force which spread out in the space around the center of the vortex and diminishes in proportion to the square of the distance from the center of the vortex [18].

These lines are real and represent the direction and strength of the field.

Both electron and positron vortices have electromagnetic field, magnetic moment and magnetic dipole.

In the electron vortex, the flow of Higgs particles that moves in spirals downward in the funnel creates a pressure gradient normal to the vortex center and acts along the central axis of vortex spin. It follows moving up around the spiral and returns from the upper side of the central axis generating the magnetic momentum and magnetic dipole. The vertical magnetic pressure gradient is normal to the horizontal electrostatic pressure gradient creating by the vortex and acts along the central axis of spin Figure 2.

The acting forces electrostatic and magnetic are now interlinked in self-balancing feedback loops that give great stability to the vortex structure shape of the particle as a whole. These are the two forces that generate movement and create currents. The currents are the avenues of movement made up of

Figure 2. Artistic presentation of the magnetic field around the electron.

Higgs particles, surrounding which are spaces or crevices through which flow currents of lesser density comprising Higgs particles.

The interaction between vortices takes place in three different ways:

1) The electrostatic force which is attractive (gravitational) in the electron and repulsive (anti-gravitational) in the positron;

2) Magnetic force which is attractive in the opposite polarity, expressed by spin value −1/2 or +1/2;

3) Electrostatic centripetal force which depends on the rotation direction, is attractive if one vortex rotates clockwise rotation and the other counter clockwise rotation.

The electron can have a magnetic dipole is oriented in a way that the negative pole is up and the positive pole down. In this case, the projection value said to be −1/2, while in the opposite direction said to be +1/2. The projection can be changed, but the total spin of 1/2 related to the spiral arm curl is fixed for all time.

Electron annihilation [23] [24] [25] is the phenomenon that consists in the collision of electrons with positrons. This phenomena, can take place in Thibaud’ s experiment where free positrons were launched against a metal lamina (tungsten) which is rich in conductive electrons or collision between free electrons and free positrons with low speed.

The two particles disappear and generally energy quanta appear in their place. As per the conservation law of momentum the two quanta have by practise opposite directions with an angle 90 degrees.

Each quantum has the energy of about 0.51 MeV, with frequency and wavelength placed in the spectrum of gamma radiation (gamma rays): f = 1.2 × 1020 Hz; lambda = 2.5 × 10−2 Angstroms. As per the conservation law of energy, because the intrinsic total energy of both, electron and positron, is 1.02 MeV, the produced quanta has about 1.02 MeV. This process is presented schematically by Feynman diagram Figure 3.

Feynman diagram does not explain the interaction mechanism. However, whirlpool structure of both electron and positron and rotation direction give us good mechanical explanation

Figure 3. Feynman diagram of the electron-positron collision at low energy.

The interaction between electron and positron takes place in the mouth of the electron and in the apex of the positron which have attractive the force, therefore the positron will be swallowed by the mouth of the electron, however, the collision at low energies causes overlapping opposite rotation direction, destructive wave interference and annulation the rotation of both vortices, the annihilation of the electron and positron, and materialisation of gamma photons Figure 4.

Electrons mostly repel each other due to having the same charge. However, electrons with opposite spins not only lack of repulsion but they partially attracted. The vortex model of the electron explains completely this behaviour.

The interaction between two opposite electrons, combines two different forces: the first the opposite attractive electrostatic force of the spiral arm of the vortices Figure 5.

Therefore, opposite spin electrons have this attraction, without any Coulomb’s repulsion.

The second is the dipole opposite spin and magnetic force, the stream flows mesh, the particles will attract one another Figure 6.

When two electrons are in the same rotation direction, the stream flows clash and repel the two electron vortices Figure 7.

Furthermore, there is magnetic repulsion between similar magnetic dipole moments. Each is like a tiny metal bar magnet that are directed in the same direction. This is the origin of Pauli exclusion principle.

The description of magnetic pole attraction and repulsion will be discussed separately in other articles that describe the internal structure of the monopole.

4. The Essence of Electron Charge

In hydrodynamics, the rotation of a vortex creates a drag force that attracts the medium to the center of the vortex. This force is directly related to the density of the vacuum, the speed of rotation, and the area according to the equation

F=1/2ρc2AF=1/2ρc2A,(3)

where, ρ is the density of the vortex, c is the speed of light and A is the area of the vortex.

Figure 4. Electron–positron annihilation process caused by the collision between the apex of the positron (upper vortex) which has clockwise rotation and the mouth of the electron (down vortex) which has counter clockwise rotation.

Figure 5. Partial attraction between two opposite spins the one has projection value said to be up with spin −1/2 and the other as +1/2.

Figure 6. Right −1/2 spin electron, left, +1/2. The stream flows mesh, the particles will attract one another.

Figure 7. The two-opposite head to head flux leads to electron repulsion.

However, any motion in a curved path represents accelerated motion, and requires a centripetal force directed toward the center of curvature of the path which inversely related to the radius according to the equation

F=1/2ρc2A/rF=1/2ρc2A/r .(4)

Multiplying and dividing the right side of Equation (4) by time t, we obtain

F=1/2ρctAc/rt=1/2ρVc/rtF=1/2ρctAc/rt=1/2ρVc/rt,(5)

where ctA is the volume V. However, this force is reduced owing to interactions with the adjacent vacuum. If the density of the vortex is ρ and the rotation speed of the vortex is c, dividing the momentum ρc by the length of the circumference of the vortex λ = 2πr will give the momentum Pd for a unit of length, thus:

Pd=ρc/λPd=ρc/λ.(6)

Therefore, the momentum of the vortex is multiplied for every unit of length by ρc according to the equation

F=1/2ρVρc2/rtλF=1/2ρVρc2/rtλ. .(7)

If λ = 2πr, then

F=1/2ρVρc2/rt2πr=ρVρc2/4tπr2F=1/2ρVρc2/rt2πr=ρVρc2/4tπr2.(8)

In hydrodynamics, ρc2 is the elasticity of the vacuum. In fact, the speed of a particle in an elastic medium can be expressed by the formula

c=(E/ρ)1/2c=(E/ρ)1/2,(9)

where c, the speed of light, E is the elasticity, and ρ the density of the medium.

Therefore, the elasticity of the vacuum, E, can be written as

E=ρc2E=ρc2,(10)

which is the inverse of the stiffness of the vacuum and has the same value as the electric permittivity, i.e., ρc2=ε−10ρc2=ε0−1.

This makes sense in terms of dimensions because the elasticity modulus is Newton × m−2 whereas the permittivity is Newton−1 × m−2 (C2/N m2).

Then, the Equation (6) becomes

F=ρV/4tπr2ε0F=ρV/4tπr2ε0.(11)

The force at a point in a fluid divided by the density is the acceleration of the fluid at that point known in fluid mechanics, as the force density ff [26].

Therefore Equation (11) become

F/ρ=f=(V/t)/4πr2ε0F/ρ=f=(V/t)/4πr2ε0.(12)

Force density is the negative gradient of the pressure which has physical dimensions of force per unit volume. The force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid.

In fluid dynamics, the volume of a fluid that passes per unit of time, V/t, is the volume flow rate, which is usually represented by the symbol q. Its SI unit is m3/s. therefore force density is expressed as:

f=q/4πr2ε0f=q/4πr2ε0,(13)

this is the same formula of the force of electric charge. Therefore, the electric charge is the volume flow rate of vacuum flux from the vacuum to the center of the electron vortex that can be expressed as:

q=f4πr2ε0q=f4πr2ε0,(14)

the q charge equals to Force x Area of the sphere (4πr2) which is the cross product between the potential energy and the radial distance of the sphere charge, diminished by the vacuum stiffness ε0.

The SI unit of quantity of electric charge is the coulomb, which is equivalent to about 6.242 × 1018 e (e is the charge of a proton). Hence, the charge of an electron is approximately −1.602 × 10−19 C. The coulomb is defined as the quantity of charge that has passed through the cross section of an electrical conductor carrying one ampere within one second.

According to Newton Law f = ma, thus we substitute f in Equation (14) to obtain

q=ma4πr2ε0q=ma4πr2ε0,(15)

This is an explicit combination of mass, length and time. If the a is c/t (a) its units are L/T2 and 4πr2 units are L2 the final charge units will be 4πε0 ML3/T2. That indicates that the charge is the mass quantity M that pass area L2 per time T at speed of light L/T diminished by the vacuum stiffness ε0.

This equation demonstrates that the electric charge is equivalent to mass change in a particle. This is a momentum equation which is conserved, and the net charge is always conserved, and this is the origin of law of conservation of charge.

In this article, the nature and the essence of a single charged was discussed, the charge interaction and Coulomb Law will be discussed in detail in separate article.

5. Conclusions

Herein, a new theory connects the structure of the electron and presents a new and explicit description of the obscure physical parameter of electric charge. The electron is presented as a frictionless vortex with conserved momentum made out of condensed vacuum.

The electron as a vortex rotates around an axis in such a way, that it possesses an angular momentum, spin and charge. This understanding enables us to apply hydrodynamic laws to derive and calculate the electron attributes including spin and charge.

This model shed light on the difference between electron and positron, comparing them to water whirlpool and tornado. The electron negative charge is related to the attractive force toward the center of the vortex, while the positron has repulsive force from the center to the periphery. The attraction or repulsion between charged particles depends on three different forces:

1) The kind of vortex (whirlpool or tornado type) that determines the charge negative or positive respectively.

2) Clockwise or counter clockwise rotation of the vortex that is related to the spin.

3) The dipole orientation.

The attraction between two oppositely oriented electrons despite they have the same charge is explained by dipole attraction and opposite spin rotation direction.

The centripetal force of the electron vortex that attracts Higgs particles to the center of the vortex which depends on the density of the vacuum, the area and the radius of the vortex is formulated. Taking into consideration the reduced momentum of the vortex, the density force in a giving point in the vortex and the net final momentum in that point is formulated. This is actually the flux density of the hydrostatic force within the bulk of a fluid.

The force density equation is an expression of volume flow rate which is equivalent to the electric charge q per unit of area of a sphere 4πr2 reduced by the stiffness of the vacuum expressed as the constant of permittivity ε0. This comes to indicate that the charge has a sphere shape.

Accordingly, the electric charge is an expression of Force x Area which is the cross product between the potential energy and the radial distance, diminished by the vacuum stiffness ε0. In other words, it’s the accelerated mass per area reduced by the stiffness of the vacuum which has the units ε0 ML3/T2. It appears that dimensional analysis is not only a reliable method for assessing the validity of equations, but also it can help to find a meaningful interpretation for a category of unknown physical parameters.

The vortex model of the electron may turn out to have far-reaching consequences, for theoretical physics and to be indeed very useful and even almost essential auxiliaries of reasoning. The essence and nature of the electric charge could make a major breakthrough in the field of electromagnetics.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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More information: Kai-Qiang Lin et al, Narrow-band high-lying excitons with negative-mass electrons in monolayer WSe2, Nature Communications (2021). DOI: 10.1038/s41467-021-25499-2

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