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What is the Spin?

Spin & Time- Inverse Symmetry.

Spin and Charge Transport

Abstract:

The spin describes the properties related to the breaking of the time-inverse symmetry for an elementary particle. An electron has a magnetic moment and angular moment due to the spin (broken time-inverse symmetry).

The time inverse symmetry is broken, when a quantum state is occupied by one electron. Such a state is spin active. The time inverse symmetry is not broken, when a quantum state is occupied by two electrons. Such a state is spin inactive.


Content

click on the chapter for the shortcut

(Part 1) Origin of the Spin

1.1. Spin & Time- Inverse symmetry
1.2. Incorrect view of the spin as an internal rotation of an electron
1.3.Spin & the time-inverse symmetry
1.4. Spin & Magnetic Moment
1.5.Spin & Dirac Equations
1.6 Quantum Mechanic and Magic in Physics
1.7. Magical (Incorrect) explanation of the Spin
1.8. Stern–Gerlach experiment. Magic, which lived over a hundred years.
1.9. Classical explanation of the Spin by Dr. Matt O`Dowt

(Part 2) Mechanical forces & Mechanical torque due to the Spin & Magnetic field

(2.1) Difference of mechanical force acting on a single electron and on an assembly of electrons
(2.2) Origin of a mechanical force
(2.2) Mechanical force 1:Due to a gradient of magnetic field
(2.3) Mechanical force 2: Due to an artificial magnetic charge. The torque of compass pointer.
(2.4) Mechanical force 3: Due to Einstein–de Haas effect.

(Part 3) What is the magnetic field?

(3.1) What is the magnetic field? 3 origins of the magnetic field.
(3.2) 3 types of the magnetic field: (1) conventional magnetic field; (2) Spin-orbit magnetic field; (3) magnetic field of the exchange interaction.

(part 5) Inflation, breaking symmetry, origin of an elementary particle & Spin

() Why is understanding of the Inflation important for understanding of the spin?
() A few facts aboaut the Inflation
() How to create a particle from the vacuum
() Size of an elementary particle
() Standard model and "post- Standard model"
() Symmetry & Conservation Laws
() Transformation of two elementary particles into one particle.
() Exchange interaction. Spin-inactive electrons

(). Questions & Answers

()about spin-mixed state

 

 

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Spin & Time- Inverse symmetry

(fact) The spin describes the degree of breaking of the time- inverse symmetry. The spin is not magnetic moment or angular momentum or anything else. The breaking if the time- inverse symmetry is only parameter, which corresponds to the spin and is measured by the spin.

 

(note) Each conserved property of an elementary particle (like an electron) correspond to some breaking of the spacetime symmetry.

For example, the particle energy corresponds to the continuity of the time. The continuity of the time means that the Laws of Physics are the same today and tomorrow. A particle with a non-zero energy, which is always the case, breaks the symmetry of the continuity of the time. Each moment of time is individually different for the particle. For example, when the particle is moving, its spatial position is different at each moment of time and each moment of time is different and not symmetrical for the particle.

The particle momentum corresponds to the continuity of the space, which means that the laws of the Physics are the same here and near the Moon. A particle with a non-zero momentum breaks the symmetry of the continuity of the space. The spatial positions, which are one meter away from the center of the particle and, therefore, the symmetry of the continuity of the space is individually broken for the particle.

. Each moment of time is individually different for the particle. For example, when the particle is moving, its spatial position is different at each moment of time and each moment of time is different and not symmetrical for the particle.

The spin corresponds to the breaking of the time- inverse symmetry. It means that some of particle properties changes if the direction of time flow would be reversed..

 

(note) The spin magnetic moment and the spin angular momentum are the properties, which are consequence of breaking of the time inverse symmetry. E.g. the breaking of the time-inverse symmetry makes the number of Dirac equation twice as many. There are 4 Dirac equations.

 

 


Incorrect view of the spin as an internal rotation of an electron

 

Q. Is it possible that the origin of the electron spin is the rotation of the electron around itself??

Electron can not rotate around itself (its own axis)

 

An object should have parts in order to able to rotates around itself. The electron does not have parts!! Or an object should have a asymmetrical shape in order to able to rotates around itself. The electron does not have a shape!!

The rotation of electron around its own axis

When the electron has parts, the rotation can be seen. When the parts vanish, the rotation can not be distinguished.

The real electron is an elementary particle, which does not has parts. Therefore, electron can not rotate around its own axis.

An electron can rotate around another object like nuclear.

When the electron has asymmetrical shape, the rotation can be seen. When the shape is spherical, the rotation can not be distinguished.

The real electron dos not have a shape. Therefore, electron can not rotate around its own axis.

The electron shape is defined by its environment. It is fixed and it can not be rotated.

 

A. No. It is not correct assumption.

An electron does does not have parts and it does not have a defined shape. Therefore, it can not rotate around its own axis.

The electron is an elementary particle and it does have any parts. Therefore, the electron can not be rotated around itself

The rotation of an object around itself literally means that the parts of the object rotates relatively each other. In case when the object is monolithic without any parts, it can not be rotated around itself, because there is nothing, which could be rotated.

An electron may rotate around another object. For example, in an atom an electron rotates around a nuclear.

An electron has length, which equals to the electron mean-free path. The length of conduction electrons in a semiconductor could be as long as micrometers. In a metal, the electron length is about of a few nanometers. A localized electron has a size of atom, which is about ~0.1 nm. An electron has a width as well. It is defined by electron wave vector and the mean-free path.

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Note:

The spin and charge are two independent features of the electron. For example, when two electrons of opposite spin occupy one quantum state. The state has the charge of -2e, but no spin. The neutron has no charge, but it has the spin.

 

Incorrect view: The spin of electron is not due to the movement (the rotation) of charge inside the electron.

The spin of electron is not due to the charge of the electron.!!!!! It is due the time-inverse breaking for the electron!!

However, the magnetic moment of electron is because the electron is a charged elementary particle.



 

All particles in Universe are created by breaking of spatial symmetry of vacuum.(See Fig. 10)

When additionally the time-inverse symmetry of vacuum is broken, an elementary particle has the Spin.

 

 



 

Spin & the time-inverse symmetry

The time-inverse symmetry breaking is the most common and simple breaking of symmetry of the vacuum. Therefore, nearly all particles have the spin

 

Since the spin describes the breaking of the time-inverse symmetry, there are only two possible spin eigen values for any elementary particle!! For this reason, the spin of an elementary particle is described maximum by two wave functions. Often it is called states of the left-rotation and the state of the right-rotation. In case of an electron, the states are called the spin-up and spin-down states. In the case of a photon, the states correspond to left- and right circular polarized photon.

The time-inverse symmetry symmetry of the vacuum is not broken. Therefore, the spin can interact with the field, which time-symmetry symmetry is broken, and the result of such interaction should be the time-inverse symmetric. The time-inverse symmetry symmetry of the magnetic field is broken. As result, the spin interacts with the magnetic field.

 

If an elementary particle with the spin is not charged (like the neutrino), does it interact with magnetic field?

The magnetic field represents the time-inverse-breaking part of the electromagnetic interaction. The neutrino, which does not interact electromagnetically, should not interact with the magnetic field. However, the common origin of the weak and the electromagnetic interactions, it could be some a very weak interaction of the neutrino with a magnetic field.

 

 

 

 

In atom an electron is circulating around a proton. Why a reversed atom, where a proton is circulating around an electron, can not be observed? Is that because of the differences of masses (the proton is heavier)?

It is because the electron is an elementary particle, but the proton is a composite particle, which consists of three quarks. The electron can not have a fix tiny length (size), but a composite particle is more close to a point-like particle. Because the proton is a composite particle, its mass is ~2000 times larger than mass of the electron. The difference of masses has some influence, but it is not major influence. For example, the proton has a diameter about 1 femtometer. It is defined by a longest- possible length of a gluon.

See Wikipedia about point-like particles (There are many parts, with which I do not agree)

 

 


Spin & Magnetic Moment

 

Origin of the spin-related magnetic moment:

The origin of the electron magnetic moment is nearly the same as the origin of the electron charge. The electron charge is originated from the breaking of the symmetry of the phase of the electron wave function with respect to spatial transformation. Similarly, the electron magnetic moment (spin-related) is originated from the breaking of the symmetry of the phase of the electron wave function with respect to time-reversal.

 

(gauge symmetry) The electron wave function has both the phase and magnitude. Only magnitude has a physical meaning which the probability of electron to be at certain spacial point at fixed moment of time (See here for more details). The phase has no physical meaning for a single electron in absence of any neighbor particle. In this case, the changing of the phase does not affect any of the physical parameter of the electron. However, in the electromagnetic field, the phase of the electron wavefunction is locally changed by the electromagnetic the electron energy

 

(origin of charge) The gauge symmetry becomes locally broken for a spacial transition (e.g. transition along the x-axis)

(origin of spin-related magnetic moment) The gauge symmetry becomes locally broken for a time inverse+ rotation

 


Spin & Dirac Equations

 

 

Dirac Equation & Spinors

Each specific electron of a fixed spin is described by a scalar wave function Ψ(r,t), |Ψ(r,t)|2 describes probability to be (to interact with another particle) at point r at a time moment t.
(breaking C-symmetry) : The symmetry, that the charge can be either negative (electron) or positive (positron), doubles the rank of spinor or number of wavefunction, which describes the electron quantum field.
(breaking T- symmetry) : The symmetry, that the spin direction can be either up or down, doubles the rank of spinor or number of wavefunction, which describes the electron quantum field.
In total, the C-symmetry (x 2) and T- symmetry (x 2) makes the rank of 4 for the spinor, which describes the electron quantum field, and, therefore, requires 4 equations (the Dirac Eqs.) to describe this electron quantum field.
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(fact 1)

The Dirac equations describes the quantum mechanical properties of an electron. The solution of the Dirac equation is a 4-rank spinor. The 4-rank spinor is a 4 dimensional vector of 4 wave functions, which transformation properties are following the symmetry of a spinor.

(fact 2): The Dirac tensor for electron quantum field describes all states of the electron. A possibility to have either a negative or positive charge and a possibility to have either spin-up or spin-down spin direction.

( C- symmetry): The symmetry of reversal sign of the charge

The plus and minus charge are fully equivalent. There is nothing, which makes the plus charge better than the minus charge or vice versa. As a result, the spinor of electron quantum field should describe equally the particle of the minus charge (the electron) and the particle of the plus charge (the positron).

( T- symmetry): The time- inverse symmetry, which is described by the spin.

The breaking of the time-inverse symmetry means that for any state (e.g. spin-up state), there is a state (the spin-down state), which is the time- inverse transform from the original state. It means that if the time flow is inverse, the spin-up state becomes spin-down state and the spin-down state becomes the spin-up states. Additionally, the breaking the time-inverse symmetry causes some new properties of particle such as the magnetic moment and the angular moment.

 

The electron can never be transformed to the positron. Why does the Dirac spinor describe both the positron and electron wave functions?

A1. (general description of all symmetries of quantum field) An actual particle (e.g. an electron) is described by a scalar wavefunction. In contrast, the Dirac spinor describes all possible states of the electron Quantum

A2. (possibility of the annihilation of the electron and positron. Restoring of the C-symmetry) For each the electron and the positron, the C - symmetry is broken. However, the symmetry breaking is opposite. The charge of the electron is negative, but the charge of the positron is positive. When the electron and positron collide to each other, the breaking of the C-symmetry disappears and a result of the colliding is a charge-free photon.

A3. (relativistic decrease of the charge, when the particle speed becomes close to the light speed) An In fact, a moving electron has a small component of the positron wave function. The positron component becomes larger and the charge of the electron becomes smaller, when the electron speed becomes close to the light speed. A particle, which moves at the light speed, cannot have a charge, because the charge is originated from breaking the gauge transformation symmetry (See above) and such symmetry breaking is not possible at the light speed.

The time flows in one direction from the past to the future. There is no time flow from the future to the past. Since time inverse can never occur, why the time- inverse wave function is included into the Dirac spinor?

A1. It only means that a specific symmetry for a particle is broken.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Quantum Mechanic and Magic in Physics

click on image to enlarge it

 

Physics has no magic

Maybe the desire to create a magic lies deep in the human nature. Anything what humans were not able to explain, is considered to be the magical until a scientist logically explains it and all magic vanishes.

 

Everything in Quantum Mechanic can be explained with logic and reasons.

All magic in Quantum Mechanic is originated from poor knowledge, tricks and lies.

There is nothing in Quantum Mechanic which could not be explained logically and based on the Laws of the Symmetries and the Conservation Laws of the Physics.

 

 

 

 

 

 

 


Magical (Incorrect) explanation of the nature of the Spin

Following incorrect explanation of the results of the Stern–Gerlach experiment (See below), the magical nature of the Spin was accepted for a long time. Even though the magical nature of the spin contradicts with several Laws of Physics and Quantum Mechanics

 

Perpetual motion machine cannot ever exist because of the energy conservation law

The energy conservation law does not allow to built a perpetual motion machine of any design
For hundreds years "engineers" and "scientists" are unsuccessfully challenging the fundamental energy law trying to built the perpetual motion machine.
Similarly, the fundamental spin conservation law are challenged by many scientists, which support the magical spin nature.

(magical nature of the Spin)

The direction of the electron spin is not fixed, but depends on the measurement geometry. When the direction is fixed (e.g. the vertical direction), it fixed the possible spin direction and the spin can have either spin-up or spin-down directions along the fixed measurement direction

 

 

Contradictions of the magical nature of the spin with several well- known well- verified Laws of Physics and Quantum Mechanics

(contradiction with spin conservation law): The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly contradicts with the well-verified spin conservation law.

Any the conservation law in Physics corresponds to some symmetry of the space- time of our Universe (See below). The spin conservation law corresponds to the time- inverse symmetry of our Universe. This symmetry is a similar to the symmetry of continuos time flow, which means that all Physics laws will be same tomorrow as they are today. Therefore, the violation of the spin-conservation law as incorrect as the violation of the energy conservation law!

(contradiction with Dirac equations): The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly contradicts with the Dirac equations, which only have a physical meaning when both the electron charge and the electron spin are fixed.

The solution of the 4 Dirac equations is a 4-rank spinor. However, a particle (an electron) is described by a scalar wave function. The 2 x functions describe a particle with opposite charge and 2x functions of the opposite spin. In order for spinor to become a scalar wavefunction both the electron charge and the electron spin should be firmly fixed. As a result, any realistic particle (an electron or a positron) has the fixed charge -e or +e and the fixed spin (the fixed spin direction)

(contradiction with fact of a single direction of the time flow): The time flows in one direction in our Universe from the past to the future. The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly means that the flow of time is not fixed.

The spin describes the breaking of time inverse symmetry. The breaking of time-inverse symmetry is described by a 2-rank spinor, which contains two wavefunction. The first wavefunction describes the actual wavefunction of the electron. The second function describes the wave function of electron, which would be if the direction of the time flow were reversed. The claim, that the spin direction is not fixed, but determined by the measurement geometry, directly means that the direction of the time flow is not fixed, but is determined by the measurement geometry. It is clear that it is a nonsense.

(contradiction with experimentally- observed spin-related effects): The

 

Why so many people, including some science, does not accept the fundamental conservation Laws like the energy conservation law and the spin conservation law?

The people need a magic. The straightforward facts and laws of Physics are bored. For the magic people are willing to pay.


Stern–Gerlach experiment. Magic, which lived over a hundred years.

wiki page about Stern–Gerlach experiment is here
See classical explanation below in Dr. Matt O`Dowt video time: 5:10

(idea of experiment): Electrons of different spin polarization, which are emit by an electron gun, pass through a spatially varying magnetic field and are at a detection screen. In a spatial gradient of a magnetic field, an electron experience a mechanical force (See above), which pushes the electron to move along the gradient in order to minimize its magnetic energy.

(result of experiment): The electrons are detected at two spots (the left and the right spot). When the gradient of the magnetic field is rotated 90 deg, the two spots are also rotated 90 deg.

Stern–Gerlach experiment

gradient of magnetic field from right to left

gradient of magnetic field from down to up

(experiment details & result) A beam of electrons of different direction is passes through a gradient of magnetic field. In a gradient of a magnetic field an electron experience a mechanical force (See here) and moves along the gradient in order to minimize its magnetic energy. The force and direction of the electron movement depends on the electron spin direction. The electron final position is detected by the electron detection screen (the screen, which used to be in an old TV set). Two spots are detected, which correspond to the spin up and spin-down directions. When the gradient of the magnetic field is rotated 90 degrees, the positions of two spots are rotated as well.

( puzzle of experimental observation) At electron gun, the spins of electrons are distributed equally in all directions. Since electrons of a different spin direction experience a different force. Therefore, the electrons should be distributed continuously through the screen. Instead only two discreet spots are observed experimentally.
( magical & incorrect explanation) The direction of the electron spin is not fixed, but depends on the measurement geometry. When the direction is fixed (e.g. the vertical direction), it fixed the possible spin direction and the spin can have either spin-up or spin-down directions along the fixed measurement direction. Even though this explanation violates several laws of Physics and Quantum mechanics (e.g. Dirac equations), the magical spin behavior is used for a long time.
( simple & correct explanation) Additionally to the movement along the gradient of magnetic field, the electron experiences another effect, which is completely ignored by the magical explanation. The electron spin is aligned along the magnetic field due to the effect of the precession damping (See here). In a gradient of magnetic field, the magnetic changes from a positive value (up-direction) to a negative direction (down- direction). In the middle there is a point when the field is zero. Independently of the initial spin direction, the spin of all electrons, which move from the left side of the zero- field point) are aligned up along the up direction of the magnetic field in this region. As a result, all electrons in this region are forced to move to the left. The spin of all electrons, which move from the right side of the zero- field point) are aligned down along the down- direction of the magnetic field in this region. As a result, all electrons in this region are forced to move to the right. Since the electron spin is aligned along the magnetic field very quickly, the final position of electrons on the detection screen practically does not depends on initial spin it only depends on the electron position with respect to the zero- field point. naturally, there are two detection spots. When the gradient is rotated, the position of the detection spots are rotated as well. Therefore, the results of Stern–Gerlach experiment are 100 % fit to known Laws of Physics and Quantum Mechanics without any magic.
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(why the measured result is a problem? Why the magic needs to be introduced?): At the muzzle of the electron gun, the electron are not spin- polarized and may have any spin direction. The mechanical force, which an electron experience, is proportional to the spin direction with respect to the gradient. Since spin direction of each electron is different, each electron should experience a different force and therefore be detected and different spots of screen. The suggested problem is that the electrons are detected at two spots instead of a continuous distribution

(Magical explanation of Stern–Gerlach experiment): As a quantum- mechanical parameter, the direction of the electron spin cannot be defined exactly, but defined by a measurement. When measurement is from the right to the left ( the magnetic field increases from the right side to the left side ), the direction of electron spin can be only to the left or to the right. There are no up or forward or up/left directions. When the measurement direction is changed, the spin directions at the gun muzzle are magically change. For example, when measurement is from the down to the up ( the magnetic field increases from the bottom side to the top side), the direction of electron spin can be only to the up or to the down. There are no left or right or forward or up/left directions.

(Non-Magical explanation of Stern–Gerlach experiment ): There is an additional effect, which the electron spin is experiences and which is ignored in the magical explanation. (additional ignored effect): The electron spin is aligned along the magnetic field.

 

 

 

(problems of magical explanation) The magical explanation severely violates several very fundamental and well-verified laws of the Physics:

(problem 1) Spin conservation law

The conservation of the spin, which corresponds to the conservation of the time inverse symmetry.

The spin conservation law is similar and as strong as the energy conservation law.

(note): Each conservation law (e.g. the energy conservation law, the momentum conservation law) is originated from a specific symmetry of our Universe (See below). The energy conservation law is originated from the symmetry of continuos time flow. It means that all Physics laws will be same tomorrow as they are today. The spin conservation law is originated from the time- inverse symmetry. It means that all Physics laws will be same if the flow direction of the time is reversed. Therefore, the Energy and Spin conservation Laws are very similar and have very similar origins.

(incorrect claim of Stern–Gerlach experiment): The direction of the electron spins is determined by a measuring device. It means that the electron spin is not conserved and can change the direction influenced by a different measurement device. It is a fully incorrect claim, which severely violate the fundamental spin conservation law.

(problem 2) Dirac equations

The solution of the Dirac equations is a 4-rank spinor. However, a particle (an electron) is described by a scalar wave function. The 2 x functions describe a particle with opposite charge and 2x functions of the opposite spin. In order for spinor to become a wavefunction both the electron charge and the electron spin should be firmly fixed. As a result, any realistic particle (an electron or a positron) has the fixed charge -e or +e and the fixed spin (the fixed spin direction)

The statement, that the electron spin is not fixed, but defined by a measurement, is fully equivalent to the statement, that the charge of the electron is not fixed, but defined by a measurement.

 

(problem 3) Precise definition of the direction of the time flow in our Universe.

The requirement that the spin direction is precisely fixed also means that the direction of the time flow in our Universe is fixed.

At any moment of time, the electron has a possibility to have one two wave functions. The first wavefunction corresponds to the forward time flow. The second wavefunction corresponds to the reversed time flow. From these two possible wave functions, the electron always has the first one, because the direction of the time flow is firmly fixed. The direction of the time flow is only in the forward direction. Assumption, that the spin direction is undefined, directly means the direction of the time flow is not defined.

 


 

 

 


Classical explanation of the Spin by Dr. Matt O`Dowt Video

Classical explanation of spin by Dr. Matt O`Dowt

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Mechanical forces & Mechanical torque due to the Spin & Magnetic field

(fact) There are more magnetic- field- induced mechanical forces acting on assembly of electrons with a non zero spin spins than on a single electron

 

Electrical charge and electrical dipole in a homogeneous (constant) electrical field

(electrical charge): The electrical charge experiences a mechanical force in a homogeneous electrical field, which accelerates the electron movement from the negative to positive electrode.
(electrical dipole or electrical moment):: An electrical dipole does not experience any mechanical force in a homogeneous electrical field as if it does not exists
The electrical field is a constant between electrodes because of the same size of the electrodes
Click on image to enlarge it

Mechanical force, act on a single electron,

(only force) gradient of magnetic field

 

Mechanical force/torque, act on an assembly of electrons,

(force 1, strongest) gradient of magnetic field

(force 2, moderate) artificial magnetic charge. Compass torque.

(force 3) Einstein–de Haas torque

 

vs

Q. Why mechanical force & torque are acting differently on a single electron and on an assembly of electrons?

As an elementary particle, the electron does not have parts. For this reason, it cannot have the north part , for example, at the left part and the south part at the right side. Both the south and north are distributed homogeneously and equally all over whole volume of the electron. Additionally, a single electron cannot experience different forces at its different parts. The electron experience the same mechanical force for its all parts. For example, the left part of electron cannot experience a different mechanical force than its left part. Since the electron does not have the parts, the left and right parts always experiences the same force.

In contrast, an assemble of electrons can experience different forces at different parts. For example, the electrons at the left part may experience the larger mechanical force than the electron at the right part.


Origin of the mechanical force

An object is forced to accelerate in space when object energy is dependent on its spacial position. For example, the object is forced to accelerated towards the left or, similarly, experiences a mechanical force towards the left, when the object energy is smaller when it is shifted to the left.

Electrical dipole in a inhomogeneous electrical field

An electrical dipole or an electrical moment experiences a mechanical force in a inhomogeneous electrical field, which accelerates movement of the electrical dipole towards a larger electrical field
The electrical field is smaller at the left (negative) electrode and larger at the right positive electrode because of different sizes of the electrodes
Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

(Mechanical force 1 (strongest)):Due to a gradient of magnetic field

 

According to the Laws of Mechanics, a force acts on an object in the direction, in which the total energy of the is minimized. The electron energy in a magnetic field is S*H/2.

In a gradient of magnetic field, a force acts on an electron. The direction of this force depends on the electron spin.

When spin is parallel to the magnetic field, the force acts so that electron moves in the direction from a smaller to a larger magnetic field.

When spin is antiparallel to the magnetic field, the force acts so that electron moves in the direction from a larger to smaller magnetic field.

 

 

(note) This force causes the repelling or attraction between two permanent magnets, which we may experience in everyday life.

 

Why and at which condition does a particle experience a mechanical force?

A particle experiences a mechanical force, when the particle energy depends on the particle special position. The particle is mechanically forced into the position where its total energy is smaller.

Why particle is forced to the position of a lower energy?

interpretation of the mechanical force:

(interpretation 1): classic quantum electrodynamics. Gaining a momentum

In a gradient of electrical field (e.g. from the left to right) , the number of virtual photons, which are absorbed from the left and from the right side, are different. Since each photon transforms a mechanical moment to the particle, the mechanical moment of the particle is changes and the particle is forced to accelerate.

(interpretation 2): quantum vibrations. Gaining energy.

Due to interaction with virtual particles, the elementary particle position is randomly changed in time. The change is extremely tiny and it is called the quantum oscillations. In the absence of the gradient of the field, the distribution of the virtual particle and, therefore, the quantum vibrations are fully symmetrical. as a result, the particle average position remains a constant. However, in the case when at one spacial point the particle energy is smaller and at another special point the energy is larger, the quantum vibrations became asymmetrical and the particle is forced to accelerate towards the larger quantum vibration.

A virtual particle of a fixed energy makes a quantum oscillation larger into region of a lower energy and a shorter in region of a higher energy. It is because the movement into the the region of the higher energy requires a virtual particle of a higher energy, which live time of the virtual particle is shorter and, therefore, the movement distance of the elementary particle shorter. This is the reason why the particle is forced to accelerate towards the region of the lower energy.

Mechanical force due to a gradient of magnetic field

Levitation Gradient to the left Gradient to the right
The "South" and "North" poles are of the same size. As a result, there is no gradient of magnetic field towards each pole and the small magnet is levitating in the center between them The smaller area of "south" poles makes the magnetic field near "S" pole more denser and, therefore, larger. There is a gradient of the magnetic field. The magnetic field is smaller at "N" pole and larger at "S" pole . The smaller area of "north" poles makes the magnetic field near "N" pole more denser and, therefore, larger. There is a gradient of the magnetic field. The magnetic field is smaller at "S" pole and larger at "N" pole
(levitation): The levitation point is middle between poles, where the density of magnetic field is largest. When the object moves out of the levitation point, it experiences a smaller magnetic field and its magnetic energy becomes smaller. The gradient of magnetic field forces the object back to the levitation point in order to increase the object magnetic energy (mechanical force to the left) The object is forced to the left toward the smaller "S" pole, where the magnetic field is larger and, therefore, the object magnetic energy is larger. (mechanical force to the right) The object is forced to the right toward the smaller "N" pole, where the magnetic field is larger and, therefore, the object magnetic energy is larger.
A small magnet, which have a magnetic moment, in a magnetic field created by two poles of a larger magnet.
There is a gradient of magnetic filed in the space between two poles. An object with a magnetic moment experiences a mechanical force from the gradient, which forces the object to the spacial point where the magnetic field is the largest.
click on image to enlarge it

 

 

(Levitation):

When an object with a magnetic moment is placed in a local maximum of magnetic field, the object is forced to stay there. In the case when the object moves out of the levitation point towards a region of a smaller magnetic field, its magnetic energy decrease. As a result, there is a mechanical force which moves the object back to the levitation point.

 

 


(Mechanical force 2 (moderate) ): Due to an artificial magnetic charge. The mechanical force of compass pointer.

(fact) An elementary particle cannot have a magnetic charge. An elementary particle only can have an electrical charge and/or a magnetic moment.

Mechanical force of compass pointer

(Mechanical force in a homogeneous magnetic field)): There are artificial magnetic charges at each tip of the compass arrow. Each magnetic charge experience a mechanical force in a homogeneous magnetic field, which is created by the large magnet. The "N" magnetic charge is attracted to "S" pole of the large magnet. The "N" magnetic charge is attracted to "S" pole.
(mechanical torque)): Neither amplitude nor direction of the mechanical force changes, when compass arrow rotates. However, the mechanical torque, which aligns the compass arrow along the magnetic field..
Click on image to enlarge it

(reason) why an elementary particle cannot have a magnetic charge

Any property of an elementary particle corresponds to a breaking of a very specific symmetry of the time-space of our universe. The electrical charge corresponds to the breaking of the gauge symmetry, the spin corresponds to the breaking of the time-inverse symmetry and the magnetic moment corresponds to the breaking of the breaking of both the time-inverse symmetry and the gauge symmetry (See here)

There is no symmetry, the breaking of which, could create the magnetic charge.

 

(fact) A single elementary particle cannot create an artificial magnetic charge.

(fact) An assembly of elementary particles with spin can create an artificial magnetic charge at a boundary of the assembly.

 

 

 

How to distinguish an existence of a magnetic charge?

If an assembly of particle has a magnetic charge inside, it will experience a mechanical force in a homogeneous magnetic field (a constant magnetic field).

If an assembly of particle does not have a magnetic charge inside, there is any mechanical force on the assembly when it is in a homogeneous magnetic field .

 

 

Magnetic charge is also called a pole. The two opposite magnetic charges are called the "North pole" and "South pole".

 

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(fact) (rotation torque vs. linear force) Conventional understanding is that the compass arrow experiences a mechanical torque in a magnetic field. However, the compass arrow can experience a linear force in one direction. For example, if the external magnetic field chance its direction at positions of "N" and "S" magnetic charges.

Difference of spin-related magnetic moment of a single electron and a bulk object

Bulk magnet (right): There are specially- separated regions of "N" magnetic charge (shown in blue color) and and of "S" magnetic charge (shown in red color)
A single electron (left): As an elementary particle, an electron cannot have separated parts. As a result, the electron does not have specially- separated "N" and "S" regions and the "S" and "N" regions are homogeneously distributed over the volume of the electron.
See about size and volume of a single electron here
Click on image to enlarge it

 

 

Artificial magnetic charge: (origin)

The artificial magnetic charge or the magnetic pole is originated in an assemble of electrons with aligned spins, when the electron magnetic moment is only partiality compensated by magnetic moments of its neighbor electrons. The magnetic moment is not fully compensated at edge of the sample along direction of aligned magnetic moments.

Each localized electron has a magnetic moment, but it does not have a magnetic charge. Each "S" pole is in contact with "N" pole of a neighbor electron and, therefore, the "S" pole is compensated, the "N" pole is not compensated by this electron. Similarity, if there is an electron at other side, each "N" pole is compensated by "S" pole of the neighbor electron at other side. At the edges of the bulk nanomagnet, there is no compensation. As a result, the artificial magnetic charge (a magnetic pole) is formed at the edges.

 

How large the artificial magnetic charge?

 

Does artificial magnetic charge exists in an antiferromagnetic material?

 

Compass arrow and artificial magnetic charge:

A bar of ferromagnetic material, which is fixed on a rotation axis and can be rotated around this axis under an external force, aligned itself along an external magnetic filed (e.g. Earth magnetic field). The ferromagnetic bar experiences the mechanical torque due to the magnetic charges (magnetic poles) on sides of the bar. The mechanical force acts on the magnetic charges from the external magnetic field causing the mechanical torque.

In contrast to a single electron, the compass arrow experience a magnetic force in a homogenous (constant) magnetic field.

(fact ) (difference between magnetic moments of an electron and compass error)

The electron does not have any magnetic charge or magnetic poles. The electron only has a magnetic moment. In contrast, the compass arrow has two opposite magnetic charges (poles) on its sides, which are separated by a substantial distance. Such configuration of opposite magnetic charges makes a magnetic moment. Therefore, the primary property of the compass arrow is the magnetic charge. The magnetic moment is the result of specific configuration of the magnetic cha

Artificial magnetic charge created at the edges of magnet

Bulk magnet ( shown as a transparent box) contains of a stack of aligned magnetic moments of localized electrons ( shown as red/blue magnets). At edges of the bulk magnet, the artificial magnetic charge or a magnetic pole is created (shown as balls). At the left side, the "N" artificial magnetic charge (pole) is created (shown as red ball). At the right side, the "S" artificial magnetic charge (pole) is created (shown as blue ball).
Due to the artificial magnetic charge, the bulk magnet experiences a mechanical force in a homogeneous magnetic field.

Each localized electron has a magnetic moment (shown as blue/red bars in figure), but it does not have a magnetic charge. Each "S" pole is in contact with "N" pole of a neighbor electron and< therefore, it is compensated. Similarity, Each "N" pole is compensated by "S" pole of the neighbor electron. At the edges of the bulk nanomagnet, there is no compensation. As a result, the artificial magnetic charge (a magnetic pole) is formed art the edges.

Even though each individual electron does not experience a mechanical force in a homogeneous magnetic field. An assembly of exchanged coupled electrons experience a mechanical force in a homogeneous magnetic field.
Click on image to enlarge it

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


(Mechanical force 3 (weakest) ): Due to Einstein–de Haas effect.

wiki page is here
See classical explanation below in Dr. Matt O`Dowt video time: 0:24

This torque occurs due to a change of the rotational moment of an object, when the total spin of the object is change.

(case 1) changing of domain structure

A relatively- large ferromagnetic object (sizes > domain size) has a multi- domain structure and its total spin is close to zero. In an external magnetic field, the magnetic domains are realign in one direction and the total spin of the object becomes a substantial. The rotation moment related to the spin become larger,, but the total orbital momentum of the object should not change due to the domain rearrangement. As a result, the whole bulk object gains

 

 


 

 

 

 

 

 

 

 


 

 



What is the magnetic field?

 

3 origins of the magnetic field.

 

(Origin 1 of magnetic field ) Relativistic component of the electromagnetic field

(source of magnetic field): electrical charge

Magnetic field of source 1: magnetic field generated by an electromagnet

Magnetic field in an electromagnet is generated by the electron current flowing in a metallic wire.

Electromagnetic field has two components; electrical field and magnetic field, which relativistically transformed to each other. The magnitudes of the observed components of the electric and magnetic fields dependent on the speed of an observer. E.g. if in the first coordinate system an observer experiences only an electrical field, but no magnetic field, in coordinate system, which is moving with respect to the first coordinate system, the observer experiences both the electrical and magnetic fields. The transformations between field are described by the the Lorentz transformation rules as

where Estatic, Hstatic are the electric and magnetic field in the static coordinate system (reference frame) and Emove, Hmove are the electric and magnetic field in the coordinate system, which moves with a constant speed v.

This magnetic field is originated from the nature of the electromagnetic field itself. There are two effects due to this source of the magnetic field

(effect 1): Ampère's law

The Ampère's law describes the fact that an electron current creates a magnetic field.

 

Relativistic origin of the Spin-Orbit Interaction
An electron (shown in red) is moving in a static electric field. In the coordinate system moving together with the electron, the static electric field is relativistically transformed into the effective electric field Eeff and the effective magnetic field Heff. The Heff is called the magnetic field of the spin-orbit interaction.

The charge of the electron creates an electrical field. There is no magnetic field component of this field only coordinate system, which the electron does not move. When the electron move, the electrical field, which has only the electrical-field component in the coordinate system moving together with the electron, has both the electrical-field and magnetic-field components in a static coordinate system.

(effect 2): Spin-orbit interaction

The spin-orbit interaction describes the fact that an electron, which moves perpendicularly to an electrical field, experience a magnetic field and the electron spin is aligned along that magnetic field.

See here more details about the spin-orbit interaction.

Even though there is only an electrical field there is no a magnetic field in a static coordinate system, there is a magnetic field in a coordinate system moving together with the electron and this magnetic field interacts with the electron spin.

Dependence on electron movement speed

Magnetic field of source 1 increases, when the electron moves faster

 

(Origin 2 of magnetic field ) magnetic moment due to the spin of electron

(source of magnetic field ): electrical charge+ broken time-inverse symmetry +

Magnetic field of source 2: magnetic field generated by a permanent magnet

In a permanent magnet the electron spins are aligned in one direction. Each such electron has a magnetic moment due to its spin. The sum of all aligned magnetic moments creates magnetic field of a permanent magnet.

Due to its spin and its charge, the electron has a magnetic moment, which generates a magnetic field

An elementary particle, which has a non-zero spin and non-zero charge, has a non-zero magnetic moment, which induces a magnetic field around the electron.

(note) The electron has a spin, because its time-inverse symmetry is broken. The electron has a charge, because its gauge symmetry is broken. Simultaneous breaking the time-inverse symmetry and the gauge symmetry creates a magnetic moment for an elementary particle (See here for more details)

 

(Zero spin + non-zero charge) spin-inactive electron no magnetic moment

For example, the electron of filled orbitals are charged, but their spin is compensated, has no magnetic moment. Formally the time-inverse symmetry is not broken for these electrons and therefore they have no spin.

(Non-zero spin + zero charge) circular- polarized photon no magnetic moment

For example, the spin of a circular- polarized photon is 1, but the the photon has no charge. As a result, the photon has no magnetic moment and does not produce any permanent magnetic field. Of course, the electromagnetic field of a photon has a magnetic component.

Dependence on electron movement speed

Magnetic field of source 2 decreases, when the electron moves faster

It is because the electron electron charge decreases with a faster speed. Since the magnetic moment is proportional to the electron charge, the magnetic moment decreases as well. A particle, which moves at speed of light, can not be charged and therefore cannot have a magnetic moment. It is a feature of the gauge symmetry.

 

 

 

(Origin 3 of magnetic field ): spin- dependent Coulomb interaction (exchange interaction)

(source of magnetic field ): broken time-inverse symmetry

Two electrons of opposite spins, when combined, form an elementary particle without spin.

Each quantum state can be occupied by two electrons of opposite spins. When a quantum state is occupied by one electron, it is an elementary particle with charge -e and spin=1/2, When a quantum state is occupied by two electrons, it is an elementary particle with charge -2e and spin=0
click on image to enlarge it

The Coulomb interaction between electrons depends on their mutual direction of their spins. It makes the electron energy dependent on its spin direction. There is a spin direction, at which the electron energy is smallest and which is the equilibrium spin direction. There is a spin precession for any any different spin direction and spin damping align the electron spin along its equilibrium direction. All these features are exactly the same of the case of the magnetic field of origins 1 and 2. Therefore, the exchange field can be assigned as a magnetic field of origin 3.

(note) Even though the exchange field is completely different from the relativistic magnetic component of the electromagnetic field, which is usually associated with a magnetic field, in a solid its feature are nearly- indistinguishable from features of the conventional magnetic field. It is convenient to handle the exchange field in a solid as a magnetic field. For example, the features and properties of antiferromagnetic resonance, which is created by the exchange field, are very similar to that of the ferromagnetic resonance (FMR), which is created by the conventional magnetic field.

 

 

(effect ): Exchange interaction

The exchange interaction describes the spin-dependent Coulomb interaction between electrons. The Coulomb repulsion between two electrons is smaller, when their spins are opposite, and is larger, when their spins are parallel. When two electrons of opposite spins approach each other, the breaking of time- inverse symmetry slowly disappears and system of two elementary particles transforms into a system of one particle. As a result, their mutual repulsion decreases and their interaction with surrounding electrons and nuclears is changed

 

The time-inverse symmetry is not broken for an electron state, which occupied by two electrons of opposite spins. It literally means that such state does not have any spin at all. It also means that the state should be considered as one particle without spin with charge -2e instead of two electrons with opposite spins and charge -e and -e. When two electrons of opposite spins approach each other, they are monotonically transformed from the system of elementary particles into a system of only one elementary particle. As a result, the Coulomb repulsion between these two electrons monotonically decreases and the Coulomb interaction between each and surrounding electrons and nuclears is changed.

 

 

Dependence on electron movement speed

Magnetic field of source 3 is independent of the electron movement speed.

The exchange interaction only depends on the distance between electrons and their spin direction.

 


3 types of the magnetic field: (1) conventional magnetic field; (2) Spin-orbit magnetic field; (3) magnetic field of the exchange interaction.

 

3 types of magnetic field

Type 1: Conventional magnetic field Type 2: Magnetic field of Spin-orbit interaction Type 3: effective magnetic field of the exchange interaction
This is the conventional magnetic filed. This magnetic field "fills" all the space and all electrons experience equally this magnetic field.

The magnetic field HSO of the spin- orbit interaction is the component of the electromagnetic field similar to the conventional magnetic field. However, each electron experiences an individual HSO of different magnitude and direction. The HSO of each electron does not influence the spin any neighbor electron. Even electrons, which rotate around the same nuclear, may have different HSO when their orbital symmetry is different.

In the exchange field the electron spin is aligned either parallel or anti parallel to the spin direction of its neighbor electrons. The exchange field is not a component of the electromagnetic field. However, in a solid the spin properties of the electron in a exchange field are exactly the same as in a conventional magnetic field. Therefore, the exchange field can be assigned as an effective magnetic field.
  The HSO is originated from electric field of a nuclear and depends on the orbital symmetry of the electron. That is why the HSO is individual for each electron. Details about the spin-orbit interaction are here. Details about the exchange interaction are here
The spin properties of electrons are exactly the same for each type of the magnetic field. In an equilibrium the electron spin is aligned along the total magnetic field, which is a vector sum of all three types of the magnetic field. There is a spin precession before the alignment.
click on image to enlarge it

 

 

 

 


 

(part 5) Inflation, breaking symmetry, origin of an elementary particle & Spin

Content

click on the chapter for the shortcut
() Why is understanding of the Inflation important for understanding of the spin?
() A few facts aboaut the Inflation
() How to create a particle from the vacuum
() Size of an elementary particle
() Standard model and "post- Standard model"
() Symmetry & Conservation Laws
() Transformation of two elementary particles into one particle. Exchange interaction.

 

From simplest (symmetrical) to complex

All elementary particle are originated from breaking a symmetry of vacuum

The spin of any particle is originated from breaking the time-inverse symmetry of vacuum.

The vacuum is are absolutely symmetrical and simplest staff. Any elementary particles comes from breaking some of different symmetries of the vacuum. Click on image to enlarge it

 

The The Inflation is an event, which occurred just before the Big Bang and during which there was a self-sustained breaking of the symmetry of the Universe. As a result, all matter of the Universe was created during the Inflation event. Before the Inflation the Universe was fully symmetrical and contained no matter at all. After the Inflation created all matter and diversity (broken symmetries) in our Universe. The Big Bang event shaped the Universe into the present form.

 

Why should one care about a cosmic event like the Inflation in order to understand the spin? Why is understanding of the Inflation important for understanding of the spin?

The spin describes the broken-time inverse symmetry. The Inflation is a big event of the breaking of all possible symmetries of the Universe. Some properties of the spin can be evaluated from general properties of the broken symmetry, which are magnified during the Inflation and, therefore, can be easily understood.

 

There are several such examples:

(example 1: Spin conservation law)

In the case when the symmetry of the vacuum (the Emptiness) is broken (something is created from nothing), the total sum of the created quantities should be zero:

particle + antiparticle =0;

negative charge (-e electron) + positive charge (+e positron) = 0;

negative energy (gravitational energy) + negative energy (kinetic energy) =0;

spin-up + spin-down =0;

 

Evolution from symmetric to complex and less symmetric

Both the evolution of life and the evolution of matter is a pass from a simplest and very symmetric to a complex and less symmetric form

evolution of life
evolution of matter

 

The evolution of life and the matter is constant breaking of the symmetry.

The spin descibes the breaking of the time- inverse symmetry for an elementary particle.

Click on image to enlarge it

 

(example 2: spin-active and spin-inactive states)

If a symmetry can be broken, it can be unbroken.

(broken/unbroken symmetry of the charge:)

Annihilation of a negatively-charged electron and a positively-charged positron results in particles without any electrical charge. Therefore, two opposite charges (two opposite breaking of a symmetry), when interact, fully disappears

 

(broken/unbroken symmetry of spin:)

Each quantum electron state can be occupied either by none or one or two electrons of opposite spin. The time inverse symmetry is broken, when a quantum state is occupied by one electron. Such a state is spin active. The time inverse symmetry is not broken, when a quantum state is occupied by two electrons. Such a state is spin inactive.

 

As a symmetry can be broken and next unbroken. The spin and the spin properties can appear and disappear for an electron. For example, deep-energy electrons in an atom do not have any spin properties.The spin-inactive states are important for the "hole" transport (See here), important for the spin distribution (See here) and important for a spin transport (e.g. the Hall transport).

 


 


 

The Greatest Discovery of 21st century!!

Undoubtable proof that the the inflation is the creation mechanism of all matter in the Universe is the Greatest discovery of the 21st century

Even though we are now in the first quarter of the 21 century, it is clear that the proof that the the inflation is the creation mechanism of all matter in the Universe is the greatest discovery of this century. It is because all known laws of Physics and our present understanding of the Universe should be adjusted to this important fact.

The inflation - the mechanism of the creation of all matter in the Universe.

The inflation explains how all matter was created in our Universe.

 

The model of the inflation was introduced in70th-80th as the model of the launching mechanism of the Big Bang. At beginning, the accelerating expansion of the Universe at earliest time of our Universe was called the inflation.

Now there are several proofs that the sum of all energies of the Universe (the positive energy of all matter and the negative energy of gravitational attractions between all matter) equals to exact zero. It proves that all matter in Universe was created from vacuum (from nothing) during inflation time.

 

How the fact of inflation influences the Law of Physics?

1. It explains many facts, which were experimentally found before and which postulated the Quantum Mechanics and the Standard Model.

2. It slightly modifies all laws of Physics to comply to the important fact that all particles should be generated from vacuum and they be able to annihilate into vacuum.

 

The Facts of Physics, which are consequence of the Inflation origin of our Universe:

(1) All elementary particles in the Universe are waves. There are no point-like particles

proof: Any existed particle should be created from vacuum. The mechanism how to create a wave-like particle is clear (See Fig.10). There is no any known mechanism, which could create a point-like particle from vacuum.

(2) An elementary particle does not have a fixed size. The size of the elementary particle is determined by its environment

proof:Since any elementary particle is a wave, the size of the wave is the size of the wave package. The size of the elementary particle is determined by the process how the elementary particle is created from vacuum (See Fig. 4).

It is the basic principle, which is postulated by the Quantum Mechanics.

(3) All forces of the nature (except the gravitation force) are originated from the processes of creation of particles from the vacuum and processes of annihilation of particles into vacuum

proof:When two particles are relatively far from each other and their wave functions are not overcrossed, only possible way of their interaction is by generating and annihilating of other particles. For example, the electrical interaction between two electrons is mediated by a photon.

(4) An elementary particle does not have parts. An elementary particle does not interact with itself.

proof:

(5) Elementary particles do not transform into each other abruptly. The process of transforming from particle to particle is continuous.

proof:Since any

(6) Any interaction between particles (except gravitational interaction) significantly changes when the distance between particles becomes smaller than their size. Any interaction between two particles are finite, even if distance between two particles approaches to zero.

proof:The classical physics states that any interaction between particles (gravitational or electromagnetic interaction) is infinite, when distance between two particles is zero. Since all particles are cracked from vacuum, initially before cracking two particles of opposite phase should be at exactly the same location (therefore, they form the vacuum). However, in the case if the interaction between these two particles (including gravitational interaction and the electromagnetic interaction) is infinite, the particle cold not ever be moved away from each other and any particle could not be created.

 

 

 

 


How to create a particle from the vacuum?

When two waves of opposite phase experience different force, they move in different positions and two particles are created from vacuum (from nothing)

Get something from "nothing" (from vacuum)
Creation of two particle by Cracking the vacuum
The sum of two waves, which have phase difference of 180 degrees, is the zero or nothing
The red and blue waves are in anti phase (180 degrees phase difference). At beginning, they are at exactly same point and their sum is "nothing" or vacuum. Next, due to some reason the red and blue interact differently with some particle. This difference causes a little bit difference in movement of the red and blue waves. The position of blue and red waves become different and two individual particle is created from vacuum.

Fig. 10 The creation of two particles from vacuum

The creation of two particles is a breaking of spacial symmetry. In case when the waves are in the x-axis direction, the breaking of the symmetry is in the x-direction.

Click on image to enlarge it

fact 1: All elementary particles in the Universe are waves. There are no point-like particles

proof: Any existed particle should be created from vacuum. The mechanism how to create a wave-like particle is clear (See Fig.10). There is no any known mechanism, which could create a point-like particle from vacuum.

How to create a particle from vacuum?

The sum of two waves, which are exactly the same but have phase difference of 180 degrees, is the zero or nothing or vacuum (See Fig.10 left). When the waves stay at an exactly the same point, they form the vacuum or nothing. In this case two waves are not yet particle, but they are a "virtual possibility for creation of particles". If there is a force, which interacts differently with the wave of opposite phase, two waves move in different locations and from virtual they become real particles

. Two waves of opposite phase are very similar. How it is possible that they interact differently with the field?

For example, two particles of opposite phase may have different charge. Than, in an electrical field they move in opposite directions.

if in a electrical field, the particle are so easily created, why do not we observe the creation of a huge number of particles in an electrical field?

From a view of a classic physics, the attraction between two particles of opposite charge are infinite, when the particles are located at the same point. It requires an infinite electrical field in order to move the particles away from each other. The case of real quantum world is different. Still the process of the creation of a particle from a vacuum is very subtle process, which requires existence of additional one, two or more particles at the same location.

 

Cases of creation of particles from vacuum:

case 1. The electromagnetic interaction

in this case a charged particle breaks a photon from vacuum. The photon reaches the second charge particle and annihilate itself (it is converted back into vacuum) at the location of the second charged particle. As result, two charged particles repel or attract each other.

case 2. The strong interaction

in this case a quark breaks a gluon from vacuum. The gluon reaches the second quark and annihilate itself (it is converted back into vacuum) at its location. As result, two quarks attract each other.

case 3. The weak interaction

in this case three quarks (u-,d-,d-) breaks a W- boson from vacuum. Next, the W- boson breaks an electron, a neutrino and a quark from the vacuum. As result, a neutron (u-,d-,d-) beta- decays into a proton (u-,u-,d-), an electron and a neutrino.

case 4. The dark energy

It is the energy of the vacuum, which fills up all Universe. The dark energy is only a substance in the Universe, which was not created during the inflation. The origin of the dark energy is the short-leave particles, which are broken from the vacuum.

There is a very small, but a finite probability that particles are broken from the vacuum. However, if there is no other particle in their proximity, these two particles quickly annihilate back into vacuum. The gravitation of these short-live particles has a substantial influence on our Universe. Even though the probability of such particles from is very small and life time of these particles is very short, in cosmological scale their gravitation is strong and it causes the accelerating expansion of our Universe. It is because these short-lived particles are created at all points of space.

case 5. The inflation

It is a self-sustained process of constant breaking of particles from vacuum. During the inflation, the particles, which are just created, make the conditions for the breaking additional particles from vacuum. These particles make another particles and so on. During inflation the number of particles increases exponentially. All substance of our Universe, except the dark energy, were created during the Inflation.

The conditions to keep self-sustained breaking of vacuum is extremely subtle. The accelerating expansion of the Universe and an extremely high density of particles are the key conditions to keep self-sustained breaking of vacuum. Only about 100-200 consequence breaking of particles by new- created particles occurred during the Inflation. It was sufficient to create all matter in our Universe.

 

The conditions, at which particles can broken from vacuum, are very subtle. First of all, all Conservation Laws should be satisfied!!!

Q. The vacuum energy is zero. When two particles are broken from vacuum, each particle has the energy mc² . How the energy is conserved during this process?

A. The particles have a positive energy, which the sum of the kinetic energy and mc². The attraction energy between particles is negative energy. The energy of the gravitational attraction is always negative. If charge of particles is opposite, the energy of the Coulomb attraction is also negative. It is very important that during breaking the particles from vacuum the total energy is always zero. As it has been proved already the sum of all energies in our Universe exactly equals to zero. That means that during all existence of our Universe and after unimaginable number of breaking of particles from vacuum the Conservation of the energy has never been compromised.

Of course, in the case when another particle participating in breaking of particles from vacuum, its energy can be transferred into the energy of new particles.

 


 

Fig.4. Length of photon

Emission of photon by an excited atom

A photon is emitted only between two subsequent colliding or scattering of the excited atom. Next, another photon is emitted.

The length of the photon is determined by time between two subsequent scatterings of the excited atom.

Similarly the effective length of an electron is determined by time between two subsequent scatterings of the electron.

The photons are in yellow color. The red balls are atoms (molecules).

Click on image to enlarge it or here for a middle size

fact An elementary particle does not have a fixed size. The size of the elementary particle is determined by its environment

proof:Since any elementary particle is a wave, the size of the wave is the size of the wave package.

proof: An elementary particle is a wave package, which length is the distance between two consequence scatterings of the particle or the distance between two events of the interaction of the particle with other particles.

For example, the electrons is

(1) 1-10 μm in a high-crystal quality semiconductor.

(2) 10-100 nm in a metal

(3) 0.1 nm in an atom

Length of a photon

It is called the photon coherence length. It is important characteristic of any light source. Simply it could be understood as an average length of wave packages in an optical beam.

In my optical experiments I use light sources of different coherence length. I use Santec tunable laser at lambda=1550 nm. Its light has the coherence length longer than 1 meter. I have a tunable Ti:sapphire laser. When I bought it it has a very short coherence length less than one millimeter. I have installed additional option in order to increase the coherence length. Now the the coherence length of light from this laser is a few centimeters. The coherence length of light from a light bulb is about 0.1 millimeter.

 

Length of an electron

The electron is a wave. Its length is not fixed, but it is determined by the electron environment.

In a conductor, the the effective length of a conduction electron equals to its mean-free path λmean or a distance between two subsequent electron scatterings. It is between 10 nm and 1000 nm in a semiconductor and between 1 nm and 10 nm in a metal.

 

The size of a localized electron equals to the size of atom (~0.1 nm).

 

 


The size of elementary particle and forces of the nature

The size of elementary particle matters for its interaction with other particles!!

An interaction between two particles depends on their size

Click on image to enlarge it

Important point: The forces between particles depend on the size of particles

The classical physics and the standard model postulate that all forces between particles (the gravitational force, the electromagnetic force, the strong force and the weak force) depends on the distance between particles and some parameter of the particle (the mass, the electrical and color charge).

An elementary particle does not have parts, it attracts or repel other particle as a whole. There are no parts of the particle, which could interact with other particle individually.

The interaction between particles (except gravitational interaction) is always mediated by a creation and annihilation of another particle from the vacuum.

(1) electromagnetic interaction is mediated by

 

 

 

 

 

 



Elementary Particles of Standard Model

The Standard model assumes that our Universe consists of above-set of the elementary particles of fix like properties the energy, spin, charge, rest mass, color charge etc.. The interactions between these particles describes all processes in our Universe

The "post- Standard" model describes all elementary particles as a "stable" "stand-alone" states of symmetry breaking. The parameters of each particle (rest mass, spin etc.) are just degree (amount) of breaking of a specific symmetry, at which a set of broken symmetries are locally stable.
Click on image to enlarge it

Standard model and "post- Standard model"

The Standard Model of particle physics

The Standard Model assumes that our Universe consists of a finite set of a particles. All possible processes and events in our Universe are only interactions between those particles. Each particle has very fixed number of properties like the energy, spin, charge, rest mass, color charge etc.. These properties of an elementary particle are firmly fixed and are the internal features of each particle. The interactions between these particles describes all processes in our Universe.

The elementary particle may be transformed between each other when they crash into each other at a high energy. In this case one elementary particle disappears into nowhere and another particle appears from nowhere. There is only one limitation for this process: The Conservation Laws. As soon as all required conservation Laws are hold, the transformation between elementary particles occurs.

 

The "post- Standard" Model 

The "post-Standard" Model assumes that our University has a set of different symmetries. One of symmetries or several symmetries can broken locally. The breaking of symmetry is hard and the symmetry is trying to return to its unbroken state. However, some rare cases exists when several symmetries can be broken simultaneously and this set of the broken symmetries is locally stable. This stand-alone set of broken symmetries is called an elementary particle. The conditions, at which a set of broken symmetries are locally stable, is subtle and can be possible at very specific parameters or at very specific degree (amount) of breaking of a specific symmetry. This is why each elementary particle has specific parameter (rest mass, spin etc.)

 

Symmetry & Conservation Laws

Emma Noether (1882-1935)

She is the first who pointed that the symmetry and the breaking of the symmetry are the major mechanisms (maybe only mechanisms) governing our Universe

She is the Mother of "post Standard Model" understating of our Universe
She proved that each existed conservation Law corresponds to one type of the Symmetry of our Universe.
See video here , Wiki is here

Each Conservation Law of Physics always corresponds to one of the continues symmetry of our Universe

This rule was discovered by Emma Noether. This discovery is one of greatest discoveries in Physics. Along the Quantum Mechanics and the Theory of relativity, it made a largest impact on our modern understanding of our Universe.
See Noether's Theorem here

Examples:

The time transfer symmetry The energy conservation law

The time transfer symmetry The momentum conservation law

The time-inverse symmetry The spin conservation law

The phase symmetry of electron wavefunctionThe electrical-charge conservation law

 

 

 


 

 


 

How two elemental particles (two electrons) are transformed into one elementary particle?

Origin of exchange interaction. Spin-inactive electrons.

Fig.3. Two electrons of opposite spins, when combined, form an elementary particle without spin.

Each quantum state can be occupied by two electrons of opposite spins.

When a quantum state is occupied by one electron, it is an elementary particle with charge -e and spin=1/2

When a quantum state is occupied by two electrons, it is an elementary particle with charge -2e and spin=0

click here to enlarge

(about spin-inactive electrons)

Two electrons of an opposite spin, which occupy one quantum state, are one particle or two particles?

A. It is one particle. At least, its properties are closer to that of one elementary particle than to that of two elementary particles. Two electrons do not repel each other, do not interact with each other and cannot be distinguished as two separated subjects (wave function symmetry, orbital moment etc.) . Such a state fully loses all single- electron property. For example, Two electrons of opposite spin, which occupy one quantum state, do not have any exchange interaction with any other electrons.

(virtual electrons) Such a state can be considered as a sum of two separate subjects only virtually. When such a state interacts with a photon or other external particle only one of two electrons is transformed to another energy level or to another quantum state. The spin direction of the transformed electrons is either random or is defined by the external particle. The spin of the remaining electron is opposite to the spin of the transformed electron. Only from this virtual point of view, this state can be considered as two electrons.

(fact) Two electrons of an opposite spin, which occupy one quantum state, should be considered as one elemental particle. These electrons lose their spin properties and are called the spin-inactive electrons.

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How is it possible that two elementary particles are transformed into one elementary particle and vice versa?

A.Since all known elementary particles are waves, it is very common that during an interaction between them, the number of particles changes. For example, the result of interaction of an electron and a positron is only a photon.

All matter in the universe was created literally from nothing 13.8 billion years ago during the inflation period.

Creation or annihilation of particles waves is very common process. How two particles (waves) can be created from nothing could be understood as follows: When there are two absolutely identical waves, but phase shifted 180 degrees relatively each other, their sum gives zero or nothing. Therefore, two particles (for example, an electron and a positron) can combine that result will be nothing. Similarly, if some force changes the phase shift between particles from 180 degrees to any other, from nothing two particles can be created.

 

Mathematically the process when two electrons of opposite spins combine and create one elementary particle without spin ("full" state) can be understood as follows.

Two electrons with opposite spins, which occupy different states, are described by two spinors

They are described by different sets of coordinates (x1,y1,z1) and (x2,y2,z2). It means they are two elementary particles, which interact with other.

When these two electrons of opposite spins occupy one state, they are described by a scalar wave function, which is product of spinors (1.1) and (1.2)

It is important that the scalar wave function (1.3) is described by one set of coordinate. It means (1.3) describes one elementary particle.

More about spin basic properties see here

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(about exchange interaction)

How is it possible that two elementary particles are transformed into one elementary particle and vice versa?

A. Continuous. When the distance between two electrons of an opposite spin decreases, the Coulomb repelling force between them decreases and becomes zero when they occupy exactly one spot. It looks like two electrons continuously transformed into one particle as the distance between electrons decreases. In Quantum Mechanics, this process is described by using a symmetrical and asymmetrical wavefunction (See here for details).

Such a reduction of the Coulomb repulsion only occurs only when the spins of two electrons are opposite. Otherwise, the Coulomb repulsion regains its full strength. As a result, the Coulomb repulsion between two electrons is spin- dependent. The spin- dependency of the Coulomb interaction is called the exchange interaction. It is a very interesting and complex effect. (For details see here)

 


Questions & Answers

(about spin-mixed state)

Does a spin-mixed state exist? Is the spin-mixed state just a simple sum of spin-up and spin-down electrons? Can you comment on properties of a spin-mixed state?

No. The spin-mixed state can not exist in reality. The spin-mixed state is a trick used sometimes in some theoretical approximations. The spin describes a breaking of the time inverse symmetry. The time inverse symmetry cannot be broken partly. The time inverse symmetry is either broken or not. The time inverse symmetry is broken, when a quantum state is occupied by one electron. Such a state is spin active. The time inverse symmetry is not broken, when a quantum state is occupied by two electrons. Such a state is spin inactive.

The spin can be either along (spin-up) or opposite (spin-down) to the direction of the broken time inverse symmetry. Only another possible and allowed state for the spin (or any subject of the broken time-inverse symmetry) is the spin precession state. The spin precession is a superposition of the spin-up and spin-down state, but it is not a spin-mixed state. Besides, the spin-precession state is not a static state. During the spin precession a photon or a magnon is unavoidably emitted and the spin is aligned along the up- direction.

Also, either spin-up or spin-down can be decomposed into components ( e.g. into a sum of spin-left and spin-right components). Such a sum of spin-left and spin-right components is not a spin-mixed state as well.


 

 

 

 

 


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