more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11
more Chapters on this topic:IntroductionTransport Eqs.Spin Proximity/ Spin InjectionSpin DetectionBoltzmann Eqs.Band currentScattering currentMeanfree pathCurrent near InterfaceOrdinary Hall effectAnomalous Hall effect, AMR effectSpinOrbit interactionSpin Hall effectNonlocal Spin DetectionLandau Lifshitz equationExchange interactionspd exchange interactionCoercive fieldPerpendicular magnetic anisotropy (PMA)Voltage controlled magnetism (VCMA effect)Allmetal transistorSpinorbit torque (SO torque)What is a hole?spin polarizationCharge accumulationMgObased MTJMagnetoopticsSpin vs Orbital momentWhat is the Spin?model comparisonQuestions & AnswersEB nanotechnologyReticle 11

What is the Spin? Spin & Time Inverse Symmetry. Spin and Charge TransportAbstract:The spin is a quantity, which describes the degree of the broken time inverse symmetry for an elementary particle. If additionally the elementary particle has an electrical charge, there is a magnetic moment associated with the spin and the elementary particle interacts with the magnetic field.
Contentclick on the chapter for the shortcut(Part 1) Origin of the Spin1.1. Spin & Time Inverse symmetry1.2. Incorrect view of the spin as an internal rotation of an electron1.3.Spin & the timeinverse symmetry1.3.1 Spin as a parameter of degree of breaking of the time inverse symmetry() Spin of a photon() Absence of magnetic moment in a photon() Einstein's representation of particle with a rest mass() Reflection of a quantum field from the Giggs field() Origin of the Spin of a particle with a rest mass1.4. Spin & Magnetic Moment() Origin of the magnetic moment and symmetry() Visualization of the spin & orbital moment() Spin vs. Orbital moment. Time inverse symmetry vs. rotational symmetry() Interaction of the spin & orbital moment() How to distinguish the spin from the orbital moment() Dirac and Non Dirac representations of the Spin() Dirac representations of the Spin() Non Dirac representations of the Spin() Dirac equations. vs Maxwell equations() Why does the spin have a direction in space?1.5.Spin & Dirac Equations1.6 Quantum Mechanic and Magic in Physics1.7ncorrect explanation of the Spin Nature1.8. Stern–Gerlach experiment. Longlived Incorrect interpretation.1.9. Classical explanation of the Spin by Dr. Matt O`Dowt() Spin Conservation Law against Quantum explanation for the Stern–Gerlach experiment() Similarity of Energy Conservation Law and the Spin Conservation Law() Two possibilities of magnet design in the original Stern–Gerlach experiment() Is the spin a quantum parameter?(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) Spinorbit magnetic field; (3) magnetic field of the exchange interaction.(). Questions & Answers() about Misinterpretation of the Stern–Gerlach experiment()about spinmixed state
.........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 nonzero 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 nonzero 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 timeinverse 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??
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 nucleus. An electron has length, which equals to the electron meanfree 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 meanfree path. 
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 timeinverse 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 timeinverse symmetry of vacuum is broken, an elementary particle has the Spin.
Spin & the timeinverse symmetryThe timeinverse 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 timeinverse 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 leftrotation and the state of the rightrotation. In case of an electron, the states are called the spinup and spindown states. In the case of a photon, the states correspond to left and right circular polarized photon. The timeinverse symmetry symmetry of the vacuum is not broken. Therefore, the spin can interact with the field, which timesymmetry symmetry is broken, and the result of such interaction should be the timeinverse symmetric. The timeinverse 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 timeinversebreaking 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 pointlike 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 pointlike particles (There are many parts, with which I do not agree)
Spin as a parameter of degree of breaking of the time inverse symmetryThe time inverse symmetry for an object means that no property of the object changes when the direction of the time is reversed. Let me give you some examples, when the time inverse symmetry is broken. (example 1): An object rotating around some axis. When the time is inverse, the clockwise rotation changes into the counterclockwise rotation. (example 2): An electrical current. When the time is inverse, the electron flow to the left changes to the flow to the right. The direction of a magnetic field, which is induced by the current, reverses its direction. In contrast, the electrical charge, the electrical field, and electron mass are not affected by the timereversal. Symmetry is critically important in Physics. Emptiness or "nothing" or vacuum is a state of full symmetry. As a result, the "nothing" can not be distinguished by any means. In contrast, an elementary particle is a bunch of broken symmetries, which is stable in time. As a result, an elementary particle can be distinguished from the "nothing". Additionally, any symmetry corresponds to one conserved parameter. For example, the symmetry of absolute value of time corresponds to a conserved parameter called the energy. The symmetry of absolute value of time means that all Law of Physics is absolutely the same yesterday, today and tomorrow. The existence itself of any elementary particle breaks this symmetry. The particle might exist today, but will not exist tomorrow. As a result, any elementary particle has the conserved parameter called the energy. Similarly, any property of an elementary particle has corresponding symmetry. For example, the electrical charge corresponds to the symmetry of a change of the phase of the wavefunction. It means if the phase of the wavefunction of one separated electron is changed, nothing happens to the electron. The spin is the conserved parameter corresponding to the symmetry of the time reversal. If an elementary particle remains exactly the same, when the time is reversed, the particle has no spin. If some property of a particle changes, when the time is reversed, the particle has a nonzero spin. General Origin of the Spin:The rotation between components of the quantum field_____For example, in the case of a photon, the photon spin is due to the rotation between two components of the photon's electrical field (see below).The spin of a particle with a rest mass can be understood from Einstein's view of an elementary particle (see below).The quantum field has a spin, because the rotation between its components is affected by the time reversal. For example, if the rotation between components of the quantum field is in the clockwise direction, the time reversal changes the rotation into the counterclockwise direction. This fact can be understood on an example of the spin of a photon. Spin of a photon
(fact) A photon may have spin equal +1 or 1, or be without spin. (why does a photon have a spin?) A photon has two components of the electrical field, which are directed perpendicular to the photon propagation direction. E.g., if a photon propagates along the z direction, the photon may have components along the x and y directions. There are 3 possibilities for the polarization of a photon. The electrical field or polarization can be fixed along one direction. In this case, the photon has no spin, because the polarization is not changed, when the time is reversed. Another possibility is the electrical field rotates between Ex and Ey components. Such a photon does have a spin, because its polarization is affected by the time reversal. For example, if the rotation of the electrical field is in the clockwise direction, the time reversal changes the rotation into the counterclockwise direction. The clockwise and counterclockwise polarization rotations correspond to the photon spin of +1 and 1. (substantial difference between the spin of an electron and a photon): The spin of a photon is always directed along or opposite to the photon propagation direction. In contrast, the spin of an electron can be directed in any direction and is independent of the electron moving direction. Absence of magnetic moment in a photonIf a photon has the spin, does it have the magnetic moment associated with the spin? No, the photon does not have a magnetic moment, even though it does have the spin. In order to have a magnetic moment, a particle should have the spin (meaning that the timeinverse symmetry for the particle is broken) and the particle should possess an electrical charge (see below). Since the photon does not carry any electrical charge, it does not have a magnetic moment. Facts proving the absence of a magnetic moment in a photon: (fact 1): There is no precession of the spin of a photon in a magnetic field (fact 2): The energy of a photon is exactly the same in cases when the photon spin is along and opposite to the magnetic field.
Einstein's representation of particle with a rest mass
(fact) Einstein considered that any particle with a rest mass (for example, an electron) consists of a massless quantum field, which is moving at speed of light and which is bounced back and forward between two mirrors. The mirrors represent the Higgs field, from which the massless quantum field is reflected. The energy of this confined state gives the electron rest mass. This representation of a particle with a rest mass gives a simple and understandable explanation of all effects of the special theory of relativity. For example, (1) why does the mass of the particle increase with its speed; (2) why the speed a particle with a rest mass cannot exceed the speed of light.
Einstein's representation of a particle with a rest mass means that (1) additionally to the fact, that any particle or quantum field cannot move faster than the light speed c (2) the quantum field cannot move slower than the speed of light
All elementary particles, which have a nonzero rest mass (like an electron), gain their rest mass due to backward and forward reflections in the Gibbs field (like light backward and forward reflections between two parallel mirrors).
Reflection of a quantum field from the Giggs field
(continuous reflection) The reflection is not a point like, for example, as a reflection of light from a mirror. The quantum field is continuously reflected from the Giggs field as it propagates in it. Such a reflection is called the distributed feedback reflection (DFR) Nowadays, the DBR mirrors are used in the most of commercial semiconductor lasers (See here). (interaction of a quantum field and the Giggs field ) There is a mutual interaction between any quantum field and the Giggs field. The quantum field is reflected backward by the Giggs field. As a result, the elementary particle gains a rest mass from the Giggs field. The quantum field modulates the Giggs field with its own spatial frequency.
Origin of the Spin of a particle with a rest mass
(spin & quantum field) A quantum field has two or more components. A rotation between the two components of the quantum field breaks the time inverse symmetry. The spin of an elementary particle describes this breaking of the timeinverse symmetry.
A particle with a rest mass is represented as a massless quantum field of the electron, which is bounced back and forward between two mirrors (See above). The mirrors represent the Higgs field, from which the quantum field is continuously reflected in backward
(Origin of the spin): a rotation between the two components of the quantum fieldIn order to have a spin, the quantum field should change (not be equal) when the direction of the time flow is reversed. For example, if the quantum field rotates in the clockwise direction, the rotation becomes counterclockwise after the time reversal. It means that the quantum field should have at least two components, which should correspond to the opposite direction of the time flow. For example, the clockwise and counterclockwise rotation of the quantum field. (note) The quantum field describes a breaking one or several symmetries of our Universe (see here)(note) Even though the direction of the time flow cannot be literally reversed, the time inverse symmetry is one of the important symmetries , which determines the particle's existence and which the particle may have or may not have..
Spin conservation during reflection of quantum field from Higgs field
The spin is a conserved quantity. When the quantum field is reflected backward, the direction of the spin remains the same, which means that with respect to the movement direction of the quantum field, the direction of the spin is reversed. For example, if the quantum field rotates in the clockwise direction along its moving direction, after reflection the field rotates in the counterclockwise direction along its moving direction (See the left picture)
(fact) the Einstein's representation of particle with a rest mass gives two possible representation of the spin: Dirac and Non Dirac representations of the Spin (see below for details)
Spin & Magnetic MomentThe magnetic moment is a quantity, which describe an interaction of a particle with an external magnetic field Two vital conditions for a particle to have a magnetic moment:(vital condition 1): The timeinverse symmetry for a particle should be broken. (vital condition 2): The particle should possess an electrical charge. Any charged particle, which timeinversesymmetry is broken, always has a magnetic moment
(fact): The timeinverse symmetry is broken only for a particle, which has a nonzero spin or/and a nonzero orbital moment (fact): An uncharged photon has a spin, but does not have a magnetic moment
Properties due to existence of a magnetic moment:(property 1): There is a precession of the spin in a magnetic field (property 2): The energy of a particle is different when the spin of the particle is along and opposite to the magnetic field. (note) A photon, which does not possess a magnetic moment, does not have those two properties.
Origin of the magnetic moment and symmetryOrigin of the 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 (spinrelated) is originated from the breaking of the symmetry of the phase of the electron wave function with respect to timereversal.
(gauge symmetry: origin of electrical charge:) 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 xaxis) (origin of spinrelated magnetic moment) The gauge symmetry becomes locally broken for a time inverse transformation
Spin vs. Orbital moment. Time inverse symmetry vs. rotational symmetry.
(fact): The spin and the orbital moment describe breaking of the different symmetries. Even though both the spin and the orbital moment describe a quantum state with a broken time inverse symmetry, the rotational symmetry, which is described by the orbital moment, has an additional component (the spatial symmetry)
Visualization of the spin & orbital moment
Interaction of the spin & orbital moment(fact) Both the spin and the orbital moment describes the degree of breaking of the time inverse symmetry. The orbital moment describes breaking of the rotational symmetry, which includes the breaking of the time inverse symmetry. (fact) An elementary particle has only one time inverse symmetry, which could be broken only once. Therefore, in case when a particle has both the orbital moment and the spin, the degree of the breaking of the time inverse symmetry has both contributions from the the spin and from the orbital moment. fact) The spin and the orbital moment are not always aligned along each other.
How to distinguish the spin from the orbital moment(How to do it): If you know the wavefunction of the quantum state you should to following: (step 1) Inverse the time direction for the wave function (step 2) Sumup the original wavefunction and the wave function with reversed time. Spin & Dirac Equations
(fact 1) The Dirac equations describes the quantum mechanical properties of an electron. The solution of the Dirac equation is a 4rank spinor. The 4rank 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 spinup or spindown spin direction. ( C symmetry): The symmetry of reversal sign of the chargeThe 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 timeinverse symmetry means that for any state (e.g. spinup state), there is a state (the spindown state), which is the time inverse transform from the original state. It means that if the time flow is inverse, the spinup state becomes spindown state and the spindown state becomes the spinup states. Additionally, the breaking the timeinverse 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 Csymmetry) 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 Csymmetry disappears and a result of the colliding is a chargefree 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
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.
Incorrect explanation of the nature of the SpinFollowing incorrect explanation of the results of the Stern–Gerlach experiment (See below), the incorrectly assumed Quantum 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
(incorrectly assumed Quantum 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 spinup or spindown directions along the fixed measurement direction
Contradictions of the Quantum 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 wellverified 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 spinconservation 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 4rank 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 timeinverse symmetry is described by a 2rank 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 spinrelated effects): All known experiments in magnetism are well explained using the Spin Conservation Law and without use of the incorrectly assumed Quantum Nature of the Spin
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. Incorrect interpretation.Magic, which lived over a hundred years.Original paper translated in English is herewiki page about Stern–Gerlach experiment is hereSee the incorrect explanation of the results Stern–Gerlach experiment in Dr. Matt O`Dowt video time: 5:10many details about the Stern–Gerlach experiment are explained in this YouTube VideoMisinterpretation of the Stern–Gerlach experiment is one of longest lived misinterpretations of an experiment in Physics. short explanaition about misinterpretation of the Stern–Gerlach experiment is below in question section
(goal of experiment): A measurement of distribution of the spin directions in an atomic gas or an electron gas. (effect behind the experiment):In a gradient of the magnetic field, a particle with the spin experiences a mechanical force. The direction and the strength of the force depends on the particle' spin direction with respect to the gradient. As a result, a particle with a different spin direction moves in a slightly different direction due to a different mechanical force. A measurement of distribution of the particles passing a gradient of the magnetic field gives the distribution of the spin directions of these particles. (result of experiment): The electrons are detected at two lines or 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.
(incorrect quantum explanation): (incorrect conclusion 1) Since there are only two detectible lines, the spin may have only two directions, for example, spinup and spindown.The spin directions cannot have some 3D distribution, for example, a spherical distribution. (incorrect conclusion 2) Since the detected lines are rotated when the magnet is rotated, the spin is not a defined property until it is measured. For example, until an event of measurement, the spin can be in either of spinup/spindown or spinleft/spinright or spinfront/spinback configurations. (Why is the quantum explanation incorrect?): Similar to the energy, the spin is a strictly conserved parameter. According to the Noether rule, the spin conservation law is due to the time inversion symmetry. As a conservation parameter, the spin cannot be undefined or be changed depending on a measurement. The spin can be changed only when a particle interacts with another with the spin. It is similar as the energy of a particle cannot be changed unless a particle interacts with another particle. The quantum explanation of the spin behavior in the Stern–Gerlach experiment violates the strict spin conservation law. (missing effect for the correct and simple explanation): It is very important that the results of the Stern–Gerlach experiment are influenced not by one, but by two effects. The 2nd effect is the alignment of the spin along the direction of the magnetic field.There is a spin precession and a spin precession damping in a magnetic field. As a result of the damping, the spin is aligned along the direction of the magnetic field. The alignment time is usually very short. (the correct and simple explanation of Stern–Gerlach experiment): A gradient of a magnetic field means that the magnetic field changes from one value to another value. There are only two possibilities for a design of the magnet for this experiment. The 1st possibility, which I guess was used in the Stern–Gerlach experiment, when there is only one gradient. In this case, the magnetic field changes from a minus value to a plus value along the magnet gap. E.g. at the left side of the gap at x=a H=H0 and at the right side of the gap at x=+a H=+H0. The gradient equals =H0/a The spins of particles, which enter the gap between x=a and x=0, are aligned in the minus direction along H. As a result, the particles are moved to the left along the gradient. The spins of particles, which enter the gap between x=0 and x=+a, are aligned in the plus direction along +H. As a result, the particles are moved to the right along the gradient. As a result, there are two detected lines!!!!
(details of Stern–Gerlach experiment): Electrons of different spin polarization, which are emitted by an electron gun, pass through a spatially varying magnetic field and are detected at a detection screen. In a spatial gradient of a magnetic field, an electron experiences a mechanical force (See below), which pushes the electron to move along the gradient. The direction and the strength of the force depends on the particle' spin direction with respect to the gradient. As soon as the particle enters the magnetic field, its spin is aligned along the magnetic field. At different sides of the spatial point where the magnetic field changes its polarity, the spins of moving particles are opposite. As a result, the particles in two regions of the opposite directions of the magnetic field, moving in the opposite directions resulting in two detected spots.
(result of experiment): The electrons are detected at two lines or 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. Both the gradient of the magnetic field and the regions of opposite polarities of the magnetic field are rotated with a rotation of the magnet. As a result, the detected lines are rotated when the magnet is rotated!!!
(Why was the measured result considered a problem for a long time? ): Why was the measured result considered a problem for a long time? ): At the muzzle of the electron gun, the electrons are not spin polarized and, therefore, their spins should be distributed equally in all directions. Since the spin direction of each electron is different, each electron should experience a different force and therefore be detected at different spots of screen. The problem was that the electrons are detected at two spots instead of a continuous distribution meaning there is something unusual about the spin distribution as if there are two possible quantum states for the spin. Additionally, the detected distribution is rotated as the magnate is rotated as if the spin distribution is dependent on the detection method. (solution: influence by other effect): All spins are aligned inside the magnet in one direction along the magnetic field. The measured distribution of the spin direction is not isotropic spin unpolarized as at the muzzle of the electron gun, but the fullyspin polarized as it is inside of the magnet. (Incorrect Quantum 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. (Simple non Quantum explanation of Stern–Gerlach experiment ): There is an additional effect, which the electron spin is experiences and which is ignored in the Quantum explanation. (additional ignored effect): The electron spin is aligned along the magnetic field.
Spin Conservation Law against Quantum explanation of Stern–Gerlach experiment >
(problems of the Quantum explanation) (problem 1) The Quantum explanation violates the spin conservation law, which is wellverified law of the Physics. (problem 2) The Quantum explanation violates the Dirac equations; (problem 3) The Quantum explanation violates the observed direction of the time flow in our Universe (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. The quantum explanation assumes that the spin direction is not defined and, therefore, is not conserved until the spin is measured. This assumption violates the fundamental spin 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 violates the fundamental spin conservation law.
(problem 2) Dirac equations The solution of the Dirac equations is a 4rank 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 of 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. Similarity of Energy Conservation Law and the Spin Conservation LawThe spin conservation law is as strict as the energy conservation law. The quantum explanation of the spin behavior in the Stern–Gerlach experiment clearly violates the spin conservation law. According to the Noether rule, any conservation law originates from some symmetry. The energy conservation law is due to the time continuity symmetry. The laws of Physics will be the same tomorrow as they are today. The spin conservation law is due to the time inversion symmetry. The laws of Physics will be the same if the direction of the flow of the time is reversed. Therefore, the energy and spin conservation laws are so similar!! (fact) It took more than 100 years for people to accept the fundamental energy conservation Law. Still now some people are trying unsuccessfully to fabricate a perpetual motion machine, which will provide energy infinitely. However, the fact is the energy conservation Law cannot be broken I hope, someday the spin conservation law will be as respected as the energy conservation law is respected now.
Two options of design of a magnet with a gradient of magnetic field, which was used in the original Stern–Gerlach experimentSee magnet design in the original paper here.It is difficult to guess the exact design of the magnet, which was originally used in the Stern–Gerlach experiment. There was a gradient of the magnetic field. A gradient of a magnetic field means that the magnetic field changes from one value to another value. There are two options of design of a magnet with a gradient of magnetic field, any of which gives two detected lines (as was observed in the experiment!!):
(magnet option 1: radient of magnetic field does not change the polarity, but he polarity of the magnetic field changes): most probable shown in Fig. 44 (click here)In this case, there are two detected lines as particles with opposite spin directions are moved in opposite directions along the gradient. In this case, the magnetic field changes from a minus value to a plus value along the magnet gap. E.g. at the left side of the gap at x=a H=H0 and at the right side of the gap at x=+a H=+H0. The gradient equals =H0/a The spins of particles, which enter the gap between x=a and x=0, are aligned in the minus direction along H. As a result, the particles are moved to the left along the gradient. The spins of particles, which enter the gap between x=0 and x=+a, are aligned in the plus direction along +H. As a result, the particles are moved to the right along the gradient. As a result, there are two detected lines!!!! (magnet option 2: the magnetic field does not change polarity, but there are two opposite gradients.):: less probable, but simpler shown in Fig. 45 (click here)In this case, there are two detected lines as particles with opposite spin directions are moved in opposite directions along the gradient. The simplest example of such a magnet is the magnet, which consists of two connected cylindrical poles with a gap at one side (the simplest case of a magnet). In this magnet, the magnetic field changes from zero value (far from magnet) to some value H ( at center between poles) and next back to zero (far from magnet in the opposite direction). The polarity of the magnetic field is the same, but there are positive and negative gradients. In this case all spins are aligned in one direction, but the opposite gradients again make two detected lines !!!!!
Is the spin a quantum parameter?No. Similar to the energy, the spin is a general conserved parameter of an object. The spin describes the degree of the broken timeinversion symmetry. Its quantization originates from two possible opposite directions of the time flow. Correspondingly, the broken timeinversion symmetry and, therefore, the spin have only two components: spinup and spindown. The spin can manifest itself in the large world (a permanent magnet) and in small quantum world (spin dependency of the energy levels of an atom)
Classical explanation of the Spin by Dr. Matt O`Dowt Video
Dirac and Non Dirac representations of the Spin(what is it about?): The spin of an elementary particle always represents the rotation between its two components of the quantum field or, the same, the broken timeinverse symmetry. The Dirac and Non Dirac representations of the Spin are distinguished on how the rotation of the quantum field occurs in the 3D space. (Dirac representation): The spin direction is independent of the propagation direction of the quantum field (Non Dirac representation): The spin direction field dependents on the propagation direction of the quantum field The elementary particle, which spin is represented either by Dirac or NonDirac representation:(note) For many elementary particles, it is difficult to verify experimentally which of either the Dirac or the NonDirac representation describes the particle spin.(Non Dirac representation): (we know for sure): The spin of the photon and the the electromagnetic field is described by the Non Dirac representation. (note): From all quantum fields, the electromagnetic field is most understood, because all its properties can be measured directly.(very probably): Neutrino and the quantum field of the weak interaction. (note): The weak and electromagnetic fields are very similar and originated from a breaking of one single quantum field.(Non Dirac representation): (very probably): The Electron (note): The Dirac equation describes all properties of the electron and the electron quantum field rather well.
(it is more natural): In fact, the nonDirac representation of the spin is more natural. (Why is that?): The movement of the quantum field by itself breaks the time inverse symmetry. When the direction of the time flow is reversed, the movement direction of the quantum field. Therefore, it is very natural that the breaking of the time inverse symmetry for the quantum field is related to the breaking of the time inverse symmetry due to the movement of the quantum field and, therefore, is related to the movement direction of the quantum field. In fact, for the electromagnetic field, which we have measured and studied most, the spin direction of a photon is always in the movement direction of the photon.
Dirac representations of the Spin(key fact): In the Dirac representations of the Spin, the rotation direction between two components of the quantum field is independent of the propagation direction of the quantum field In the Dirac representations of the Spin, the the axis of the rotation of the quantum field can be both along and perpendicular to the movement direction of the quantum field. (it is very probably): that the Electron is described by the Dirac representation
Two components of the quantum field are describes by two components of a spinor.
Non Dirac representations of the Spin(key fact): In the Non Dirac representations of the Spin, the rotation direction between two components of the quantum field is dependents on the propagation direction of the quantum field In the Non Dirac representations of the Spin, the the axis of the rotation of the quantum field is fixed with respect to the movement direction of the quantum field.
Two components of the quantum field are describes by two components of a spinor.
Dirac equations. vs Maxwell equations(fact): The Dirac equation is the simplest description of a quantum field of an elementary particle, which has a rest mass, and whose broken time inverse symmetry is described by the Dirac representation of the spin. (note) In fact, the Dirac equation describes the quantum field of 4 components. A pair of two components correspond to a particle (the electron) and antiparticle (the positron). Only 2 components describe the broken timeinverse symmetry (the spin) for each the particle and the antiparticle.(fact): The Maxwell equations are the simplest description of a quantum field of an elementary particle, which does not have a rest mass, and whose broken time inverse symmetry is described by the nonDirac representation of the spin.
(Complexity of Maxwell' equations) The Maxwell' equations are more complex, for example in comparison to the Dirac equations, because of the complexity to describe the dependence of the broken time inverse symmetry of the quantum field on the movement direction of the quantum field. Still Maxwell' equations is the simplest form to describe the NonDirac type broken time inverse symmetry of the quantum field.
Why does the spin have a direction in space? Why doesn't the spin have only two states corresponding to "+" and "" as similar as the charge has? Instead the spin has a spatial direction? Since the spin describes the time inversion, the "+" would correspond to the forward flow of time and the "" would correspond to the backforward flow of time.It is correct. The time inversion symmetry can be broken by two methods and, therefore, be described either by a spin scalar or a spin vector. When the spin is a vector, the spin properties are somehow similar to the rotation. The broken rotation symmetry, which is described by the orbital moment, has also broken timeinverse symmetry, which is described by the vector. The direction of this vector corresponds to the rotation axis. (see here) The example of the scalar spin is the spin of the photon. The spin of the photon may have only two possibilities (two directions). The spin can be either along or opposite to the direction of the photon propagation. Therefore, the spin of the photon is scalar, has only two possible values and, similar to the charge, the spin value can be assigned as "+" and "" values. Only the quantum field of the Non Dirac representation of the Spin has the spin as a scalar. An elementary particle with a rest mass of both the Dirac and Non Dirac representations of the Spin has the spin as a vector. An elementary particle without a rest mass of the Dirac and Non Dirac representation of the Spin has spin as a vector.
Mechanical forces & Mechanical torque due to the Spin & Magnetic field(fact) A single elementary particle with the spin experiences only one mechanical force in a magnetic field, while an assembly of the particles with spins, like a permanent magnet, experiences three different mechanical forces in a magnetic field
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 forceAn 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.
(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.
(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.
(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 timespace of our universe. The electrical charge corresponds to the breaking of the gauge symmetry, the spin corresponds to the breaking of the timeinverse symmetry and the magnetic moment corresponds to the breaking of the breaking of both the timeinverse 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". . (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.
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 charge
(Mechanical force 3 (weakest) ): Due to Einstein–de Haas effect.wiki page is hereSee classical explanation below in Dr. Matt O`Dowt video time: 0:24This 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
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 E_{static}, H_{static}_{} are the electric and magnetic field in the static coordinate system (reference frame) and E_{move}, H_{move}_{} 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.
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 electricalfield component in the coordinate system moving together with the electron, has both the electricalfield and magneticfield components in a static coordinate system. (effect 2): Spinorbit interaction The spinorbit 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 spinorbit 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 speedMagnetic 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 timeinverse symmetry +
Due to its spin and its charge, the electron has a magnetic moment, which generates a magnetic field An elementary particle, which has a nonzero spin and nonzero charge, has a nonzero magnetic moment, which induces a magnetic field around the electron. (note) The electron has a spin, because its timeinverse symmetry is broken. The electron has a charge, because its gauge symmetry is broken. Simultaneous breaking the timeinverse symmetry and the gauge symmetry creates a magnetic moment for an elementary particle (See here for more details)
(Zero spin + nonzero charge) spininactive electron no magnetic moment For example, the electron of filled orbitals are charged, but their spin is compensated, has no magnetic moment. Formally the timeinverse symmetry is not broken for these electrons and therefore they have no spin. (Nonzero 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 speedMagnetic 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 timeinverse symmetry
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 spindependent 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 nuclei is changed
The timeinverse 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 nuclei is changed.
Dependence on electron movement speedMagnetic 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) Spinorbit magnetic field; (3) magnetic field of the exchange interaction.
Questions & Answers(about Misinterpretation of the Stern–Gerlach experiment) There is an alternative interpretation of the SternGerlach experiment that does not violate any fundamental laws of physics and does not rely on "quantum magic" explanations. It is crucial to note that the experiment's results are influenced by two effects. The first effect is a mechanical force along a gradient of the magnetic field that moves a particle along the gradient. The force's direction and strength depend on the particle's spin direction with respect to the gradient, with particles of opposite spin directions moving in opposite directions. The second effect is the alignment of the spin along the direction of the magnetic field, regardless of gradient. In any magnetic field, there is a spin precession and, consequently, a spin precession damping. As a result of the spin precession damping, the spin aligns along the magnetic field direction. The spin alignment occurs very quickly. When a beam of particles with any complex distribution of spin directions enters a magnetic field, the spins of all particles quickly align along the magnetic field direction. As a result, all particles experience an equal mechanical force, leading to a line shape in the detected pattern. Two detected lines result from a polarity change of either magnetic field or a gradient of the magnetic inside the gap of the magnet. There are two options of design of a magnet with a gradient of magnetic field, any of which gives two detected lines: (magnet option 1): gradient of magnetic field does not change the polarity, but he polarity of the magnetic field changes This case of magnet shown in Fig.44 aboveIn this case, there are two detected lines as particles with opposite spin directions are moved in opposite directions along the samepolarity gradient. In this case, the magnetic field changes from a minus value to a plus value along the magnet gap. E.g. at the left side of the gap at x=a H=H0 and at the right side of the gap at x=+a H=+H0. The gradient equals =H0/a The spins of particles, which enter the gap between x=a and x=0, are aligned in the minus direction along H. As a result, the particles are moved to the left along the gradient. The spins of particles, which enter the gap between x=0 and x=+a, are aligned in the plus direction along +H. As a result, the particles are moved to the right along the gradient. Therefore, there are two detected lines in this case!!!! (magnet option 2): the magnetic field does not change polarity, but there are two opposite gradients. This case of magnet shown in Fig.45 aboveIn this case, all spins are aligned in one direction, but the opposite gradients produce two detected lines. The simplest example of such a magnet is the magnet, which consists of two connected cylindrical poles with a gap at one side (the simplest case of a magnet). In this magnet, the magnetic field changes from zero value (far from magnet) to some value H ( at center between poles) and next back to zero (far from magnet in the opposite direction). The polarity of the magnetic field is the same, but there are positive and negative gradients. In this case all spins are aligned in one direction, but the opposite gradients again make two detected lines !!!!! (the reason why the detected lines are rotated when the magnet is rotated): It is not because the spin direction is not defined and, therefore, is not conserved until the spin is measured. The spin is always well defined and well conserved.When the magnet is rotated, the detected lines are also rotated because both the magnetic field gradient and the regions of opposite polarities are rotated with the magnet. (the spin conservation law): The spin conservation law originates from the timeinversion symmetryIt is essential to note that the spin conservation law is as strict as the energy conservation law, and the quantum explanation of the spin behavior in the SternGerlach experiment violates the spin conservation law.
Does a spinmixed state exist? Is the spinmixed state just a simple sum of spinup and spindown electrons? Can you comment on properties of a spinmixed state?No. The spinmixed state can not exist in reality. The spinmixed 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 (spinup) or opposite (spindown) to the direction of the broken time inverse symmetry. Only another possible and allowed state for the spin (or any subject of the broken timeinverse symmetry) is the spin precession state. The spin precession is a superposition of the spinup and spindown state, but it is not a spinmixed state. Besides, the spinprecession 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 spinup or spindown can be decomposed into components ( e.g. into a sum of spinleft and spinright components). Such a sum of spinleft and spinright components is not a spinmixed state as well.
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